Mathematical Tasks without Words and Word Problems: Perceptions of Reluctant Problem Solvers
Holbert, Sydney Margaret
2013-01-01
This qualitative research study used a multiple, holistic case study approach (Yin, 2009) to explore the perceptions of reluctant problem solvers related to mathematical tasks without words and word problems. Participants were given a choice of working a mathematical task without words or a word problem during four problem-solving sessions. Data…
Graphic Organizer in Action: Solving Secondary Mathematics Word Problems
Directory of Open Access Journals (Sweden)
Khoo Jia Sian
2016-09-01
Full Text Available Mathematics word problems are one of the most challenging topics to learn and teach in secondary schools. This is especially the case in countries where English is not the first language for the majority of the people, such as in Brunei Darussalam. Researchers proclaimed that limited language proficiency and limited Mathematics strategies are the possible causes to this problem. However, whatever the reason is behind difficulties students face in solving Mathematical word problems, it is perhaps the teaching and learning of the Mathematics that need to be modified. For example, the use of four-square-and-a-diamond graphic organizer that infuses model drawing skill; and Polya’s problem solving principles, to solve Mathematical word problems may be some of the strategies that can help in improving students’ word problem solving skills. This study, through quantitative analysis found that the use of graphic organizer improved students’ performance in terms of Mathematical knowledge, Mathematical strategy and Mathematical explanation in solving word problems. Further qualitative analysis revealed that the use of graphic organizer boosted students’ confidence level and positive attitudes towards solving word problems.Keywords: Word Problems, Graphic Organizer, Algebra, Action Research, Secondary School Mathematics DOI: http://dx.doi.org/10.22342/jme.7.2.3546.83-90
The Association between Mathematical Word Problems and Reading Comprehension
Vilenius-Tuohimaa, Piia Maria; Aunola, Kaisa; Nurmi, Jari-Erik
2008-01-01
This study aimed to investigate the interplay between mathematical word problem skills and reading comprehension. The participants were 225 children aged 9-10 (Grade 4). The children's text comprehension and mathematical word problem-solving performance was tested. Technical reading skills were investigated in order to categorise participants as…
Language and modeling word problems in mathematics among bilinguals.
Bernardo, Allan B I
2005-09-01
The study was conducted to determine whether the language of math word problems would affect how Filipino-English bilingual problem solvers would model the structure of these word problems. Modeling the problem structure was studied using the problem-completion paradigm, which involves presenting problems without the question. The paradigm assumes that problem solvers can infer the appropriate question of a word problem if they correctly grasp its problem structure. Arithmetic word problems in Filipino and English were given to bilingual students, some of whom had Filipino as a first language and others who had English as a first language. The problem-completion data and solution data showed similar results. The language of the problem had no effect on problem-structure modeling. The results were discussed in relation to a more circumscribed view about the role of language in word problem solving among bilinguals. In particular, the results of the present study showed that linguistic factors do not affect the more mathematically abstract components of word problem solving, although they may affect the other components such as those related to reading comprehension and understanding.
How Can One Learn Mathematical Word Problems in a Second Language? A Cognitive Load Perspective
Moussa-Inaty, Jase; Causapin, Mark; Groombridge, Timothy
2015-01-01
Language may ordinarily account for difficulties in solving word problems and this is particularly true if mathematical word problems are taught in a language other than one's native language. Research into cognitive load may offer a clear theoretical framework when investigating word problems because memory, specifically working memory, plays a…
Directory of Open Access Journals (Sweden)
Yinghui Lai
Full Text Available Mathematics is one of the most objective, logical, and practical academic disciplines. Yet, in addition to cognitive skills, mathematical problem solving also involves affective factors. In the current study, we first investigated effects of mathematics anxiety (MA and mathematical metacognition on word problem solving (WPS. We tested 224 children (116 boys, M = 10.15 years old, SD = 0.56 with the Mathematics Anxiety Scale for Children, the Chinese Revised-edition Questionnaire of Pupil's Metacognitive Ability in Mathematics, and WPS tasks. The results indicated that mathematical metacognition mediated the effect of MA on WPS after controlling for IQ. Second, we divided the children into four mathematics achievement groups including high achieving (HA, typical achieving (TA, low achieving (LA, and mathematical learning difficulty (MLD. Because mathematical metacognition and MA predicted mathematics achievement, we compared group differences in metacognition and MA with IQ partialled out. The results showed that children with MLD scored lower in self-image and higher in learning mathematics anxiety (LMA than the TA and HA children, but not in mathematical evaluation anxiety (MEA. MLD children's LMA was also higher than that of their LA counterparts. These results provide insight into factors that may mediate poor WPS performance which emerges under pressure in mathematics. These results also suggest that the anxiety during learning mathematics should be taken into account in mathematical learning difficulty interventions.
Lai, Yinghui; Zhu, Xiaoshuang; Chen, Yinghe; Li, Yanjun
2015-01-01
Mathematics is one of the most objective, logical, and practical academic disciplines. Yet, in addition to cognitive skills, mathematical problem solving also involves affective factors. In the current study, we first investigated effects of mathematics anxiety (MA) and mathematical metacognition on word problem solving (WPS). We tested 224 children (116 boys, M = 10.15 years old, SD = 0.56) with the Mathematics Anxiety Scale for Children, the Chinese Revised-edition Questionnaire of Pupil's Metacognitive Ability in Mathematics, and WPS tasks. The results indicated that mathematical metacognition mediated the effect of MA on WPS after controlling for IQ. Second, we divided the children into four mathematics achievement groups including high achieving (HA), typical achieving (TA), low achieving (LA), and mathematical learning difficulty (MLD). Because mathematical metacognition and MA predicted mathematics achievement, we compared group differences in metacognition and MA with IQ partialled out. The results showed that children with MLD scored lower in self-image and higher in learning mathematics anxiety (LMA) than the TA and HA children, but not in mathematical evaluation anxiety (MEA). MLD children's LMA was also higher than that of their LA counterparts. These results provide insight into factors that may mediate poor WPS performance which emerges under pressure in mathematics. These results also suggest that the anxiety during learning mathematics should be taken into account in mathematical learning difficulty interventions.
Lai, Yinghui; Zhu, Xiaoshuang; Chen, Yinghe; Li, Yanjun
2015-01-01
Mathematics is one of the most objective, logical, and practical academic disciplines. Yet, in addition to cognitive skills, mathematical problem solving also involves affective factors. In the current study, we first investigated effects of mathematics anxiety (MA) and mathematical metacognition on word problem solving (WPS). We tested 224 children (116 boys, M = 10.15 years old, SD = 0.56) with the Mathematics Anxiety Scale for Children, the Chinese Revised-edition Questionnaire of Pupil’s Metacognitive Ability in Mathematics, and WPS tasks. The results indicated that mathematical metacognition mediated the effect of MA on WPS after controlling for IQ. Second, we divided the children into four mathematics achievement groups including high achieving (HA), typical achieving (TA), low achieving (LA), and mathematical learning difficulty (MLD). Because mathematical metacognition and MA predicted mathematics achievement, we compared group differences in metacognition and MA with IQ partialled out. The results showed that children with MLD scored lower in self-image and higher in learning mathematics anxiety (LMA) than the TA and HA children, but not in mathematical evaluation anxiety (MEA). MLD children’s LMA was also higher than that of their LA counterparts. These results provide insight into factors that may mediate poor WPS performance which emerges under pressure in mathematics. These results also suggest that the anxiety during learning mathematics should be taken into account in mathematical learning difficulty interventions. PMID:26090806
Strategies of solving arithmetic word problems in students with learning difficulties in mathematics
Kalan, Marko
2015-01-01
Problem solving as an important skill is, beside arithmetic, measure and algebra, included in standards of school mathematics (National Council of Teachers of Mathematics) (NCTM, 2000) and needed as a necessary skill for successfulness in science, technology, engineering and mathematics (STEM) (National Mathematics Advisory Panel, 2008). Since solving of human problems is connected to the real life, the arithmetic word problems (in short AWP) are an important kind of mathematics tasks in scho...
The Motivation of Secondary School Students in Mathematical Word Problem Solving
Gasco, Javier; Villarroel, Jose-Domingo
2014-01-01
Introduction: Motivation is an important factor in the learning of mathematics. Within this area of education, word problem solving is central in most mathematics curricula of Secondary School. The objective of this research is to detect the differences in motivation in terms of the strategies used to solve word problems. Method: It analyzed the…
Adeneye Olarewaju Awofala
2016-01-01
This study investigated the effect of personalisation of instruction on the motivation to learn mathematics word problems of 450 senior secondary students in Nigeria within the blueprint of quasi-experimental research of Solomon Four non-equivalent control group design. It also examined the influence of gender on motivation to learn mathematics word problems and personalisation was accomplished by incorporating selected information with students’ personal preferences into their mathematics wo...
Helping Students with Emotional and Behavioral Disorders Solve Mathematics Word Problems
Alter, Peter
2012-01-01
The author presents a strategy for helping students with emotional and behavioral disorders become more proficient at solving math word problems. Math word problems require students to go beyond simple computation in mathematics (e.g., adding, subtracting, multiplying, and dividing) and use higher level reasoning that includes recognizing relevant…
Students’ Representation in Mathematical Word Problem-Solving: Exploring Students’ Self-efficacy
Sahendra, A.; Budiarto, M. T.; Fuad, Y.
2018-01-01
This descriptive qualitative research aims at investigating student represented in mathematical word problem solving based on self-efficacy. The research subjects are two eighth graders at a school in Surabaya with equal mathematical ability consisting of two female students with high and low self-efficacy. The subjects were chosen based on the results of test of mathematical ability, documentation of the result of middle test in even semester of 2016/2017 academic year, and results of questionnaire of mathematics word problem in terms of self-efficacy scale. The selected students were asked to do mathematical word problem solving and be interviewed. The result of this study shows that students with high self-efficacy tend to use multiple representations of sketches and mathematical models, whereas students with low self-efficacy tend to use single representation of sketches or mathematical models only in mathematical word problem-solving. This study emphasizes that teachers should pay attention of student’s representation as a consideration of designing innovative learning in order to increase the self-efficacy of each student to achieve maximum mathematical achievement although it still requires adjustment to the school situation and condition.
Bernardo, Allan B I; Calleja, Marissa O
2005-03-01
Researchers have suggested that among bilinguals, solving word problems in mathematics is influenced by linguistic factors (K. Durkin & B. Shire, 1991; L. Verschaffel, B. Greer, & E. De Corte, 2000). Others have suggested that students exhibit a strong tendency to exclude real-world constraints in solving mathematics word problems (L. Verschaffel, E. De Corte, & S. Lasure, 1994). In the present study, the authors explored the effects of stating word problems in either Filipino or English on how Filipino-English bilingual students solved word problems in which the solution required the application of real-world knowledge. The authors asked bilingual students to solve word problems in either their first or second language. For some of the word problems, real-life constraints prevented straightforward application of mathematical procedures. The authors analyzed the students' solutions to determine whether the language of the word problems affected the tendency to apply real-life constraints in the solution. Results showed that the bilingual students (a) rarely considered real-life constraints in their solutions, (b) were more successful in understanding and solving word problems that were stated in their first language, and (c) were more likely to experience failure in finding a solution to problems stated in their second language. The results are discussed in terms of the relationship between linguistic and mathematical problem-solving processes among bilinguals.
Usman, Ahmed Ibrahim
2015-01-01
Knowledge and understanding of mathematical operations serves as a pre-reequisite for the successful translation of algebraic word problems. This study explored pre-service teachers' ability to recognize mathematical operations as well as use of those capabilities in constructing algebraic expressions, equations, and their solutions. The outcome…
Students' Mathematics Word Problem-Solving Achievement in a Computer-Based Story
Gunbas, N.
2015-01-01
The purpose of this study was to investigate the effect of a computer-based story, which was designed in anchored instruction framework, on sixth-grade students' mathematics word problem-solving achievement. Problems were embedded in a story presented on a computer as computer story, and then compared with the paper-based version of the same story…
Exploring the Learning of Mathematics Word Problems by African Immigrant Early Learners
Mahofa, Ernest; Adendorff, Stanley; Kwenda, Chiwimbiso
2018-01-01
The aim of this study was to explore the learning of mathematics word problems by African immigrant early learners in the Western Cape Province of South Africa (SA). Phenomenology was used as the philosophical underpinning for this study and also informed the research method. Purposive sampling methods were used to select 10 African immigrant…
Björn, Piia Maria; Aunola, Kaisa; Nurmi, Jari-Erik
2016-01-01
This longitudinal study aimed to investigate the extent to which primary school text comprehension predicts mathematical word problem-solving skills in secondary school among Finnish students. The participants were 224 fourth graders (9-10 years old at the baseline). The children's text-reading fluency, text comprehension and basic calculation…
Rosales, Javier; Vicente, Santiago; Chamoso, Jose M.; Munez, David; Orrantia, Josetxu
2012-01-01
Word problem solving involves the construction of two different mental representations, namely, mathematical and situational. Although educational research in word problem solving has documented different kinds of instruction at these levels, less is known about how both representational levels are evoked during word problem solving in day-to-day…
Jitendra, Asha K.; Petersen-Brown, Shawna; Lein, Amy E.; Zaslofsky, Anne F.; Kunkel, Amy K.; Jung, Pyung-Gang; Egan, Andrea M.
2015-01-01
This study examined the quality of the research base related to strategy instruction priming the underlying mathematical problem structure for students with learning disabilities and those at risk for mathematics difficulties. We evaluated the quality of methodological rigor of 18 group research studies using the criteria proposed by Gersten et…
Are middle school mathematics teachers able to solve word problems without using variable?
Gökkurt Özdemir, Burçin; Erdem, Emrullah; Örnek, Tuğba; Soylu, Yasin
2018-01-01
Many people consider problem solving as a complex process in which variables such as x, y are used. Problems may not be solved by only using 'variable.' Problem solving can be rationalized and made easier using practical strategies. When especially the development of children at younger ages is considered, it is obvious that mathematics teachers should solve problems through concrete processes. In this context, middle school mathematics teachers' skills to solve word problems without using variables were examined in the current study. Through the case study method, this study was conducted with 60 middle school mathematics teachers who have different professional experiences in five provinces in Turkey. A test consisting of five open-ended word problems was used as the data collection tool. The content analysis technique was used to analyze the data. As a result of the analysis, it was seen that the most of the teachers used trial-and-error strategy or area model as the solution strategy. On the other hand, the teachers who solved the problems using variables such as x, a, n or symbols such as Δ, □, ○, * and who also felt into error by considering these solutions as without variable were also seen in the study.
Morin, Lisa L.; Watson, Silvana M. R.; Hester, Peggy; Raver, Sharon
2017-01-01
For students with mathematics difficulties (MD), math word problem solving is especially challenging. The purpose of this study was to examine the effects of a problem-solving strategy, bar model drawing, on the mathematical problem-solving skills of students with MD. The study extended previous research that suggested that schematic-based…
Working memory components as predictors of children's mathematical word problem solving.
Zheng, Xinhua; Swanson, H Lee; Marcoulides, George A
2011-12-01
This study determined the working memory (WM) components (executive, phonological loop, and visual-spatial sketchpad) that best predicted mathematical word problem-solving accuracy of elementary school children in Grades 2, 3, and 4 (N=310). A battery of tests was administered to assess problem-solving accuracy, problem-solving processes, WM, reading, and math calculation. Structural equation modeling analyses indicated that (a) all three WM components significantly predicted problem-solving accuracy, (b) reading skills and calculation proficiency mediated the predictive effects of the central executive system and the phonological loop on solution accuracy, and (c) academic mediators failed to moderate the relationship between the visual-spatial sketchpad and solution accuracy. The results support the notion that all components of WM play a major role in predicting problem-solving accuracy, but basic skills acquired in specific academic domains (reading and math) can compensate for some of the influence of WM on children's mathematical word problem solving. Copyright © 2011 Elsevier Inc. All rights reserved.
Jitendra, Asha K; Petersen-Brown, Shawna; Lein, Amy E; Zaslofsky, Anne F; Kunkel, Amy K; Jung, Pyung-Gang; Egan, Andrea M
2015-01-01
This study examined the quality of the research base related to strategy instruction priming the underlying mathematical problem structure for students with learning disabilities and those at risk for mathematics difficulties. We evaluated the quality of methodological rigor of 18 group research studies using the criteria proposed by Gersten et al. and 10 single case design (SCD) research studies using criteria suggested by Horner et al. and the What Works Clearinghouse. Results indicated that 14 group design studies met the criteria for high-quality or acceptable research, whereas SCD studies did not meet the standards for an evidence-based practice. Based on these findings, strategy instruction priming the mathematics problem structure is considered an evidence-based practice using only group design methodological criteria. Implications for future research and for practice are discussed. © Hammill Institute on Disabilities 2013.
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Marija Kavkler
2014-05-01
Full Text Available BACKGROUND Difficulties in solving mathematical word problems (MWP are one of the most common reasons for weak mathematics performance, and poor mathematical literacy has important implications for an individual’s further education, employment opportunities, mental health and quality of life in today’s modern technological society. The purpose of the study was to examine whether Slovenian good and poor MWP solvers differ in arithmetic knowledge and skills, non-verbal reasoning, pupils’ self-evaluations of MWP abilities, teachers’ assessment of their mathematical knowledge and what strategies fifth- grade learners use in solving MWP. PARTICIPANTS AND PROCEDURE The larger sample included 233 pupils from 14 fifth-grade classes (mean age 10 years 3 months and 14 teachers. On the basis of the teachers’ opinions and the results of MWP solving two sub-samples of 24 students were formed, good and poor MWP solvers. Several tests were used to determine MWP solving ability, automation of arithmetic facts and procedures as well as Raven’s SPM. Questionnaires for pupils were used to assess pupils’ estimations of MWP tasks’ difficulty, their own ability to solve them and the strategies used. To assess pupils’ knowledge a questionnaire for teachers was used. RESULTS Slovenian 5 th graders in the larger sample generally used very few empirically proven effective cognitive and metacognitive strategies to solve MWP. Pupils with lower achievement in solving MWP, compared to pupils with higher achievement demonstrated significantly less automated arithmetic facts and procedures of the algorithm, less flexible use of arithmetic skills, as well as qualitatively different MWP solving, which is also related to their lower non-verbal reasoning. Teachers’ assessments and pupils’ self-assessments matched the achieved test results. CONCLUSIONS The results exposed important key factors for successful solving of mathematical word problems with
Powell, Sarah R; Fuchs, Lynn S
2010-05-01
Elementary school students often misinterpret the equal sign (=) as an operational rather than a relational symbol. Such misunderstanding is problematic because solving equations with missing numbers may be important for higher-order mathematics skills including word problems. Research indicates equal-sign instruction can alter how typically-developing students use the equal sign, but no study has examined effects for students with mathematics difficulty (MD) or how equal-sign instruction contributes to word-problem skill for students with or without MD. The present study assessed the efficacy of equal-sign instruction within word-problem tutoring. Third-grade students with MD (n = 80) were assigned to word-problem tutoring, word-problem tutoring plus equal-sign instruction (combined) tutoring, or no-tutoring control. Combined tutoring produced better improvement on equal sign tasks and open equations compared to the other 2 conditions. On certain forms of word problems, combined tutoring but not word-problem tutoring alone produced better improvement than control. When compared at posttest to 3(rd)-grade students without MD on equal sign tasks and open equations, only combined tutoring students with MD performed comparably.
Abdullah, Nasarudin; Halim, Lilia; Zakaria, Effandi
2014-01-01
This study aimed to determine the impact of strategic thinking and visual representation approaches (VStops) on the achievement, conceptual knowledge, metacognitive awareness, awareness of problem-solving strategies, and student attitudes toward mathematical word problem solving among primary school students. The experimental group (N = 96)…
Kribbs, Elizabeth E.; Rogowsky, Beth A.
2016-01-01
Mathematics word-problems continue to be an insurmountable challenge for many middle school students. Educators have used pictorial and schematic illustrations within the classroom to help students visualize these problems. However, the data shows that pictorial representations can be more harmful than helpful in that they only display objects or…
MONTO: A Machine-Readable Ontology for Teaching Word Problems in Mathematics
Lalingkar, Aparna; Ramnathan, Chandrashekar; Ramani, Srinivasan
2015-01-01
The Indian National Curriculum Framework has as one of its objectives the development of mathematical thinking and problem solving ability. However, recent studies conducted in Indian metros have expressed concern about students' mathematics learning. Except in some private coaching academies, regular classroom teaching does not include problem…
Oostermeijer, M.; Boonen, A.J.H.; Jolles, J.
2014-01-01
The scientific literature shows that constructive play activities are positively related to children's spatial ability. Likewise, a close positive relation is found between spatial ability and mathematical word problem-solving performances. The relation between children's constructive play and their
Bjork, Isabel Maria; Bowyer-Crane, Claudine
2013-01-01
This study investigates the relationship between skills that underpin mathematical word problems and those that underpin numerical operations, such as addition, subtraction, division and multiplication. Sixty children aged 6-7 years were tested on measures of mathematical ability, reading accuracy, reading comprehension, verbal intelligence and…
Are Middle School Mathematics Teachers Able to Solve Word Problems without Using Variable?
Gökkurt Özdemir, Burçin; Erdem, Emrullah; Örnek, Tugba; Soylu, Yasin
2018-01-01
Many people consider problem solving as a complex process in which variables such as "x," "y" are used. Problems may not be solved by only using "variable." Problem solving can be rationalized and made easier using practical strategies. When especially the development of children at younger ages is considered, it is…
Walkington, Candace; Clinton, Virginia; Shivraj, Pooja
2018-01-01
The link between reading and mathematics achievement is well known, and an important question is whether readability factors in mathematics problems are differentially impacting student groups. Using 20 years of data from the National Assessment of Educational Progress and the Trends in International Mathematics and Science Study, we examine how…
Cassidy, Jack
1991-01-01
Presents suggestions for teaching math word problems to elementary students. The strategies take into consideration differences between reading in math and reading in other areas. A problem-prediction game and four self-checking activities are included along with a magic password challenge. (SM)
González-Castro, Paloma; Cueli, Marisol; Areces, Débora; Rodríguez, Celestino; Sideridis, Georgios
2016-01-01
Problem solving represents a salient deficit in students with mathematical learning difficulties (MLD) primarily caused by difficulties with informal and formal mathematical competencies. This study proposes a computerized intervention tool, the integrated dynamic representation (IDR), for enhancing the early learning of basic mathematical…
Directory of Open Access Journals (Sweden)
Tuba Aydogdu Iskenderoglu
2018-04-01
Full Text Available It is important for pre-service teachers to know the conceptual difficulties they have experienced regarding the concepts of multiplication and division in fractions and problem posing is a way to learn these conceptual difficulties. Problem posing is a synthetic activity that fundamentally has multiple answers. The purpose of this study is to analyze the multiplication and division of fractions problems posed by pre-service elementary mathematics teachers and to investigate how the problems posed change according to the year of study the pre-service teachers are in. The study employed developmental research methods. A total of 213 pre-service teachers enrolled in different years of the Elementary Mathematics Teaching program at a state university in Turkey took part in the study. The “Problem Posing Test” was used as the data collecting tool. In this test, there are 3 multiplication and 3 division operations. The data were analyzed using qualitative descriptive analysis. The findings suggest that, regardless of the year, pre-service teachers had more conceptual difficulties in problem posing about the division of fractions than in problem posing about the multiplication of fractions.
Nash, Jr, John Forbes
2016-01-01
The goal in putting together this unique compilation was to present the current status of the solutions to some of the most essential open problems in pure and applied mathematics. Emphasis is also given to problems in interdisciplinary research for which mathematics plays a key role. This volume comprises highly selected contributions by some of the most eminent mathematicians in the international mathematical community on longstanding problems in very active domains of mathematical research. A joint preface by the two volume editors is followed by a personal farewell to John F. Nash, Jr. written by Michael Th. Rassias. An introduction by Mikhail Gromov highlights some of Nash’s legendary mathematical achievements. The treatment in this book includes open problems in the following fields: algebraic geometry, number theory, analysis, discrete mathematics, PDEs, differential geometry, topology, K-theory, game theory, fluid mechanics, dynamical systems and ergodic theory, cryptography, theoretical computer sc...
Embedding Number-Combinations Practice Within Word-Problem Tutoring
Powell, Sarah R.; Fuchs, Lynn S.; Fuchs, Douglas
2012-01-01
Two aspects of mathematics with which students with mathematics learning difficulty (MLD) often struggle are word problems and number-combination skills. This article describes a math program in which students receive instruction on using algebraic equations to represent the underlying problem structure for three word-problem types. Students also learn counting strategies for answering number combinations that they cannot retrieve from memory. Results from randomized-control trials indicated that embedding the counting strategies for number combinations produces superior word-problem and number-combination outcomes for students with MLD beyond tutoring programs that focus exclusively on number combinations or word problems. PMID:22661880
Chinese Number Words, Culture, and Mathematics Learning
Ng, Sharon Sui Ngan; Rao, Nirmala
2010-01-01
This review evaluates the role of language--specifically, the Chinese-based system of number words and the simplicity of Chinese mathematical terms--in explaining the relatively superior performance of Chinese and other East Asian students in cross-national studies of mathematics achievement. Relevant research is critically reviewed focusing on…
Math word problems for dummies
Sterling, Mary Jane
2008-01-01
Covers percentages, probability, proportions, and moreGet a grip on all types of word problems by applying them to real lifeAre you mystified by math word problems? This easy-to-understand guide shows you how to conquer these tricky questions with a step-by-step plan for finding the right solution each and every time, no matter the kind or level of problem. From learning math lingo and performing operations to calculating formulas and writing equations, you''ll get all the skills you need to succeed!Discover how to: * Translate word problems into plain English* Brush up on basic math skills* Plug in the right operation or formula* Tackle algebraic and geometric problems* Check your answers to see if they work
How to solve mathematical problems
Wickelgren, Wayne A
1995-01-01
Seven problem-solving techniques include inference, classification of action sequences, subgoals, contradiction, working backward, relations between problems, and mathematical representation. Also, problems from mathematics, science, and engineering with complete solutions.
Mathematical problems for chemistry students
Pota, Gyorgy
2011-01-01
Mathematical Problems for Chemistry Students has been compiled and written (a) to help chemistrystudents in their mathematical studies by providing them with mathematical problems really occurring in chemistry (b) to help practising chemists to activate their applied mathematical skills and (c) to introduce students and specialistsof the chemistry-related fields (physicists, mathematicians, biologists, etc.) intothe world of the chemical applications.Some problems of the collection are mathematical reformulations of those in the standard textbooks of chemistry, others we
Word Problems: A "Meme" for Our Times.
Leamnson, Robert N.
1996-01-01
Discusses a novel approach to word problems that involves linear relationships between variables. Argues that working stepwise through intermediates is the way our minds actually work and therefore this should be used in solving word problems. (JRH)
Students' errors in solving linear equation word problems: Case ...
African Journals Online (AJOL)
kofi.mereku
Development in most areas of life is based on effective knowledge of science and ... Problem solving, as used in mathematics education literature, refers ... word problems, on the other hand, are those linear equation tasks or ... taught LEWPs in the junior high school, many of them reach the senior high school without a.
Boonen, Anton J. H.; de Koning, Björn B.; Jolles, Jelle; van der Schoot, Menno
2016-01-01
Successfully solving mathematical word problems requires both mental representation skills and reading comprehension skills. In Realistic Math Education (RME), however, students primarily learn to apply the first of these skills (i.e., representational skills) in the context of word problem solving. Given this, it seems legitimate to assume that students from a RME curriculum experience difficulties when asked to solve semantically complex word problems. We investigated this assumption under 80 sixth grade students who were classified as successful and less successful word problem solvers based on a standardized mathematics test. To this end, students completed word problems that ask for both mental representation skills and reading comprehension skills. The results showed that even successful word problem solvers had a low performance on semantically complex word problems, despite adequate performance on semantically less complex word problems. Based on this study, we concluded that reading comprehension skills should be given a (more) prominent role during word problem solving instruction in RME. PMID:26925012
Directory of Open Access Journals (Sweden)
Anton eBoonen
2016-02-01
Full Text Available Successfully solving mathematical word problems requires both mental representation skills and reading comprehension skills. In Realistic Math Education (RME, however, students primarily learn to apply the first of these skills (i.e., representational skills in the context of word problem solving. Given this, it seems legitimate to assume that students from a RME curriculum experience difficulties when asked to solve semantically complex word problems. We investigated this assumption under 80 sixth grade students who were classified as successful and less successful word problem solvers based on a standardized mathematics test. To this end, students completed word problems that ask for both mental representation skills and reading comprehension skills. The results showed that even successful word problem solvers had a low performance on semantically complex word problems, despite adequate performance on semantically less complex word problems. Based on this study, we concluded that reading comprehension skills should be given a (more prominent role during word problem solving instruction in RME.
Boonen, Anton J H; de Koning, Björn B; Jolles, Jelle; van der Schoot, Menno
2016-01-01
Successfully solving mathematical word problems requires both mental representation skills and reading comprehension skills. In Realistic Math Education (RME), however, students primarily learn to apply the first of these skills (i.e., representational skills) in the context of word problem solving. Given this, it seems legitimate to assume that students from a RME curriculum experience difficulties when asked to solve semantically complex word problems. We investigated this assumption under 80 sixth grade students who were classified as successful and less successful word problem solvers based on a standardized mathematics test. To this end, students completed word problems that ask for both mental representation skills and reading comprehension skills. The results showed that even successful word problem solvers had a low performance on semantically complex word problems, despite adequate performance on semantically less complex word problems. Based on this study, we concluded that reading comprehension skills should be given a (more) prominent role during word problem solving instruction in RME.
Three-M in Word Problem Solving
Hajra, Sayonita Ghosh; Kofman, Victoria
2018-01-01
We describe three activities that help undergraduates (pre-service teachers) to develop scientific vocabulary on measurable attributes and units of measurement. Measurable attributes are important features in understanding a word problem and solving the problem. These activities help students comprehend word problems better by identifying…
The compressed word problem for groups
Lohrey, Markus
2014-01-01
The Compressed Word Problem for Groups provides a detailed exposition of known results on the compressed word problem, emphasizing efficient algorithms for the compressed word problem in various groups. The author presents the necessary background along with the most recent results on the compressed word problem to create a cohesive self-contained book accessible to computer scientists as well as mathematicians. Readers will quickly reach the frontier of current research which makes the book especially appealing for students looking for a currently active research topic at the intersection of group theory and computer science. The word problem introduced in 1910 by Max Dehn is one of the most important decision problems in group theory. For many groups, highly efficient algorithms for the word problem exist. In recent years, a new technique based on data compression for providing more efficient algorithms for word problems, has been developed, by representing long words over group generators in a compres...
Mathematical problems in meteorological modelling
Csomós, Petra; Faragó, István; Horányi, András; Szépszó, Gabriella
2016-01-01
This book deals with mathematical problems arising in the context of meteorological modelling. It gathers and presents some of the most interesting and important issues from the interaction of mathematics and meteorology. It is unique in that it features contributions on topics like data assimilation, ensemble prediction, numerical methods, and transport modelling, from both mathematical and meteorological perspectives. The derivation and solution of all kinds of numerical prediction models require the application of results from various mathematical fields. The present volume is divided into three parts, moving from mathematical and numerical problems through air quality modelling, to advanced applications in data assimilation and probabilistic forecasting. The book arose from the workshop “Mathematical Problems in Meteorological Modelling” held in Budapest in May 2014 and organized by the ECMI Special Interest Group on Numerical Weather Prediction. Its main objective is to highlight the beauty of the de...
Bae, Young Seh
2013-01-01
Mathematical Word Problem Solving of Students with Autistic Spectrum Disorders and Students with Typical Development Young Seh Bae This study investigated mathematical word problem solving and the factors associated with the solution paths adopted by two groups of participants (N=40), students with autism spectrum disorders (ASDs) and typically…
Problem solving through recreational mathematics
Averbach, Bonnie
1999-01-01
Historically, many of the most important mathematical concepts arose from problems that were recreational in origin. This book takes advantage of that fact, using recreational mathematics - problems, puzzles and games - to teach students how to think critically. Encouraging active participation rather than just observation, the book focuses less on mathematical results than on how these results can be applied to thinking about problems and solving them. Each chapter contains a diverse array of problems in such areas as logic, number and graph theory, two-player games of strategy, solitaire ga
Problem Solving Frameworks for Mathematics and Software Development
McMaster, Kirby; Sambasivam, Samuel; Blake, Ashley
2012-01-01
In this research, we examine how problem solving frameworks differ between Mathematics and Software Development. Our methodology is based on the assumption that the words used frequently in a book indicate the mental framework of the author. We compared word frequencies in a sample of 139 books that discuss problem solving. The books were grouped…
Modern problems in insurance mathematics
Martin-Löf, Anders
2014-01-01
This book is a compilation of 21 papers presented at the International Cramér Symposium on Insurance Mathematics (ICSIM) held at Stockholm University in June, 2013. The book comprises selected contributions from several large research communities in modern insurance mathematics and its applications. The main topics represented in the book are modern risk theory and its applications, stochastic modelling of insurance business, new mathematical problems in life and non-life insurance, and related topics in applied and financial mathematics. The book is an original and useful source of inspiration and essential reference for a broad spectrum of theoretical and applied researchers, research students and experts from the insurance business. In this way, Modern Problems in Insurance Mathematics will contribute to the development of research and academy–industry co-operation in the area of insurance mathematics and its applications.
Applied Mathematical Problems in Engineering
Directory of Open Access Journals (Sweden)
Carlos Llopis-Albert
2016-10-01
Full Text Available There is a close relationship between engineering and mathematics, which has led to the development of new techniques in recent years. Likewise the developments in technology and computers have led to new ways of teaching mathematics for engineering students and the use of modern techniques and methods. This research aims to provide insight on how to deal with mathematical problems for engineering students. This is performed by means of a fuzzy set/Qualitative Comparative Analysis applied to conflict resolution of Public Participation Projects in support to the EU Water Framework Directive.
Obstacle problems in mathematical physics
Rodrigues, J-F
1987-01-01
The aim of this research monograph is to present a general account of the applicability of elliptic variational inequalities to the important class of free boundary problems of obstacle type from a unifying point of view of classical Mathematical Physics.The first part of the volume introduces some obstacle type problems which can be reduced to variational inequalities. Part II presents some of the main aspects of the theory of elliptic variational inequalities, from the abstract hilbertian framework to the smoothness of the variational solution, discussing in general the properties of the free boundary and including some results on the obstacle Plateau problem. The last part examines the application to free boundary problems, namely the lubrication-cavitation problem, the elastoplastic problem, the Signorini (or the boundary obstacle) problem, the dam problem, the continuous casting problem, the electrochemical machining problem and the problem of the flow with wake in a channel past a profile.
Solving applied mathematical problems with Matlab
Xue, Dingyu
2008-01-01
Computer Mathematics Language-An Overview. Fundamentals of MATLAB Programming. Calculus Problems. MATLAB Computations of Linear Algebra Problems. Integral Transforms and Complex Variable Functions. Solutions to Nonlinear Equations and Optimization Problems. MATLAB Solutions to Differential Equation Problems. Solving Interpolations and Approximations Problems. Solving Probability and Mathematical Statistics Problems. Nontraditional Solution Methods for Mathematical Problems.
The semantic system is involved in mathematical problem solving.
Zhou, Xinlin; Li, Mengyi; Li, Leinian; Zhang, Yiyun; Cui, Jiaxin; Liu, Jie; Chen, Chuansheng
2018-02-01
Numerous studies have shown that the brain regions around bilateral intraparietal cortex are critical for number processing and arithmetical computation. However, the neural circuits for more advanced mathematics such as mathematical problem solving (with little routine arithmetical computation) remain unclear. Using functional magnetic resonance imaging (fMRI), this study (N = 24 undergraduate students) compared neural bases of mathematical problem solving (i.e., number series completion, mathematical word problem solving, and geometric problem solving) and arithmetical computation. Direct subject- and item-wise comparisons revealed that mathematical problem solving typically had greater activation than arithmetical computation in all 7 regions of the semantic system (which was based on a meta-analysis of 120 functional neuroimaging studies on semantic processing). Arithmetical computation typically had greater activation in the supplementary motor area and left precentral gyrus. The results suggest that the semantic system in the brain supports mathematical problem solving. Copyright © 2017 Elsevier Inc. All rights reserved.
Open problems in mathematical physics
International Nuclear Information System (INIS)
Coley, Alan A
2017-01-01
We present a list of open questions in mathematical physics. After a historical introduction, a number of problems in a variety of different fields are discussed, with the intention of giving an overall impression of the current status of mathematical physics, particularly in the topical fields of classical general relativity, cosmology and the quantum realm. This list is motivated by the recent article proposing 42 fundamental questions (in physics) which must be answered on the road to full enlightenment (Allen and Lidstrom 2017 Phys. Scr . 92 012501). But paraphrasing a famous quote by the British football manager Bill Shankly, in response to the question of whether mathematics can answer the Ultimate Question of Life, the Universe, and Everything, mathematics is, of course, much more important than that. (invited comment)
Open problems in mathematical physics
Coley, Alan A.
2017-09-01
We present a list of open questions in mathematical physics. After a historical introduction, a number of problems in a variety of different fields are discussed, with the intention of giving an overall impression of the current status of mathematical physics, particularly in the topical fields of classical general relativity, cosmology and the quantum realm. This list is motivated by the recent article proposing 42 fundamental questions (in physics) which must be answered on the road to full enlightenment (Allen and Lidstrom 2017 Phys. Scr. 92 012501). But paraphrasing a famous quote by the British football manager Bill Shankly, in response to the question of whether mathematics can answer the Ultimate Question of Life, the Universe, and Everything, mathematics is, of course, much more important than that.
Language and mathematical problem solving among bilinguals.
Bernardo, Allan B I
2002-05-01
Does using a bilingual's 1st or 2nd language have an effect on problem solving in semantically rich domains like school mathematics? The author conducted a study to determine whether Filipino-English bilingual students' understanding and solving of word problems in arithmetic differed when the problems were in the students' 1st and 2nd languages. Two groups participated-students whose 1st language was Filipino and students whose 1st language was English-and easy and difficult arithmetic problems were used. The author used a recall paradigm to assess how students understood the word problems and coded the solution accuracy to assess problem solving. The results indicated a 1st-language advantage; that is, the students were better able to understand and solve problems in their 1st language, whether the 1st language was English or Filipino. Moreover, the advantage was more marked with the easy problems. The theoretical and practical implications of the results are discussed.
Mathematical problems in image processing
International Nuclear Information System (INIS)
Chidume, C.E.
2000-01-01
This is the second volume of a new series of lecture notes of the Abdus Salam International Centre for Theoretical Physics. This volume contains the lecture notes given by A. Chambolle during the School on Mathematical Problems in Image Processing. The school consisted of two weeks of lecture courses and one week of conference
A Comparative Analysis of Word Problems in Selected United States and Russian First Grade Textbooks
Grishchenko, Svetlana
2009-01-01
The purpose of this study was to explore word problems as a subject matter in mathematics textbook curricula. The motivation for the study derived from the following evidence: (a) American students find some word problems are more difficult than others (Garcia, Jimenez, & Hess, 2006; Riley & Green, 1988; Stern, 2001), and (b) one of the…
Cognitive Strategy Instruction for Teaching Word Problems to Primary-Level Struggling Students
Pfannenstiel, Kathleen Hughes; Bryant, Diane Pedrotty; Bryant, Brian R.; Porterfield, Jennifer A.
2015-01-01
Students with mathematics difficulties and learning disabilities (LD) typically struggle with solving word problems. These students often lack knowledge about efficient, cognitive strategies to utilize when solving word problems. Cognitive strategy instruction has been shown to be effective in teaching struggling students how to solve word…
Young Filipino Students Making Sense of Arithmetic Word Problems in English
Bautista, Debbie; Mulligan, Joanne; Mitchelmore, Michael
2009-01-01
Young Filipino children are expected to solve mathematical word problems in English, a task which they typically encounter only in schools. In this exploratory study, task-based interviews were conducted with seven Filipino children from a public school. The children were asked to read and solve addition and subtraction word problems in English or…
Why Do Disadvantaged Filipino Children Find Word Problems in English Difficult?
Bautista, Debbie; Mulligan, Joanne
2010-01-01
Young Filipino students are expected to solve mathematical word problems in English, a language that many encounter only in schools. Using individual interviews of 17 Filipino children, we investigated why word problems in English are difficult and the extent to which the language interferes with performance. Results indicate that children could…
Improving mathematical problem solving : A computerized approach
Harskamp, EG; Suhre, CJM
Mathematics teachers often experience difficulties in teaching students to become skilled problem solvers. This paper evaluates the effectiveness of two interactive computer programs for high school mathematics problem solving. Both programs present students with problems accompanied by instruction
Solving Mathematical Problems A Personal Perspective
Tao, Terence
2006-01-01
Authored by a leading name in mathematics, this engaging and clearly presented text leads the reader through the tactics involved in solving mathematical problems at the Mathematical Olympiad level. With numerous exercises and assuming only basic mathematics, this text is ideal for students of 14 years and above in pure mathematics.
MATHEMATICAL PROBLEMS OF INTEGRATIVE CONTENTS
Directory of Open Access Journals (Sweden)
V. Kushnir
2014-09-01
Full Text Available The tasks of integrative content requires the use of knowledge and skills on various themes both one discipline and different disciplines. Mostly in the classroom (or in homework the tasks on the properties absorption of different concepts using different theories are considered. Thus knowledge within only one discipline is formed, knowledge of the narrow sense (one subject. Such knowledge is "prescriptional", we call it idealized. After all, it is far from models of the real professional problems and problems of life in general, in order to solve them it is necessary to apply knowledge and skills acquired in different themes of the same objects,life experience. Practical formation of integrative knowledge requires statement of the educational problems before the subjects of studying, the problems within the "narrow objectivity" can not be resolved at all, or such kind of solving is too difficult to solve, for example, the nature and the context of solving problems (scientific approaches to solving problems, creating mathematical models, methods for solving such models, means of solving, application of methods, analysis of the models solution and the right choice, the inspection of solutions, etc. will sink in the conglomeration of technical operations. The problems with integrative content are usually more complicated than the problems of "narrow objectivity." In our problems the index of such difficulty is the essence of educational content, which is disclosed in the previous paragraph. The problems solution proposed in this article requires knowledge of the structural geometry (circle construction, touching two or three laps: with analytic geometry (method of coordinates on the plane; the distance between two points on the coordinate plane; algebra (system drawing irrational equations, method for solving such system, the solution of the system, analysis of the results and the right choose of the desired solution for found criterion, testing
Mathematical Thinking and Creativity through Mathematical Problem Posing and Solving
Directory of Open Access Journals (Sweden)
María F. Ayllón
2016-04-01
Full Text Available This work shows the relationship between the development of mathematical thinking and creativity with mathematical problem posing and solving. Creativity and mathematics are disciplines that do not usually appear together. Both concepts constitute complex processes sharing elements, such as fluency (number of ideas, flexibility (range of ideas, novelty (unique idea and elaboration (idea development. These factors contribute, among others, to the fact that schoolchildren are competent in mathematics. The problem solving and posing are a very powerful evaluation tool that shows the mathematical reasoning and creative level of a person. Creativity is part of the mathematics education and is a necessary ingredient to perform mathematical assignments. This contribution presents some important research works about problem posing and solving related to the development of mathematical knowledge and creativity. To that end, it is based on various beliefs reflected in the literature with respect to notions of creativity, problem solving and posing.
Some unsolved problems in discrete mathematics and mathematical cybernetics
Energy Technology Data Exchange (ETDEWEB)
Korshunov, Aleksei D [S.L. Sobolev Institute for Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk (Russian Federation)
2009-10-31
There are many unsolved problems in discrete mathematics and mathematical cybernetics. Writing a comprehensive survey of such problems involves great difficulties. First, such problems are rather numerous and varied. Second, they greatly differ from each other in degree of completeness of their solution. Therefore, even a comprehensive survey should not attempt to cover the whole variety of such problems; only the most important and significant problems should be reviewed. An impersonal choice of problems to include is quite hard. This paper includes 13 unsolved problems related to combinatorial mathematics and computational complexity theory. The problems selected give an indication of the author's studies for 50 years; for this reason, the choice of the problems reviewed here is, to some extent, subjective. At the same time, these problems are very difficult and quite important for discrete mathematics and mathematical cybernetics. Bibliography: 74 items.
Some unsolved problems in discrete mathematics and mathematical cybernetics
Korshunov, Aleksei D.
2009-10-01
There are many unsolved problems in discrete mathematics and mathematical cybernetics. Writing a comprehensive survey of such problems involves great difficulties. First, such problems are rather numerous and varied. Second, they greatly differ from each other in degree of completeness of their solution. Therefore, even a comprehensive survey should not attempt to cover the whole variety of such problems; only the most important and significant problems should be reviewed. An impersonal choice of problems to include is quite hard. This paper includes 13 unsolved problems related to combinatorial mathematics and computational complexity theory. The problems selected give an indication of the author's studies for 50 years; for this reason, the choice of the problems reviewed here is, to some extent, subjective. At the same time, these problems are very difficult and quite important for discrete mathematics and mathematical cybernetics. Bibliography: 74 items.
Some unsolved problems in discrete mathematics and mathematical cybernetics
International Nuclear Information System (INIS)
Korshunov, Aleksei D
2009-01-01
There are many unsolved problems in discrete mathematics and mathematical cybernetics. Writing a comprehensive survey of such problems involves great difficulties. First, such problems are rather numerous and varied. Second, they greatly differ from each other in degree of completeness of their solution. Therefore, even a comprehensive survey should not attempt to cover the whole variety of such problems; only the most important and significant problems should be reviewed. An impersonal choice of problems to include is quite hard. This paper includes 13 unsolved problems related to combinatorial mathematics and computational complexity theory. The problems selected give an indication of the author's studies for 50 years; for this reason, the choice of the problems reviewed here is, to some extent, subjective. At the same time, these problems are very difficult and quite important for discrete mathematics and mathematical cybernetics. Bibliography: 74 items.
Research Mathematicians' Practices in Selecting Mathematical Problems
Misfeldt, Morten; Johansen, Mikkel Willum
2015-01-01
Developing abilities to create, inquire into, qualify, and choose among mathematical problems is an important educational goal. In this paper, we elucidate how mathematicians work with mathematical problems in order to understand this mathematical process. More specifically, we investigate how mathematicians select and pose problems and discuss to…
Mathematical Profiles and Problem Solving Abilities of Mathematically Promising Students
Budak, Ibrahim
2012-01-01
Mathematically promising students are defined as those who have the potential to become the leaders and problem solvers of the future. The purpose of this research is to reveal what problem solving abilities mathematically promising students show in solving non-routine problems and type of profiles they present in the classroom and during problem…
Mathematical Thinking and Creativity through Mathematical Problem Posing and Solving
Ayllón, María F.; Gómez, Isabel A.; Ballesta-Claver, Julio
2016-01-01
This work shows the relationship between the development of mathematical thinking and creativity with mathematical problem posing and solving. Creativity and mathematics are disciplines that do not usually appear together. Both concepts constitute complex processes sharing elements, such as fluency (number of ideas), flexibility (range of ideas),…
de Guzman, Niño Jose P.; Belecina, Rene R.
2012-01-01
The teaching of mathematics involves problem solving skills which prove to be difficult on the part of the pupils due to misrepresentation of the word problems. Oftentimes, pupils tend to represent the phrase "more than" as addition and the word difference as "- ". This paper aims to address the problem solving skills of grade…
Current problems in applied mathematics and mathematical physics
Samarskii, A. A.
Papers are presented on such topics as mathematical models in immunology, mathematical problems of medical computer tomography, classical orthogonal polynomials depending on a discrete variable, and boundary layer methods for singular perturbation problems in partial derivatives. Consideration is also given to the computer simulation of supernova explosion, nonstationary internal waves in a stratified fluid, the description of turbulent flows by unsteady solutions of the Navier-Stokes equations, and the reduced Galerkin method for external diffraction problems using the spline approximation of fields.
Factors Influencing Filipino Children's Solutions to Addition and Subtraction Word Problems
Bautista, Debbie; Mitchelmore, Michael; Mulligan, Joanne
2009-01-01
Young Filipino children are expected to solve mathematical word problems in English, which is not their mother tongue. Because of this, it is often assumed that Filipino children have difficulties in solving problems because they cannot read or comprehend what they have read. This study tested this assumption by determining whether presenting word…
The Model Method: Singapore Children's Tool for Representing and Solving Algebraic Word Problems
Ng, Swee Fong; Lee, Kerry
2009-01-01
Solving arithmetic and algebraic word problems is a key component of the Singapore elementary mathematics curriculum. One heuristic taught, the model method, involves drawing a diagram to represent key information in the problem. We describe the model method and a three-phase theoretical framework supporting its use. We conducted 2 studies to…
Elementary Students' Spontaneous Metacognitive Functions in Different Types of Mathematical Problems
Mokos, Evagelos; Kafoussi, Sonia
2013-01-01
Metacognition is the mind's ability to monitor and control itself or, in other words, the ability to know about our knowing (Dunlosky & Bjork, 2008). In mathematics education, the importance of the investigation of students' metacognition during their mathematical activity has been focused on the area of mathematics problem solving. This study…
Exploring mathematics problem-solving and proof
Grieser, Daniel
2018-01-01
Have you ever faced a mathematical problem and had no idea how to approach it? Or perhaps you had an idea but got stuck halfway through? This book guides you in developing your creativity, as it takes you on a voyage of discovery into mathematics. Readers will not only learn strategies for solving problems and logical reasoning, but they will also learn about the importance of proofs and various proof techniques. Other topics covered include recursion, mathematical induction, graphs, counting, elementary number theory, and the pigeonhole, extremal and invariance principles. Designed to help students make the transition from secondary school to university level, this book provides readers with a refreshing look at mathematics and deep insights into universal principles that are valuable far beyond the scope of this book. Aimed especially at undergraduate and secondary school students as well as teachers, this book will appeal to anyone interested in mathematics. Only basic secondary school mathematics is requi...
Powell, Sarah R; Fuchs, Lynn S
2014-08-01
According to national mathematics standards, algebra instruction should begin at kindergarten and continue through elementary school. Most often, teachers address algebra in the elementary grades with problems related to solving equations or understanding functions. With 789 2 nd - grade students, we administered (a) measures of calculations and word problems in the fall and (b) an assessment of pre-algebraic reasoning, with items that assessed solving equations and functions, in the spring. Based on the calculation and word-problem measures, we placed 148 students into 1 of 4 difficulty status categories: typically performing, calculation difficulty, word-problem difficulty, or difficulty with calculations and word problems. Analyses of variance were conducted on the 148 students; path analytic mediation analyses were conducted on the larger sample of 789 students. Across analyses, results corroborated the finding that word-problem difficulty is more strongly associated with difficulty with pre-algebraic reasoning. As an indicator of later algebra difficulty, word-problem difficulty may be a more useful predictor than calculation difficulty, and students with word-problem difficulty may require a different level of algebraic reasoning intervention than students with calculation difficulty.
Powell, Sarah R.; Fuchs, Lynn S.
2014-01-01
According to national mathematics standards, algebra instruction should begin at kindergarten and continue through elementary school. Most often, teachers address algebra in the elementary grades with problems related to solving equations or understanding functions. With 789 2nd- grade students, we administered (a) measures of calculations and word problems in the fall and (b) an assessment of pre-algebraic reasoning, with items that assessed solving equations and functions, in the spring. Based on the calculation and word-problem measures, we placed 148 students into 1 of 4 difficulty status categories: typically performing, calculation difficulty, word-problem difficulty, or difficulty with calculations and word problems. Analyses of variance were conducted on the 148 students; path analytic mediation analyses were conducted on the larger sample of 789 students. Across analyses, results corroborated the finding that word-problem difficulty is more strongly associated with difficulty with pre-algebraic reasoning. As an indicator of later algebra difficulty, word-problem difficulty may be a more useful predictor than calculation difficulty, and students with word-problem difficulty may require a different level of algebraic reasoning intervention than students with calculation difficulty. PMID:25309044
Advanced Problems in Mathematics : Preparing for University
Siklos, Stephen
2016-01-01
" This book is intended to help candidates prepare for entrance examinations in mathematics and scientific subjects, including STEP (Sixth Term Examination Paper). STEP is an examination used by Cambridge colleges as the basis for conditional offers. They are also used by Warwick University, and many other mathematics departments recommend that their applicants practice on the past papers even if they do not take the examination. Advanced Problems in Mathematics is recommended as preparati...
Plato's problem an introduction to mathematical platonism
Panza, M
2013-01-01
What is mathematics about? And how can we have access to the reality it is supposed to describe? The book tells the story of this problem, first raised by Plato, through the views of Aristotle, Proclus, Kant, Frege, Gödel, Benacerraf, up to the most recent debate on mathematical platonism.
Students' errors in solving linear equation word problems: Case ...
African Journals Online (AJOL)
The study examined errors students make in solving linear equation word problems with a view to expose the nature of these errors and to make suggestions for classroom teaching. A diagnostic test comprising 10 linear equation word problems, was administered to a sample (n=130) of senior high school first year Home ...
Understanding the Role of Linguistic Processes in the Solution of Arithmetic Word Problems.
LeBlanc, Mark D.
Ongoing work toward developing a learning environment that will perform real-time diagnoses of students' difficulties in solving mathematical word problems is described. The learning environment designed consists of a microworld and expert modules. The microworld (or toolbox) is a collection of mouse-driven interfaces that facilitate a transition…
Automatic Item Generation via Frame Semantics: Natural Language Generation of Math Word Problems.
Deane, Paul; Sheehan, Kathleen
This paper is an exploration of the conceptual issues that have arisen in the course of building a natural language generation (NLG) system for automatic test item generation. While natural language processing techniques are applicable to general verbal items, mathematics word problems are particularly tractable targets for natural language…
Peake, Christian; Jiménez, Juan E.; Rodríguez, Cristina; Bisschop, Elaine; Villarroel, Rebeca
2015-01-01
Arithmetic word problem (AWP) solving is a highly demanding task for children with learning disabilities (LD) since verbal and mathematical information have to be integrated. This study examines specifically how syntactic awareness (SA), the ability to manage the grammatical structures of language, affects AWP solving. Three groups of children in…
How to solve applied mathematics problems
Moiseiwitsch, B L
2011-01-01
This workbook bridges the gap between lectures and practical applications, offering students of mathematics, engineering, and physics the chance to practice solving problems from a wide variety of fields. 2011 edition.
Are Mathematics Problems a Problem for Women and Girls?
Schonberger, Ann K.
The primary questions investigated are: Is it true that males excel in mathematical problem solving and, if so, when does this superiority develop? An examination of recent research showed that sex-related differences did exist, although small, even after controlling for mathematics background. Differences appeared in early adolescence and were…
Processes involved in solving mathematical problems
Shahrill, Masitah; Putri, Ratu Ilma Indra; Zulkardi, Prahmana, Rully Charitas Indra
2018-04-01
This study examines one of the instructional practices features utilized within the Year 8 mathematics lessons in Brunei Darussalam. The codes from the TIMSS 1999 Video Study were applied and strictly followed, and from the 183 mathematics problems recorded, there were 95 problems with a solution presented during the public segments of the video-recorded lesson sequences of the four sampled teachers. The analyses involved firstly, identifying the processes related to mathematical problem statements, and secondly, examining the different processes used in solving the mathematical problems for each problem publicly completed during the lessons. The findings revealed that for three of the teachers, their problem statements coded as `using procedures' ranged from 64% to 83%, while the remaining teacher had 40% of his problem statements coded as `making connections.' The processes used when solving the problems were mainly `using procedures', and none of the problems were coded as `giving results only'. Furthermore, all four teachers made use of making the relevant connections in solving the problems given to their respective students.
Ingenious mathematical problems and methods
Graham, Louis A
2013-01-01
Collection of 100 of the best submissions to a math puzzle column features problems in engineering situations, logic, number theory, and geometry. Most solutions include details of several different methods.
Developing Mathematics Problems Based on Pisa Level
Directory of Open Access Journals (Sweden)
Shahibul Ahyan
2014-01-01
Full Text Available This research aims to produce mathematics problems based on PISA level with valid and practical content of change and relationships and has potential effect for Junior High School students. A development research method developed by Akker, Gravemeijer, McKenney and Nieveen is used this research. In the first stage, the researcher analyzed students, algebra material in school-based curricula (KTSP and mathematics problems of PISA 2003 of change and relationships content. The second stage, the researcher designed 13 problems with content of change and relationships. The last, the researcher used formative evaluation design developed by Tessmer which includes self evaluation, one-to-one, expert review, small group, and field test. The data collect by walk through, interview, and questionnaire. The result of this research indicated that 12 mathematical problems based on PISA level of change and relationships content that developed have validity, practically, and potential effects for Junior High School students.
Understanding the Problems of Learning Mathematics.
Semilla-Dube, Lilia
1983-01-01
A model is being developed to categorize problems in teaching and learning mathematics. Categories include problems due to language difficulties, lack of prerequisite knowledge, and those related to the affective domain. This paper calls on individuals to share teaching and learning episodes; those submitted will then be compiled and categorized.…
Word-based Morphology: Some Problems from a Polysynthetic Language.
Axelrod, Melissa
Some of the problems inherent in a word-based hypothesis asserting that the word/stem is taken as the minimal sign not only for syntax but also for morphology are examined in an analysis of a polysynthetic language, Koyukon, an Athabaskan language of Alaska. Data from the Central dialect is considered in the analysis. A brief sketch of the verbal…
Student’s thinking process in solving word problems in geometry
Khasanah, V. N.; Usodo, B.; Subanti, S.
2018-05-01
This research aims to find out the thinking process of seventh grade of Junior High School in solve word problem solving of geometry. This research was descriptive qualitative research. The subject of the research was selected based on sex and differences in mathematical ability. Data collection was done based on student’s work test, interview, and observation. The result of the research showed that there was no difference of thinking process between male and female with high mathematical ability, and there were differences of thinking process between male and female with moderate and low mathematical ability. Also, it was found that male with moderate mathematical ability took a long time in the step of making problem solving plans. While female with moderate mathematical ability took a long time in the step of understanding the problems. The importance of knowing the thinking process of students in solving word problem solving were that the teacher knows the difficulties faced by students and to minimize the occurrence of the same error in problem solving. Teacher could prepare the right learning strategies which more appropriate with student’s thinking process.
Problems in mathematical analysis III integration
Kaczor, W J
2003-01-01
We learn by doing. We learn mathematics by doing problems. This is the third volume of Problems in Mathematical Analysis. The topic here is integration for real functions of one real variable. The first chapter is devoted to the Riemann and the Riemann-Stieltjes integrals. Chapter 2 deals with Lebesgue measure and integration. The authors include some famous, and some not so famous, integral inequalities related to Riemann integration. Many of the problems for Lebesgue integration concern convergence theorems and the interchange of limits and integrals. The book closes with a section on Fourier series, with a concentration on Fourier coefficients of functions from particular classes and on basic theorems for convergence of Fourier series. The book is primarily geared toward students in analysis, as a study aid, for problem-solving seminars, or for tutorials. It is also an excellent resource for instructors who wish to incorporate problems into their lectures. Solutions for the problems are provided in the boo...
Mathematical Problems in Biology : Victoria Conference
1974-01-01
A conference on "Some Mathematical Problems in Biology" was held at the University of Victoria, Victoria, B. C. , Canada, from May 7 - 10, 1973. The participants and invited speakers were mathematicians interested in problems of a biological nature, and scientists actively engaged in developing mathematical models in biological fields. One aim of the conference was to attempt to assess what the recent rapid growth of mathematical interaction with the biosciences has accomplished and may accomplish in the near future. The conference also aimed to expose the problems of communication bet~",een mathematicians and biological scientists, and in doing so to stimulate the interchange of ideas. It was recognised that the topic spans an enormous breadth, and little attempt was made to balance the very diverse areas. Widespread active interest was shown in the conference, and just over one hundred people registered. The varied departments and institutions across North America from which the participants came made it bo...
On Teaching Problem Solving in School Mathematics
Directory of Open Access Journals (Sweden)
Erkki Pehkonen
2013-12-01
Full Text Available The article begins with a brief overview of the situation throughout the world regarding problem solving. The activities of the ProMath group are then described, as the purpose of this international research group is to improve mathematics teaching in school. One mathematics teaching method that seems to be functioning in school is the use of open problems (i.e., problem fields. Next we discuss the objectives of the Finnish curriculum that are connected with problem solving. Some examples and research results are taken from a Finnish–Chilean research project that monitors the development of problem-solving skills in third grade pupils. Finally, some ideas on “teacher change” are put forward. It is not possible to change teachers, but only to provide hints for possible change routes: the teachers themselves should work out the ideas and their implementation.
Learning via problem solving in mathematics education
Directory of Open Access Journals (Sweden)
Piet Human
2009-09-01
Full Text Available Three forms of mathematics education at school level are distinguished: direct expository teaching with an emphasis on procedures, with the expectation that learners will at some later stage make logical and functional sense of what they have learnt and practised (the prevalent form, mathematically rigorous teaching in terms of fundamental mathematical concepts, as in the so-called “modern mathematics” programmes of the sixties, teaching and learning in the context of engaging with meaningful problems and focused both on learning to become good problem solvers (teaching for problem solving andutilising problems as vehicles for the development of mathematical knowledge andproﬁciency by learners (problem-centred learning, in conjunction with substantialteacher-led social interaction and mathematical discourse in classrooms.Direct expository teaching of mathematical procedures dominated in school systems after World War II, and was augmented by the “modern mathematics” movement in the period 1960-1970. The latter was experienced as a major failure, and was soon abandoned. Persistent poor outcomes of direct expository procedural teaching of mathematics for the majority of learners, as are still being experienced in South Africa, triggered a world-wide movement promoting teaching mathematics for and via problem solving in the seventies and eighties of the previous century. This movement took the form of a variety of curriculum experiments in which problem solving was the dominant classroom activity, mainly in the USA, Netherlands, France and South Africa. While initially focusing on basic arithmetic (computation with whole numbers and elementary calculus, the problem-solving movement started to address other mathematical topics (for example, elementary statistics, algebra, differential equations around the turn of the century. The movement also spread rapidly to other countries, including Japan, Singapore and Australia. Parallel with the
Examples and problems in mathematical statistics
Zacks, Shelemyahu
2013-01-01
This book presents examples that illustrate the theory of mathematical statistics and details how to apply the methods for solving problems. While other books on the topic contain problems and exercises, they do not focus on problem solving. This book fills an important niche in the statistical theory literature by providing a theory/example/problem approach. Each chapter is divided into four parts: Part I provides the needed theory so readers can become familiar with the concepts, notations, and proven results; Part II presents examples from a variety of fields including engineering, mathem
Mathematical model in economic environmental problems
Energy Technology Data Exchange (ETDEWEB)
Nahorski, Z. [Polish Academy of Sciences, Systems Research Inst. (Poland); Ravn, H.F. [Risoe National Lab. (Denmark)
1996-12-31
The report contains a review of basic models and mathematical tools used in economic regulation problems. It starts with presentation of basic models of capital accumulation, resource depletion, pollution accumulation, and population growth, as well as construction of utility functions. Then the one-state variable model is discussed in details. The basic mathematical methods used consist of application of the maximum principle and phase plane analysis of the differential equations obtained as the necessary conditions of optimality. A summary of basic results connected with these methods is given in appendices. (au) 13 ills.; 17 refs.
Applying Lakatos' Theory to the Theory of Mathematical Problem Solving.
Nunokawa, Kazuhiko
1996-01-01
The relation between Lakatos' theory and issues in mathematics education, especially mathematical problem solving, is investigated by examining Lakatos' methodology of a scientific research program. (AIM)
Banerjee, Banmali
Methods and procedures for successfully solving math word problems have been, and continue to be a mystery to many U.S. high school students. Previous studies suggest that the contextual and mathematical understanding of a word problem, along with the development of schemas and their related external representations, positively contribute to students' accomplishments when solving word problems. Some studies have examined the effects of diagramming on students' abilities to solve word problems that only involved basic arithmetic operations. Other studies have investigated how instructional models that used technology influenced students' problem solving achievements. Still other studies have used schema-based instruction involving students with learning disabilities. No study has evaluated regular high school students' achievements in solving standard math word problems using a diagramming technique without technological aid. This study evaluated students' achievement in solving math word problems using a diagramming technique. Using a quasi-experimental experimental pretest-posttest research design, quantitative data were collected from 172 grade 11 Hispanic English language learners (ELLS) and African American learners whose first language is English (EFLLs) in 18 classes at an inner city high school in Northern New Jersey. There were 88 control and 84 experimental students. The pretest and posttest of each participating student and samples of the experimental students' class assignments provided the qualitative data for the study. The data from this study exhibited that the diagramming method of solving math word problems significantly improved student achievement in the experimental group (pvocabulary and symbols used in word problems and that both ELLs and EFLLs improved their problem solving success through careful attention to the creation and labeling of diagrams to represent the mathematics involved in standard word problems. Although Learnertype (ELL, EFLL
The Effect of Contextual and Conceptual Rewording on Mathematical Problem-Solving Performance
Haghverdi, Majid; Wiest, Lynda R.
2016-01-01
This study shows how separate and combined contextual and conceptual problem rewording can positively influence student performance in solving mathematical word problems. Participants included 80 seventh-grade Iranian students randomly assigned in groups of 20 to three experimental groups involving three types of rewording and a control group. All…
Bibliography on moving boundary problems with key word index
International Nuclear Information System (INIS)
Wilson, D.G.; Solomon, A.D.; Trent, J.S.
1979-10-01
This bibliography concentrates mainly on time-dependent moving-boundary problems of heat and mass transfer. The bibliography is in two parts, a list of the references ordered by last name of the first author and a key word index to the titles. Few references from before 1965 are included
Bibliography on moving boundary problems with key word index
Energy Technology Data Exchange (ETDEWEB)
Wilson, D.G.; Solomon, A.D.; Trent, J.S.
1979-10-01
This bibliography concentrates mainly on time-dependent moving-boundary problems of heat and mass transfer. The bibliography is in two parts, a list of the references ordered by last name of the first author and a key word index to the titles. Few references from before 1965 are included. (RWR)
Is Word-Problem Solving a Form of Text Comprehension?
Fuchs, Lynn S.; Fuchs, Douglas; Compton, Donald L.; Hamlett, Carol L.; Wang, Amber Y.
2015-01-01
This study's hypotheses were that (a) word-problem (WP) solving is a form of text comprehension that involves language comprehension processes, working memory, and reasoning, but (b) WP solving differs from other forms of text comprehension by requiring WP-specific language comprehension as well as general language comprehension. At the start of…
Freeman-Green, Shaqwana M.; O'Brien, Chris; Wood, Charles L.; Hitt, Sara Beth
2015-01-01
This study examined the effects of explicit instruction in the SOLVE Strategy on the mathematical problem solving skills of six Grade 8 students with specific learning disabilities. The SOLVE Strategy is an explicit instruction, mnemonic-based learning strategy designed to help students in solving mathematical word problems. Using a multiple probe…
Hickendorff, M.
2013-01-01
Mathematics education and assessments increasingly involve arithmetic problems presented in context: a realistic situation that requires mathematical modeling. This study assessed the effects of such typical school mathematics contexts on two aspects of problem solving: performance and strategy use.
Lectures on mathematical theory of extremum problems
1972-01-01
The author of this book, Igor' Vladimirovich Girsanov, was one of the first mathematicians to study general extremum problems and to realize the feasibility and desirability of a unified theory of extremal problems, based on a functional analytic approach. He actively advocated this view, and his special course, given at the Faculty of Mechanics and Mathematics of the Moscow State University in 1963 and 1964, was apparently the first systematic exposition of a unified approach to the theory of extremal problems. This approach was based on the ideas of Dubovitskii and Milyutin [1]. The general theory of extremal problems has developed so intensely during the past few years that its basic concepts may now be considered finalized. Nevertheless, as yet the basic results of this new field of mathematics have not been presented in a form accessible to a wide range of readers. (The profound paper of Dubovitskii and Milyutin [2] can hardly be recommended for a first study of the theory, since, in particular, it doe...
The Role of Expository Writing in Mathematical Problem Solving
Craig, Tracy S.
2016-01-01
Mathematical problem-solving is notoriously difficult to teach in a standard university mathematics classroom. The project on which this article reports aimed to investigate the effect of the writing of explanatory strategies in the context of mathematical problem solving on problem-solving behaviour. This article serves to describe the…
Thevenot, Catherine; Devidal, Michel; Barrouillet, Pierre; Fayol, Michel
2007-01-01
The aim of this paper is to investigate the controversial issue of the nature of the representation constructed by individuals to solve arithmetic word problems. More precisely, we consider the relevance of two different theories: the situation or mental model theory (Johnson-Laird, 1983; Reusser, 1989) and the schema theory (Kintsch & Greeno, 1985; Riley, Greeno, & Heller, 1983). Fourth-graders who differed in their mathematical skills were presented with problems that varied in difficulty and with the question either before or after the text. We obtained the classic effect of the position of the question, with better performance when the question was presented prior to the text. In addition, this effect was more marked in the case of children who had poorer mathematical skills and in the case of more difficult problems. We argue that this pattern of results is compatible only with the situation or mental model theory, and not with the schema theory.
Molecular Phylogenetics: Mathematical Framework and Unsolved Problems
Xia, Xuhua
Phylogenetic relationship is essential in dating evolutionary events, reconstructing ancestral genes, predicting sites that are important to natural selection, and, ultimately, understanding genomic evolution. Three categories of phylogenetic methods are currently used: the distance-based, the maximum parsimony, and the maximum likelihood method. Here, I present the mathematical framework of these methods and their rationales, provide computational details for each of them, illustrate analytically and numerically the potential biases inherent in these methods, and outline computational challenges and unresolved problems. This is followed by a brief discussion of the Bayesian approach that has been recently used in molecular phylogenetics.
Ozdemir, S.; Reis, Z. Ayvaz
2013-01-01
Mathematics is an important discipline, providing crucial tools, such as problem solving, to improve our cognitive abilities. In order to solve a problem, it is better to envision and represent through multiple means. Multiple representations can help a person to redefine a problem with his/her own words in that envisioning process. Dynamic and…
Wijaya, A.
2018-03-01
Creativity is often seen as one of the fundamental aspects of character education. As one of the 21st century skills, creativity has also been considered as an important goal of education across the world. This paper reports a study on promoting mathematical creativity through the use of open-ended mathematics problems. A total of 53 undergraduate students participated in the study. These students worked on open-ended problems in two types, i.e. bare mathematics problem and contextual problem. The contextual problem was presented in the form of paper-based and Geogebra-based. The students’ works were analysed qualitatively in order to describe how students’ mathematical creativity developed. It was found that the open-ended problems successfully promote students’ creativity as indicated by various solutions or strategies that were used by students to solve the problems. The analysis of students’ works show that students’ creativity developed through three kinds of exploration, i. e. (1) exploration of contexts, (2) exploration of software features, and (3) exploration of mathematics concepts. The use of metacognitive questioning was found to be helpful to develop the first two explorations into mathematical exploration.
Mathematical problems in wave propagation theory
1970-01-01
The papers comprising this collection are directly or indirectly related to an important branch of mathematical physics - the mathematical theory of wave propagation and diffraction. The paper by V. M. Babich is concerned with the application of the parabolic-equation method (of Academician V. A. Fok and M. A, Leontovich) to the problem of the asymptotic behavior of eigenfunc tions concentrated in a neighborhood of a closed geodesie in a Riemannian space. The techniques used in this paper have been föund useful in solving certain problems in the theory of open resonators. The topic of G. P. Astrakhantsev's paper is similar to that of the paper by V. M. Babich. Here also the parabolic-equation method is used to find the asymptotic solution of the elasticity equations which describes Love waves concentrated in a neighborhood of some surface ray. The paper of T. F. Pankratova is concerned with finding the asymptotic behavior of th~ eigenfunc tions of the Laplace operator from the exact solution for the surf...
Mathematical Problems in Synthetic Aperture Radar
Klein, Jens
2010-10-01
This thesis is concerned with problems related to Synthetic Aperture Radar (SAR). The thesis is structured as follows: The first chapter explains what SAR is, and the physical and mathematical background is illuminated. The following chapter points out a problem with a divergent integral in a common approach and proposes an improvement. Numerical comparisons are shown that indicate that the improvements allow for a superior image quality. Thereafter the problem of limited data is analyzed. In a realistic SAR-measurement the data gathered from the electromagnetic waves reflected from the surface can only be collected from a limited area. However the reconstruction formula requires data from an infinite distance. The chapter gives an analysis of the artifacts which can obscure the reconstructed images due to this problem. Additionally, some numerical examples are shown that point to the severity of the problem. In chapter 4 the fact that data is available only from a limited area is used to propose a new inversion formula. This inversion formula has the potential to make it easier to suppress artifacts due to limited data and, depending on the application, can be refined to a fast reconstruction formula. In the penultimate chapter a solution to the problem of left-right ambiguity is presented. This problem exists since the invention of SAR and is caused by the geometry of the measurements. This leads to the fact that only symmetric images can be obtained. With the solution from this chapter it is possible to reconstruct not only the even part of the reflectivity function, but also the odd part, thus making it possible to reconstruct asymmetric images. Numerical simulations are shown to demonstrate that this solution is not affected by stability problems as other approaches have been. The final chapter develops some continuative ideas that could be pursued in the future.
Benincasa, Luciana
2017-01-01
The paper applies Goffman's frame analysis and ethnomethodology to student performance on mathematical word problems. In educational research, frame analysis has usually been limited to primary frames. Instead, in this paper I focus on the kind of secondary frame that Goffman calls 'utilitarian make-believe'. The data consist of a fragment of…
The Construction of Mathematical Literacy Problems for Geometry
Malasari, P. N.; Herman, T.; Jupri, A.
2017-09-01
The students of junior high school should have mathematical literacy ability to formulate, apply, and interpret mathematics in problem solving of daily life. Teaching these students are not enough by giving them ordinary mathematics problems. Teaching activities for these students brings consequence for teacher to construct mathematical literacy problems. Therefore, the aim of this study is to construct mathematical literacy problems to assess mathematical literacy ability. The steps of this study that consists of analysing, designing, theoretical validation, revising, limited testing to students, and evaluating. The data was collected with written test to 38 students of grade IX at one of state junior high school. Mathematical literacy problems consist of three essays with three indicators and three levels at polyhedron subject. The Indicators are formulating and employing mathematics. The results show that: (1) mathematical literacy problems which are constructed have been valid and practical, (2) mathematical literacy problems have good distinguishing characteristics and adequate distinguishing characteristics, (3) difficulty levels of problems are easy and moderate. The final conclusion is mathematical literacy problems which are constructed can be used to assess mathematical literacy ability.
ABC Problem in Elementary Mathematics Education: Arithmetic "before" Comprehension
Boote, Stacy K.; Boote, David N.
2018-01-01
Mathematical habits of prospective teachers affect problem comprehension and success and expose their beliefs about mathematics. Prospective elementary teachers (PSTs) (n = 121) engaged in a problem solving activity each week in class. Data were collected from PSTs enrolled in an undergraduate elementary mathematics methods course at a…
Metacognition Process of Students with High Mathematics Anxiety in Mathematics Problem-Solving
Patrisius Afrisno Udil; Tri Atmojo Kusmayadi; Riyadi Riyadi
2017-01-01
This study aims to find out students’ metacognition process while solving the mathematics problem. It focuses on analyzing the metacognition process of students with high mathematics anxiety based on Polya’s problem solving phases. This study uses qualitative research with case study strategy. The subjects consist of 8 students of 7th grade selected through purposive sampling. Data in the form of Mathematics Anxiety Scale (MAS) result and recorded interview while solving mathematics problems ...
Kartal, Ozgul; Dunya, Beyza Aksu; Diefes-Dux, Heidi A.; Zawojewski, Judith S.
2016-01-01
Critical to many science, technology, engineering, and mathematics (STEM) career paths is mathematical modeling--specifically, the creation and adaptation of mathematical models to solve problems in complex settings. Conventional standardized measures of mathematics achievement are not structured to directly assess this type of mathematical…
Mathematical Problems in Creating Large Astronomical Catalogs
Directory of Open Access Journals (Sweden)
Prokhorov M. E.
2016-12-01
Full Text Available The next stage after performing observations and their primary reduction is to transform the set of observations into a catalog. To this end, objects that are irrelevant to the catalog should be excluded from observations and gross errors should be discarded. To transform such a prepared data set into a high-precision catalog, we need to identify and correct systematic errors. Therefore, each object of the survey should be observed several, preferably many, times. The problem formally reduces to solving an overdetermined set of equations. However, in the case of catalogs this system of equations has a very specific form: it is extremely sparse, and its sparseness increases rapidly with the number of objects in the catalog. Such equation systems require special methods for storing data on disks and in RAM, and for the choice of the techniques for their solving. Another specific feature of such systems is their high “stiffiness”, which also increases with the volume of a catalog. Special stable mathematical methods should be used in order not to lose precision when solving such systems of equations. We illustrate the problem by the example of photometric star catalogs, although similar problems arise in the case of positional, radial-velocity, and parallax catalogs.
Mathematical problems in modeling artificial heart
Directory of Open Access Journals (Sweden)
Ahmed N. U.
1995-01-01
Full Text Available In this paper we discuss some problems arising in mathematical modeling of artificial hearts. The hydrodynamics of blood flow in an artificial heart chamber is governed by the Navier-Stokes equation, coupled with an equation of hyperbolic type subject to moving boundary conditions. The flow is induced by the motion of a diaphragm (membrane inside the heart chamber attached to a part of the boundary and driven by a compressor (pusher plate. On one side of the diaphragm is the blood and on the other side is the compressor fluid. For a complete mathematical model it is necessary to write the equation of motion of the diaphragm and all the dynamic couplings that exist between its position, velocity and the blood flow in the heart chamber. This gives rise to a system of coupled nonlinear partial differential equations; the Navier-Stokes equation being of parabolic type and the equation for the membrane being of hyperbolic type. The system is completed by introducing all the necessary static and dynamic boundary conditions. The ultimate objective is to control the flow pattern so as to minimize hemolysis (damage to red blood cells by optimal choice of geometry, and by optimal control of the membrane for a given geometry. The other clinical problems, such as compatibility of the material used in the construction of the heart chamber, and the membrane, are not considered in this paper. Also the dynamics of the valve is not considered here, though it is also an important element in the overall design of an artificial heart. We hope to model the valve dynamics in later paper.
Is Word-Problem Solving a Form of Text Comprehension?
Fuchs, Lynn S.; Fuchs, Douglas; Compton, Donald L.; Hamlett, Carol L.; Wang, Amber Y.
2015-01-01
This study’s hypotheses were that (a) word-problem (WP) solving is a form of text comprehension that involves language comprehension processes, working memory, and reasoning, but (b) WP solving differs from other forms of text comprehension by requiring WP-specific language comprehension as well as general language comprehension. At the start of the 2nd grade, children (n = 206; on average, 7 years, 6 months) were assessed on general language comprehension, working memory, nonlinguistic reasoning, processing speed (a control variable), and foundational skill (arithmetic for WPs; word reading for text comprehension). In spring, they were assessed on WP-specific language comprehension, WPs, and text comprehension. Path analytic mediation analysis indicated that effects of general language comprehension on text comprehension were entirely direct, whereas effects of general language comprehension on WPs were partially mediated by WP-specific language. By contrast, effects of working memory and reasoning operated in parallel ways for both outcomes. PMID:25866461
Beal, Carole R.; Rosenblum, L. Penny
2018-01-01
Introduction: The authors examined a tablet computer application (iPad app) for its effectiveness in helping students studying prealgebra to solve mathematical word problems. Methods: Forty-three visually impaired students (that is, those who are blind or have low vision) completed eight alternating mathematics units presented using their…
Affect and mathematical problem solving a new perspective
Adams, Verna
1989-01-01
Research on cognitive aspects of mathematical problem solving has made great progress in recent years, but the relationship of affective factors to problem-solving performance has been a neglected research area. The purpose of Affect and Mathematical Problem Solving: A New Perspective is to show how the theories and methods of cognitive science can be extended to include the role of affect in mathematical problem solving. The book presents Mandler's theory of emotion and explores its implications for the learning and teaching of mathematical problem solving. Also, leading researchers from mathematics, education, and psychology report how they have integrated affect into their own cognitive research. The studies focus on metacognitive processes, aesthetic influences on expert problem solvers, teacher decision-making, technology and teaching problem solving, and beliefs about mathematics. The results suggest how emotional factors like anxiety, frustration, joy, and satisfaction can help or hinder performance in...
The Music of Mathematics: Toward a New Problem Typology
Quarfoot, David
Halmos (1980) once described problems and their solutions as "the heart of mathematics". Following this line of thinking, one might naturally ask: "What, then, is the heart of problems?". In this work, I attempt to answer this question using techniques from statistics, information visualization, and machine learning. I begin the journey by cataloging the features of problems delineated by the mathematics and mathematics education communities. These dimensions are explored in a large data set of students working thousands of problems at the Art of Problem Solving, an online company that provides adaptive mathematical training for students around the world. This analysis is able to concretely show how the fabric of mathematical problems changes across different subjects, difficulty levels, and students. Furthermore, it locates problems that stand out in the crowd -- those that synergize cognitive engagement, learning, and difficulty. This quantitatively-heavy side of the dissertation is partnered with a qualitatively-inspired portion that involves human scoring of 105 problems and their solutions. In this setting, I am able to capture elusive features of mathematical problems and derive a fuller picture of the space of mathematical problems. Using correlation matrices, principal components analysis, and clustering techniques, I explore the relationships among those features frequently discussed in mathematics problems (e.g., difficulty, creativity, novelty, affective engagement, authenticity). Along the way, I define a new set of uncorrelated features in problems and use these as the basis for a New Mathematical Problem Typology (NMPT). Grounded in the terminology of classical music, the NMPT works to quickly convey the essence and value of a problem, just as terms like "etude" and "mazurka" do for musicians. Taken together, these quantitative and qualitative analyses seek to terraform the landscape of mathematical problems and, concomitantly, the current thinking
COMPUTER TOOLS OF DYNAMIC MATHEMATIC SOFTWARE AND METHODICAL PROBLEMS OF THEIR USE
Directory of Open Access Journals (Sweden)
Olena V. Semenikhina
2014-08-01
Full Text Available The article presents results of analyses of standard computer tools of dynamic mathematic software which are used in solving tasks, and tools on which the teacher can support in the teaching of mathematics. Possibility of the organization of experimental investigating of mathematical objects on the basis of these tools and the wording of new tasks on the basis of the limited number of tools, fast automated check are specified. Some methodological comments on application of computer tools and methodological features of the use of interactive mathematical environments are presented. Problems, which are arising from the use of computer tools, among which rethinking forms and methods of training by teacher, the search for creative problems, the problem of rational choice of environment, check the e-solutions, common mistakes in the use of computer tools are selected.
De Corte, E.; And Others
One important finding from recent research on multiplication word problems is that children's performances are strongly affected by the nature of the multiplier (whether it is an integer, decimal larger than 1 or a decimal smaller than 1). On the other hand, the size of the multiplicand has little or no effect on problem difficulty. The aim of the…
The Effect of Some Constraints on Mathematics Instructors' Problem ...
African Journals Online (AJOL)
This study was designed to examine the effect of perceived constraints on four universities mathematics department instructors' classroom practices of problem solving in teaching mathematics. To this end, the target population of the study includes mathematics instructors in the Amhara Regional state universities. From a ...
The universe in zero words the story of mathematics as told through equations
Mackenzie, Dana
2012-01-01
Most popular books about science, and even about mathematics, tiptoe around equations as if they were something to be hidden from the reader's tender eyes. Dana Mackenzie starts from the opposite premise: He celebrates equations. No history of art would be complete without pictures. Why, then, should a history of mathematics--the universal language of science--keep the masterpieces of the subject hidden behind a veil? The Universe in Zero Words tells the history of twenty-four great and beautiful equations that have shaped mathematics, science, and society--from the elementary
Boonen, Anton J. H.; Reed, Helen C.; Schoonenboom, Judith; Jolles, Jelle
2016-01-01
Non-routine word problem solving is an essential feature of the mathematical development of elementary school students worldwide. Many students experience difficulties in solving these problems due to erroneous problem comprehension. These difficulties could be alleviated by instructing students how to use visual representations that clarify the…
The 'thousand words' problem: Summarizing multi-dimensional data
International Nuclear Information System (INIS)
Scott, David M.
2011-01-01
Research highlights: → Sophisticated process sensors produce large multi-dimensional data sets. → Plant control systems cannot handle images or large amounts of data. → Various techniques reduce the dimensionality, extracting information from raw data. → Simple 1D and 2D methods can often be extended to 3D and 4D applications. - Abstract: An inherent difficulty in the application of multi-dimensional sensing to process monitoring and control is the extraction and interpretation of useful information. Ultimately the measured data must be collapsed into a relatively small number of values that capture the salient characteristics of the process. Although multiple dimensions are frequently necessary to isolate a particular physical attribute (such as the distribution of a particular chemical species in a reactor), plant control systems are not equipped to use such data directly. The production of a multi-dimensional data set (often displayed as an image) is not the final step of the measurement process, because information must still be extracted from the raw data. In the metaphor of one picture being equal to a thousand words, the problem becomes one of paraphrasing a lengthy description of the image with one or two well-chosen words. Various approaches to solving this problem are discussed using examples from the fields of particle characterization, image processing, and process tomography.
THE QUALITY OF MATHEMATICAL PROBLEMS - EVALUATION AND SELF-EVALUATION
Directory of Open Access Journals (Sweden)
Patáková, Eva
2013-09-01
Full Text Available The research presented in the article consists of two parts. Firstly, opinions on mathematical problem quality are explored within four groups of participants (novices, specialists and experts in problem posing; high school students who never posed their own problems. Secondly, self-reflections written by the participants who have some experience in problem posing (novices, specialists and experts are explored and compared with the general view of problem quality received in the first part of the research. The more experienced problem posers have more requirements on problem quality (both as general requirements and within their own work on posing problems. There is a slight decrease in ability to notice important features of mathematical problem quality after the first experience in problem posing. Experts lay stress on mathematical features of the problem whilst novices and specialists more on problem – student interaction.
Addressing Mathematization Obstacles with Unformalized Problems in Physics Education
DEFF Research Database (Denmark)
Niss, Martin
2018-01-01
Abstract: Solving a physics problem requires that the problem solver either implicitly or explicitly structure the problem situation in such a way that she can set up the mathematical equations based on the relevant physics. This part of the mathematization process has been shown to cause obstacles...... for students (Niss, 2016). In the paper, we show how the students’ ability to perform this mathematization process can be trained by using so-called unformalized physics problems. Some examples of how this training can be done are provided from a course on problem solving in physics taught at Roskilde...
What Is the Problem in Problem-Based Learning in Higher Education Mathematics
Dahl, Bettina
2018-01-01
Problem and Project-Based Learning (PBL) emphasise collaborate work on problems relevant to society and emphases the relation between theory and practice. PBL fits engineering students as preparation for their future professions but what about mathematics? Mathematics is not just applied mathematics, but it is also a body of abstract knowledge…
Directory of Open Access Journals (Sweden)
Benincasa Luciana
2017-12-01
Full Text Available The paper applies Goffman’s frame analysis and ethnomethodology to student performance on mathematical word problems. In educational research, frame analysis has usually been limited to primary frames. Instead, in this paper I focus on the kind of secondary frame that Goffman calls ‘utilitarian make-believe’. The data consist of a fragment of verbal interaction between a teacher and a 12-year-old pupil during an oral mathematics exam. By evoking the idea of ‘as-ifness’, word problems introduce pupils to a make-believe world. The text consists only of ‘filler words’ because what really matters are the figures. Word problems and possibly other aspects of schooling can be interpreted in terms of a utilitarian make-believe key. Readiness to adopt this make-believe frame when required may be the difference between school success and failure. I argue that maths achievement takes more than just ‘being good with numbers’. It is a joint enterprise of people interacting within a culturally-shaped setting, organized so as to make some phenomena stand out rather than others. Finally, I argue that ‘word problems and possibly other ‘school genres’ could be added to the list of utilitarian make-believe frames provided by Goffman.
What is the problem in problem-based learning in higher education mathematics
Dahl, Bettina
2018-01-01
Problem and Project-Based Learning (PBL) emphasise collaborate work on problems relevant to society and emphases the relation between theory and practice. PBL fits engineering students as preparation for their future professions but what about mathematics? Mathematics is not just applied mathematics, but it is also a body of abstract knowledge where the application in society is not always obvious. Does mathematics, including pure mathematics, fit into a PBL curriculum? This paper argues that it does for two reasons: (1) PBL resembles the working methods of research mathematicians. (2) The concept of society includes the society of researchers to whom theoretical mathematics is relevant. The paper describes two cases of university PBL projects in mathematics; one in pure mathematics and the other in applied mathematics. The paper also discusses that future engineers need to understand the world of mathematics as well as how engineers fit into a process of fundamental-research-turned-into-applied-science.
Aljaberi, Nahil M.; Gheith, Eman
2016-01-01
This study aims to investigate the ability of pre-service class teacher at University of Petrain solving mathematical problems using Polya's Techniques, their level of problem solving skills in daily-life issues. The study also investigates the correlation between their ability to solve mathematical problems and their level of problem solving…
Rasiman
2015-01-01
This research aims to determine the leveling of critical thinking abilities of students of mathematics education in mathematical problem solving. It includes qualitative-explorative study that was conducted at University of PGRI Semarang. The generated data in the form of information obtained problem solving question and interview guides. The…
Secondary Teachers’ Mathematics-related Beliefs and Knowledge about Mathematical Problem-solving
E Siswono, T. Y.; Kohar, A. W.; Hartono, S.
2017-02-01
This study investigates secondary teachers’ belief about the three mathematics-related beliefs, i.e. nature of mathematics, teaching mathematics, learning mathematics, and knowledge about mathematical problem solving. Data were gathered through a set of task-based semi-structured interviews of three selected teachers with different philosophical views of teaching mathematics, i.e. instrumental, platonist, and problem solving. Those teachers were selected from an interview using a belief-related task from purposively selected teachers in Surabaya and Sidoarjo. While the interviews about knowledge examine teachers’ problem solving content and pedagogical knowledge, the interviews about beliefs examine their views on several cases extracted from each of such mathematics-related beliefs. Analysis included the categorization and comparison on each of beliefs and knowledge as well as their interaction. Results indicate that all the teachers did not show a high consistency in responding views of their mathematics-related beliefs, while they showed weaknesses primarily on problem solving content knowledge. Findings also point out that teachers’ beliefs have a strong relationship with teachers’ knowledge about problem solving. In particular, the instrumental teacher’s beliefs were consistent with his insufficient knowledge about problem-solving, while both platonist and problem-solving teacher’s beliefs were consistent with their sufficient knowledge of either content or pedagogical problem solving.
The Place of Problem Solving in Contemporary Mathematics Curriculum Documents
Stacey, Kaye
2005-01-01
This paper reviews the presentation of problem solving and process aspects of mathematics in curriculum documents from Australia, UK, USA and Singapore. The place of problem solving in the documents is reviewed and contrasted, and illustrative problems from teachers' support materials are used to demonstrate how problem solving is now more often…
The philosophical aspect of learning inverse problems of mathematical physics
Directory of Open Access Journals (Sweden)
Виктор Семенович Корнилов
2018-12-01
Full Text Available The article describes specific questions student learning inverse problems of mathematical physics. When teaching inverse problems of mathematical physics to the understanding of the students brought the information that the inverse problems of mathematical physics with a philosophical point of view are the problems of determining the unknown causes of known consequences, and the search for their solutions have great scientific and educational potential. The reasons are specified in the form of unknown coefficients, right side, initial conditions of the mathematical model of inverse problems, and as a consequence are functionals of the solution of this mathematical model. In the process of learning the inverse problems of mathematical physics focuses on the philosophical aspects of the phenomenon of information and identify cause-effect relations. It is emphasized that in the process of logical analysis applied and humanitarian character, students realize that information is always related to the fundamental philosophical questions that the analysis applied and the humanitarian aspects of the obtained results the inverse problem of mathematical physics allows students to make appropriate inferences about the studied process and to, ultimately, new information, to study its properties and understand its value. Philosophical understanding of the notion of information opens up to students a new methodological opportunities to comprehend the world and helps us to reinterpret existing science and philosophy of the theory related to the disclosure of the interrelationship of all phenomena of reality.
Forms of Understanding in Mathematical Problem Solving.
1982-08-01
mathematical concepts, but more recent studies (e.g., Gelman & Gallistel , 1978) indicate that significant understanding of those concepts should be...Beranek, & Newman, 1980. Gelman, R., & Gallistel , C. R. The child’s understanding of number. Cambridge, Mass.: Harvard University Press, 1978. 43 Greeno
Directory of Open Access Journals (Sweden)
Syarifah Fadillah
2017-03-01
Full Text Available The problem in this research is to know how the process of developing mathematics physics instructional book based on inquiry approach and its supporting documents to improve students' mathematical problem-solving ability. The purpose of this research is to provide mathematical physics instruction based on inquiry approach and its supporting documents (semester learning activity plan, lesson plan and mathematical problem-solving test to improve students' mathematical problem-solving ability. The development of textbook refers to the ADDIE model, including analysis, design, development, implementation, and evaluation. The validation result from the expert team shows that the textbook and its supporting documents are valid. The test results of the mathematical problem-solving skills show that all test questions are valid and reliable. The result of the incorporation of the textbook in teaching and learning process revealed that students' mathematical problem-solving ability using mathematical physics instruction based on inquiry approach book was better than the students who use the regular book.
Pattern of mathematic representation ability in magnetic electricity problem
Hau, R. R. H.; Marwoto, P.; Putra, N. M. D.
2018-03-01
The mathematic representation ability in solving magnetic electricity problem gives information about the way students understand magnetic electricity. Students have varied mathematic representation pattern ability in solving magnetic electricity problem. This study aims to determine the pattern of students' mathematic representation ability in solving magnet electrical problems.The research method used is qualitative. The subject of this study is the fourth semester students of UNNES Physics Education Study Program. The data collection is done by giving a description test that refers to the test of mathematical representation ability and interview about field line topic and Gauss law. The result of data analysis of student's mathematical representation ability in solving magnet electric problem is categorized into high, medium and low category. The ability of mathematical representations in the high category tends to use a pattern of making known and asked symbols, writing equations, using quantities of physics, substituting quantities into equations, performing calculations and final answers. The ability of mathematical representation in the medium category tends to use several patterns of writing the known symbols, writing equations, using quantities of physics, substituting quantities into equations, performing calculations and final answers. The ability of mathematical representations in the low category tends to use several patterns of making known symbols, writing equations, substituting quantities into equations, performing calculations and final answer.
Notes on the students’ solutions of Mathematical Olympiad problems
Veilande, Ingrida
2015-01-01
The quality of mathematics education in schools of Latvia can be evaluated by several criteria: on national level – by the results of centralized examination, by diagnostic tests, by students’ achievements in educational Olympiads, and in international comparison – by analysis of results of students’ assessment programs such as TIMSS and PISA. These statistics identify the major problems in mathematics education.
Robotic Toys as a Catalyst for Mathematical Problem Solving
Highfield, Kate
2010-01-01
Robotic toys present unique opportunities for teachers of young children to integrate mathematics learning with engaging problem-solving tasks. This article describes a series of tasks using Bee-bots and Pro-bots, developed as part a larger project examining young children's use of robotic toys as tools in developing mathematical and metacognitive…
University Students' Problem Posing Abilities and Attitudes towards Mathematics.
Grundmeier, Todd A.
2002-01-01
Explores the problem posing abilities and attitudes towards mathematics of students in a university pre-calculus class and a university mathematical proof class. Reports a significant difference in numeric posing versus non-numeric posing ability in both classes. (Author/MM)
Improving mathematical problem solving skills through visual media
Widodo, S. A.; Darhim; Ikhwanudin, T.
2018-01-01
The purpose of this article was to find out the enhancement of students’ mathematical problem solving by using visual learning media. The ability to solve mathematical problems is the ability possessed by students to solve problems encountered, one of the problem-solving model of Polya. This preliminary study was not to make a model, but it only took a conceptual approach by comparing the various literature of problem-solving skills by linking visual learning media. The results of the study indicated that the use of learning media had not been appropriated so that the ability to solve mathematical problems was not optimal. The inappropriateness of media use was due to the instructional media that was not adapted to the characteristics of the learners. Suggestions that can be given is the need to develop visual media to increase the ability to solve problems.
Ünlü, Melihan
2017-01-01
The aim of the study was to determine mathematics teacher candidates' knowledge about problem solving strategies through problem posing. This qualitative research was conducted with 95 mathematics teacher candidates studying at education faculty of a public university during the first term of the 2015-2016 academic year in Turkey. Problem Posing…
Mathematical problem solving in primary school
Kolovou, A.
2011-01-01
A student is engaged in (non-routine) problem solving when there is no clear pathway to the solution. In contrast to routine problems, non-routine ones cannot be solved through the direct application of a standard procedure. Consider the following problem: In a quiz you get two points for each
Glogs as Non-Routine Problem Solving Tools in Mathematics
Devine, Matthew T.
2013-01-01
In mathematical problem solving, American students are falling behind their global peers because of a lack of foundational and reasoning skills. A specific area of difficulty with problem solving is working non-routine, heuristic-based problems. Many students are not provided with effective instruction and often grow frustrated and dislike math.…
The Influence of Cognitive Abilities on Mathematical Problem Solving Performance
Bahar, Abdulkadir
2013-01-01
Problem solving has been a core theme in education for several decades. Educators and policy makers agree on the importance of the role of problem solving skills for school and real life success. A primary purpose of this study was to investigate the influence of cognitive abilities on mathematical problem solving performance of students. The…
Using What Matters to Students in Bilingual Mathematics Problems
Dominguez, Higinio
2011-01-01
In this study, the author represented what matters to bilingual students in their everyday lives--namely bilingualism and everyday experiences--in school-based mathematical problems. Solving problems in pairs, students demonstrated different patterns of organizing and coordinating talk across problem contexts and across languages. Because these…
Comparison of mathematical problem solving strategies of primary school pupils
Wasilewská, Eliška
2016-01-01
The aim of this dissertation is to describe the role of educational strategy especially in field of the teaching of mathematics and to compare the mathematical problem solving strategies of primary school pupils which are taught by using different educational strategies. In the theoretical part, the main focus is on divergent educational strategies and their characteristics, next on factors affected teaching/learning process and finally on solving the problems. The empirical part of the disse...
Exercises and problems in mathematical methods of physics
Cicogna, Giampaolo
2018-01-01
This book presents exercises and problems in the mathematical methods of physics with the aim of offering undergraduate students an alternative way to explore and fully understand the mathematical notions on which modern physics is based. The exercises and problems are proposed not in a random order but rather in a sequence that maximizes their educational value. Each section and subsection starts with exercises based on first definitions, followed by groups of problems devoted to intermediate and, subsequently, more elaborate situations. Some of the problems are unavoidably "routine", but others bring to the forenontrivial properties that are often omitted or barely mentioned in textbooks. There are also problems where the reader is guided to obtain important results that are usually stated in textbooks without complete proofs. In all, some 350 solved problems covering all mathematical notions useful to physics are included. While the book is intended primarily for undergraduate students of physics, students...
ÖÇAL, Mehmet Fatih; ŞİMŞEK, Mertkan
2016-01-01
Problem solving skill is the core of mathematics education and its importance cannot be denied. This study specifically examined 56 freshmen pre-service mathematics teachers’ problem solving processes on a specific problem with the help of Geometer’s Sketchpad (GSP). They were grouped into two-person teams to solve a problem called "the mirror problem". They were expected to solve it by means of GSP. According to their works on GSP and related reflections, there appeared two differe...
USING TASK LIKE PISA’S PROBLEM TO SUPPORT STUDENT’S CREATIVITY IN MATHEMATICS
Directory of Open Access Journals (Sweden)
Rita Novita
2016-01-01
Full Text Available Creativity is one of keys to success in the evolving global economy and also be a fundamental skill that is absolutely necessary in the 21st century. Also In mathematics, creativity or thinking creatively is important to be developed because creativity is an integral part of mathematics. However, limiting the use of creativity in the classroom reduces mathematics to a set of skills to master and rules to memorize. Doing so causes many children’s natural curiosity and enthusiasm for mathematics to disappear as they get older, creating a tremendous problem for mathematics educators who are trying to instil these very qualities. In order to investigate the increase in awareness of elementary school students’ creativity in solving mathematics’ problems by using task like PISA’s Question, a qualitative research emphasizing on holistic description was conducted. We used a formative evaluation type of development research as a mean to develop mathematical tasks like PISA’s question that have potential effect to support students’ creativity in mathematics. Ten elementary school students of grade 6 in Palembang were involved in this research. They judged the task given for them is very challenging and provokes their curiosity. The result showed that task like PISA’s question can encourage students to more creatively in mathematics.Key Words: PISA, Problem Solving, Creativity in Mathematics DOI: http://dx.doi.org/10.22342/jme.7.1.2815.31-42
Nasution, M. L.; Yerizon, Y.; Gusmiyanti, R.
2018-04-01
One of the purpose mathematic learning is to develop problem solving abilities. Problem solving is obtained through experience in questioning non-routine. Improving students’ mathematical problem-solving abilities required an appropriate strategy in learning activities one of them is models problem based learning (PBL). Thus, the purpose of this research is to determine whether the problem solving abilities of mathematical students’ who learn to use PBL better than on the ability of students’ mathematical problem solving by applying conventional learning. This research included quasi experiment with static group design and population is students class XI MIA SMAN 1 Lubuk Alung. Class experiment in the class XI MIA 5 and class control in the class XI MIA 6. The instrument of final test students’ mathematical problem solving used essay form. The result of data final test in analyzed with t-test. The result is students’ mathematical problem solving abilities with PBL better then on the ability of students’ mathematical problem solving by applying conventional learning. It’s seen from the high percentage achieved by the group of students who learn to use PBL for each indicator of students’ mathematical problem solving.
Tyagi, Tarun Kumar
2016-01-01
The relationship between mathematical creativity (MC) and mathematical problem-solving performance (MP) has often been studied but the causal relation between these two constructs has yet to be clearly reported. The main purpose of this study was to define the causal relationship between MC and MP. Data from a representative sample of 480…
Research mathematicians’ practices in selecting mathematical problems
DEFF Research Database (Denmark)
Misfeldt, Morten; Johansen, Mikkel Willum
2015-01-01
mathematicians select and pose problems and discuss to what extent our results can be used to inform, criticize, and develop educational practice at various levels. Selecting and posing problems is far from simple. In fact, it is considered hard, complex, and of crucial importance. A number of criteria...
A Mathematical Optimization Problem in Bioinformatics
Heyer, Laurie J.
2008-01-01
This article describes the sequence alignment problem in bioinformatics. Through examples, we formulate sequence alignment as an optimization problem and show how to compute the optimal alignment with dynamic programming. The examples and sample exercises have been used by the author in a specialized course in bioinformatics, but could be adapted…
Using CAS to Solve Classical Mathematics Problems
Burke, Maurice J.; Burroughs, Elizabeth A.
2009-01-01
Historically, calculus has displaced many algebraic methods for solving classical problems. This article illustrates an algebraic method for finding the zeros of polynomial functions that is closely related to Newton's method (devised in 1669, published in 1711), which is encountered in calculus. By exploring this problem, precalculus students…
Developing non-routine problems for assessing students’ mathematical literacy
Murdiyani, N. M.
2018-03-01
The purpose of this study is to develop non-routine problems for assessing the mathematics literacy skills of students, which is valid, practical, and effective. It is based on the previous research said that Indonesian students’ mathematical literacy is still low. The results of this study can be used as a guide in developing the evaluation questions that can train students to improve the ability of solving non-routine problems in everyday life. This research type is formative evaluation that consists of preliminary, self evaluation, expert reviews, one-to-one, small group, and field test. The sample of this research is grade 8 students at one of Junior High School in Yogyakarta. This study results in mathematics literacy problems prototype consisting of level 1 to level 6 problems similar to PISA problems. This study also discusses the examples of students’ answer and their reasoning.
Effectiveness of discovery learning model on mathematical problem solving
Herdiana, Yunita; Wahyudin, Sispiyati, Ririn
2017-08-01
This research is aimed to describe the effectiveness of discovery learning model on mathematical problem solving. This research investigate the students' problem solving competency before and after learned by using discovery learning model. The population used in this research was student in grade VII in one of junior high school in West Bandung Regency. From nine classes, class VII B were randomly selected as the sample of experiment class, and class VII C as control class, which consist of 35 students every class. The method in this research was quasi experiment. The instrument in this research is pre-test, worksheet and post-test about problem solving of mathematics. Based on the research, it can be conclude that the qualification of problem solving competency of students who gets discovery learning model on level 80%, including in medium category and it show that discovery learning model effective to improve mathematical problem solving.
Bullock, Audrey N.
2017-01-01
Problem solving in mathematics has been a goal for students for decades. In the reviewed literature, problem solving was most often treated as the dependent variable and was defined very broadly; however, few studies were found that included problem solving as a treatment or independent variable. The purpose of this study was to investigate the…
Using Video Prompting to Teach Mathematical Problem Solving of Real-World Video-Simulation Problems
Saunders, Alicia F.; Spooner, Fred; Ley Davis, Luann
2018-01-01
Mathematical problem solving is necessary in many facets of everyday life, yet little research exists on how to teach students with more severe disabilities higher order mathematics like problem solving. Using a multiple probe across participants design, three middle school students with moderate intellectual disability (ID) were taught to solve…
Problem Posing with Realistic Mathematics Education Approach in Geometry Learning
Mahendra, R.; Slamet, I.; Budiyono
2017-09-01
One of the difficulties of students in the learning of geometry is on the subject of plane that requires students to understand the abstract matter. The aim of this research is to determine the effect of Problem Posing learning model with Realistic Mathematics Education Approach in geometry learning. This quasi experimental research was conducted in one of the junior high schools in Karanganyar, Indonesia. The sample was taken using stratified cluster random sampling technique. The results of this research indicate that the model of Problem Posing learning with Realistic Mathematics Education Approach can improve students’ conceptual understanding significantly in geometry learning especially on plane topics. It is because students on the application of Problem Posing with Realistic Mathematics Education Approach are become to be active in constructing their knowledge, proposing, and problem solving in realistic, so it easier for students to understand concepts and solve the problems. Therefore, the model of Problem Posing learning with Realistic Mathematics Education Approach is appropriately applied in mathematics learning especially on geometry material. Furthermore, the impact can improve student achievement.
Open-Start Mathematics Problems: An Approach to Assessing Problem Solving
Monaghan, John; Pool, Peter; Roper, Tom; Threlfall, John
2009-01-01
This article describes one type of mathematical problem, open-start problems, and discusses their potential for use in assessment. In open-start problems how one starts to address the problem can vary but they have a correct answer. We argue that the use of open-start problems in assessment could positively influence classroom mathematics…
Writing and mathematical problem solving in Grade 3
Directory of Open Access Journals (Sweden)
Belinda Petersen
2017-06-01
Full Text Available This article looks at writing tasks as a methodology to support learners’ mathematical problemsolving strategies in the South African Foundation Phase context. It is a qualitative case study and explores the relation between the use of writing in mathematics and development of learners’ problem-solving strategies and conceptual understanding. The research was conducted in a suburban Foundation Phase school in Cape Town with a class of Grade 3 learners involved in a writing and mathematics intervention. Writing tasks were modelled to learners and implemented by them while they were engaged in mathematical problem solving. Data were gathered from a sample of eight learners of different abilities and included written work, interviews, field notes and audio recordings of ability group discussions. The results revealed an improvement in the strategies and explanations learners used when solving mathematical problems compared to before the writing tasks were implemented. Learners were able to reflect critically on their thinking through their written strategies and explanations. The writing tasks appeared to support learners in providing opportunities to construct and apply mathematical knowledge and skills in their development of problem-solving strategies.
Mathematical modelling and numerical simulation of oil pollution problems
2015-01-01
Written by outstanding experts in the fields of marine engineering, atmospheric physics and chemistry, fluid dynamics and applied mathematics, the contributions in this book cover a wide range of subjects, from pure mathematics to real-world applications in the oil spill engineering business. Offering a truly interdisciplinary approach, the authors present both mathematical models and state-of-the-art numerical methods for adequately solving the partial differential equations involved, as well as highly practical experiments involving actual cases of ocean oil pollution. It is indispensable that different disciplines of mathematics, like analysis and numerics, together with physics, biology, fluid dynamics, environmental engineering and marine science, join forces to solve today’s oil pollution problems. The book will be of great interest to researchers and graduate students in the environmental sciences, mathematics and physics, showing the broad range of techniques needed in order to solve these poll...
Diversity of problems of international mathematical olympiads (imo)
Kukuraitis, Nerijus
2012-01-01
Šiame darbe yra pateikta 16 Pasaulinių olimpiadų uždavinių ir jų sprendimų. Uždaviniai yra lyginami pagal jų sudėtingumo lygį. Sixteen problems and their solutions from International Mathematical Olympiads are presented in this work. Problems are compared by their difficulty.
Unfinished Student Answer in PISA Mathematics Contextual Problem
Lutfianto, Moch.; Zulkardi; Hartono, Yusuf
2013-01-01
Solving mathematics contextual problems is one way that can be used to enable students to have the skills needed to live in the 21st century. Completion contextual problem requires a series of steps in order to properly answer the questions that are asked. The purpose of this study was to determine the steps performed students in solving…
Great Problems of Mathematics: A Course Based on Original Sources.
Laubenbacher, Reinhard C.; Pengelley, David J.
1992-01-01
Describes the history of five selected problems from mathematics that are included in an undergraduate honors course designed to utilize original sources for demonstrating the evolution of ideas developed in solving these problems: area and the definite integral, the beginnings of set theory, solutions of algebraic equations, Fermat's last…
Assessing the Effect of Language Demand in Bundles of Math Word Problems
Banks, Kathleen; Jeddeeni, Ahmad; Walker, Cindy M.
2016-01-01
Differential bundle functioning (DBF) analyses were conducted to determine whether seventh and eighth grade second language learners (SLLs) had lower probabilities of answering bundles of math word problems correctly that had heavy language demands, when compared to non-SLLs of equal math proficiency. Math word problems on each of four test forms…
Sharp, Emily; Shih Dennis, Minyi
2017-01-01
This study used a multiple probe across participants design to examine the effects of a model drawing strategy (MDS) intervention package on fraction comparing and ordering word problem-solving performance of three Grade 4 students. MDS is a form of cognitive strategy instruction for teaching word problem solving that includes explicit instruction…
The Impact of Metacognitive Strategies and Self-Regulating Processes of Solving Math Word Problems
Vula, Eda; Avdyli, Rrezarta; Berisha, Valbona; Saqipi, Blerim; Elezi, Shpetim
2017-01-01
This empirical study investigates the impact of metacognitive strategies and self-regulating processes in learners' achievement on solving math word problems. It specifically analyzes the impact of the linguistic factor and the number of steps and arithmetical operations that learners need to apply during the process of solving math word problems.…
Students’ mathematical representations on secondary school in solving trigonometric problems
Istadi; Kusmayadi, T. A.; Sujadi, I.
2017-06-01
This research aimed to analyse students’ mathematical representations on secondary school in solving trigonometric problems. This research used qualitative method. The participants were 4 students who had high competence of knowledge taken from 20 students of 12th natural-science grade SMAN-1 Kota Besi, Central Kalimantan. Data validation was carried out using time triangulation. Data analysis used Huberman and Miles stages. The results showed that their answers were not only based on the given figure, but also used the definition of trigonometric ratio on verbal representations. On the other hand, they were able to determine the object positions to be observed. However, they failed to determine the position of the angle of depression at the sketches made on visual representations. Failure in determining the position of the angle of depression to cause an error in using the mathematical equation. Finally, they were unsuccessful to use the mathematical equation properly on symbolic representations. From this research, we could recommend the importance of translations between mathematical problems and mathematical representations as well as translations among mathematical representaions (verbal, visual, and symbolic) in learning mathematics in the classroom.
Pre-service teachers’ challenges in presenting mathematical problems
Desfitri, R.
2018-01-01
The purpose of this study was to analyzed how pre-service teachers prepare and assigned tasks or assignments in teaching practice situations. This study was also intended to discuss about kind of tasks or assignments they gave to students. Participants of this study were 15 selected pre-service mathematics teachers from mathematics education department who took part on microteaching class as part of teaching preparation program. Based on data obtained, it was occasionally found that there were hidden errors on questions or tasks assigned by pre-service teachers which might lead their students not to be able to reach a logical or correct answer. Although some answers might seem to be true, they were illogical or unfavourable. It is strongly recommended that pre-service teachers be more careful when posing mathematical problems so that students do not misunderstand the problems or the concepts, since both teachers and students were sometimes unaware of errors in problems being worked on.
Calculus Problem Solving Behavior of Mathematic Education Students
Rizal, M.; Mansyur, J.
2017-04-01
The purpose of this study is to obtain a description of the problem-solving behaviour of mathematics education students. The attainment of the purpose consisted of several stages: (1) to gain the subject from the mathematic education of first semester students, each of them who has a high, medium, and low competence of mathematic case. (2) To give two mathematical problems with different characteristics. The first problem (M1), the statement does not lead to a resolution. The second problem (M2), a statement leads to problem-solving. (3) To explore the behaviour of problem-solving based on the step of Polya (Rizal, 2011) by way of thinking aloud and in-depth interviews. The obtained data are analysed as suggested by Miles and Huberman (1994) but at first, time triangulation is done or data’s credibility by providing equivalent problem contexts and at different times. The results show that the behavioral problem solvers (mathematic education students) who are capable of high mathematic competency (ST). In understanding M1, ST is more likely to pay attention to an image first, read the texts piecemeal and repeatedly, then as a whole and more focus to the sentences that contain equations, numbers or symbols. As a result, not all information can be received well. When understanding the M2, ST can link the information from a problem that is stored in the working memory to the information on the long-term memory. ST makes planning to the solution of M1 and M2 by using a formula based on similar experiences which have been ever received before. Another case when implementing the troubleshooting plans, ST complete the M1 according to the plan, but not all can be resolved correctly. In contrast to the implementation of the solving plan of M2, ST can solve the problem according to plan quickly and correctly. According to the solving result of M1 and M2, ST conducts by reading the job based on an algorithm and reasonability. Furthermore, when SS and SR understand the
Reynolds, Thomas D.; And Others
This compilation of 138 problems illustrating applications of high school mathematics to various aspects of space science is intended as a resource from which the teacher may select questions to supplement his regular course. None of the problems require a knowledge of calculus or physics, and solutions are presented along with the problem…
Handayani, I.; Januar, R. L.; Purwanto, S. E.
2018-01-01
This research aims to know the influence of Missouri Mathematics Project Learning Model to Mathematical Problem-solving Ability of Students at Junior High School. This research is a quantitative research and uses experimental research method of Quasi Experimental Design. The research population includes all student of grade VII of Junior High School who are enrolled in the even semester of the academic year 2016/2017. The Sample studied are 76 students from experimental and control groups. The sampling technique being used is cluster sampling method. The instrument is consisted of 7 essay questions whose validity, reliability, difficulty level and discriminating power have been tested. Before analyzing the data by using t-test, the data has fulfilled the requirement for normality and homogeneity. The result of data shows that there is the influence of Missouri mathematics project learning model to mathematical problem-solving ability of students at junior high school with medium effect.
Students’ Mathematical Creative Thinking through Problem Posing Learning
Ulfah, U.; Prabawanto, S.; Jupri, A.
2017-09-01
The research aims to investigate the differences in enhancement of students’ mathematical creative thinking ability of those who received problem posing approach assisted by manipulative media and students who received problem posing approach without manipulative media. This study was a quasi experimental research with non-equivalent control group design. Population of this research was third-grade students of a primary school in Bandung city in 2016/2017 academic year. Sample of this research was two classes as experiment class and control class. The instrument used is a test of mathematical creative thinking ability. Based on the results of the research, it is known that the enhancement of the students’ mathematical creative thinking ability of those who received problem posing approach with manipulative media aid is higher than the ability of those who received problem posing approach without manipulative media aid. Students who get learning problem posing learning accustomed in arranging mathematical sentence become matter of story so it can facilitate students to comprehend about story
Use of the Fox derivatives in the solution of the word problem for groups
International Nuclear Information System (INIS)
Majumdar, S.
1988-09-01
Applying Fox's free partial derivative, the word problem of a finitely presented group has been reduced to the problem of finding an algorithm for determining the existence of a root of a system of linear equations over the integral group ring. The solubility of the word problem for torsion-free one-relator groups and torsion-free polycyclic-by-finite groups has been deduced. (author). 10 refs
Student’s scheme in solving mathematics problems
Setyaningsih, Nining; Juniati, Dwi; Suwarsono
2018-03-01
The purpose of this study was to investigate students’ scheme in solving mathematics problems. Scheme are data structures for representing the concepts stored in memory. In this study, we used it in solving mathematics problems, especially ratio and proportion topics. Scheme is related to problem solving that assumes that a system is developed in the human mind by acquiring a structure in which problem solving procedures are integrated with some concepts. The data were collected by interview and students’ written works. The results of this study revealed are students’ scheme in solving the problem of ratio and proportion as follows: (1) the content scheme, where students can describe the selected components of the problem according to their prior knowledge, (2) the formal scheme, where students can explain in construct a mental model based on components that have been selected from the problem and can use existing schemes to build planning steps, create something that will be used to solve problems and (3) the language scheme, where students can identify terms, or symbols of the components of the problem.Therefore, by using the different strategies to solve the problems, the students’ scheme in solving the ratio and proportion problems will also differ.
Problem Solving Abilities and Perceptions in Alternative Certification Mathematics Teachers
Evans, Brian R.
2012-01-01
It is important for teacher educators to understand new alternative certification middle and high school teachers' mathematical problem solving abilities and perceptions. Teachers in an alternative certification program in New York were enrolled in a proof-based algebra course. At the beginning and end of a semester participants were given a…
Towards efficient measurement of metacognition in mathematical problem solving
Jacobse, Annemieke E.; Harskamp, Egbert G.
Metacognitive monitoring and regulation play an essential role in mathematical problem solving. Therefore, it is important for researchers and practitioners to assess students' metacognition. One proven valid, but time consuming, method to assess metacognition is by using think-aloud protocols.
Directory of Open Access Journals (Sweden)
Lorena Salazar Solórzano
2015-06-01
Full Text Available Beginning university training programs must focus on different competencies for mathematics teachers, i.e., not only on solving problems, but also on posing them and analyzing the mathematical activity. This paper reports the results of an exploratory study conducted with future secondary school mathematics teachers on the introduction of problem-posing tasks in formal mathematics courses, specifically in abstract algebra and real analysis courses. Evidence was found that training which includes problem-posing tasks has a positive impact on the students’ understanding of definitions, theorems and exercises within formal mathematics, as well as on their competency in reflecting on the mathematical activity.
Processing of Words Related to the Demands of a Previously Solved Problem
Directory of Open Access Journals (Sweden)
Kowalczyk Marek
2014-06-01
Full Text Available Earlier research by the author brought about findings suggesting that people in a special way process words related to demands of a problem they previously solved, even when they do not consciously notice this relationship. The findings concerned interference in the task in which the words appeared, a shift in affective responses to them that depended on sex of the participants, and impaired memory of the words. The aim of this study was to replicate these effects and to find out whether they are related to working memory (WM span of the participants, taken as a measure of the individual’s ability to control attention. Participants in the experimental group solved a divergent problem, then performed an ostensibly unrelated speeded affective classification task concerning each of a series of nouns, and then performed an unexpected cued recall task for the nouns. Afterwards, a task measuring WM span was administered. In the control group there was no problem-solving phase. Response latencies for words immediately following problem-related words in the classification task were longer in the experimental than in the control group, but there was no relationship between this effect and WM span. Solving the problem, in interaction with sex of the participants and, independently, with their WM span, influenced affective responses to problem-related words. Recall of these words, however, was not impaired in the experimental group.
Cognitive Backgrounds of Problem Solving: A Comparison of Open-Ended vs. Closed Mathematics Problems
Bahar, Abdulkadir; Maker, C. June
2015-01-01
Problem solving has been a core theme in education for several decades. Educators and policy makers agree on the importance of the role of problem solving skills for school and real life success. A primary purpose of this study was to investigate the influence of cognitive abilities on mathematical problem solving performance of elementary…
Keuning, J.; Verhoeven, L.T.W.
2008-01-01
The purpose of the present study was to explore whether the Item Response Theory (IRT) provides a suitable framework to screen for word reading and spelling problems during the elementary school period. The following issues were addressed from an IRT perspective: (a) the dimensionality of word
Fuchs, Lynn S.; Gilbert, Jennifer K.; Powell, Sarah R.; Cirino, Paul T.; Fuchs, Douglas; Hamlett, Carol L.; Seethaler, Pamela M.; Tolar, Tammy D.
2016-01-01
The purpose of this study was to examine child-level pathways in development of pre-algebraic knowledge versus word-problem solving, while evaluating the contribution of calculation accuracy and fluency as mediators of foundational skills/processes. Children (n = 962; mean 7.60 years) were assessed on general cognitive processes and early calculation, word-problem, and number knowledge at start of grade 2; calculation accuracy and calculation fluency at end of grade 2; and pre-algebraic knowledge and word-problem solving at end of grade 4. Important similarities in pathways were identified, but path analysis also indicated that language comprehension is more critical for later word-problem solving than pre-algebraic knowledge. We conclude that pathways in development of these forms of 4th-grade mathematics performance are more alike than different, but demonstrate the need to fine-tune instruction for strands of the mathematics curriculum in ways that address individual students’ foundational mathematics skills or cognitive processes. PMID:27786534
Flexibility in Mathematics Problem Solving Based on Adversity Quotient
Dina, N. A.; Amin, S. M.; Masriyah
2018-01-01
Flexibility is an ability which is needed in problem solving. One of the ways in problem solving is influenced by Adversity Quotient (AQ). AQ is the power of facing difficulties. There are three categories of AQ namely climber, camper, and quitter. This research is a descriptive research using qualitative approach. The aim of this research is to describe flexibility in mathematics problem solving based on Adversity Quotient. The subjects of this research are climber student, camper student, and quitter student. This research was started by giving Adversity Response Profile (ARP) questioner continued by giving problem solving task and interviews. The validity of data measurement was using time triangulation. The results of this research shows that climber student uses two strategies in solving problem and doesn’t have difficulty. The camper student uses two strategies in solving problem but has difficulty to finish the second strategies. The quitter student uses one strategy in solving problem and has difficulty to finish it.
Algebraic Reasoning in Solving Mathematical Problem Based on Learning Style
Indraswari, N. F.; Budayasa, I. K.; Ekawati, R.
2018-01-01
This study aimed to describe algebraic reasoning of secondary school’s pupils with different learning styles in solving mathematical problem. This study begins by giving the questionnaire to find out the learning styles and followed by mathematical ability test to get three subjects of 8th-grade whereas the learning styles of each pupil is visual, auditory, kinesthetic and had similar mathematical abilities. Then it continued with given algebraic problems and interviews. The data is validated using triangulation of time. The result showed that in the pattern of seeking indicator, subjects identified the things that were known and asked based on them observations. The visual and kinesthetic learners represented the known information in a chart, whereas the auditory learner in a table. In addition, they found the elements which makes the pattern and made a relationship between two quantities. In the pattern recognition indicator, they created conjectures on the relationship between two quantities and proved it. In the generalization indicator, they were determining the general rule of pattern found on each element of pattern using algebraic symbols and created a mathematical model. Visual and kinesthetic learners determined the general rule of equations which was used to solve problems using algebraic symbols, but auditory learner in a sentence.
Problems of Mathematical Finance by Stochastic Control Methods
Stettner, Łukasz
The purpose of this paper is to present main ideas of mathematics of finance using the stochastic control methods. There is an interplay between stochastic control and mathematics of finance. On the one hand stochastic control is a powerful tool to study financial problems. On the other hand financial applications have stimulated development in several research subareas of stochastic control in the last two decades. We start with pricing of financial derivatives and modeling of asset prices, studying the conditions for the absence of arbitrage. Then we consider pricing of defaultable contingent claims. Investments in bonds lead us to the term structure modeling problems. Special attention is devoted to historical static portfolio analysis called Markowitz theory. We also briefly sketch dynamic portfolio problems using viscosity solutions to Hamilton-Jacobi-Bellman equation, martingale-convex analysis method or stochastic maximum principle together with backward stochastic differential equation. Finally, long time portfolio analysis for both risk neutral and risk sensitive functionals is introduced.
The comprehension of mathematic problems in primary school
Directory of Open Access Journals (Sweden)
Karel Pérez Ariza
2015-05-01
Full Text Available The paper describes the result of the research project “A study of causes of difficulties in learning comprehension from an interdisciplinary perspective in Camagüey. The main objective of that study is to propose a methodology for the comprehension of mathematic problems in primary school. In designing the methodology, the characteristics of this text variety, basic principle of the theory of reading comprehension and problem solving were taking into account. In this research work several theoretical methods were used —analysis-synthesis, historical-logical, inductive-deductive— to elaborate the theoretical framework, while modeling and system approach in the methodology construction. Additionally, empirical methods were used in order to assess the knowledge about comprehension of mathematic problems; among them observation and analysis of the activity results.
Students’ Algebraic Reasonsing In Solving Mathematical Problems With Adversity Quotient
Aryani, F.; Amin, S. M.; Sulaiman, R.
2018-01-01
Algebraic reasoning is a process in which students generalize mathematical ideas from a set of particular instances and express them in increasingly formal and age-appropriate ways. Using problem solving approach to develop algebraic reasoning of mathematics may enhace the long-term learning trajectory of the majority students. The purpose of this research was to describe the algebraic reasoning of quitter, camper, and climber junior high school students in solving mathematical problems. This research used qualitative descriptive method. Subjects were determined by purposive sampling. The technique of collecting data was done by task-based interviews.The results showed that the algebraic reasoning of three students in the process of pattern seeking by identifying the things that are known and asked in a similar way. But three students found the elements of pattern recognition in different ways or method. So, they are generalize the problem of pattern formation with different ways. The study of algebraic reasoning and problem solving can be a learning paradigm in the improve students’ knowledge and skills in algebra work. The goal is to help students’ improve academic competence, develop algebraic reasoning in problem solving.
Mathematical mechanic using physical reasoning to solve problems
Levi, Mark
2009-01-01
Everybody knows that mathematics is indispensable to physics--imagine where we'd be today if Einstein and Newton didn't have the math to back up their ideas. But how many people realize that physics can be used to produce many astonishing and strikingly elegant solutions in mathematics? Mark Levi shows how in this delightful book, treating readers to a host of entertaining problems and mind-bending puzzlers that will amuse and inspire their inner physicist. Levi turns math and physics upside down, revealing how physics can simplify proofs and lead to quicker solutions and new theorems, and how physical solutions can illustrate why results are true in ways lengthy mathematical calculations never can
The impact of metacognitive strategies and self-regulating processes of solving math word problems
Eda Vula; Rrezarta Avdyli; Valbona Berisha; Blerim Saqipi; Shpetim Elezi
2017-01-01
This empirical study investigates the impact of metacognitive strategies and self-regulating processes in learners’ achievement on solving math word problems. It specifically analyzes the impact of the linguistic factor and the number of steps and arithmetical operations that learners need to apply during the process of solving math word problems. Two hundred sixty-three learners, of three classes of third graders (N=130) and four classes of fifth ...
Artzt, Alice F.; Armour-Thomas, Eleanor
1998-01-01
Uses a "teaching as problem solving" perspective to examine the components of metacognition underlying the instructional practice of seven experienced and seven beginning secondary-school mathematics teachers. Data analysis of observations, lesson plans, videotapes, and audiotapes of structured interviews suggests that the metacognition of…
The Efficacy of Using Diagrams When Solving Probability Word Problems in College
Beitzel, Brian D.; Staley, Richard K.
2015-01-01
Previous experiments have shown a deleterious effect of visual representations on college students' ability to solve total- and joint-probability word problems. The present experiments used conditional-probability problems, known to be more difficult than total- and joint-probability problems. The diagram group was instructed in how to use tree…
Parmar, Rene S.; Cawley, John F.
1994-01-01
Matrix organization can be used to construct math word problems for children with mild disabilities. Matrix organization specifies the characteristics of problems, such as problem theme or setting, operations, level of computation complexity, reading vocabulary level, and need for classification. A sample scope and sequence and 16 sample word…
To what extent do student teachers develop their mathematical problem solving ability by self-study?
Kool, Marjolein; Keijzer, Ronald
2017-01-01
A primary teacher needs mathematical problem solving ability. That is why Dutch student teachers have to show this ability in a nationwide mathematics test that contains many non-routine problems. Most student teachers prepare for this test by working on their own solving test-like problems. To what extent does these individual problem solving activities really contribute to their mathematical problem solving ability? Developing mathematical problem solving ability requires reflective mathema...
Fasni, N.; Turmudi, T.; Kusnandi, K.
2017-09-01
This research background of this research is the importance of student problem solving abilities. The purpose of this study is to find out whether there are differences in the ability to solve mathematical problems between students who have learned mathematics using Ang’s Framework for Mathematical Modelling Instruction (AFFMMI) and students who have learned using scientific approach (SA). The method used in this research is a quasi-experimental method with pretest-postest control group design. Data analysis of mathematical problem solving ability using Indepent Sample Test. The results showed that there was a difference in the ability to solve mathematical problems between students who received learning with Ang’s Framework for Mathematical Modelling Instruction and students who received learning with a scientific approach. AFFMMI focuses on mathematical modeling. This modeling allows students to solve problems. The use of AFFMMI is able to improve the solving ability.
Cheng, Lu Pien
2015-01-01
In this study, ways in which 9-year old students from one Singapore school solved 1-step and 2-step word problems based on the three semantic structures were examined. The students' work and diagrams provided insights into the range of errors in word problem solving for 1- step and 2-step word problems. In particular, the errors provided some…
Schoppek, Wolfgang; Tulis, Maria
2010-01-01
The fluency of basic arithmetical operations is a precondition for mathematical problem solving. However, the training of skills plays a minor role in contemporary mathematics instruction. The authors proposed individualization of practice as a means to improve its efficiency, so that the time spent with the training of skills is minimized. As a…
Mathematical Approaches to Problems in Resource Management and Epidemiology
Levin, Simon; Shoemaker, Christine
1989-01-01
Increasingly, mathematical methods are being used to advantage in addressing the problems facing humanity in managing its environment. Problems in resource management and epidemiology especially have demonstrated the utility of quantitative modeling. To explore these approaches, the Center of Applied Mathematics at Cornell University organized a conference in Fall, 1987, with the objective of surveying and assessing the state of the art. This volume records the proceedings of that conference. Underlying virtually all of these studies are models of population growth, from individual cells to large vertebrates. Cell population growth presents the simplest of systems for study, and is of fundamental importance in its own right for a variety of medical and environmental applications. In Part I of this volume, Michael Shuler describes computer models of individual cells and cell populations, and Frank Hoppensteadt discusses the synchronization of bacterial culture growth. Together, these provide a valuable introdu...
The heat treatment of steel. A mathematical control problem
Energy Technology Data Exchange (ETDEWEB)
Hoemberg, Dietmar; Kern, Daniela
2009-07-21
The goal of this paper is to show how the heat treatment of steel can be modelled in terms of a mathematical optimal control problem. The approach is applied to laser surface hardening and the cooling of a steel slab including mechanical effects. Finally, it is shown how the results can be utilized in industrial practice by a coupling with machine-based control. (orig.)
Takahashi, Akihiko
2016-01-01
Problem solving has been a major theme in Japanese mathematics curricula for nearly 50 years. Numerous teacher reference books and lesson plans using problem solving have been published since the 1960s. Government-authorized mathematics textbooks for elementary grades, published by six private companies, have had more and more problem solving over…
Open mathematical problems regarding non-Newtonian fluids
International Nuclear Information System (INIS)
Wilson, Helen J
2012-01-01
We present three open problems in the mathematical modelling of the flow of non-Newtonian fluids. The first problem is rather long standing: a discontinuity in the dependence of the rise velocity of a gas bubble on its volume. This is very well characterized experimentally but not, so far, fully reproduced either numerically or analytically. The other two are both instabilities. The first is observed experimentally but never predicted analytically or numerically. In the second instability, numerical studies reproduce the experimental observations but there is as yet no analytical or semi-analytical prediction of the linear instability which must be present. (invited article)
Using the Wonder of Inequalities between Averages for Mathematics Problems Solving
Shaanan, Rachel Mogilevsky; Gordon, Moshe Stupel
2016-01-01
The study presents an introductory idea of using mathematical averages as a tool for enriching mathematical problem solving. Throughout students' activities, a research was conducted on their ability to solve mathematical problems, and how to cope with a variety of mathematical tasks, in a variety of ways, using the skills, tools and experiences…
Mathematical programming methods for large-scale topology optimization problems
DEFF Research Database (Denmark)
Rojas Labanda, Susana
for mechanical problems, but has rapidly extended to many other disciplines, such as fluid dynamics and biomechanical problems. However, the novelty and improvements of optimization methods has been very limited. It is, indeed, necessary to develop of new optimization methods to improve the final designs......, and at the same time, reduce the number of function evaluations. Nonlinear optimization methods, such as sequential quadratic programming and interior point solvers, have almost not been embraced by the topology optimization community. Thus, this work is focused on the introduction of this kind of second...... for the classical minimum compliance problem. Two of the state-of-the-art optimization algorithms are investigated and implemented for this structural topology optimization problem. A Sequential Quadratic Programming (TopSQP) and an interior point method (TopIP) are developed exploiting the specific mathematical...
Application of a Mathematical Model to an Advertisement Reservation Problem
Directory of Open Access Journals (Sweden)
Ozlem COSGUN
2013-01-01
Full Text Available Television networks provide TV programs free of charge to the public. However, they acquire their revenue by telecasting advertisements in the midst of continuing programs or shows. A key problem faced by the TV networks in Turkey is how to accept and televise the advertisements reserved by a client on a specified advertisement break which we called “Advertisement Reservation Problem” (ARP. The problem is complicated by limited time inventory, by different rating points for different target groups, competition avoidance and the relationship between TV networks and clients. In this study we have developed a mathematical model for advertisement reservation problem and extended this model for some cases encountered in real business life. We have also discussed how these cases affect the decisions of a TV network. Mixed integer linear programming approach is proposed to solve these problems. This approach has been implemented to a case taken from one of the biggest TV networks of Turkey.
A Cognitive Analysis of Students’ Mathematical Problem Solving Ability on Geometry
Rusyda, N. A.; Kusnandi, K.; Suhendra, S.
2017-09-01
The purpose of this research is to analyze of mathematical problem solving ability of students in one of secondary school on geometry. This research was conducted by using quantitative approach with descriptive method. Population in this research was all students of that school and the sample was twenty five students that was chosen by purposive sampling technique. Data of mathematical problem solving were collected through essay test. The results showed the percentage of achievement of mathematical problem solving indicators of students were: 1) solve closed mathematical problems with context in math was 50%; 2) solve the closed mathematical problems with the context beyond mathematics was 24%; 3) solving open mathematical problems with contexts in mathematics was 35%; And 4) solving open mathematical problems with contexts outside mathematics was 44%. Based on the percentage, it can be concluded that the level of achievement of mathematical problem solving ability in geometry still low. This is because students are not used to solving problems that measure mathematical problem solving ability, weaknesses remember previous knowledge, and lack of problem solving framework. So the students’ ability of mathematical problems solving need to be improved with implement appropriate learning strategy.
Fuchs, Lynn S.; Fuchs, Douglas; Compton, Donald L.; Powell, Sarah R.; Seethaler, Pamela M.; Capizzi, Andrea M.; Schatschneider, Christopher; Fletcher, Jack M.
2006-01-01
The purpose of this study was to examine the cognitive correlates of RD-grade skill in arithmetic, algorithmic computation, and arithmetic word problems. Third graders (N = 312) were measured on language, nonverbal problem solving, concept formation, processing speed, long-term memory, working memory, phonological decoding, and sight word…
Munez, David; Orrantia, Josetxu; Rosales, Javier
2013-01-01
This study explored the effectiveness of external representations presented together with compare word problems, and whether such effectiveness was moderated by working memory. Participants were 49 secondary school students. Each participant solved 48 problems presented in 4 presentation types that included 2 difficulty treatments (number of steps…
The Strategies of Mathematics Teachers When Solving Number Sense Problems
Directory of Open Access Journals (Sweden)
Sare Şengül
2014-04-01
Full Text Available Number sense involves efficient strategies and the ability to think flexibly with numbers and number operations and flexible thinking ability and the inclination getting for making sound mathematical judgements. The aim of this study was to investigate the strategies used by mathematics teachers while solving number sense problems. Eleven mathematics teachers from a graduate program in education were the participants. A number sense test which has a total of 12 problems is used as the data gathering tool. Teachers’ responses and strategies were analyzed both qualitatively and quantitatively.First, participants’ responses were evaluated for correctness. Then the strategies teachers used were analyzed. The strategies were categorized as based on the use of number sense or rule based strategies. When the correct and incorrect responses were considered together, in the 46% of the responses number sense strategies were used and in 54% the rule-based strategies were used. The results of this study showed that even though teachers can use number sense strategies at some level, there is still room for development in teachers’ number sense.
LEVELING STUDENTS’ CREATIVE THINKING IN SOLVING AND POSING MATHEMATICAL PROBLEM
Directory of Open Access Journals (Sweden)
Tatag Yuli Eko Siswono
2010-07-01
Full Text Available Many researchers assume that people are creative, but their degree ofcreativity is different. The notion of creative thinking level has beendiscussed .by experts. The perspective of mathematics creative thinkingrefers to a combination of logical and divergent thinking which is basedon intuition but has a conscious aim. The divergent thinking is focusedon flexibility, fluency, and novelty in mathematical problem solving andproblem posing. As students have various backgrounds and differentabilities, they possess different potential in thinking patterns,imagination, fantasy and performance; therefore, students have differentlevels of creative thinking. A research study was conducted in order todevelop a framework for students’ levels of creative thinking inmathematics. This research used a qualitative approach to describe thecharacteristics of the levels of creative thinking. Task-based interviewswere conducted to collect data with ten 8thgrade junior secondary schoolstudents. The results distinguished five levels of creative thinking,namely level 0 to level 4 with different characteristics in each level.These differences are based on fluency, flexibility, and novelty inmathematical problem solving and problem posing.Keywords: student’s creative thinking, problem posing, flexibility,fluency, novelty DOI: http://dx.doi.org/10.22342/jme.1.1.794.17-40
An inverse problem for a mathematical model of aquaponic agriculture
Bobak, Carly; Kunze, Herb
2017-01-01
Aquaponic agriculture is a sustainable ecosystem that relies on a symbiotic relationship between fish and macrophytes. While the practice has been growing in popularity, relatively little mathematical models exist which aim to study the system processes. In this paper, we present a system of ODEs which aims to mathematically model the population and concetrations dynamics present in an aquaponic environment. Values of the parameters in the system are estimated from the literature so that simulated results can be presented to illustrate the nature of the solutions to the system. As well, a brief sensitivity analysis is performed in order to identify redundant parameters and highlight those which may need more reliable estimates. Specifically, an inverse problem with manufactured data for fish and plants is presented to demonstrate the ability of the collage theorem to recover parameter estimates.
Sheriff, Kelli A; Boon, Richard T
2014-08-01
The purpose of this study was to examine the effects of computer-based graphic organizers, using Kidspiration 3© software, to solve one-step word problems. Participants included three students with mild intellectual disability enrolled in a functional academic skills curriculum in a self-contained classroom. A multiple probe single-subject research design (Horner & Baer, 1978) was used to evaluate the effectiveness of computer-based graphic organizers to solving mathematical one-step word problems. During the baseline phase, the students completed a teacher-generated worksheet that consisted of nine functional word problems in a traditional format using a pencil, paper, and a calculator. In the intervention and maintenance phases, the students were instructed to complete the word problems using a computer-based graphic organizer. Results indicated that all three of the students improved in their ability to solve the one-step word problems using computer-based graphic organizers compared to traditional instructional practices. Limitations of the study and recommendations for future research directions are discussed. Copyright © 2014 Elsevier Ltd. All rights reserved.
Problem solving of student with visual impairment related to mathematical literacy problem
Pratama, A. R.; Saputro, D. R. S.; Riyadi
2018-04-01
The student with visual impairment, total blind category depends on the sense of touch and hearing in obtaining information. In fact, the two senses can receive information less than 20%. Thus, students with visual impairment of the total blind categories in the learning process must have difficulty, including learning mathematics. This study aims to describe the problem-solving process of the student with visual impairment, total blind category on mathematical literacy issues based on Polya phase. This research using test method similar problems mathematical literacy in PISA and in-depth interviews. The subject of this study was a student with visual impairment, total blind category. Based on the result of the research, problem-solving related to mathematical literacy based on Polya phase is quite good. In the phase of understanding the problem, the student read about twice by brushing the text and assisted with information through hearing three times. The student with visual impairment in problem-solving based on the Polya phase, devising a plan by summoning knowledge and experience gained previously. At the phase of carrying out the plan, students with visual impairment implement the plan in accordance with pre-made. In the looking back phase, students with visual impairment need to check the answers three times but have not been able to find a way.
Interference thinking in constructing students’ knowledge to solve mathematical problems
Jayanti, W. E.; Usodo, B.; Subanti, S.
2018-04-01
This research aims to describe interference thinking in constructing students’ knowledge to solve mathematical problems. Interference thinking in solving problems occurs when students have two concepts that interfere with each other’s concept. Construction of problem-solving can be traced using Piaget’s assimilation and accommodation framework, helping to know the students’ thinking structures in solving the problems. The method of this research was a qualitative method with case research strategy. The data in this research involving problem-solving result and transcripts of interviews about students’ errors in solving the problem. The results of this research focus only on the student who experience proactive interference, where student in solving a problem using old information to interfere with the ability to recall new information. The student who experience interference thinking in constructing their knowledge occurs when the students’ thinking structures in the assimilation and accommodation process are incomplete. However, after being given reflection to the student, then the students’ thinking process has reached equilibrium condition even though the result obtained remains wrong.
Hong, Jee Yun; Kim, Min Kyeong
2016-01-01
Ill-structured problems can be regarded as one of the measures that meet recent social needs emphasizing students' abilities to solve real-life problems. This study aimed to analyze the mathematical abstraction process in solving such problems, and to identify the mathematical abstraction level ([I] Recognition of mathematical structure through…
Artzt, Alice F.; Armour-Thomas, Eleanor
The roles of cognition and metacognition were examined in the mathematical problem-solving behaviors of students as they worked in small groups. As an outcome, a framework that links the literature of cognitive science and mathematical problem solving was developed for protocol analysis of mathematical problem solving. Within this framework, each…
Investigating and Developing Engineering Students' Mathematical Modelling and Problem-Solving Skills
Wedelin, Dag; Adawi, Tom; Jahan, Tabassum; Andersson, Sven
2015-01-01
How do engineering students approach mathematical modelling problems and how can they learn to deal with such problems? In the context of a course in mathematical modelling and problem solving, and using a qualitative case study approach, we found that the students had little prior experience of mathematical modelling. They were also inexperienced…
Tense and aspect in word problems about motion: diagram, gesture, and the felt experience of time
de Freitas, Elizabeth; Zolkower, Betina
2015-09-01
Word problems about motion contain various conjugated verb forms. As students and teachers grapple with such word problems, they jointly operationalize diagrams, gestures, and language. Drawing on findings from a 3-year research project examining the social semiotics of classroom interaction, we show how teachers and students use gesture and diagram to make sense of complex verb forms in such word problems. We focus on the grammatical category of "aspect" for how it broadens the concept of verb tense. Aspect conveys duration and completion or frequency of an event. The aspect of a verb defines its temporal flow (or lack thereof) and the location of a vantage point for making sense of this durational process.
Language, arithmetic word problems, and deaf students: Linguistic strategies used to solve tasks
Zevenbergen, Robyn; Hyde, Merv; Power, Des
2001-12-01
There has been limited examination of the intersection between language and arithmetic in the performance of deaf students, although some previous research has shown that deaf and hearing-impaired1 students are delayed in both their language acquisition and arithmetic performance. This paper examines the performance of deaf and hearing-impaired students in South-East Queensland, Australia, in solving arithmetic word problems. It was found that the subjects' solutions of word problems confirmed trends for hearing students, but that their performance was delayed in comparison. The results confirm other studies where deaf and hearing-impaired students are delayed in their language acquisition and this impacts on their capacity to successfully undertake the resolution of word problems.
A review of mathematical models in economic environmental problems
DEFF Research Database (Denmark)
Nahorski, Z.; Ravn, H.F.
2000-01-01
The paper presents a review of mathematical models used,in economic analysis of environmental problems. This area of research combines macroeconomic models of growth, as dependent on capital, labour, resources, etc., with environmental models describing such phenomena like natural resources...... exhaustion or pollution accumulation and degradation. In simpler cases the models can be treated analytically and the utility function can be optimized using, e.g., such tools as the maximum principle. In more complicated cases calculation of the optimal environmental policies requires a computer solution....
de Mul, F.F.M.; Martin Batlle, C.; Martin i Batlle, Cristina; de Bruijn, Imme; Rinzema, K.; Rinzema, Kees
2003-01-01
Teaching physics to first-year university students (in the USA: junior/senior level) is often hampered by their lack of skills in the underlying mathematics, and that in turn may block their understanding of the physics and their ability to solve problems. Examples are vector algebra, differential
Analysis of mathematical problem-solving ability based on metacognition on problem-based learning
Mulyono; Hadiyanti, R.
2018-03-01
Problem-solving is the primary purpose of the mathematics curriculum. Problem-solving abilities influenced beliefs and metacognition. Metacognition as superordinate capabilities can direct, regulate cognition and motivation and then problem-solving processes. This study aims to (1) test and analyzes the quality of problem-based learning and (2) investigate the problem-solving capabilities based on metacognition. This research uses mixed method study with The subject research are class XI students of Mathematics and Science at High School Kesatrian 2 Semarang which divided into tacit use, aware use, strategic use and reflective use level. The collecting data using scale, interviews, and tests. The data processed with the proportion of test, t-test, and paired samples t-test. The result shows that the students with levels tacit use were able to complete the whole matter given, but do not understand what and why a strategy is used. Students with aware use level were able to solve the problem, be able to build new knowledge through problem-solving to the indicators, understand the problem, determine the strategies used, although not right. Students on the Strategic ladder Use can be applied and adopt a wide variety of appropriate strategies to solve the issues and achieved re-examine indicators of process and outcome. The student with reflective use level is not found in this study. Based on the results suggested that study about the identification of metacognition in problem-solving so that the characteristics of each level of metacognition more clearly in a more significant sampling. Teachers need to know in depth about the student metacognitive activity and its relationship with mathematical problem solving and another problem resolution.
Ei, Shin-ichiro; Koiso, Miyuki; Ochiai, Hiroyuki; Okada, Kanzo; Saito, Shingo; Shirai, Tomoyuki
2014-01-01
This book deals with one of the most novel advances in mathematical modeling for applied scientific technology, including computer graphics, public-key encryption, data visualization, statistical data analysis, symbolic calculation, encryption, error correcting codes, and risk management. It also shows that mathematics can be used to solve problems from nature, e.g., slime mold algorithms. One of the unique features of this book is that it shows readers how to use pure and applied mathematics, especially those mathematical theory/techniques developed in the twentieth century, and developing now, to solve applied problems in several fields of industry. Each chapter includes clues on how to use "mathematics" to solve concrete problems faced in industry as well as practical applications. The target audience is not limited to researchers working in applied mathematics and includes those in engineering, material sciences, economics, and life sciences.
From immunology to MRI data anlysis: Problems in mathematical biology
Waters, Ryan Samuel
This thesis represents a collection of four distinct biological projects rising from immunology and metabolomics that required unique and creative mathematical approaches. One project focuses on understanding the role IL-2 plays in immune response regulation and exploring how these effects can be altered. We developed several dynamic models of the receptor signaling network which we analyze analytically and numerically. In a second project focused also on MS, we sought to create a system for grading magnetic resonance images (MRI) with good correlation with disability. The goal is for these MRI scores to provide a better standard for large-scale clinical drug trials, which limits the bias associated with differences in available MRI technology and general grader/participant variability. The third project involves the study of the CRISPR adaptive immune system in bacteria. Bacterial cells recognize and acquire snippets of exogenous genetic material, which they incorporate into their DNA. In this project we explore the optimal design for the CRISPR system given a viral distribution to maximize its probability of survival. The final project involves the study of the benefits for colocalization of coupled enzymes in metabolic pathways. The hypothesized kinetic advantage, known as `channeling', of putting coupled enzymes closer together has been used as justification for the colocalization of coupled enzymes in biological systems. We developed and analyzed a simple partial differential equation of the diffusion of the intermediate substrate between coupled enzymes to explore the phenomena of channeling. The four projects of my thesis represent very distinct biological problems that required a variety of techniques from diverse areas of mathematics ranging from dynamical modeling to statistics, Fourier series and calculus of variations. In each case, quantitative techniques were used to address biological questions from a mathematical perspective ultimately providing
Gender differences in algebraic thinking ability to solve mathematics problems
Kusumaningsih, W.; Darhim; Herman, T.; Turmudi
2018-05-01
This study aimed to conduct a gender study on students' algebraic thinking ability in solving a mathematics problem, polyhedron concept, for grade VIII. This research used a qualitative method. The data was collected using: test and interview methods. The subjects in this study were eight male and female students with different level of abilities. It was found that the algebraic thinking skills of male students reached high group of five categories. They were superior in terms of reasoning and quick understanding in solving problems. Algebraic thinking ability of high-achieving group of female students also met five categories of algebraic thinking indicators. They were more diligent, tenacious and thorough in solving problems. Algebraic thinking ability of male students in medium category only satisfied three categories of algebraic thinking indicators. They were sufficient in terms of reasoning and understanding in solving problems. Algebraic thinking ability group of female students in medium group also satisfied three categories of algebraic thinking indicators. They were fairly diligent, tenacious and meticulous on working on the problems.
COMPUTER TOOLS OF DYNAMIC MATHEMATIC SOFTWARE AND METHODICAL PROBLEMS OF THEIR USE
Olena V. Semenikhina; Maryna H. Drushliak
2014-01-01
The article presents results of analyses of standard computer tools of dynamic mathematic software which are used in solving tasks, and tools on which the teacher can support in the teaching of mathematics. Possibility of the organization of experimental investigating of mathematical objects on the basis of these tools and the wording of new tasks on the basis of the limited number of tools, fast automated check are specified. Some methodological comments on application of computer tools and ...
Directory of Open Access Journals (Sweden)
Anja Drame
2011-10-01
Full Text Available
Abstract: Languages are not static systems. They develop and change, add new items while others become outdated. These changes can be clearly observed in the lexicon especially. No language can afford to ignore or neglect foreign influence. Due to globalisation, especially English gains more and more influence on other (also European languages. In developing countries, the languages of the former colonisers also still have an enormous impact on the indigenous languages. Some of these nations are slowly heading towards endogenous language policies which demands the modernisation of the technical vocabulary. This is however a costly and time-consuming process. In this regard language planners often prefer borrowing from foreign sources as a quick and therefore cheap method. The first part of this paper deals with the discussion amongst linguists, sociolinguists and lexicographers about the extent to which foreign words should be allowed in an indigenous language. The second part looks at the example of isiXhosa, one of South Africa's eleven official languages, which is strongly influenced by foreign words, especially English and Afrikaans, and shows problems and methods of the integration of foreign words into the isiXhosa grammatical structure.
Keywords: FOREIGN WORDS, ISIXHOSA, ENGLISH, AFRIKAANS, BAHASA INDONESIA, RUSSIAN, ESTONIAN, GERMAN, LANGUAGE POLICY, LANGUAGE PURISM, LSP, MORPHOLOGY, SEMANTICS, PHONOLOGY
Zusammenfassung: Fremdwörter als Problem in der Standardisierung/Lexikographie: Englische und afrikaanse Lehnwörter in isiXhosa. Sprachen sindkeine statischen Systeme. Sie entwickeln und verändern sich, fügen neue Bestandteile hinzu,während andere veralten. Diese Vorgänge lassen sich besonders deutlich im Lexikon einer Sprachebeobachten. Keine Sprache kann es sich leisten fremde Einflüsse zu ignorieren oder zurückzuweisen.Aufgrund von Globalisation gewinnt vor allem das Englisch immer mehr Einfluss aufandere (auch
The impact of metacognitive strategies and self-regulating processes of solving math word problems
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Eda Vula
2017-09-01
Full Text Available This empirical study investigates the impact of metacognitive strategies and self-regulating processes in learners’ achievement on solving math word problems. It specifically analyzes the impact of the linguistic factor and the number of steps and arithmetical operations that learners need to apply during the process of solving math word problems. Two hundred sixty-three learners, of three classes of third graders (N=130 and four classes of fifth graders (N=133 of the elementary cycle from two urban schools of Kosovo, participated in the study. Almost half of the total number of the third and fifth-graderswere exposed to metacognitive instruction. The rest of the learners were included in control classes in which they performed tasks without having been given any specific guidance, based exclusively on traditional methods and respective textbooks. All the learners were tested in math word problems twice, before the intervention and after it. Research findings have shown that metacognitive strategies and self-regulating processes that learners use to control their actions, to reason, and to reflect, are one of the main resources that influence their success in solving a math word problem. Although the difference between the pre-test and the post-test resultswas statistically significant solely with the fifth-grade experimental classes, yet an improved performance was observed in third-grade experimental learners’ classes compared to control classes. Theoretical and practical implications of the research are discussed in the end of the study.
Learning to Solve Addition and Subtraction Word Problems in English as an Imported Language
Verzosa, Debbie Bautista; Mulligan, Joanne
2013-01-01
This paper reports an intervention phase of a design study aimed to assist second-grade Filipino children in solving addition word problems in English, a language they primarily encounter only in school. With Filipino as the medium of instruction, an out-of-school pedagogical intervention providing linguistic and representational scaffolds was…
Darma, I. K.
2018-01-01
This research is aimed at determining: 1) the differences of mathematical problem solving ability between the students facilitated with problem-based learning model and conventional learning model, 2) the differences of mathematical problem solving ability between the students facilitated with authentic and conventional assessment model, and 3) interaction effect between learning and assessment model on mathematical problem solving. The research was conducted in Bali State Polytechnic, using the 2x2 experiment factorial design. The samples of this research were 110 students. The data were collected using a theoretically and empirically-validated test. Instruments were validated by using Aiken’s approach of technique content validity and item analysis, and then analyzed using anova stylistic. The result of the analysis shows that the students facilitated with problem-based learning and authentic assessment models get the highest score average compared to the other students, both in the concept understanding and mathematical problem solving. The result of hypothesis test shows that, significantly: 1) there is difference of mathematical problem solving ability between the students facilitated with problem-based learning model and conventional learning model, 2) there is difference of mathematical problem solving ability between the students facilitated with authentic assessment model and conventional assessment model, and 3) there is interaction effect between learning model and assessment model on mathematical problem solving. In order to improve the effectiveness of mathematics learning, collaboration between problem-based learning model and authentic assessment model can be considered as one of learning models in class.
Fletcher, Nicole
2014-01-01
Mathematics curriculum designers and policy decision makers are beginning to recognize the importance of problem solving, even at the earliest stages of mathematics learning. The Common Core includes sense making and perseverance in solving problems in its standards for mathematical practice for students at all grade levels. Incorporating problem…
Koichu, Boris
2010-01-01
This article discusses an issue of inserting mathematical knowledge within the problem-solving processes. Relatively advanced mathematical knowledge is defined in terms of "three mathematical worlds"; relatively advanced problem-solving behaviours are defined in terms of taxonomies of "proof schemes" and "heuristic behaviours". The relationships…
DEFF Research Database (Denmark)
Niss, Martin
2017-01-01
This paper studies the cognitive obstacles related to one aspect of mathematization in physics problem-solving, namely, what might be called structuring for mathematization, where the problem situation is structured in such a way that a translation to a mathematical universe can be done. We report...
From inverse problems in mathematical physiology to quantitative differential diagnoses.
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Sven Zenker
2007-11-01
Full Text Available The improved capacity to acquire quantitative data in a clinical setting has generally failed to improve outcomes in acutely ill patients, suggesting a need for advances in computer-supported data interpretation and decision making. In particular, the application of mathematical models of experimentally elucidated physiological mechanisms could augment the interpretation of quantitative, patient-specific information and help to better target therapy. Yet, such models are typically complex and nonlinear, a reality that often precludes the identification of unique parameters and states of the model that best represent available data. Hypothesizing that this non-uniqueness can convey useful information, we implemented a simplified simulation of a common differential diagnostic process (hypotension in an acute care setting, using a combination of a mathematical model of the cardiovascular system, a stochastic measurement model, and Bayesian inference techniques to quantify parameter and state uncertainty. The output of this procedure is a probability density function on the space of model parameters and initial conditions for a particular patient, based on prior population information together with patient-specific clinical observations. We show that multimodal posterior probability density functions arise naturally, even when unimodal and uninformative priors are used. The peaks of these densities correspond to clinically relevant differential diagnoses and can, in the simplified simulation setting, be constrained to a single diagnosis by assimilating additional observations from dynamical interventions (e.g., fluid challenge. We conclude that the ill-posedness of the inverse problem in quantitative physiology is not merely a technical obstacle, but rather reflects clinical reality and, when addressed adequately in the solution process, provides a novel link between mathematically described physiological knowledge and the clinical concept of
From Inverse Problems in Mathematical Physiology to Quantitative Differential Diagnoses
Zenker, Sven; Rubin, Jonathan; Clermont, Gilles
2007-01-01
The improved capacity to acquire quantitative data in a clinical setting has generally failed to improve outcomes in acutely ill patients, suggesting a need for advances in computer-supported data interpretation and decision making. In particular, the application of mathematical models of experimentally elucidated physiological mechanisms could augment the interpretation of quantitative, patient-specific information and help to better target therapy. Yet, such models are typically complex and nonlinear, a reality that often precludes the identification of unique parameters and states of the model that best represent available data. Hypothesizing that this non-uniqueness can convey useful information, we implemented a simplified simulation of a common differential diagnostic process (hypotension in an acute care setting), using a combination of a mathematical model of the cardiovascular system, a stochastic measurement model, and Bayesian inference techniques to quantify parameter and state uncertainty. The output of this procedure is a probability density function on the space of model parameters and initial conditions for a particular patient, based on prior population information together with patient-specific clinical observations. We show that multimodal posterior probability density functions arise naturally, even when unimodal and uninformative priors are used. The peaks of these densities correspond to clinically relevant differential diagnoses and can, in the simplified simulation setting, be constrained to a single diagnosis by assimilating additional observations from dynamical interventions (e.g., fluid challenge). We conclude that the ill-posedness of the inverse problem in quantitative physiology is not merely a technical obstacle, but rather reflects clinical reality and, when addressed adequately in the solution process, provides a novel link between mathematically described physiological knowledge and the clinical concept of differential diagnoses
Surya, Edy; Sabandar, Jozua; Kusumah, Yaya S.; Darhim
2013-01-01
The students' difficulty which was found is in the problem of understanding, drawing diagrams, reading the charts correctly, conceptual formal mathematical understanding, and mathematical problem solving. The appropriate problem representation is the basic way in order to understand the problem itself and make a plan to solve it. This research was…
PROBLEMS RELATED TO THE ADAPTATION OF SOME ENGLISH LOAN WORDS IN CROATIAN AND POLISH LANGUAGE
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Maciek Czerwiński
2000-01-01
Full Text Available Many languages in the new era are open to the influence of English language. There is no doubt about it but process of adaptation in various languages can run quite different. I focused in the article on such problems. Adaptation itself of every single loan word (and thus English loan word as well runs on the three basic levels: phonological, morphological and semantic. On every level we find some particular tendencies in particular language. To research them properly we should look at another language and compare them.
Quantum mechanics problems in observer's mathematics
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Khots, Boris; Khots, Dmitriy [Compressor Controls Corp, Des Moines, Iowa (United States); iMath Consulting LLC, Omaha, Nebraska (United States)
2012-11-06
This work considers the ontology, guiding equation, Schrodinger's equation, relation to the Born Rule, the conditional wave function of a subsystem in a setting of arithmetic, algebra and topology provided by Observer's Mathematics (see www.mathrelativity.com). Observer's Mathematics creates new arithmetic, algebra, geometry, topology, analysis and logic which do not contain the concept of continuum, but locally coincide with the standard fields. Certain results and communications pertaining to solutions of these problems are provided. In particular, we prove the following theorems: Theorem I (Two-slit interference). Let {Psi}{sub 1} be a wave from slit 1, {Psi}{sub 2} - from slit 2, and {Psi} = {Psi}{sub 1}+{Psi}{sub 2}. Then the probability of {Psi} being a wave equals to 0.5. Theorem II (k-bodies solution). For W{sub n} from m-observer point of view with m>log{sub 10}((2 Multiplication-Sign 10{sup 2n}-1){sup 2k}+1), the probability of standard expression of Hamiltonian variation is less than 1 and depends on n,m,k.
Parameter Subset Selection Techniques for Problems in Mathematical Biology
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Olsen, Christian; Smith, Ralph; Tran, Hien
2015-01-01
Patient-specific models for diagnostics and treatment planning require reliable parameter estimation and model predictions. Mathematical models of physiological systems are often formulated as systems of nonlinear ODEs with many parameters and few options for measuring all state variables....... Consequently, it can be difficult to determine which parameters can reliably be estimated from the available data. This investigation highlights some pitfalls associated with parameters that are unidentifiable in the sense that they are not uniquely determined by responses, and presents methods for recognizing...... and addressing identifiability problems. These methods quantify the magnitude of parameter influence through sensitivity analysis, and parameter interactions that might complicate unambiguous parameter estimation. The methods will be demonstrated using five examples of increasing complexity, as well...
A broad look at the literature on math word problem-solving interventions for third graders
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Sheri Kingsdorf
2016-12-01
Full Text Available Though research on effective instruction in math word problem solving is prominent at the middle and secondary levels, much less work has been done in elementary grades. In this article, we review the research on varied problem-solving instructional interventions at the third-grade level for students across ability levels. Third grade was chosen as the focus due to the fact that word problem-solving requirements are first introduced into the curriculum and standardized assessment at this point in time. Drawing on quantitative studies using single subject, quasi-experimental, and randomized controlled trial designs, we examine the instructional components and instructional content identified as effective across the 13 studies that met search criteria. Conclusions focus on current understanding of best practices, limitations of the existing research, and important considerations for future research.
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Bashirah Ibrahim
2017-10-01
Full Text Available We examine students’ mathematical performance on quantitative “synthesis problems” with varying mathematical complexity. Synthesis problems are tasks comprising multiple concepts typically taught in different chapters. Mathematical performance refers to the formulation, combination, and simplification of equations. Generally speaking, formulation and combination of equations require conceptual reasoning; simplification of equations requires manipulation of equations as computational tools. Mathematical complexity is operationally defined by the number and the type of equations to be manipulated concurrently due to the number of unknowns in each equation. We use two types of synthesis problems, namely, sequential and simultaneous tasks. Sequential synthesis tasks require a chronological application of pertinent concepts, and simultaneous synthesis tasks require a concurrent application of the pertinent concepts. A total of 179 physics major students from a second year mechanics course participated in the study. Data were collected from written tasks and individual interviews. Results show that mathematical complexity negatively influences the students’ mathematical performance on both types of synthesis problems. However, for the sequential synthesis tasks, it interferes only with the students’ simplification of equations. For the simultaneous synthesis tasks, mathematical complexity additionally impedes the students’ formulation and combination of equations. Several reasons may explain this difference, including the students’ different approaches to the two types of synthesis problems, cognitive load, and the variation of mathematical complexity within each synthesis type.
Problem solving in the borderland between mathematics and physics
DEFF Research Database (Denmark)
Jensen, Jens Højgaard; Niss, Martin; Jankvist, Uffe Thomas
2017-01-01
The article addresses the problématique of where mathematization is taught in the educational system, and who teaches it. Mathematization is usually not a part of mathematics programs at the upper secondary level, but we argue that physics teaching has something to offer in this respect, if it fo......The article addresses the problématique of where mathematization is taught in the educational system, and who teaches it. Mathematization is usually not a part of mathematics programs at the upper secondary level, but we argue that physics teaching has something to offer in this respect...
Mills, Nadia Monrose
2015-01-01
The ability to succeed in Science, Technology, Engineering, and Mathematics (STEM) careers is contingent on a student's ability to engage in mathematical problem solving. As a result, there has been increased focus on students' ability to think critically by providing them more with problem solving experiences in the classroom. Much research has…
Mahendra, Rengga; Slamet, Isnandar; Budiyono
2017-12-01
One of the difficulties of students in learning mathematics is on the subject of geometry that requires students to understand abstract things. The aim of this research is to determine the effect of learning model Problem Posing and Problem Solving with Realistic Mathematics Education Approach to conceptual understanding and students' adaptive reasoning in learning mathematics. This research uses a kind of quasi experimental research. The population of this research is all seventh grade students of Junior High School 1 Jaten, Indonesia. The sample was taken using stratified cluster random sampling technique. The test of the research hypothesis was analyzed by using t-test. The results of this study indicate that the model of Problem Posing learning with Realistic Mathematics Education Approach can improve students' conceptual understanding significantly in mathematics learning. In addition tu, the results also showed that the model of Problem Solving learning with Realistic Mathematics Education Approach can improve students' adaptive reasoning significantly in learning mathematics. Therefore, the model of Problem Posing and Problem Solving learning with Realistic Mathematics Education Approach is appropriately applied in mathematics learning especially on the subject of geometry so as to improve conceptual understanding and students' adaptive reasoning. Furthermore, the impact can improve student achievement.
New Readings in Greek Mathematics: Sources, Problems, Publications.
Knorr, Wilbur R.
1990-01-01
The field of ancient Greek mathematics is discussed in terms of how representative is the surviving corpus of the ancient achievement in mathematics, the patterns of thought by which they were discovered, and the construction of mathematics during this period. The research being done in this field is described. (KR)
Earth's Rotation: A Challenging Problem in Mathematics and Physics
Ferrándiz, José M.; Navarro, Juan F.; Escapa, Alberto; Getino, Juan
2015-01-01
A suitable knowledge of the orientation and motion of the Earth in space is a common need in various fields. That knowledge has been ever necessary to carry out astronomical observations, but with the advent of the space age, it became essential for making observations of satellites and predicting and determining their orbits, and for observing the Earth from space as well. Given the relevant role it plays in Space Geodesy, Earth rotation is considered as one of the three pillars of Geodesy, the other two being geometry and gravity. Besides, research on Earth rotation has fostered advances in many fields, such as Mathematics, Astronomy and Geophysics, for centuries. One remarkable feature of the problem is in the extreme requirements of accuracy that must be fulfilled in the near future, about a millimetre on the tangent plane to the planet surface, roughly speaking. That challenges all of the theories that have been devised and used to-date; the paper makes a short review of some of the most relevant methods, which can be envisaged as milestones in Earth rotation research, emphasizing the Hamiltonian approach developed by the authors. Some contemporary problems are presented, as well as the main lines of future research prospected by the International Astronomical Union/International Association of Geodesy Joint Working Group on Theory of Earth Rotation, created in 2013.
Fuchs, Lynn S; Gilbert, Jennifer K; Fuchs, Douglas; Seethaler, Pamela M; Martin, BrittanyLee N
2018-01-01
This study was designed to deepen insights on whether word-problem (WP) solving is a form of text comprehension (TC) and on the role of language in WPs. A sample of 325 second graders, representing high, average, and low reading and math performance, was assessed on (a) start-of-year TC, WP skill, language, nonlinguistic reasoning, working memory, and foundational skill (word identification, arithmetic) and (b) year-end WP solving, WP-language processing (understanding WP statements, without calculation demands), and calculations. Multivariate, multilevel path analysis, accounting for classroom and school effects, indicated that TC was a significant and comparably strong predictor of all outcomes. Start-of-year language was a significantly stronger predictor of both year-end WP outcomes than of calculations, whereas start-of-year arithmetic was a significantly stronger predictor of calculations than of either WP measure. Implications are discussed in terms of WP solving as a form of TC and a theoretically coordinated approach, focused on language, for addressing TC and WP-solving instruction.
Fuchs, Lynn S.; Gilbert, Jennifer K.; Fuchs, Douglas; Seethaler, Pamela M.; Martin, BrittanyLee N.
2018-01-01
This study was designed to deepen insights on whether word-problem (WP) solving is a form of text comprehension (TC) and on the role of language in WPs. A sample of 325 second graders, representing high, average, and low reading and math performance, was assessed on (a) start-of-year TC, WP skill, language, nonlinguistic reasoning, working memory, and foundational skill (word identification, arithmetic) and (b) year-end WP solving, WP-language processing (understanding WP statements, without calculation demands), and calculations. Multivariate, multilevel path analysis, accounting for classroom and school effects, indicated that TC was a significant and comparably strong predictor of all outcomes. Start-of-year language was a significantly stronger predictor of both year-end WP outcomes than of calculations, whereas start-of-year arithmetic was a significantly stronger predictor of calculations than of either WP measure. Implications are discussed in terms of WP solving as a form of TC and a theoretically coordinated approach, focused on language, for addressing TC and WP-solving instruction. PMID:29643723
Towards the Construction of a Framework to Deal with Routine Problems to Foster Mathematical Inquiry
Santos-Trigo, Manuel; Camacho-Machin, Matias
2009-01-01
To what extent does the process of solving textbook problems help students develop a way of thinking that is consistent with mathematical practice? Can routine problems be transformed into problem solving activities that promote students' mathematical reflection? These questions are used to outline and discuss features of an inquiry framework…
To what extent do student teachers develop their mathematical problem solving ability by self-study?
Marjolein Kool; Ronald Keijzer
2017-01-01
A primary teacher needs mathematical problem solving ability. That is why Dutch student teachers have to show this ability in a nationwide mathematics test that contains many non-routine problems. Most student teachers prepare for this test by working on their own solving test-like problems. To what
Using Metacognitive Strategies to Improve Reading Comprehension and Solve a Word Problem
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Tomo Djudin
2017-03-01
Full Text Available This article describes briefly the theories of metacognition and the impacts of metacognitive skills on learning. The differences between cognitive strategy and metacognitive strategy were mentioned. Some strategies to improve students’ meta cognition skills in the classroom explored as well. Based on the theories, two models of metacognitive strategies instruction for deeply understanding in reading textbook and for finding a solution of words physics problem solving were developed. These models will enable students to be independent and strategic learners.
Using Mathematics and Engineering to Solve Problems in Secondary Level Biology
Cox, Charles; Reynolds, Birdy; Schunn, Christian; Schuchardt, Anita
2016-01-01
There are strong classroom ties between mathematics and the sciences of physics and chemistry, but those ties seem weaker between mathematics and biology. Practicing biologists realize both that there are interesting mathematics problems in biology, and that viewing classroom biology in the context of another discipline could support students'…
Science Modelling in Pre-Calculus: How to Make Mathematics Problems Contextually Meaningful
Sokolowski, Andrzej; Yalvac, Bugrahan; Loving, Cathleen
2011-01-01
"Use of mathematical representations to model and interpret physical phenomena and solve problems is one of the major teaching objectives in high school math curriculum" [National Council of Teachers of Mathematics (NCTM), "Principles and Standards for School Mathematics", NCTM, Reston, VA, 2000]. Commonly used pre-calculus textbooks provide a…
Students Use Graphic Organizers to Improve Mathematical Problem-Solving Communications
Zollman, Alan
2009-01-01
Improving students' problem-solving abilities is a major, if not the major, goal of middle grades mathematics. To address this goal, the author, who is a university mathematics educator, and nine inner-city middle school teachers developed a math/science action research project. This article describes their unique approach to mathematical problem…
Lein, Amy E.; Jitendra, Asha K.; Starosta, Kristin M.; Dupuis, Danielle N.; Hughes-Reid, Cheyenne L.; Star, Jon R.
2016-01-01
In this study, the authors assessed the contribution of engagement (on-task behavior) to the mathematics problem-solving performance of seventh-grade students after accounting for prior mathematics achievement. A subsample of seventh-grade students in four mathematics classrooms (one high-, two average-, and one low-achieving) from a larger…
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Hasan KARAL
2010-06-01
Full Text Available The purpose of this study is to make the students involve with the simulation environment with the developed practice and to develop their problem solving abilities by making easy their understanding of word problems. For this goal, a web based simulation environment which could be manipulated related to the defined movement and pool problems was designed in the light of the defined questions in the curriculum. The research was designed according to semi-experimental pattern which has equalized control group. It was applied in two different 8th grade classes on 44 students in total in the city center of Trabzon in 2008-2009 spring semester. In the research it was benefited from both quantitative and qualitative data collection methods, in the study as the data collection instrument to measure students’ cognitive achievements, it was benefited from word problems achievement test which had 20 items and its KR-20 coefficient was 0,86, observations and from the interviews which were made with the students. The study involved 19 students in experiment group and 25 students in the controlled group. It was used web based education in the experiment group, however, in controlled group, traditional education was used. For the analysis of the data collected in the research, t-test as used for the independent groups. At the end of the research, it was seen that in understanding and solving the word problems, the students in the experiment group who used web based education environment which included simulation environment was more successful than the controlled group who used the traditional method. After the interviews it was concluded that the students in the experiment group had positive thoughts about the web based simulations environment. It is defined that students are more motivated to the lesson and they have an increasing self-confident in problem solving in simulation environment
An Investigation of Secondary Teachers’ Understanding and Belief on Mathematical Problem Solving
Yuli Eko Siswono, Tatag; Wachidul Kohar, Ahmad; Kurniasari, Ika; Puji Astuti, Yuliani
2016-02-01
Weaknesses on problem solving of Indonesian students as reported by recent international surveys give rise to questions on how Indonesian teachers bring out idea of problem solving in mathematics lesson. An explorative study was undertaken to investigate how secondary teachers who teach mathematics at junior high school level understand and show belief toward mathematical problem solving. Participants were teachers from four cities in East Java province comprising 45 state teachers and 25 private teachers. Data was obtained through questionnaires and written test. The results of this study point out that the teachers understand pedagogical problem solving knowledge well as indicated by high score of observed teachers‘ responses showing understanding on problem solving as instruction as well as implementation of problem solving in teaching practice. However, they less understand on problem solving content knowledge such as problem solving strategies and meaning of problem itself. Regarding teacher's difficulties, teachers admitted to most frequently fail in (1) determining a precise mathematical model or strategies when carrying out problem solving steps which is supported by data of test result that revealed transformation error as the most frequently observed errors in teachers’ work and (2) choosing suitable real situation when designing context-based problem solving task. Meanwhile, analysis of teacher's beliefs on problem solving shows that teachers tend to view both mathematics and how students should learn mathematics as body static perspective, while they tend to believe to apply idea of problem solving as dynamic approach when teaching mathematics.
Problem representation and mathematical problem solving of students of varying math ability.
Krawec, Jennifer L
2014-01-01
The purpose of this study was to examine differences in math problem solving among students with learning disabilities (LD, n = 25), low-achieving students (LA, n = 30), and average-achieving students (AA, n = 29). The primary interest was to analyze the processes students use to translate and integrate problem information while solving problems. Paraphrasing, visual representation, and problem-solving accuracy were measured in eighth grade students using a researcher-modified version of the Mathematical Processing Instrument. Results indicated that both students with LD and LA students struggled with processing but that students with LD were significantly weaker than their LA peers in paraphrasing relevant information. Paraphrasing and visual representation accuracy each accounted for a statistically significant amount of variance in problem-solving accuracy. Finally, the effect of visual representation of relevant information on problem-solving accuracy was dependent on ability; specifically, for students with LD, generating accurate visual representations was more strongly related to problem-solving accuracy than for AA students. Implications for instruction for students with and without LD are discussed.
Wardono; Waluya, S. B.; Mariani, Scolastika; Candra D, S.
2016-02-01
This study aims to find out that there are differences in mathematical literacy ability in content Change and Relationship class VII Junior High School 19, Semarang by Problem Based Learning (PBL) model with an Indonesian Realistic Mathematics Education (called Pendidikan Matematika Realistik Indonesia or PMRI in Indonesia) approach assisted Elearning Edmodo, PBL with a PMRI approach, and expository; to know whether the group of students with learning PBL models with PMRI approach and assisted E-learning Edmodo can improve mathematics literacy; to know that the quality of learning PBL models with a PMRI approach assisted E-learning Edmodo has a good category; to describe the difficulties of students in working the problems of mathematical literacy ability oriented PISA. This research is a mixed methods study. The population was seventh grade students of Junior High School 19, Semarang Indonesia. Sample selection is done by random sampling so that the selected experimental class 1, class 2 and the control experiment. Data collected by the methods of documentation, tests and interviews. From the results of this study showed average mathematics literacy ability of students in the group PBL models with a PMRI approach assisted E-learning Edmodo better than average mathematics literacy ability of students in the group PBL models with a PMRI approach and better than average mathematics literacy ability of students in the expository models; Mathematics literacy ability in the class using the PBL model with a PMRI approach assisted E-learning Edmodo have increased and the improvement of mathematics literacy ability is higher than the improvement of mathematics literacy ability of class that uses the model of PBL learning with PMRI approach and is higher than the improvement of mathematics literacy ability of class that uses the expository models; The quality of learning using PBL models with a PMRI approach assisted E-learning Edmodo have very good category.
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Melike TURAL SÖNMEZ
2017-12-01
Full Text Available The purpose of this study is to examine the construction of mathematical modelling problems process in the content of financial literacy. It is also aimed to create design proposals for construction of mathematical modelling problems. A design based research method was used in this study. The participants were three seventh grade students, six finance experts and nine mathematics education experts. Data collection tools were transcription of video and tapes group discussions, presentations and worksheets during mathematical modelling activities, and participant experts’ feedback form about mathematical modelling problems. There were three stages in this study. First stage was application of preliminary study. This stage gave information about convenience of problems to grade level, students’ timing for solution of problems, clarity of problems and students’ background about content. In second stage, finance experts commented on convenience of mathematical modelling problems to financial literacy standards. In third stage, mathematics education experts commented on convenience of problems to students’ grade level, mathematical modelling principles and seventh grade mathematics lesson objectives. They also gave suggestion on progress. The frequency value of theme in feedback forms was calculated and experts’ expressions were given as citation. It was given suggestion about stages and application of the design guide
Guerrero-Ortiz, Carolina; Mena-Lorca, Jaime
2015-01-01
International audience; This study analyses the results obtained from comparing the paths shown by expert mathematicians on the one hand and mathematics teachers on the other, when addressing a hypothetical problem that requires the construction of a mathematical model. The research was conducted with a qualitative approach, applying a case study which involved a group of mathematics teachers and three experts from different mathematical areas. The results show that the process of constructin...
An empirical approach to the mathematical values of problem choice and argumentation
DEFF Research Database (Denmark)
Johansen, Mikkel Willum; Misfeldt, Morten
2016-01-01
In this paper we describe and discuss how mathematical values influence researchers’ choices when practicing mathematics. Our paper is based on a qualitative investigation of mathematicians’ practices, and its goal is to gain an empirically grounded understanding of mathematical values. More...... specifically, we will analyze the values connected to mathematicians’ choice of problems and their choice of argumentative style when communicating their results. We suggest that these two situations can be understood as relating to the three mathematical values: recognizability, formalizability...
Scientific Approach to Improve Mathematical Problem Solving Skills Students of Grade V
Roheni; Herman, T.; Jupri, A.
2017-09-01
This study investigates the skills of elementary school students’ in problem solving through the Scientific Approach. The purpose of this study is to determine mathematical problem solving skills of students by using Scientific Approach is better than mathematical problem solving skills of students by using Direct Instruction. This study is using quasi-experimental method. Subject of this study is students in grade V in one of state elementary school in Cirebon Regency. Instrument that used in this study is mathematical problem solving skills. The result of this study showed that mathematical problem solving skills of students who learn by using Scientific Approach is more significant than using Direct Instruction. Base on result and analysis, the conclusion is that Scientific Approach can improve students’ mathematical problem solving skills.
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Edy Surya
2013-01-01
Full Text Available The students’ difficulty which was found is in the problem of understanding, drawing diagrams, reading the charts correctly, conceptual formal mathematical understanding, and mathematical problem solving. The appropriate problem representation is the basic way in order to understand the problem itself and make a plan to solve it. This research was the experimental classroom design with a pretest-posttest control in order to increase the representation of visual thinking ability on mathematical problem solving approach with contextual learning. The research instrument was a test, observation and interviews. Contextual approach increases of mathematical representations ability increases in students with high initial category, medium, and low compared to conventional approaches. Keywords: Visual Thinking Representation, Mathematical Problem Solving, Contextual Teaching Learning Approach DOI: http://dx.doi.org/10.22342/jme.4.1.568.113-126
PROBLEMS OF MATHEMATICAL MODELING OF THE ENTERPRISES ORGANIZATIONAL STRUCTURE
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N. V. Andrianov
2006-01-01
Full Text Available The analysis of the mathematical models which can be used at optimization of the control system of the enterprise organizational structure is presented. The new approach to the mathematical modeling of the enterprise organizational structure, based on using of temporary characteristics of the control blocks working, is formulated
Teaching Mathematical Problem Solving to Students with Limited English Proficiency.
Kaplan, Rochelle G.; Patino, Rodrigo A.
Many mainstreamed students with limited English proficiency continue to face the difficulty of learning English as a second language (ESL) while studying mathematics and other content areas framed in the language of native speakers. The difficulty these students often encounter in mathematics classes and their poor performance on subsequent…
Strategies That Help Learning-Disabled Students Solve Verbal Mathematical Problems.
Giordano, Gerard
1990-01-01
Strategies are presented for dealing with factors that can be responsible for failure in mathematical problem solving. The suggestions include personalization of verbal problems, thematic strands based on student interests, visual representation, a laboratory approach, and paraphrasing. (JDD)
Jagals, Divan; van der Walt, Marthie
2016-01-01
Metacognition encompasses knowledge and regulation that, through reflection, sustain problem solving behaviour. How metacognitive awareness is constructed from reflection on metacognitive knowledge and regulation and how these reflections enable metacognitive skills for Mathematics problem solving remain unclear. Three secondary schools…
Edwin Musdi
2016-01-01
This research aims to develop a mathematics instructional model based realistic mathematics education (RME) to promote students' problem-solving abilities. The design research used Plomp models, which consists of preliminary phase, development or proto-typing phase and assessment phase. At this study, only the first two phases conducted. The first phase, a preliminary investigation, carried out with a literature study to examine the theory-based instructional learning RME model, characterist...
Problem solving as a challenge for mathematics education in The Netherlands
Doorman, M.; Drijvers, P.; Dekker, T.; Heuvel-Panhuizen, T. van; Lange, J. de; Wijers, M.
2007-01-01
This paper deals with the challenge to establish problem solving as a living domain in mathematics education in The Netherlands. While serious attempts are made to implement a problem-oriented curriculum based on principles of realistic mathematics education with room for modelling and with
Ramnarain, Umesh
2014-01-01
A major impediment to problem solving in mathematics in the great majority of South African schools is that disadvantaged students from seriously impoverished learning environments are lacking in the necessary informal mathematical knowledge to develop their own strategies for solving non-routine problems. A randomized pretest-posttest control…
Context problems in realistic mathematics education: A calculus course as an example
Gravemeijer, K.P.E.; Doorman, L.M.
1999-01-01
This article discusses the role of context problems, as they are used in the Dutch approach that is known as realistic mathematics education (RME). In RME, context problems are intended for supporting a reinvention process that enables students to come to grips with formal mathematics. This approach
Djukic, Dusan; Matic, Ivan
2006-01-01
The International Mathematical Olympiad (IMO) is a prestigious competition for high-school students interested in mathematics. It offers high school students a chance to measure up with students from the rest of the world. This book contains problems and solutions that appeared on the IMO over the years. It presents a grand total of 1900 problems.
Teachers Implementing Mathematical Problem Posing in the Classroom: Challenges and Strategies
Leung, Shuk-kwan S.
2013-01-01
This paper reports a study about how a teacher educator shared knowledge with teachers when they worked together to implement mathematical problem posing (MPP) in the classroom. It includes feasible methods for getting practitioners to use research-based tasks aligned to the curriculum in order to encourage children to pose mathematical problems.…
Kaya, Deniz; Izgiol, Dilek; Kesan, Cenk
2014-01-01
The aim was to determine elementary mathematics teacher candidates' problem solving skills and analyze problem solving skills according to various variables. The data were obtained from total 306 different grade teacher candidates receiving education in Department of Elementary Mathematics Education, Buca Faculty of Education, Dokuz Eylul…
Pre-service mathematics teachers’ ability in solving well-structured problem
Paradesa, R.
2018-01-01
This study aimed to describe the mathematical problem-solving ability of undergraduate students of mathematics education in solving the well-structured problem. The type of this study was qualitative descriptive. The subjects in this study were 100 undergraduate students of Mathematics Education at one of the private universities in Palembang city. The data in this study was collected through two test items with essay form. The results of this study showed that, from the first problem, only 8% students can solve it, but do not check back again to validate the process. Based on a scoring rubric that follows Polya strategy, their answer satisfied 2 4 2 0 patterns. But, from the second problem, 45% students satisfied it. This is because the second problem imitated from the example that was given in learning process. The average score of undergraduate students mathematical problem-solving ability in solving well-structured problems showed 56.00 with standard deviation was 13.22. It means that, from 0 - 100 scale, undergraduate students mathematical problem-solving ability can be categorized low. From this result, the conclusion was undergraduate students of mathematics education in Palembang still have a problem in solving mathematics well-structured problem.
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Sunisa Sumirattana
2017-09-01
This study was based on research and development design. The main purposes of this study were to develop an instructional process for enhancing mathematical literacy among students in secondary school and to study the effects of the developed instructional process on mathematical literacy. The instructional process was developed by analyzing and synthesizing realistic mathematics education and the DAPIC problem-solving process. The developed instructional process was verified by experts and was trialed. The designated pre-test/post-test control method was used to study the effectiveness of the developed instructional process on mathematical literacy. The sample consisted of 104 ninth grade students from a secondary school in Bangkok, Thailand. The developed instructional process consisted of five steps, namely (1 posing real life problems, (2 solving problems individually or in a group, (3 presenting and discussing, (4 developing formal mathematics, and (5 applying knowledge. The mathematical literacy of the experimental group was significantly higher after being taught through the instructional process. The same results were obtained when comparing the results of the experimental group with the control group.
Analytical derivation: An epistemic game for solving mathematically based physics problems
Bajracharya, Rabindra R.; Thompson, John R.
2016-06-01
Problem solving, which often involves multiple steps, is an integral part of physics learning and teaching. Using the perspective of the epistemic game, we documented a specific game that is commonly pursued by students while solving mathematically based physics problems: the analytical derivation game. This game involves deriving an equation through symbolic manipulations and routine mathematical operations, usually without any physical interpretation of the processes. This game often creates cognitive obstacles in students, preventing them from using alternative resources or better approaches during problem solving. We conducted hour-long, semi-structured, individual interviews with fourteen introductory physics students. Students were asked to solve four "pseudophysics" problems containing algebraic and graphical representations. The problems required the application of the fundamental theorem of calculus (FTC), which is one of the most frequently used mathematical concepts in physics problem solving. We show that the analytical derivation game is necessary, but not sufficient, to solve mathematically based physics problems, specifically those involving graphical representations.
Problem of mathematical deduction of the existence of black holes
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Yuan-Shun Chin
1990-01-01
Full Text Available The mathematical proof of existence of Black Hole is based on the assumption of mass being independent of speed. Considering the effect of special relativity of the dependence of mass with speed there is no Black hole.
Agustan, S.; Juniati, Dwi; Siswono, Tatag Yuli Eko
2017-08-01
Reflective thinking is an important component in the world of education, especially in professional education of teachers. In learning mathematics, reflective thinking is one way to solve mathematical problem because it can improve student's curiosity when student faces a mathematical problem. Reflective thinking is also a future competence that should be taught to students to face the challenges and to respond of demands of the 21st century. There are many factors which give impact toward the student's reflective thinking when student solves mathematical problem. One of them is cognitive style. For this reason, reflective thinking and cognitive style are important things in solving contextual mathematical problem. This research paper describes aspect of reflective thinking in solving contextual mathematical problem involved solution by using some mathematical concept, namely linear program, algebra arithmetic operation, and linear equations of two variables. The participant, in this research paper, is a male-prospective teacher who has Field Dependent. The purpose of this paper is to describe aspect of prospective teachers' reflective thinking in solving contextual mathematical problem. This research paper is a descriptive by using qualitative approach. To analyze the data, the researchers focus in four main categories which describe prospective teacher's activities using reflective thinking, namely; (a) formulation and synthesis of experience, (b) orderliness of experience, (c) evaluating the experience and (d) testing the selected solution based on the experience.
Investigating and developing engineering students' mathematical modelling and problem-solving skills
Wedelin, Dag; Adawi, Tom; Jahan, Tabassum; Andersson, Sven
2015-09-01
How do engineering students approach mathematical modelling problems and how can they learn to deal with such problems? In the context of a course in mathematical modelling and problem solving, and using a qualitative case study approach, we found that the students had little prior experience of mathematical modelling. They were also inexperienced problem solvers, unaware of the importance of understanding the problem and exploring alternatives, and impeded by inappropriate beliefs, attitudes and expectations. Important impacts of the course belong to the metacognitive domain. The nature of the problems, the supervision and the follow-up lectures were emphasised as contributing to the impacts of the course, where students show major development. We discuss these empirical results in relation to a framework for mathematical thinking and the notion of cognitive apprenticeship. Based on the results, we argue that this kind of teaching should be considered in the education of all engineers.
The role of problem solving method on the improvement of mathematical learning
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Saeed Mokhtari-Hassanabad
2012-10-01
Full Text Available In history of education, problem solving is one of the important educational goals and teachers or parents have intended that their students have capacity of problem solving. In present research, it is tried that study the problem solving method for mathematical learning. This research is implemented via quasi-experimental method on 49 boy students at high school. The results of Leven test and T-test indicated that problem solving method has more effective on the improvement of mathematical learning than traditional instruction method. Therefore it seems that teachers of mathematics must apply the problem solving method in educational systems till students became self-efficiency in mathematical problem solving.
Science modelling in pre-calculus: how to make mathematics problems contextually meaningful
Sokolowski, Andrzej; Yalvac, Bugrahan; Loving, Cathleen
2011-04-01
'Use of mathematical representations to model and interpret physical phenomena and solve problems is one of the major teaching objectives in high school math curriculum' (National Council of Teachers of Mathematics (NCTM), Principles and Standards for School Mathematics, NCTM, Reston, VA, 2000). Commonly used pre-calculus textbooks provide a wide range of application problems. However, these problems focus students' attention on evaluating or solving pre-arranged formulas for given values. The role of scientific content is reduced to provide a background for these problems instead of being sources of data gathering for inducing mathematical tools. Students are neither required to construct mathematical models based on the contexts nor are they asked to validate or discuss the limitations of applied formulas. Using these contexts, the instructor may think that he/she is teaching problem solving, where in reality he/she is teaching algorithms of the mathematical operations (G. Kulm (ed.), New directions for mathematics assessment, in Assessing Higher Order Thinking in Mathematics, Erlbaum, Hillsdale, NJ, 1994, pp. 221-240). Without a thorough representation of the physical phenomena and the mathematical modelling processes undertaken, problem solving unintentionally appears as simple algorithmic operations. In this article, we deconstruct the representations of mathematics problems from selected pre-calculus textbooks and explicate their limitations. We argue that the structure and content of those problems limits students' coherent understanding of mathematical modelling, and this could result in weak student problem-solving skills. Simultaneously, we explore the ways to enhance representations of those mathematical problems, which we have characterized as lacking a meaningful physical context and limiting coherent student understanding. In light of our discussion, we recommend an alternative to strengthen the process of teaching mathematical modelling - utilization
le Roux, Kate; Adler, Jill
2016-01-01
Mathematical problems that make links to the everyday and to disciplines other than mathematics--variously referred to as practical, realistic, real-world or applied problems in the literature--feature in school and undergraduate mathematics reforms aimed at increasing mathematics participation in contexts of inequity and diversity. In this…
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Natal’ya Yur’evna Gorbunova
2017-06-01
Full Text Available We described several aspects of organizing student research work, as well as solving a number of mathematical modeling problems: professionally-oriented, multi-stage, etc. We underlined the importance of their economic content. Samples of using such problems in teaching Mathematics at agricultural university were given. Several questions connected with information material selection and peculiarities of research problems application were described. Purpose. The author aims to show the possibility and necessity of using professionally-oriented problems of mathematical modeling in teaching Mathematics at agricultural university. The subject of analysis is including such problems into educational process. Methodology. The main research method is dialectical method of obtaining knowledge of finding approaches to selection, writing and using mathematical modeling and professionally-oriented problems in educational process; the methodology is study of these methods of obtaining knowledge. Results. As a result of analysis of literature, students opinions, observation of students work, and taking into account personal teaching experience, it is possible to make conclusion about importance of using mathematical modeling problems, as it helps to systemize theoretical knowledge, apply it to practice, raise students study motivation in engineering sphere. Practical implications. Results of the research can be of interest for teachers of Mathematics in preparing Bachelor and Master students of engineering departments of agricultural university both for theoretical research and for modernization of study courses.
Mathematical models of physics problems (physics research and technology)
Anchordoqui, Luis Alfredo
2013-01-01
This textbook is intended to provide a foundation for a one-semester introductory course on the advanced mathematical methods that form the cornerstones of the hard sciences and engineering. The work is suitable for first year graduate or advanced undergraduate students in the fields of Physics, Astronomy and Engineering. This text therefore employs a condensed narrative sufficient to prepare graduate and advanced undergraduate students for the level of mathematics expected in more advanced graduate physics courses, without too much exposition on related but non-essential material. In contrast to the two semesters traditionally devoted to mathematical methods for physicists, the material in this book has been quite distilled, making it a suitable guide for a one-semester course. The assumption is that the student, once versed in the fundamentals, can master more esoteric aspects of these topics on his or her own if and when the need arises during the course of conducting research. The book focuses on two cor...
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Farhat Syyeda
2015-04-01
Full Text Available This article presents my experience of using pictures/images drawn by children as a form of data in research and discusses the merits and implications of employing this method. It comes from research of a mixed method exploratory case study to investigate the attitudes of 11 and 15 year old secondary school students (in the East Midlands towards Mathematics. The aim of this research was to gain an insight into the emotions, cognition, beliefs and behaviour of learners regarding Maths and the factors which influence their attitude. Besides using the tried and tested data collection tools such as focus groups and questionnaires, the children were asked to draw pictures illustrating their vision of Maths and its impact on their lives. The idea was to offer them an alternative medium of communication to exhibit their feelings and thoughts. Students used emoticons, numerals, figures, characters and mathematical symbols to show their favourable/unfavourable attitudes towards Maths and their understanding of the importance of Maths in future life. The results of visual data in this study conform to the findings of the other forms of data collected and show that boys and higher ability students have a more positive attitude towards Mathematics as compared to girls and low ability students.
Quinn, Diane M.; Spencer, Steven J.
2001-01-01
Investigated whether stereotype threat would depress college women's math performance. In one test, men outperformed women when solving word problems, though women performed equally when problems were converted into numerical equivalents. In another test, participants solved difficult problems in high or reduced stereotype threat conditions. Women…
Error analysis of mathematical problems on TIMSS: A case of Indonesian secondary students
Priyani, H. A.; Ekawati, R.
2018-01-01
Indonesian students’ competence in solving mathematical problems is still considered as weak. It was pointed out by the results of international assessment such as TIMSS. This might be caused by various types of errors made. Hence, this study aimed at identifying students’ errors in solving mathematical problems in TIMSS in the topic of numbers that considered as the fundamental concept in Mathematics. This study applied descriptive qualitative analysis. The subject was three students with most errors in the test indicators who were taken from 34 students of 8th graders. Data was obtained through paper and pencil test and student’s’ interview. The error analysis indicated that in solving Applying level problem, the type of error that students made was operational errors. In addition, for reasoning level problem, there are three types of errors made such as conceptual errors, operational errors and principal errors. Meanwhile, analysis of the causes of students’ errors showed that students did not comprehend the mathematical problems given.
Developing a pedagogical problem solving view for mathematics teachers with two reflection programs
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Bracha KRAMARSKI
2009-10-01
Full Text Available The study investigated the effects of two reflection support programs on elementary school mathematics teachers’ pedagogical problem solving view. Sixty-two teachers participated in a professional development program. Thirty teachers were assigned to the self-questioning (S_Q training and thirty two teachers were assigned to the reflection discourse (R_D training. The S_Q program was based on the IMPROVE self-questioning approach which emphasizes systematic discussion along the phases of mathematical or pedagogical problem solving as student and teacher. The R_D program emphasized discussion of standard based teaching and learning principles. Findings indicated that systematic reflection support (S_Q is effective for developing mathematics PCK, and strengthening metacognitive knowledge of mathematics teachers, more than reflection discourse (R_D. No differences were found between the groups in developing beliefs about teaching mathematics in using problem solving view.
Mujiasih; Waluya, S. B.; Kartono; Mariani
2018-03-01
Skills in working on the geometry problems great needs of the competence of Geometric Reasoning. As a teacher candidate, State Islamic University (UIN) students need to have the competence of this Geometric Reasoning. When the geometric reasoning in solving of geometry problems has grown well, it is expected the students are able to write their ideas to be communicative for the reader. The ability of a student's mathematical communication is supposed to be used as a marker of the growth of their Geometric Reasoning. Thus, the search for the growth of geometric reasoning in solving of analytic geometry problems will be characterized by the growth of mathematical communication abilities whose work is complete, correct and sequential, especially in writing. Preceded with qualitative research, this article was the result of a study that explores the problem: Was the search for the growth of geometric reasoning in solving analytic geometry problems could be characterized by the growth of mathematical communication abilities? The main activities in this research were done through a series of activities: (1) Lecturer trains the students to work on analytic geometry problems that were not routine and algorithmic process but many problems that the process requires high reasoning and divergent/open ended. (2) Students were asked to do the problems independently, in detail, complete, order, and correct. (3) Student answers were then corrected each its stage. (4) Then taken 6 students as the subject of this research. (5) Research subjects were interviewed and researchers conducted triangulation. The results of this research, (1) Mathematics Education student of UIN Semarang, had adequate the mathematical communication ability, (2) the ability of this mathematical communication, could be a marker of the geometric reasoning in solving of problems, and (3) the geometric reasoning of UIN students had grown in a category that tends to be good.
Kapur, Manu
2011-01-01
This paper replicates and extends my earlier work on productive failure in mathematical problem solving (Kapur, doi:10.1007/s11251-009-9093-x, 2009). One hundred and nine, seventh-grade mathematics students taught by the same teacher from a Singapore school experienced one of three learning designs: (a) traditional lecture and practice (LP), (b)…
M. Rodionov; Z. Dedovets
2015-01-01
The level and type of student academic motivation are the key factors in their development and determine the effectiveness of their education. Improving motivation is very important with regard to courses on middle school mathematics. This article examines the general position regarding the practice of academic motivation. It also examines the particular features of mathematical problem solving in a school setting.
Demitra; Sarjoko
2018-01-01
Indigenous people of Dayak tribe in Kalimantan, Indonesia have traditionally relied on a system of mutual cooperation called "handep." The cultural context has an influence on students mathematics learning. The "handep" system might be suitable for modern learning situations to develop mathematical problem-solving skill. The…
Creativity in Unique Problem-Solving in Mathematics and Its Influence on Motivation for Learning
Bishara, Saied
2016-01-01
This research study investigates the ability of students to tackle the solving of unique mathematical problems in the domain of numerical series, verbal and formal, and its influence on the motivation of junior high students with learning disabilities in the Arab sector. Two instruments were used to collect the data: mathematical series were…
Tzohar-Rozen, Meirav; Kramarski, Bracha
2014-01-01
Mathematical problem solving is one of the most valuable aspects of mathematics education. It is also the most difficult for elementary-school students (Verschaffel, Greer, & De Corte, 2000). Students experience cognitive and metacognitive difficulties in this area and develop negative emotions and poor motivation, which hamper their efforts…
Exploring a Structure for Mathematics Lessons That Foster Problem Solving and Reasoning
Sullivan, Peter; Walker, Nadia; Borcek, Chris; Rennie, Mick
2015-01-01
While there is widespread agreement on the importance of incorporating problem solving and reasoning into mathematics classrooms, there is limited specific advice on how this can best happen. This is a report of an aspect of a project that is examining the opportunities and constraints in initiating learning by posing challenging mathematics tasks…
Junsay, Merle L.
2016-01-01
This is a quasi-experimental study that explored the effects of reflective learning on prospective teachers' conceptual understanding, critical thinking, problem solving, and mathematical communication skills and the relationship of these variables. It involved 60 prospective teachers from two basic mathematics classes of an institution of higher…
Hamadneh, Iyad M.; Al-Masaeed, Aslan
2015-01-01
This study aimed at finding out mathematics teachers' attitudes towards photo math application in solving mathematical problems using mobile camera; it also aim to identify significant differences in their attitudes according to their stage of teaching, educational qualifications, and teaching experience. The study used judgmental/purposive…
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Olga V. Shipulina
2013-01-01
Full Text Available The study explores how students, who had completed the AP calculus course, mathematized the optimal navigation real-life problem simulated in the Second Life Virtual Environment. The particular research interest was to investigate whether/how students’ empirical activity in VE influences the way of their mathematizing.
The Prevalent Rate of Problem-Solving Approach in Teaching Mathematics in Ghanaian Basic Schools
Nyala, Joseph; Assuah, Charles; Ayebo, Abraham; Tse, Newel
2016-01-01
Stakeholders of mathematics education decry the rate at which students' performance are falling below expectation; they call for a shift to practical methods of teaching the subject in Ghanaian basic schools. The study explores the extent to which Ghanaian basic school mathematics teachers use problem-solving approach in their lessons. The…
Write Is Right: Using Graphic Organizers to Improve Student Mathematical Problem Solving
Zollman, Alan
2012-01-01
Teachers have used graphic organizers successfully in teaching the writing process. This paper describes graphic organizers and their potential mathematics benefits for both students and teachers, elucidates a specific graphic organizer adaptation for mathematical problem solving, and discusses results using the "four-corners-and-a-diamond"…
African Journal of Educational Studies in Mathematics and Sciences ...
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African Journal of Educational Studies in Mathematics and Sciences. ... on senior high school students' proficiency in solving linear equation word problems ... from parents and teachers' influence on students' mathematics-related self-beliefs ...
An Evaluation of Grades 9 and 10 Mathematics Textbooks Vis-À-Vis ...
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the bid system. Besides, the interview result ... Key words: Problem-solving, Mathematics textbook analysis, Heuristics. *An Associate Professor .... 1. Do mathematics textbooks contain problems that require inquiry and discovery methods of ...
Integrating packing and distribution problems and optimization through mathematical programming
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Fabio Miguel
2016-06-01
Full Text Available This paper analyzes the integration of two combinatorial problems that frequently arise in production and distribution systems. One is the Bin Packing Problem (BPP problem, which involves finding an ordering of some objects of different volumes to be packed into the minimal number of containers of the same or different size. An optimal solution to this NP-Hard problem can be approximated by means of meta-heuristic methods. On the other hand, we consider the Capacitated Vehicle Routing Problem with Time Windows (CVRPTW, which is a variant of the Travelling Salesman Problem (again a NP-Hard problem with extra constraints. Here we model those two problems in a single framework and use an evolutionary meta-heuristics to solve them jointly. Furthermore, we use data from a real world company as a test-bed for the method introduced here.
Evaluating the Use of Problem-Based Video Podcasts to Teach Mathematics in Higher Education
Kay, Robin; Kletskin, Ilona
2012-01-01
Problem-based video podcasts provide short, web-based, audio-visual explanations of how to solve specific procedural problems in subject areas such as mathematics or science. A series of 59 problem-based video podcasts covering five key areas (operations with functions, solving equations, linear functions, exponential and logarithmic functions,…
Assessing the Internal Dynamics of Mathematical Problem Solving in Small Groups.
Artzt, Alice F.; Armour-Thomas, Eleanor
The purpose of this exploratory study was to examine the problem-solving behaviors and perceptions of (n=27) seventh-grade students as they worked on solving a mathematical problem within a small-group setting. An assessment system was developed that allowed for this analysis. To assess problem-solving behaviors within a small group a Group…
PROBLEM SOLVING IN SCHOOL MATHEMATICS BASED ON HEURISTIC STRATEGIES
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NOVOTNÁ, Jarmila
2014-03-01
Full Text Available The paper describes one of the ways of developing pupils’ creative approach to problem solving. The described experiment is a part of a longitudinal research focusing on improvement of culture of problem solving by pupils. It deals with solving of problems using the following heuristic strategies: Analogy, Guess – check – revise, Systematic experimentation, Problem reformulation, Solution drawing, Way back and Use of graphs of functions. Most attention is paid to the question whether short-term work, in this case only over the period of three months, can result in improvement of pupils’ abilities to solve problems whose solving algorithms are easily accessible. It also answers the question which strategies pupils will prefer and with what results. The experiment shows that even short-term work can bear positive results as far as pupils’ approach to problem solving is concerned.
Pacheco, Mark B.; Goodwin, Amanda P.
2013-01-01
Adolescents often use root word and affix knowledge to figure out unknown words. Anglin (1993) found that younger readers favor the Part-to-Whole strategy, and Tyler and Nagy (1989) confirmed the importance of root-word knowledge for middle school students. This study seeks to understand the different strategies middle school readers use so that…
Extricating Justification Scheme Theory in Middle School Mathematical Problem Solving
Matteson, Shirley; Capraro, Mary Margaret; Capraro, Robert M.; Lincoln, Yvonna S.
2012-01-01
Twenty middle grades students were interviewed to gain insights into their reasoning about problem-solving strategies using a Problem Solving Justification Scheme as our theoretical lens and the basis for our analysis. The scheme was modified from the work of Harel and Sowder (1998) making it more broadly applicable and accounting for research…
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Delsika Pramata Sari
2017-06-01
Full Text Available The purpose of this study was to investigate the errors experienced by students learning with REACT strategy and traditional learning in solving problems of mathematical representation ability. This study used quasi experimental pattern with static-group comparison design. The subjects of this study were 47 eighth grade students of junior high school in Bandung consisting of two samples. The instrument used was a test to measure students' mathematical representation ability. The reliability coefficient about the mathematical representation ability was 0.56. The most prominent errors of mathematical representation ability of students learning with REACT strategy and traditional learning, was on indicator that solving problem involving arithmetic symbols (symbolic representation. In addition, errors were also experienced by many students with traditional learning on the indicator of making the image of a real world situation to clarify the problem and facilitate its completion (visual representation.
Refractive Thinking Profile In Solving Mathematical Problem Reviewed from Students Math Capability
Maslukha, M.; Lukito, A.; Ekawati, R.
2018-01-01
Refraction is a mental activity experienced by a person to make a decision through reflective thinking and critical thinking. Differences in mathematical capability have an influence on the difference of student’s refractive thinking processes in solving math problems. This descriptive research aims to generate a picture of refractive thinking of students in solving mathematical problems in terms of students’ math skill. Subjects in this study consisted of three students, namely students with high, medium, and low math skills based on mathematics capability test. Data collection methods used are test-based methods and interviews. After collected data is analyzed through three stages that are, condensing and displaying data, data display, and drawing and verifying conclusion. Results showed refractive thinking profiles of three subjects is different. This difference occurs at the planning and execution stage of the problem. This difference is influenced by mathematical capability and experience of each subject.
Teachers' selection and enactment of mathematical problems from textbooks
Son, Ji-Won; Kim, Ok-Kyeong
2015-12-01
In order to investigate how teachers' use of textbooks creates different kinds of opportunities for student learning, this study focused on teachers' selection and enactment of problems and tasks from the textbooks and their influence on the cognitive demand placed on students. By drawing on data from three elementary teachers in the USA, two of which used a reform-oriented textbook— Math Trailblazers and one a commercially developed textbook—this study examined kinds of problems the teachers chose and ways in which they enacted those problems in relation to the cognitive demand of the problems. In particular, we attended to the kinds of questions the teachers asked in enacting the problems and ways in which those questions influenced the cognitive demand of the textbook problems. This study also identified critical issues involved in teacher decision-making on task selection and enactment, such as the match between teachers' goals and those of the textbooks, and teachers' perception of textbook problems. Based on the results of the study, we discuss implications for teacher education and professional development.
USING TASK LIKE PISA’S PROBLEM TO SUPPORT STUDENT’S CREATIVITY IN MATHEMATICS
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Rita Novita
2016-01-01
Full Text Available Creativity is one of keys to success in the evolving global economy and also be a fundamental skill that is absolutely necessary in the 21st century. Also In mathematics, creativity or thinking creatively is important to be developed because creativity is an integral part of mathematics. However, limiting the use of creativity in the classroom reduces mathematics to a set of skills to master and rules to memorize. Doing so causes many children’s natural curiosity and enthusiasm for mathematics to disappear as they get older, creating a tremendous problem for mathematics educators who are trying to instil these very qualities. In order to investigate the increase in awareness of elementary school students’ creativity in solving mathematics’ problems by using task like PISA’s Question, a qualitative research emphasizing on holistic description was conducted. We used a formative evaluation type of development research as a mean to develop mathematical tasks like PISA’s question that have potential effect to support students’ creativity in mathematics. Ten elementary school students of grade 6 in Palembang were involved in this research. They judged the task given for them is very challenging and provokes their curiosity. The result showed that task like PISA’s question can encourage students to more creatively in mathematics.
One-dimensional inverse problems of mathematical physics
Lavrent'ev, M M; Yakhno, V G; Schulenberger, J R
1986-01-01
This monograph deals with the inverse problems of determining a variable coefficient and right side for hyperbolic and parabolic equations on the basis of known solutions at fixed points of space for all times. The problems are one-dimensional in nature since the desired coefficient of the equation is a function of only one coordinate, while the desired right side is a function only of time. The authors use methods based on the spectral theory of ordinary differential operators of second order and also methods which make it possible to reduce the investigation of the inverse problems to the in
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Edwin Musdi
2016-02-01
Full Text Available This research aims to develop a mathematics instructional model based realistic mathematics education (RME to promote students' problem-solving abilities. The design research used Plomp models, which consists of preliminary phase, development or proto-typing phase and assessment phase. At this study, only the first two phases conducted. The first phase, a preliminary investigation, carried out with a literature study to examine the theory-based instructional learning RME model, characteristics of learners, learning management descriptions by junior high school mathematics teacher and relevant research. The development phase is done by developing a draft model (an early prototype model that consists of the syntax, the social system, the principle of reaction, support systems, and the impact and effects of instructional support. Early prototype model contain a draft model, lesson plans, worksheets, and assessments. Tesssmer formative evaluation model used to revise the model. In this study only phase of one to one evaluation conducted. In the ppreliminary phase has produced a theory-based learning RME model, a description of the characteristics of learners in grade VIII Junior High School Padang and the description of teacher teaching in the classroom. The result showed that most students were still not be able to solve the non-routine problem. Teachers did not optimally facilitate students to develop problem-solving skills of students. It was recommended that the model can be applied in the classroom.
Supianto, A. A.; Hayashi, Y.; Hirashima, T.
2017-02-01
Problem-posing is well known as an effective activity to learn problem-solving methods. Monsakun is an interactive problem-posing learning environment to facilitate arithmetic word problems learning for one operation of addition and subtraction. The characteristic of Monsakun is problem-posing as sentence-integration that lets learners make a problem of three sentences. Monsakun provides learners with five or six sentences including dummies, which are designed through careful considerations by an expert teacher as a meaningful distraction to the learners in order to learn the structure of arithmetic word problems. The results of the practical use of Monsakun in elementary schools show that many learners have difficulties in arranging the proper answer at the high level of assignments. The analysis of the problem-posing process of such learners found that their misconception of arithmetic word problems causes impasses in their thinking and mislead them to use dummies. This study proposes a method of changing assignments as a support for overcoming bottlenecks of thinking. In Monsakun, the bottlenecks are often detected as a frequently repeated use of a specific dummy. If such dummy can be detected, it is the key factor to support learners to overcome their difficulty. This paper discusses how to detect the bottlenecks and to realize such support in learning by problem-posing.
Oswald, Tasha M; Beck, Jonathan S; Iosif, Ana-Maria; McCauley, James B; Gilhooly, Leslie J; Matter, John C; Solomon, Marjorie
2016-04-01
Mathematics achievement in autism spectrum disorder (ASD) has been understudied. However, the ability to solve applied math problems is associated with academic achievement, everyday problem-solving abilities, and vocational outcomes. The paucity of research on math achievement in ASD may be partly explained by the widely-held belief that most individuals with ASD are mathematically gifted, despite emerging evidence to the contrary. The purpose of the study was twofold: to assess the relative proportions of youth with ASD who demonstrate giftedness versus disability on applied math problems, and to examine which cognitive (i.e., perceptual reasoning, verbal ability, working memory) and clinical (i.e., test anxiety) characteristics best predict achievement on applied math problems in ASD relative to typically developing peers. Twenty-seven high-functioning adolescents with ASD and 27 age- and Full Scale IQ-matched typically developing controls were assessed on standardized measures of math problem solving, perceptual reasoning, verbal ability, and test anxiety. Results indicated that 22% of the ASD sample evidenced a mathematics learning disability, while only 4% exhibited mathematical giftedness. The parsimonious linear regression model revealed that the strongest predictor of math problem solving was perceptual reasoning, followed by verbal ability and test anxiety, then diagnosis of ASD. These results inform our theories of math ability in ASD and highlight possible targets of intervention for students with ASD struggling with mathematics. © 2015 International Society for Autism Research, Wiley Periodicals, Inc.
Prabawanto, Sufyani
2017-05-01
This research aims to investigate the enhancement of students' mathematical problem solving through teaching with metacognitive scaffolding approach. This research used a quasi-experimental design with pretest-posttest control. The subjects were pre-service elementary school teachers in a state university in Bandung. In this study, there were two groups: experimental and control groups. The experimental group consists of 60 studentswho acquire teaching mathematicsunder metacognitive scaffolding approach, while the control group consists of 58 studentswho acquire teaching mathematicsunder direct approach. Students were classified into three categories based on the mathematical prior ability, namely high, middle, and low. Data collection instruments consist of mathematical problem solving test instruments. By usingmean difference test, two conclusions of the research:(1) there is a significant difference in the enhancement of mathematical problem solving between the students who attended the course under metacognitive scaffolding approach and students who attended the course under direct approach, and(2) thereis no significant interaction effect of teaching approaches and ability level based on the mathematical prior ability toward enhancement of students' mathematical problem solving.
Ismail; Suwarsono, St.; Lukito, A.
2018-01-01
Critical thinking is one of the most important skills of the 21st century in addition to other learning skills such as creative thinking, communication skills and collaborative skills. This is what makes researchers feel the need to conduct research on critical thinking skills in junior high school students. The purpose of this study is to describe the critical thinking skills of junior high school female students with high mathematical skills in solving contextual and formal mathematical problems. To achieve this is used qualitative research. The subject of the study was a female student of eight grade junior high school. The students’ critical thinking skills are derived from in-depth problem-based interviews using interview guidelines. Interviews conducted in this study are problem-based interviews, which are done by the subject given a written assignment and given time to complete. The results show that critical thinking skills of female high school students with high math skills are as follows: In solving the problem at the stage of understanding the problem used interpretation skills with sub-indicators: categorization, decode, and clarify meaning. At the planning stage of the problem-solving strategy is used analytical skills with sub-indicators: idea checking, argument identification and argument analysis and evaluation skills with sub indicators: assessing the argument. In the implementation phase of problem solving, inference skills are used with subindicators: drawing conclusions, and problem solving and explanatory skills with sub-indicators: problem presentation, justification procedures, and argument articulation. At the re-checking stage all steps have been employed self-regulatory skills with sub-indicators: self-correction and selfstudy.
The effects of cumulative practice on mathematics problem solving.
Mayfield, Kristin H; Chase, Philip N
2002-01-01
This study compared three different methods of teaching five basic algebra rules to college students. All methods used the same procedures to teach the rules and included four 50-question review sessions interspersed among the training of the individual rules. The differences among methods involved the kinds of practice provided during the four review sessions. Participants who received cumulative practice answered 50 questions covering a mix of the rules learned prior to each review session. Participants who received a simple review answered 50 questions on one previously trained rule. Participants who received extra practice answered 50 extra questions on the rule they had just learned. Tests administered after each review included new questions for applying each rule (application items) and problems that required novel combinations of the rules (problem-solving items). On the final test, the cumulative group outscored the other groups on application and problem-solving items. In addition, the cumulative group solved the problem-solving items significantly faster than the other groups. These results suggest that cumulative practice of component skills is an effective method of training problem solving.
Burn, H. E.; Wenner, J. M.; Baer, E. M.
2011-12-01
The quantitative components of introductory geoscience courses can pose significant barriers to students. Many academic departments respond by stripping courses of their quantitative components or by attaching prerequisite mathematics courses [PMC]. PMCs cause students to incur additional costs and credits and may deter enrollment in introductory courses; yet, stripping quantitative content from geoscience courses masks the data-rich, quantitative nature of geoscience. Furthermore, the diversity of math skills required in geoscience and students' difficulty with transferring mathematical knowledge across domains suggest that PMCs may be ineffective. Instead, this study explores an alternative strategy -- to remediate students' mathematical skills using online modules that provide students with opportunities to build contextual quantitative reasoning skills. The Math You Need, When You Need It [TMYN] is a set of modular online student resources that address mathematical concepts in the context of the geosciences. TMYN modules are online resources that employ a "just-in-time" approach - giving students access to skills and then immediately providing opportunities to apply them. Each module places the mathematical concept in multiple geoscience contexts. Such an approach illustrates the immediate application of a principle and provides repeated exposure to a mathematical skill, enhancing long-term retention. At the same time, placing mathematics directly in several geoscience contexts better promotes transfer of learning by using similar discourse (words, tools, representations) and context that students will encounter when applying mathematics in the future. This study uses quantitative and qualitative data to explore the effectiveness of TMYN modules in remediating students' mathematical skills. Quantitative data derive from ten geoscience courses that used TMYN modules during the fall 2010 and spring 2011 semesters; none of the courses had a PMC. In all courses
Energy Technology Data Exchange (ETDEWEB)
Korsch, Hans Juergen
2013-07-01
This book mediates the fundamental terms and methods, which are necessary for an understanding of quantum mechanics. It shows, how mathematics can contribute to the understanding of quantum mechanics. The presented quantum-mechanical problems aim at the illustration and exercise of the most important mathematical methods. Because of the clear and understandable presentation and the numerous completely calculated examples and problems this book is suited for the self-study, for the accompanying of courses on quantum physics, for the accomplishment of exercise problems, and for the preparation on examinations.
DESIGN OF EDUCATIONAL PROBLEMS ON LINEAR PROGRAMMING USING SYSTEMS OF COMPUTER MATHEMATICS
Directory of Open Access Journals (Sweden)
Volodymyr M. Mykhalevych
2013-11-01
Full Text Available From a perspective of the theory of educational problems a problem of substitution in the conditions of ICT use of one discipline by an educational problem of another discipline is represented. Through the example of mathematical problems of linear programming it is showed that a student’s method of operation in the course of an educational problem solving is determinant in the identification of an educational problem in relation to a specific discipline: linear programming, informatics, mathematical modeling, methods of optimization, automatic control theory, calculus etc. It is substantiated the necessity of linear programming educational problems renovation with the purpose of making students free of bulky similar arithmetic calculations and notes which often becomes a barrier to a deeper understanding of key ideas taken as a basis of algorithms used by them.
Lee, Young-Jin
2017-01-01
Purpose: The purpose of this paper is to develop a quantitative model of problem solving performance of students in the computer-based mathematics learning environment. Design/methodology/approach: Regularized logistic regression was used to create a quantitative model of problem solving performance of students that predicts whether students can…
Enhancing Learners' Problem Solving Performance in Mathematics: A Cognitive Load Perspective
Dhlamini, Joseph J.
2016-01-01
This paper reports on a pilot study that investigated the effect of implementing a context-based problem solving instruction (CBPSI) to enhance the problem solving performance of high school mathematics learners. Primarily, the pilot study aimed: (1) to evaluate the efficiency of data collection instruments; and, (2) to test the efficacy of CBPSI…
Swanson, H. Lee
2011-01-01
The role of working memory (WM) in children's growth in mathematical problem solving was examined in a longitudinal study of children (N = 127). A battery of tests was administered that assessed problem solving, achievement, WM, and cognitive processing (inhibition, speed, phonological coding) in Grade 1 children, with follow-up testing in Grades…
Numerical methods for solution of some nonlinear problems of mathematical physics
International Nuclear Information System (INIS)
Zhidkov, E.P.
1981-01-01
The continuous analog of the Newton method and its application to some nonlinear problems of mathematical physics using a computer is considered. It is shown that the application of this method in JINR to the wide range of nonlinear problems has shown its universality and high efficiency [ru
An Examination of High School Students' Online Engagement in Mathematics Problems
Lim, Woong; Son, Ji-Won; Gregson, Susan; Kim, Jihye
2018-01-01
This article examines high school students' engagement in a set of trigonometry problems. Students completed this task independently in an online environment with access to Internet search engines, online textbooks, and YouTube videos. The findings imply that students have the resourcefulness to solve procedure-based mathematics problems in an…
The Effects of Problem Posing on Student Mathematical Learning: A Meta-Analysis
Rosli, Roslinda; Capraro, Mary Margaret; Capraro, Robert M.
2014-01-01
The purpose of the study was to meta-synthesize research findings on the effectiveness of problem posing and to investigate the factors that might affect the incorporation of problem posing in the teaching and learning of mathematics. The eligibility criteria for inclusion of literature in the meta-analysis was: published between 1989 and 2011,…
The Transitory Phase to the Attainment of Self-Regulatory Skill in Mathematical Problem Solving
Lazakidou, G.; Paraskeva, F.; Retalis, S.
2007-01-01
Three phases of development of self-regulatory skill in the domain of mathematical problem solving were designed to examine students' behaviour and the effects on their problem solving ability. Forty-eight Grade 4 students (10 year olds) participated in this pilot study. The students were randomly assigned to one of three groups, each representing…
Thai, Khanh-Phuong; Son, Ji Y.; Hoffman, Jessica; Devers, Christopher; Kellman, Philip J.
2014-01-01
Mathematics is the study of structure but students think of math as solving problems according to rules. Students can learn procedures, but they often have trouble knowing when to apply learned procedures, especially to problems unlike those they trained with. In this study, the authors rely on the psychological mechanism of perceptual learning…
Creativity of Field-dependent and Field-independent Students in Posing Mathematical Problems
Azlina, N.; Amin, S. M.; Lukito, A.
2018-01-01
This study aims at describing the creativity of elementary school students with different cognitive styles in mathematical problem-posing. The posed problems were assessed based on three components of creativity, namely fluency, flexibility, and novelty. The free-type problem posing was used in this study. This study is a descriptive research with qualitative approach. Data collections were conducted through written task and task-based interviews. The subjects were two elementary students. One of them is Field Dependent (FD) and the other is Field Independent (FI) which were measured by GEFT (Group Embedded Figures Test). Further, the data were analyzed based on creativity components. The results show thatFD student’s posed problems have fulfilled the two components of creativity namely fluency, in which the subject posed at least 3 mathematical problems, and flexibility, in whichthe subject posed problems with at least 3 different categories/ideas. Meanwhile,FI student’s posed problems have fulfilled all three components of creativity, namely fluency, in which thesubject posed at least 3 mathematical problems, flexibility, in which thesubject posed problems with at least 3 different categories/ideas, and novelty, in which the subject posed problems that are purely the result of her own ideas and different from problems they have known.
Intuitive physics knowledge, physics problem solving and the role of mathematical equations
Directory of Open Access Journals (Sweden)
Laura Buteler
2012-09-01
Full Text Available The present work explores the role that mathematical equations play in modifying students’ physical intuition (diSessa, 1993. The work is carried out assuming that students achieve a great deal of the refinement in their physical intuitions during problem solving (Sherin, 2006. The study is guided by the question of how the use of mathematical equations contributes to this refinement. The authors aim at expanding on Sherin´s (2006 hypothesis, suggesting a more bounding relation between physical intuitions and mathematics. In this scenario, intuitions play a more compelling role in “deciding” which equations are acceptable and which are not. Our hypothesis is constructed on the basis of three cases: the first published by Sherin (2006 and two more from registries of our own. The three cases are compared and analyzed in relation to the role of mathematical equations in refining – or not – the intuitive knowledge students bring to play during problem solving.
Mathematical thinking of maintenance. Problem setting and solving bases
International Nuclear Information System (INIS)
2007-01-01
Plant or mechanical facility for maintenance became more complicated than before and consisted of many subsystems made of various equipments or facilities with parts, which were a system having complicated and hierarchical structure. Maintenance was required to be properly implemented to assure reliability of a system for a long period so as for each equipment to play a specified role for a stable operation of plant. Mathematical thinking using probability theory was rational to optimize maintenance action with failure rate function of system or part of equipment. Reliability function, maintainability function and availability of plant and equipment were defined. Unreliability function was called failure time distribution function (F(t)) and failure rate function (λ(t)) was defined as the ratio of failure time density distribution function (dF(t)/dt) to reliability function (1-F(t)). λ(t) could be expressed as a simple equation with Weibull parameter. Availability at steady state was attributed to ratio of average operating time to sum of operating time and maintenance time, i.e. MTBF/(MTBF+MTTR) where MTBF was mean time between failures and MTTR was mean time to repair. Optimization of system risk and maintenance action was encouraged using computational science simulating material degradation. (T. Tanaka)
Solving cross-disciplinary problems by mathematical modelling
Panfilov, D. A.; Romanchikov, V. V.; Krupin, K. N.
2018-03-01
The article deals with the creation of a human tibia 3D model by means of “Autodesk Revit-2016” PC based on tomogram data. The model was imported into “Lira- SAPR2013 R4” software system. To assess the possibility of education and the nature of bone fracture (and their visualization), the Finite Element Analysis (FEA) method was used. The geometric parameters of the BBK model corresponded to the physical parameters of the individual. The compact plate different thickness is modeled by rigidity properties of the finite elements in accordance with the parameters on the roentgenogram. The BBK model included parameters of the outer compact plate and the spongy substance having a more developed structure of the epiphysic region. In the “Lira-SAPR2013 R4” software system, mathematical modeling of the traumatic effect was carried out and the analysis of the stress-strain state of the finite element model of the tibia was made to assess fracture conditions.
Integrating Study Skills and Problem Solving into Remedial Mathematics
Cornick, Jonathan; Guy, G. Michael; Beckford, Ian
2015-01-01
Students at a large urban community college enrolled in seven classes of an experimental remedial algebra programme, which integrated study skills instruction and collaborative problem solving. A control group of seven classes was taught in a traditional lecture format without study skills instruction. Student performance in the course was…
Elementary Teachers' Perspectives of Mathematics Problem Solving Strategies
Bruun, Faye
2013-01-01
Participants in this study were asked to report what strategies were most often used in their attempts to foster their students' problem solving abilities. Participants included 70 second through fifth-grade elementary teachers from 42 schools in a large state of the south central region in the U.S. Data analyses of the interviews revealed that…
A mathematical framework for inverse wave problems in heterogeneous media
Blazek, K.D.; Stolk, C.; Symes, W.W.
2013-01-01
This paper provides a theoretical foundation for some common formulations of inverse problems in wave propagation, based on hyperbolic systems of linear integro-differential equations with bounded and measurable coefficients. The coefficients of these time-dependent partial differential equations
Wine and Maths: Mathematical Solutions to Wine-Inspired Problems
Cadeddu, L.; Cauli, A.
2018-01-01
We deal with an application of partial differential equations to the correct definition of a wine cellar. We present some historical details about this problem. We also discuss how to build or renew a wine cellar, creating ideal conditions for the ageing process and improving the quality of wines. Our goal is to calculate the optimal depth…
Fung, Wenson; Swanson, H Lee
2017-07-01
The purpose of this study was to assess whether the differential effects of working memory (WM) components (the central executive, phonological loop, and visual-spatial sketchpad) on math word problem-solving accuracy in children (N = 413, ages 6-10) are completely mediated by reading, calculation, and fluid intelligence. The results indicated that all three WM components predicted word problem solving in the nonmediated model, but only the storage component of WM yielded a significant direct path to word problem-solving accuracy in the fully mediated model. Fluid intelligence was found to moderate the relationship between WM and word problem solving, whereas reading, calculation, and related skills (naming speed, domain-specific knowledge) completely mediated the influence of the executive system on problem-solving accuracy. Our results are consistent with findings suggesting that storage eliminates the predictive contribution of executive WM to various measures Colom, Rebollo, Abad, & Shih (Memory & Cognition, 34: 158-171, 2006). The findings suggest that the storage component of WM, rather than the executive component, has a direct path to higher-order processing in children.
Sweller, John; Clark, Richard; Kirschner, Paul A.
2010-01-01
Sweller, J., Clark, R., & Kirschner, P. A. (2010). Teaching general problem-solving skills is not a substitute for, or a viable addition to, teaching mathematics. Notices of the American Mathematical Society, 57, 1303-1304.
Mathematical conversations multicolor problems, problems in the theory of numbers, and random walks
Dynkin, E B
2006-01-01
Comprises Multicolor Problems, dealing with map-coloring problems; Problems in the Theory of Numbers, an elementary introduction to algebraic number theory; Random Walks, addressing basic problems in probability theory. 1963 edition.
Vision in elementary mathematics
Sawyer, W W
2003-01-01
Sure-fire techniques of visualizing, dramatizing, and analyzing numbers promise to attract and retain students' attention and understanding. Topics include basic multiplication and division, algebra, word problems, graphs, negative numbers, fractions, many other practical applications of elementary mathematics. 1964 ed. Answers to Problems.
Error Analysis Of Students Working About Word Problem Of Linear Program With NEA Procedure
Santoso, D. A.; Farid, A.; Ulum, B.
2017-06-01
Evaluation and assessment is an important part of learning. In evaluation process of learning, written test is still commonly used. However, the tests usually do not following-up by further evaluation. The process only up to grading stage not to evaluate the process and errors which done by students. Whereas if the student has a pattern error and process error, actions taken can be more focused on the fault and why is that happen. NEA procedure provides a way for educators to evaluate student progress more comprehensively. In this study, students’ mistakes in working on some word problem about linear programming have been analyzed. As a result, mistakes are often made students exist in the modeling phase (transformation) and process skills (process skill) with the overall percentage distribution respectively 20% and 15%. According to the observations, these errors occur most commonly due to lack of precision of students in modeling and in hastiness calculation. Error analysis with students on this matter, it is expected educators can determine or use the right way to solve it in the next lesson.
Swanson, H Lee; Lussier, Catherine M; Orosco, Michael J
2015-01-01
This study investigated the role of strategy instruction and working memory capacity (WMC) on word problem solving accuracy in children with (n = 100) and without (n = 92) math difficulties (MD). Within classrooms, children in Grades 2 and 3 were randomly assigned to one of four treatment conditions: verbal-only strategies (e.g., underlining question sentence), verbal + visual strategies, visual-only strategies (e.g., correctly placing numbers in diagrams), or untreated control. Strategy interventions included 20 sessions in both Year 1 and Year 2. The intent-to-treat as well as the "as-treated" analyses showed that treatment effects were significantly moderated by WMC. In general, treatment outcomes were higher when WMC was set to a high rather than low level. When set to a relatively high WMC level, children with MD performed significantly better under visual-only strategy conditions and children without MD performed better under verbal + visual conditions when compared to control conditions. © Hammill Institute on Disabilities 2013.
Investigating middle school students’ difficulties in mathematical literacy problems level 1 and 2
Setiawati, S.; Herman, T.; Jupri, A.
2017-11-01
The background of this study is the lack of mathematical literacy skills of students. The proficiency of students’ mathematical literacy skills based on the results of the PISA 2015 study shows that Indonesian students at the proficiency level 1. This fact gave rise to this study which aims to investigate middle school students’ difficulties in mathematical literacy problems level 1 and 2. Qualitative research was used in this study. An individual written test on mathematical literacy problems was administered, followed by interviews. The subjects of the study were 61 students grade VII in Bandung and 26 of them were interviewed afterward. Data analysis revealed that students’ error in performing arithmetic most frequently observed. Other observed difficulties concerned understanding about algebra concept, applying arithmetic operation in algebraic expressions, and interpreting symbols to represent the unknown. In solving mathematical literacy problems, students use their prior knowledge, although sometimes not relevant to the questions. Based on the results, we suggest that mathematics learning in contextual learning and which invites students to participate in the processes of understanding the concepts.
Puzzles, paradoxes, and problem solving an introduction to mathematical thinking
Reba, Marilyn A
2014-01-01
Graphs: Puzzles and Optimization Graphical Representation and Search Greedy Algorithms and Dynamic Programming Shortest Paths, DNA Sequences, and GPS Systems Routing Problems and Optimal Circuits Traveling Salesmen and Optimal Orderings Vertex Colorings and Edge Matchings Logic: Rational Inference and Computer Circuits Inductive and Deductive Arguments Deductive Arguments and Truth-Tables Deductive Arguments and Derivations Deductive Logic and Equivalence Modeling Using Deductive Logic Probability: Predictions and Expectations Probability and Counting Counting and Unordered Outcomes Independen
Dewi, N. R.; Arini, F. Y.
2018-03-01
The main purpose of this research is developing and produces a Calculus textbook model that supported with GeoGebra. This book was designed to enhancing students’ mathematical problem solving and mathematical representation. There were three stages in this research i.e. define, design, and develop. The textbooks consisted of 6 chapters which each chapter contains introduction, core materials and include examples and exercises. The textbook developed phase begins with the early stages of designed the book (draft 1) which then validated by experts. Revision of draft 1 produced draft 2. The data were analyzed with descriptive statistics. The analysis showed that the Calculus textbook model that supported with GeoGebra, valid and fill up the criteria of practicality.
One Language, Two Number-Word Systems and Many Problems: Numerical Cognition in the Czech Language
Pixner, S.; Zuber, J.; Hermanova, V.; Kaufmann, L.; Nuerk, H.-C.; Moeller, K.
2011-01-01
Comparing numerical performance between different languages does not only mean comparing different number-word systems, but also implies a comparison of differences regarding culture or educational systems. The Czech language provides the remarkable opportunity to disentangle this confound as there exist two different number-word systems within…
One language, two number-word systems and many problems: numerical cognition in the Czech language.
Pixner, S; Zuber, J; Heřmanová, V; Kaufmann, L; Nuerk, H-C; Moeller, K
2011-01-01
Comparing numerical performance between different languages does not only mean comparing different number-word systems, but also implies a comparison of differences regarding culture or educational systems. The Czech language provides the remarkable opportunity to disentangle this confound as there exist two different number-word systems within the same language: for instance, "25" can be either coded in non-inverted order "dvadsetpät" [twenty-five] or in inverted order "pätadvadset" [five-and-twenty]. To investigate the influence of the number-word system on basic numerical processing within one culture, 7-year-old Czech-speaking children had to perform a transcoding task (i.e., writing Arabic numbers to dictation) in both number-word systems. The observed error pattern clearly indicated that the structure of the number-word system determined transcoding performance reliably: In the inverted number-word system about half of all errors were inversion-related. In contrast, hardly any inversion-related errors occurred in the non-inverted number-word system. We conclude that the development of numerical cognition does not only depend on cultural or educational differences, but is indeed related to the structure and transparency of a given number-word system. Copyright © 2011 Elsevier Ltd. All rights reserved.
Fuchs, Lynn S.; Schumacher, Robin F.; Long, Jessica; Namkung, Jessica; Malone, Amelia S.; Wang, Amber; Hamlett, Carol L.; Jordan, Nancy C.; Siegler, Robert S.; Changas, Paul
2016-01-01
The purposes of this study were to (a) investigate the efficacy of a core fraction intervention program on understanding and calculation skill and (b) isolate the effects of different forms of fraction word-problem (WP) intervention. At-risk fourth graders (n = 213) were randomly assigned to the school's business-as-usual program, or one of two…
Fuchs, Lynn S.; Schumacher, Robin F.; Long, Jessica; Namkung, Jessica; Malone, Amelia S.; Wang, Amber; Hamlett, Carol L.; Jordan, Nancy C.; Siegler, Robert S.; Changas, Paul
2016-01-01
The purposes of this study were to (a) investigate the efficacy of a core fraction intervention program on understanding and calculation skill and (b) isolate the effects of different forms of fraction word-problem (WP) intervention delivered as part of the larger program. At-risk 4th graders (n = 213) were randomly assigned at the individual…
Swanson, H. Lee
2014-01-01
Cognitive strategies are important tools for children with math difficulties (MD) in learning to solve word problems. The effectiveness of strategy training, however, depends on working memory capacity (WMC). Thus, children with MD but with relatively higher WMC are more likely to benefit from strategy training, whereas children with lower WMC may…
"Seeing It on the Screen Isn't Really Seeing It": Reading Problems of Writers Using Word Processing.
Haas, Christina
An observational study examined computer writers' use of hard copy for reading. The study begins with a description, based on interviews, of four kinds of reading problems encountered by writers using word processing; formatting, proofreading, reorganizing, and critical reading ("getting a sense of the text"). Subjects, six freshmen…
On two mathematical problems of canonical quantization. 1
International Nuclear Information System (INIS)
Kirillov, A.I.
1991-01-01
Problems of choice a representation of the canonical commutation relations (CCR) and determining of Hamiltonian are investigated. It is shown that the Hamiltonians studied by H. Araki are the Dirichlet operators. The almost inverse theorem is also proved. Dirichlet operators are completely determined by measures. The same measures specify also representations of CCR and ground states. A notion of generalized density of these measures is introduced. Calculation methods of the densities and its corresponding measures, i.e. in the end, of representations of CCR and Hamiltonians interrelated in the meaning of L.Van Hove, are suggested
Mathematical models and heuristic solutions for container positioning problems in port terminals
DEFF Research Database (Denmark)
Kallehauge, Louise Sibbesen
2008-01-01
presents an efficient solution algorithm for the CPP. Based on a number of new concepts, an event-based construction heuristic is developed and its ability to solve real-life problem instances is established. The backbone of the algorithm is a list of events, corresponding to a sequence of operations...... by constructing mathematical programming formulations of the problem and developing an efficient heuristic algorithm for its solution. The thesis consists of an introduction, two main chapters concerning new mathematical formulations and a new heuristic for the CPP, technical issues, computational results...... concerning the subject is reviewed. The research presented in this thesis is divided into two main parts: Construction and investigation of new mathematical programming formulations of the CPP and development and implementation of a new event-based heuristic for the problem. The first part presents three...
A new mathematical modeling for pure parsimony haplotyping problem.
Feizabadi, R; Bagherian, M; Vaziri, H R; Salahi, M
2016-11-01
Pure parsimony haplotyping (PPH) problem is important in bioinformatics because rational haplotyping inference plays important roles in analysis of genetic data, mapping complex genetic diseases such as Alzheimer's disease, heart disorders and etc. Haplotypes and genotypes are m-length sequences. Although several integer programing models have already been presented for PPH problem, its NP-hardness characteristic resulted in ineffectiveness of those models facing the real instances especially instances with many heterozygous sites. In this paper, we assign a corresponding number to each haplotype and genotype and based on those numbers, we set a mixed integer programing model. Using numbers, instead of sequences, would lead to less complexity of the new model in comparison with previous models in a way that there are neither constraints nor variables corresponding to heterozygous nucleotide sites in it. Experimental results approve the efficiency of the new model in producing better solution in comparison to two state-of-the art haplotyping approaches. Copyright © 2016 Elsevier Inc. All rights reserved.
Hull, Michael M.; Kuo, Eric; Gupta, Ayush; Elby, Andrew
2013-06-01
Much research in engineering and physics education has focused on improving students’ problem-solving skills. This research has led to the development of step-by-step problem-solving strategies and grading rubrics to assess a student’s expertise in solving problems using these strategies. These rubrics value “communication” between the student’s qualitative description of the physical situation and the student’s formal mathematical descriptions (usually equations) at two points: when initially setting up the equations, and when evaluating the final mathematical answer for meaning and plausibility. We argue that (i) neither the rubrics nor the associated problem-solving strategies explicitly value this kind of communication during mathematical manipulations of the chosen equations, and (ii) such communication is an aspect of problem-solving expertise. To make this argument, we present a case study of two students, Alex and Pat, solving the same kinematics problem in clinical interviews. We argue that Pat’s solution, which connects manipulation of equations to their physical interpretation, is more expertlike than Alex’s solution, which uses equations more algorithmically. We then show that the types of problem-solving rubrics currently available do not discriminate between these two types of solutions. We conclude that problem-solving rubrics should be revised or repurposed to more accurately assess problem-solving expertise.
Enhancing students’ mathematical problem posing skill through writing in performance tasks strategy
Kadir; Adelina, R.; Fatma, M.
2018-01-01
Many researchers have studied the Writing in Performance Task (WiPT) strategy in learning, but only a few paid attention on its relation to the problem-posing skill in mathematics. The problem-posing skill in mathematics covers problem reformulation, reconstruction, and imitation. The purpose of the present study was to examine the effect of WiPT strategy on students’ mathematical problem-posing skill. The research was conducted at a Public Junior Secondary School in Tangerang Selatan. It used a quasi-experimental method with randomized control group post-test. The samples were 64 students consists of 32 students of the experiment group and 32 students of the control. A cluster random sampling technique was used for sampling. The research data were obtained by testing. The research shows that the problem-posing skill of students taught by WiPT strategy is higher than students taught by a conventional strategy. The research concludes that the WiPT strategy is more effective in enhancing the students’ mathematical problem-posing skill compared to the conventional strategy.
Directory of Open Access Journals (Sweden)
Antonín Hájek
2007-01-01
Full Text Available The paper is devoted to the use of mathematical modelling for analysis of the thermo-mechanical (T-M processes, which are relevant for the assessment of underground repositories of the spent nuclear fuel. Wes shall discuss mathematical formulation, numerical methods and parallel alghorithms, which are capable to solve large-scale complicated and coupled 3D problems. Particularly, we show an application of the described methods and parallel computer simulations for analysis of model problems concerning the Swedish KBS3 concept of underground repository.
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Ana Kuzle
2012-04-01
Full Text Available In this paper, I report on preservice teachers’ reflections and perceptions on theirproblem-solving process in a technological context. The purpose of the study was to to investigatehow preservice teachers experience working individually in a dynamic geometry environment andhow these experiences affect their own mathematical activity when integrating content (nonroutineproblems and context (technology environment. Careful analysis of participants’ perceptionsregarding their thinking while engaged in problem solving, provided an opportunity to explorehow they explain the emergence of problem solving when working in a dynamic geometryenvironment. The two participants communicated their experience both through the lenses ofthemselves as problem solvers and as future mathematics educators. Moreover, the results of thestudy indicated that problem solving in a technology environment does not necessarily allow focuson decision-making, reflection, and problem solving processes as reported by previous research.
Flores, Margaret M.; Hinton, Vanessa M.; Burton, Megan E.
2016-01-01
Mathematical word problems are the most common form of mathematics problem solving implemented in K-12 schools. Identifying key words is a frequent strategy taught in classrooms in which students struggle with problem solving and show low success rates in mathematics. Researchers show that using the concrete-representational-abstract (CRA)…
Development of syntax of intuition-based learning model in solving mathematics problems
Yeni Heryaningsih, Nok; Khusna, Hikmatul
2018-01-01
The aim of the research was to produce syntax of Intuition Based Learning (IBL) model in solving mathematics problem for improving mathematics students’ achievement that valid, practical and effective. The subject of the research were 2 classes in grade XI students of SMAN 2 Sragen, Central Java. The type of the research was a Research and Development (R&D). Development process adopted Plomp and Borg & Gall development model, they were preliminary investigation step, design step, realization step, evaluation and revision step. Development steps were as follow: (1) Collected the information and studied of theories in Preliminary Investigation step, studied about intuition, learning model development, students condition, and topic analysis, (2) Designed syntax that could bring up intuition in solving mathematics problem and then designed research instruments. They were several phases that could bring up intuition, Preparation phase, Incubation phase, Illumination phase and Verification phase, (3) Realized syntax of Intuition Based Learning model that has been designed to be the first draft, (4) Did validation of the first draft to the validator, (5) Tested the syntax of Intuition Based Learning model in the classrooms to know the effectiveness of the syntax, (6) Conducted Focus Group Discussion (FGD) to evaluate the result of syntax model testing in the classrooms, and then did the revision on syntax IBL model. The results of the research were produced syntax of IBL model in solving mathematics problems that valid, practical and effective. The syntax of IBL model in the classroom were, (1) Opening with apperception, motivations and build students’ positive perceptions, (2) Teacher explains the material generally, (3) Group discussion about the material, (4) Teacher gives students mathematics problems, (5) Doing exercises individually to solve mathematics problems with steps that could bring up students’ intuition: Preparations, Incubation, Illumination, and
Visual Representations in Mathematics Teaching: An Experiment with Students
Debrenti, Edith
2015-01-01
General problem-solving skills are of central importance in school mathematics achievement. Word problems play an important role not just in mathematical education, but in general education as well. Meaningful learning and understanding are basic aspects of all kinds of learning and it is even more important in the case of learning mathematics. In…
Directory of Open Access Journals (Sweden)
Kim-Leong Lai
2009-07-01
Full Text Available This study assessed the effectiveness of an online mathematical problem solving course designed using a social constructivist approach for pre-service teachers. Thirty-seven pre-service teachers at the Batu Lintang Teacher Institute, Sarawak, Malaysia were randomly selected to participate in the study. The participants were required to complete the course online without the typical face-to-face classes and they were also required to solve authentic mathematical problems in small groups of 4-5 participants based on the Polya’s Problem Solving Model via asynchronous online discussions. Quantitative and qualitative methods such as questionnaires and interviews were used to evaluate the effects of the online learning course. Findings showed that a majority of the participants were satisfied with their learning experiences in the course. There were no significant changes in the participants’ attitudes toward mathematics, while the participants’ skills in problem solving for “understand the problem” and “devise a plan” steps based on the Polya Model were significantly enhanced, though no improvement was apparent for “carry out the plan” and “review”. The results also showed that there were significant improvements in the participants’ critical thinking skills. Furthermore, participants with higher initial computer skills were also found to show higher performance in mathematical problem solving as compared to those with lower computer skills. However, there were no significant differences in the participants’ achievements in the course based on gender. Generally, the online social constructivist mathematical problem solving course is beneficial to the participants and ought to be given the attention it deserves as an alternative to traditional classes. Nonetheless, careful considerations need to be made in the designing and implementing of online courses to minimize problems that participants might encounter while
Saleh, H.; Suryadi, D.; Dahlan, J. A.
2018-01-01
The aim of this research was to find out whether 7E learning cycle under hypnoteaching model can enhance students’ mathematical problem-solving skill. This research was quasi-experimental study. The design of this study was pretest-posttest control group design. There were two groups of sample used in the study. The experimental group was given 7E learning cycle under hypnoteaching model, while the control group was given conventional model. The population of this study was the student of mathematics education program at one university in Tangerang. The statistical analysis used to test the hypothesis of this study were t-test and Mann-Whitney U. The result of this study show that: (1) The students’ achievement of mathematical problem solving skill who obtained 7E learning cycle under hypnoteaching model are higher than the students who obtained conventional model; (2) There are differences in the students’ enhancement of mathematical problem-solving skill based on students’ prior mathematical knowledge (PMK) category (high, middle, and low).
Powell, Sarah R.; Fuchs, Lynn S.
2014-01-01
According to national mathematics standards, algebra instruction should begin at kindergarten and continue through elementary school. Most often, teachers address algebra in the elementary grades with problems related to solving equations or understanding functions. With 789 second-grade students, we administered: (1) measures of calculations and…
Students’ Self-Monitoring on Mathematics Ability: Cube and Cuboid Problem Solving
Lusiana, N. T.; Lukito, A.; Khabibah, S.
2018-01-01
This study aims at describing students’ activity to understand the behaviors processes called self-monitoring in a cube and cuboid problem solving viewed from mathematics ability. The subjects were eight graders of junior high school who studied surface area and volume of cube and cuboid clussified into high, average and low mathematics abilities. Mathematics ability test to select the subjects the study. Data were collected through self-monitoring task and interviews. Data triangulation was used to verify the credibillity findings. Data analysis was done by data condensation, data display and conclusion drawing and verification. Results showed that students’ self-monitoring with high math ability is more fullfilled self-monitoring components. Students with average and low math abilities not fullfilled the component that covers verifying the results during solving the problem. It is expected that teachers must provide different learning treatments to improve students’ self-monitoring for better learning outcomes.
Whitney, Todd; Hirn, Regina G.; Lingo, Amy S.
2016-01-01
In the present study, we examined the effects of a fluency-building mathematics program called Great Leaps Math on fluency of basic addition mathematics facts zero to nine and word problem solving using a multiple probe design across participants. Three elementary students with challenging behaviors and mathematics difficulty participated in the…
Students’ Mathematical Literacy in Solving PISA Problems Based on Keirsey Personality Theory
Masriyah; Firmansyah, M. H.
2018-01-01
This research is descriptive-qualitative research. The purpose is to describe students’ mathematical literacy in solving PISA on space and shape content based on Keirsey personality theory. The subjects are four junior high school students grade eight with guardian, artisan, rational or idealist personality. Data collecting methods used test and interview. Data of Keirsey Personality test, PISA test, and interview were analysed. Profile of mathematical literacy of each subject are described as follows. In formulating, guardian subject identified mathematical aspects are formula of rectangle area and sides length; significant variables are terms/conditions in problem and formula of ever encountered question; translated into mathematical language those are measurement and arithmetic operations. In employing, he devised and implemented strategies using ease of calculation on area-subtraction principle; declared truth of result but the reason was less correct; didn’t use and switch between different representations. In interpreting, he declared result as area of house floor; declared reasonableness according measurement estimation. In formulating, artisan subject identified mathematical aspects are plane and sides length; significant variables are solution procedure on both of daily problem and ever encountered question; translated into mathematical language those are measurement, variables, and arithmetic operations as well as symbol representation. In employing, he devised and implemented strategies using two design comparison; declared truth of result without reason; used symbol representation only. In interpreting, he expressed result as floor area of house; declared reasonableness according measurement estimation. In formulating, rational subject identified mathematical aspects are scale and sides length; significant variables are solution strategy on ever encountered question; translated into mathematical language those are measurement, variable, arithmetic
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Deniz Özen
2013-03-01
Full Text Available The aim of this study is to investigate pre-service elementary mathematics teachers’ open geometric problem solving process in a Dynamic Geometry Environment. With its qualitative inquiry based research design employed, the participants of the study are three pre-service teachers from 4th graders of the Department of Elementary Mathematics Teaching. In this study, clinical interviews, screencaptures of the problem solving process in the Cabri Geomery Environment, and worksheets included 2 open geometry problems have been used to collect the data. It has been investigated that all the participants passed through similar recursive phases as construction, exploration, conjecture, validate, and justification in the problem solving process. It has been thought that this study provide a new point of view to curriculum developers, teachers and researchers
Erdogan, Ahmet
2017-01-01
The purpose of this research is to determine mathematics teacher candidates' conceptual structures about the concept of "measurement" that is the one of the important learning fields of mathematics. Qualitative research method was used in this study. Participants of this study were 58 mathematics teacher candidates studying in one of the…
Chen, Chiu-Jung; Liu, Pei-Lin
2007-01-01
This study evaluated the effects of a personalized computer-assisted mathematics problem-solving program on the performance and attitude of Taiwanese fourth grade students. The purpose of this study was to determine whether the personalized computer-assisted program improved student performance and attitude over the nonpersonalized program.…
Baltaci, Serdal
2016-01-01
It is a widely known fact that gifted students have different skills compared to their peers. However, to what extent gifted students use mathematical thinking skills during probability problem solving process emerges as a significant question. Thence, the main aim of the present study is to examine 8th grade gifted students' probability…
Root, Jenny; Saunders, Alicia; Spooner, Fred; Brosh, Chelsi
2017-01-01
The ability to solve mathematical problems related to purchasing and personal finance is important in promoting skill generalization and increasing independence for individuals with moderate intellectual disabilities (IDs). Using a multiple probe across participant design, this study investigated the effects of modified schema-based instruction…
FORMULATION OF MATHEMATICAL PROBLEM DESCRIBING PHYSICAL AND CHEMICAL PROCESSES AT CONCRETE CORROSION
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Sergey V. Fedosov
2017-06-01
Full Text Available The article deals with the relevance of new scientific research focused on modeling of physical and chemical processes occurring in the cement concrete at their exploitation. The basic types of concrete corrosion are described. The problem of mass transfer processes in a flat reinforced concrete wall at concrete corrosion of the first and the second types has been mathematically formulated.
Sari, Delsika Pramata; Darhim; Rosjanuardi, Rizky
2018-01-01
The purpose of this study was to investigate the errors experienced by students learning with REACT strategy and traditional learning in solving problems of mathematical representation ability. This study used quasi experimental pattern with static-group comparison design. The subjects of this study were 47 eighth grade students of junior high…
Some applications of fractal mathematics in the evaluation of environmental problems
Energy Technology Data Exchange (ETDEWEB)
Thimm, H. F.; Poon, D. C.; McCormack, M.
1997-11-01
Application of fractal mathematics to commonly occurring environmental problems in the petroleum industry is discussed. Examples are provided to illustrate application of the technique. The specific examples cited involve the interpretation of mercury contamination data at a gas plant and the determination of the optimal volume of soil excavation at a contaminated site. 10 refs., 4 figs.
Putra, Mulia; Novita, Rita
2015-01-01
This study aimed to describe the profile of secondary school students with high mathematics ability in solving shape and space problem in PISA (Program for International Student Assessment). It is a descriptive research with a qualitative approach, in which the subjects in this study were students of class VIII SMP N 1 Banda Aceh. The results show…
Energy Technology Data Exchange (ETDEWEB)
1979-01-01
The booklet presents the full text of 13 contributions to a Colloquium held at Karlsruhe in Sept. 1979. The main topics of the papers are the evaluation of mathematical models to solve flow problems in tide water, seas, rivers, groundwater and in the earth atmosphere. See further hints under relevant topics.
Petersen, Richard H.
1997-01-01
The objectives of the Institute were: (a) increase participants' content knowledge about aeronautics, science, mathematics, and technology, (b) model and promote the use of scientific inquiry through problem-based learning, (c) investigate the use of instructional technologies and their applications to curricula, and (d) encourage the dissemination of TEI experiences to colleagues, students, and parents.
The effect of shift-problem lessons in the mathematics classsroom
Palha, S.; Dekker, R.; Gravemeijer, K.
2015-01-01
It remains difficult to foster problem-solving and mathematical-reasoning capabilities in classrooms where students and teachers are accustomed to the more traditional forms of education. Several studies suggest that this difficulty might be related to the kind of knowledge students acquire in such
The effect of shift-problem lessons in the mathematics classroom
Palha, S.; Dekker, Rijkje; Gravemeijer, K.P.E.
2015-01-01
It remains difficult to foster problem-solving and mathematical-reasoning capabilities in classrooms where students and teachers are accustomed to the more traditional forms of education. Several studies suggest that this difficulty might be related to the kind of knowledge students acquire in such
Rutherford, Vanessa
2012-01-01
This study explores how a problem-solving based professional learning community (PLC) affects the beliefs, knowledge, and instructional practices of two sixth-grade mathematics teachers. An interview and two observations were conducted prior to beginning the year-long PLC in order to gather information about the participants' beliefs,…
Critical Thinking and Problem Solving Skills in Mathematics of Grade-7 Public Secondary Students
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Emil C. Alcantara
2017-11-01
Full Text Available The study aimed to assess the academic performance, critical thinking skills, and problem solving skills in mathematics of Grade-7 students in the five central public secondary schools of Area 2, Division of Batangas, Philippines. This study utilized descriptive method of research. Three hundred forty one (341 students of the public secondary schools out of the total of 2,324 Grade-7 students were selected through systematic random sampling as the subjects of the study. It was found out that the level of performance in Mathematics of the Grade-7 students is proficient. The level of critical thinking skills of students from the different schools is above average as well as their level of problem solving skills. The mathematics performance of the students is positively correlated to their level of critical thinking skills and problem solving skills. Students considered the following learning competencies in the different content areas of Grade-7 Mathematics as difficult to master: solving problems involving sets, describing the development of measurement from the primitive to the present international system of units, finding a solution of an equation or inequality involving one variable, using compass and straightedge to bisect line segments and angles, and analyzing, interpreting accurately and drawing conclusions from graphic and tabular presentations of statistical data.
Problem Solving Strategies of Selected Pre-Service Secondary School Mathematics Teachers in Malaysia
Yew, Wun Theam; Zamri, Sharifah Norul Akmar Syed
2016-01-01
Problem solving strategies of eight pre-service secondary school mathematics teachers (PSSMTs) were examined in this study. A case study research design was employed and clinical interview technique was used to collect the data. Materials collected for analysis consisted of audiotapes and videotapes of clinical interviews, subjects' notes and…
Kramarski, Bracha; Friedman, Sheli
2014-01-01
The study examined how student control over metacognitive prompts in a multimedia environment affects students' ability to solve mathematical problems in immediate comprehension tasks using a multimedia program and a delayed-transfer test. It also examined the effect on metacognitive discourse, mental effort, and engagement with multimedia-based…
The Effects of Group Monitoring on Fatigue-Related Einstellung during Mathematical Problem Solving
Frings, Daniel
2011-01-01
Fatigue resulting from sleep deficit can lead to decreased performance in a variety of cognitive domains and can result in potentially serious accidents. The present study aimed to test whether fatigue leads to increased Einstellung (low levels of cognitive flexibility) in a series of mathematical problem-solving tasks. Many situations involving…
Problem-Based Learning in K-8 Mathematics and Science Education: A Literature Review
Merritt, Joi; Lee, Mi Yeon; Rillero, Peter; Kinach, Barbara M.
2017-01-01
This systematic literature review was conducted to explore the effectiveness of problem-based and project-based learning (PBL) implemented with students in early elementary to grade 8 (ages 3-14) in mathematics and science classrooms. Nine studies met the following inclusion criteria: (a) focus on PBL, (b) experimental study, (c) kindergarten to…
Problem Solving Strategies of Girls and Boys in Single-Sex Mathematics Classrooms
Che, Megan; Wiegert, Elaine; Threlkeld, Karen
2012-01-01
This study examines patterns in middle-grade boys' and girls' written problem solving strategies for a mathematical task involving proportional reasoning. The students participating in this study attend a coeducational charter middle school with single-sex classrooms. One hundred nineteen sixth-grade students' responses are analyzed by gender…
Santos-Trigo, Manuel; Barrera-Mora, Fernando
2011-01-01
The study documents the extent to which high school teachers reflect on their need to revise and extend their mathematical and practicing knowledge. In this context, teachers worked on a set of tasks as a part of an inquiring community that promoted the use of different computational tools in problem solving approaches. Results indicated that the…
Bas, Fatih
2016-01-01
This study aims to observe the pre-service secondary mathematics teachers' metacognitive awareness in terms of the variables gender and class level and determine their metacognitive behaviours which showed in the non-routine problems. A partially mixed sequential dominant status design was carried out with a total of 287 participants. The data of…
Badru, Ademola K.
2016-01-01
The study investigated Problem-based Instructional Strategy and Numerical ability as determinants of Senior Secondary Achievement in Mathematics. This study used 4 x 2 x 2 non-randomised control group Pretest-Posttest Quasi-experimental Factorial design. It consisted of two independent variables (treatment and Numerical ability) and one moderating…
Yavuz, Ahmet
2015-01-01
This study aims to investigate (1) students' trust in mathematics calculation versus intuition in a physics problem solving and (2) whether this trust is related to achievement in physics in the context of epistemic game theoretical framework. To achieve this research objective, paper-pencil and interview sessions were conducted. A paper-pencil…
Evaluation of Students' Mathematical Problem Solving Skills in Relation to Their Reading Levels
Özsoy, Gökhan; Kuruyer, Hayriye Gül; Çakiroglu, Ahmet
2015-01-01
The purpose of the current study is to investigate the correlation between students' reading levels and mathematical problem solving skills. The present study was conducted in line with a qualitative research method, i.e., the phenomenological method. The study group of the current research is composed of six third grade students with different…
Parallelization of mathematical library for generalized eigenvalue problem for real band matrices
International Nuclear Information System (INIS)
Tanaka, Yasuhisa.
1997-05-01
This research has focused on a parallelization of the mathematical library for a generalized eigenvalue problem for real band matrices on IBM SP and Hitachi SR2201. The origin of the library is LASO (Lanczos Algorithm with Selective Orthogonalization), which was developed on the basis of Block Lanczos method for standard eigenvalue problem for real band matrices at Texas University. We adopted D.O.F. (Degree Of Freedom) decomposition method for a parallelization of this library, and evaluated its parallel performance. (author)
The Problem of the Object of Mathematics as Intelligible Substance in Aristotle's Metaphysics
Cattanei, Elisabetta
2013-01-01
The A. examines the problem of intermediat emathematical entities by analyzing Metaphysics l017a9-l4, since, according to Aristotle. this passage is both a source and a critique of Plato's theory. The goal is to identify four cardinal points that may ground a dialogue between two contesting positions regarding this problem. Through them, it becomes evident that Aristotle severs the question of the intelligible nature of mathematical entities by using the conceptual scalpel of his own ousiolog...
Rahmah Johar; Sri Yusniarti; Saminan Saminan
2017-01-01
The lack of Indonesian students achievement in the international assessment is due to several factors. Students are not familiar with the problems requiring reasoning, in particular the proportional reasoning. This research aims to identify the distribution and the Level of Cognitive Demands (LCD) of the proportional reasoning problems found in the Year 7 and Year 8 mathematics textbooks based on the 2013 curriculum (revised edition 2014). The data collection was conducted by identifying the ...
Anticipation Guides: Reading for Mathematics Understanding
Adams, Anne E.; Pegg, Jerine; Case, Melissa
2015-01-01
With the acceptance by many states of the Common Core State Standards for Mathematics, new emphasis is being placed on students' ability to engage in mathematical practices such as understanding problems (including word problems), reading and critiquing arguments, and making explicit use of definitions (CCSSI 2010). Engaging students in…
On the Formal-Logical Analysis of the Foundations of Mathematics Applied to Problems in Physics
Kalanov, Temur Z.
2016-03-01
Analysis of the foundations of mathematics applied to problems in physics was proposed. The unity of formal logic and of rational dialectics is methodological basis of the analysis. It is shown that critical analysis of the concept of mathematical quantity - central concept of mathematics - leads to the following conclusion: (1) The concept of ``mathematical quantity'' is the result of the following mental operations: (a) abstraction of the ``quantitative determinacy of physical quantity'' from the ``physical quantity'' at that the ``quantitative determinacy of physical quantity'' is an independent object of thought; (b) abstraction of the ``amount (i.e., abstract number)'' from the ``quantitative determinacy of physical quantity'' at that the ``amount (i.e., abstract number)'' is an independent object of thought. In this case, unnamed, abstract numbers are the only sign of the ``mathematical quantity''. This sign is not an essential sign of the material objects. (2) The concept of mathematical quantity is meaningless, erroneous, and inadmissible concept in science because it represents the following formal-logical and dialectical-materialistic error: negation of the existence of the essential sign of the concept (i.e., negation of the existence of the essence of the concept) and negation of the existence of measure of material object.
Factors involved in making post-performance judgments in mathematics problem-solving.
García Fernández, Trinidad; Kroesbergen, Evelyn; Rodríguez Pérez, Celestino; González-Castro, Paloma; González-Pienda, Julio A
2015-01-01
This study examines the impact of executive functions, affective-motivational variables related to mathematics, mathematics achievement and task characteristics on fifth and sixth graders’ calibration accuracy after completing two mathematical problems. A sample of 188 students took part in the study. They were divided into two groups as function of their judgment accuracy after completing the two tasks (accurate= 79, inaccurate= 109). Differences between these groups were examined. The discriminative value of these variables to predict group membership was analyzed, as well as the effect of age, gender, and grade level. The results indicated that accurate students showed better levels of executive functioning, and more positive feelings, beliefs, and motivation related to mathematics. They also spent more time on the tasks. Mathematics achievement, perceived usefulness of mathematics, and time spent on Task 1 significantly predicted group membership, classifying 71.3% of the sample correctly. These results support the relationship between academic achievement and calibration accuracy, suggesting the need to consider a wide range of factors when explaining performance judgments.
Lestari, N. D. S.; Juniati, D.; Suwarsono, St.
2018-04-01
The purpose of this paper is to describe to what extent the prospective teachers can be considered as mathematically literate and how they communicate their reasoning in solving the problem based on the sex differences. Data were collected through mathematics literacy test on occupational context by 157 of prospective teachers from three universities in East Java, Indonesia. Their written responses were collected, organized based on the sex differences, analyzed and categorized to one of three levels of mathematical literacy. The examples of interesting students’ response altogether with the scoring are discussed to describe their characteristic on mathematical literacy and their communication. The result showed that in general the mathematical literacy of female prospective teachers tend to be better than male prospective math teachers. Female prospective teachers are more capable of logical reasoning, using concepts, facts and procedures and algebraic operations to draw conclusions; make an interpretations and evaluations. This study has an implication that gender differences in mathematical literacy of prospective math teachers do exist, therefore this issue should be given a serious concern from the development programs of the faculty.
Umasenan a/l Thanikasalam
2017-05-01
Occupational safety health is a multidisciplinary discipline concentrating on the safety, health and welfare of workers in the working place. Healthcare Students undergoing Occupational Safety Health internships are required to apply mathematical in areas such as safety legislation, safety behavior, ergonomics, chemical safety, OSH practices, industrial hygiene, risk management and safety health practices as problem solving. The aim of this paper is to investigate the level of mathematics and logic utilization from these students during their internship looking at areas of Hazard identification, Determining the population exposed to the hazard, Assessing the risk of the exposure to the hazards and Taking preventive and control. A total of 142 returning healthcare students from their Occupational Safety Health, internship were given a questionnaire to measure their perceptions towards mathematical and logic utilization. The overall results indicated a strong positive skewed result towards the use of Mathematics during their internship. The findings showed that mathematics were well delivered by the students during their internship. Mathematics could not be separated from OSH practice as a needed precision in quantifying safety, health an d welfare of workers in addition to empiricism.
Rajotte, Thomas; Marcotte, Christine; Bureau-Levasseur, Lisa
2016-01-01
In recent decades, the dropout rate in Abitibi-Témiscamingue is a worrying phenomenon. An analysis of ministerial examination results identifies that students in Abitibi-Témiscamingue have specific difficulties with mathematical problem solving tasks. Among the activities that develop those skills, the daily routines in mathematics seem to be a…
Formal languages, automata and numeration systems introduction to combinatorics on words
Rigo, Michel
2014-01-01
Formal Languages, Automaton and Numeration Systems presents readers with a review of research related to formal language theory, combinatorics on words or numeration systems, such as Words, DLT (Developments in Language Theory), ICALP, MFCS (Mathematical Foundation of Computer Science), Mons Theoretical Computer Science Days, Numeration, CANT (Combinatorics, Automata and Number Theory). Combinatorics on words deals with problems that can be stated in a non-commutative monoid, such as subword complexity of finite or infinite words, construction and properties of infinite words, unavoidabl
Nortvedt, Guri A.
2011-01-01
This article discusses how 13-year-old students with above-average numeracy skills and below-average reading skills cope with comprehending word problems. Compared to other students who are proficient in numeracy and are skilled readers, these students are more disadvantaged when solving single-step and multistep arithmetic word problems. The…
New concepts and new words--how do languages cope with the problem of neology?
Muhvić-Dimanovski, Vesna
2004-01-01
It is a well-known fact that languages react differently when foreign words denoting new concepts have to be integrated into the native system. The procedure mostly depends on the degree of purism present in a linguistic community: some languages are rather open to foreign influences and do not demonstrate any special hostility towards new words which are easily accepted and adapted to the phonological and morphological systems of the receiving language. Languages, which have a strong puristic tradition, usually channel their borrowings into the loan translation field using internal word formation resources as a means of creating neologisms. Regardless of whether they are built of native elements or appear as loans, neologisms are necessarily the result of linguistic changes.
Fasni, Nurli; Fatimah, Siti; Yulanda, Syerli
2017-05-01
This research aims to achieve some purposes such as: to know whether mathematical problem solving ability of students who have learned mathematics using Multiple Intelligences based teaching model is higher than the student who have learned mathematics using cooperative learning; to know the improvement of the mathematical problem solving ability of the student who have learned mathematics using Multiple Intelligences based teaching model., to know the improvement of the mathematical problem solving ability of the student who have learned mathematics using cooperative learning; to know the attitude of the students to Multiple Intelligences based teaching model. The method employed here is quasi-experiment which is controlled by pre-test and post-test. The population of this research is all of VII grade in SMP Negeri 14 Bandung even-term 2013/2014, later on two classes of it were taken for the samples of this research. A class was taught using Multiple Intelligences based teaching model and the other one was taught using cooperative learning. The data of this research were gotten from the test in mathematical problem solving, scale questionnaire of the student attitudes, and observation. The results show the mathematical problem solving of the students who have learned mathematics using Multiple Intelligences based teaching model learning is higher than the student who have learned mathematics using cooperative learning, the mathematical problem solving ability of the student who have learned mathematics using cooperative learning and Multiple Intelligences based teaching model are in intermediate level, and the students showed the positive attitude in learning mathematics using Multiple Intelligences based teaching model. As for the recommendation for next author, Multiple Intelligences based teaching model can be tested on other subject and other ability.
Combining fuzzy mathematics with fuzzy logic to solve business management problems
Vrba, Joseph A.
1993-12-01
Fuzzy logic technology has been applied to control problems with great success. Because of this, many observers fell that fuzzy logic is applicable only in the control arena. However, business management problems almost never deal with crisp values. Fuzzy systems technology--a combination of fuzzy logic, fuzzy mathematics and a graphical user interface--is a natural fit for developing software to assist in typical business activities such as planning, modeling and estimating. This presentation discusses how fuzzy logic systems can be extended through the application of fuzzy mathematics and the use of a graphical user interface to make the information contained in fuzzy numbers accessible to business managers. As demonstrated through examples from actual deployed systems, this fuzzy systems technology has been employed successfully to provide solutions to the complex real-world problems found in the business environment.
Ismail
2018-01-01
This study aims to describe student’s critical thinking skill of grade VIII in solving mathematical problem. A qualitative research was conducted to a male student with high mathematical ability. Student’s critical thinking skill was obtained from a depth task-based interview. The result show that male student’s critical thinking skill of the student as follows. In understanding the problem, the student did categorization, significance decoding, and meaning clarification. In devising a plan he examined his ideas, detected his argument, analyzed his argument and evaluated his argument. During the implementation phase, the skill that appeared were analyzing of the argument and inference skill such as drawing conclusion, deliver alternative thinking, and problem solving skills. At last, in rechecking all the measures, they did self-correcting and self-examination.
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Reza Akhlaghi Garmjani
2016-10-01
Full Text Available Teaching science and math has been underdeveloped in nurturing the talents and motivations of young people who are in search of professions in these fields. Identifying and strengthening the students' problem solving beliefs and behaviors, can be a great help to those involved in teaching mathematics. This study investigates on the university and high school students, teachers and professors' problem solving beliefs and behaviors. Considering the research method, this study is a field research in which questionnaire is used. Participants in this research were senior high school and university students, math teachers and math professors. Data collection method for beliefs and behavior variables was via the use of a questionnaire. The Mann-Whitney test results showed that problem solving in high school and university was different and the main difference was in mathematical professional beliefs and behaviors.
Thomas J. Pfaff
2015-01-01
Mahajan, Sanjoy. Street-Fighting Mathematics: The Art of Educated Guessing and Opportunistic Problem Solving (The MIT Press, Cambridge, Massachusetts, 2010). 152 pp. ISBN 978--0--262--51429--3 Street-Fighting Mathematics is an engaging collection of problem-solving techniques. The book is not for a general audience, as it requires a significant level of mathematical and scientific background knowledge. In particular, most of the book requires knowledge of Calculus I and there are examples ...
Schonberger, Ann Koch
This three-volume report deals with the hypothesis that males are more successful at solving mathematical and spatial problems than females. The general relationship between visual spatial abilities and mathematical problem-solving ability is also investigated. The research sample consisted of seventh graders. Each pupil took five spatial tests…
Perrenet, J.C.; Taconis, R.
2009-01-01
This study investigates the changes in mathematical problem-solving beliefs and behaviour of mathematics students during the years after entering university. Novice bachelor students fill in a questionnaire about their problem-solving beliefs and behaviour. At the end of their bachelor programme, as
Perrenet, Jacob; Taconis, Ruurd
2009-01-01
This study investigates the changes in mathematical problem-solving beliefs and behaviour of mathematics students during the years after entering university. Novice bachelor students fill in a questionnaire about their problem-solving beliefs and behaviour. At the end of their bachelor programme, as experienced bachelor students, they again fill…
Lobato, Fran Sérgio
2017-01-01
This book is aimed at undergraduate and graduate students in applied mathematics or computer science, as a tool for solving real-world design problems. The present work covers fundamentals in multi-objective optimization and applications in mathematical and engineering system design using a new optimization strategy, namely the Self-Adaptive Multi-objective Optimization Differential Evolution (SA-MODE) algorithm. This strategy is proposed in order to reduce the number of evaluations of the objective function through dynamic update of canonical Differential Evolution parameters (population size, crossover probability and perturbation rate). The methodology is applied to solve mathematical functions considering test cases from the literature and various engineering systems design, such as cantilevered beam design, biochemical reactor, crystallization process, machine tool spindle design, rotary dryer design, among others.
Minimalism as a Guiding Principle: Linking Mathematical Learning to Everyday Knowledge
Inoue, Noriyuki
2008-01-01
Studies report that students often fail to consider familiar aspects of reality in solving mathematical word problems. This study explored how different features of mathematical problems influence the way that undergraduate students employ realistic considerations in mathematical problem solving. Incorporating familiar contents in the word…
Words, Words, Words: English, Vocabulary.
Lamb, Barbara
The Quinmester course on words gives the student the opportunity to increase his proficiency by investigating word origins, word histories, morphology, and phonology. The course includes the following: dictionary skills and familiarity with the "Oxford,""Webster's Third," and "American Heritage" dictionaries; word…
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Reviandari Widyatiningtyas
2015-07-01
Full Text Available The study was report the findings of an only post-test control group research design and aims to analyze the influence of problem-based learning approach, school level, and students’ prior mathematical ability to student’s mathematics critical thinking ability. The research subjects were 140 grade ten senior high school students coming from excellent and moderate school level. The research instruments a set of mathematical critical thinking ability test, and the data were analyzed by using two ways ANOVA and t-test. The research found that the problem based learning approach has significant impact to the ability of students’ mathematics critical thinking in terms of school level and students’ prior mathematical abilities. Furthermore. This research also found that there is no interaction between learning approach and school level, and learning approach and students’ prior mathematics ability to students’ mathematics critical thinking ability.
The effect of creative problem solving on students’ mathematical adaptive reasoning
Muin, A.; Hanifah, S. H.; Diwidian, F.
2018-01-01
This research was conducted to analyse the effect of creative problem solving (CPS) learning model on the students’ mathematical adaptive reasoning. The method used in this study was a quasi-experimental with randomized post-test only control group design. Samples were taken as many as two classes by cluster random sampling technique consisting of experimental class (CPS) as many as 40 students and control class (conventional) as many as 40 students. Based on the result of hypothesis testing with the t-test at the significance level of 5%, it was obtained that significance level of 0.0000 is less than α = 0.05. This shows that the students’ mathematical adaptive reasoning skills who were taught by CPS model were higher than the students’ mathematical adaptive reasoning skills of those who were taught by conventional model. The result of this research showed that the most prominent aspect of adaptive reasoning that could be developed through a CPS was inductive intuitive. Two aspects of adaptive reasoning, which were inductive intuitive and deductive intuitive, were mostly balanced. The different between inductive intuitive and deductive intuitive aspect was not too big. CPS model can develop student mathematical adaptive reasoning skills. CPS model can facilitate development of mathematical adaptive reasoning skills thoroughly.
METHOD OF GREEN FUNCTIONS IN MATHEMATICAL MODELLING FOR TWO-POINT BOUNDARY-VALUE PROBLEMS
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E. V. Dikareva
2015-01-01
Full Text Available Summary. In many applied problems of control, optimization, system theory, theoretical and construction mechanics, for problems with strings and nods structures, oscillation theory, theory of elasticity and plasticity, mechanical problems connected with fracture dynamics and shock waves, the main instrument for study these problems is a theory of high order ordinary differential equations. This methodology is also applied for studying mathematical models in graph theory with different partitioning based on differential equations. Such equations are used for theoretical foundation of mathematical models but also for constructing numerical methods and computer algorithms. These models are studied with use of Green function method. In the paper first necessary theoretical information is included on Green function method for multi point boundary-value problems. The main equation is discussed, notions of multi-point boundary conditions, boundary functionals, degenerate and non-degenerate problems, fundamental matrix of solutions are introduced. In the main part the problem to study is formulated in terms of shocks and deformations in boundary conditions. After that the main results are formulated. In theorem 1 conditions for existence and uniqueness of solutions are proved. In theorem 2 conditions are proved for strict positivity and equal measureness for a pair of solutions. In theorem 3 existence and estimates are proved for the least eigenvalue, spectral properties and positivity of eigenfunctions. In theorem 4 the weighted positivity is proved for the Green function. Some possible applications are considered for a signal theory and transmutation operators.
GeoGebra Assist Discovery Learning Model for Problem Solving Ability and Attitude toward Mathematics
Murni, V.; Sariyasa, S.; Ardana, I. M.
2017-09-01
This study aims to describe the effet of GeoGebra utilization in the discovery learning model on mathematical problem solving ability and students’ attitude toward mathematics. This research was quasi experimental and post-test only control group design was used in this study. The population in this study was 181 of students. The sampling technique used was cluster random sampling, so the sample in this study was 120 students divided into 4 classes, 2 classes for the experimental class and 2 classes for the control class. Data were analyzed by using one way MANOVA. The results of data analysis showed that the utilization of GeoGebra in discovery learning can lead to solving problems and attitudes towards mathematics are better. This is because the presentation of problems using geogebra can assist students in identifying and solving problems and attracting students’ interest because geogebra provides an immediate response process to students. The results of the research are the utilization of geogebra in the discovery learning can be applied in learning and teaching wider subject matter, beside subject matter in this study.
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Serdal BALTACI
2016-10-01
Full Text Available It is a widely known fact that gifted students have different skills compared to their peers. However, to what extent gifted students use mathematical thinking skills during probability problem solving process emerges as a significant question. Thence, the main aim of the present study is to examine 8th grade gifted students’ probability problem-solving process related to daily life in terms of mathematical thinking skills. In this regard, a case study was used in the study. The participants of the study were six students at 8th grade (four girls and two boys from the Science and Art Center. One of the purposeful sampling methods, maximum variation sampling was used for selecting the participants. Clinical interview and problems were used as a data collection tool. As a results of the study, it was determined that gifted students use reasoning and strategies skill, which is one of the mathematical thinking skills, mostly on the process of probability problem solving, and communication skills at least.
Strategy Instruction in Mathematics.
Goldman, Susan R.
1989-01-01
Experiments in strategy instruction for mathematics have been conducted using three models (direct instruction, self-instruction, and guided learning) applied to the tasks of computation and word problem solving. Results have implications for effective strategy instruction for learning disabled students. It is recommended that strategy instruction…
Eringen, A Cemal
2013-01-01
Continuum Physics: Volume 1 - Mathematics is a collection of papers that discusses certain selected mathematical methods used in the study of continuum physics. Papers in this collection deal with developments in mathematics in continuum physics and its applications such as, group theory functional analysis, theory of invariants, and stochastic processes. Part I explains tensor analysis, including the geometry of subspaces and the geometry of Finsler. Part II discusses group theory, which also covers lattices, morphisms, and crystallographic groups. Part III reviews the theory of invariants th
Following the Template: Transferring Modeling Skills to Nonstandard Problems
Tyumeneva, Yu. A.; Goncharova, M. V.
2017-01-01
This study seeks to analyze how students apply a mathematical modeling skill that was previously learned by solving standard word problems to the solution of word problems with nonstandard contexts. During the course of an experiment involving 106 freshmen, we assessed how well they were able to transfer the mathematical modeling skill that is…
Syukriani, Andi; Juniati, Dwi; Siswono, Tatag Yuli Eko
2017-08-01
The purpose of this study was to explore the strategic competence of senior secondary school students in solving mathematics problems. Terdapat dua subjek, satu bergaya kognitif field-independent dan satu bergaya kognitif field-dependent tetapi keduanya memiliki tingkat prestasi belajar matematika yang setara. There were two subjects, one field-independent cognitive style and one field-dependent cognitive style. They had an equivalent high level of mathematics achievement. Keduanya dipilih berdasarkan hasil tes kompetensi matematika dan GEFT (Group Embedded Figures Test). Subjects were selected based on the test results of mathematics competence and GEFT (Group Embedded Figures Test). Kompetensi strategis dapat merangsang perkembangan otonomi dan fleksibilitas dalam diri siswa karena merupakan keterampilan yang sangat dibutuhkan di sepanjang abad 21. Gaya kognitif merupakan kecenderungan siswa dalam mengolah informasi sangat mempengaruhi performance dalam menyelesaikan masalah matematika. Strategic competence can stimulate the development of autonomy and flexibility of students and they are skills which are needed in the 21st century. Cognitive style is the tendency of students in processing informations and it greatly affects the performance in solving mathematics problems. Hasil penelitian menunjukkan bahwa subjek FI cenderung analitis baik pada pembentukan bayangannya maupun pada gambar yang dibuatnya untuk memproses informasi berdasarkan dengan struktur pengetahuannya sendiri (Internally directed). The research result showed that subject FI tended to be analytical both in forming the mental imagination and the picture to process information in accordance with his own knowledge structure (internally directed). Subjek FD kurang analitis dan tidak dapat mengenal bentuk sederhana (konsep matematika) dari bentuk yang kompleks (Exeternally directed) sehingga menerima ide sebagaimana yang disajikan. Subject FD was less analytical and unable to recognize simple form
Mathematical problems of the dynamics of incompressible fluid on a rotating sphere
Skiba, Yuri N
2017-01-01
This book presents selected mathematical problems involving the dynamics of a two-dimensional viscous and ideal incompressible fluid on a rotating sphere. In this case, the fluid motion is completely governed by the barotropic vorticity equation (BVE), and the viscosity term in the vorticity equation is taken in its general form, which contains the derivative of real degree of the spherical Laplace operator. This work builds a bridge between basic concepts and concrete outcomes by pursuing a rich combination of theoretical, analytical and numerical approaches, and is recommended for specialists developing mathematical methods for application to problems in physics, hydrodynamics, meteorology and geophysics, as well for upper undergraduate or graduate students in the areas of dynamics of incompressible fluid on a rotating sphere, theory of functions on a sphere, and flow stability.
Sari, D. P.; Usodo, B.; Subanti, S.
2018-04-01
This research aims to describe metacognitive experience of mathematics education students with strong, average, and weak intrapersonal intelligence in open start problem solving. Type of this research was qualitative research. The research subject was mathematics education students in Muhammadiyah University of Surakarta in academic year 2017/2018. The selected students consisted of 6 students with details of two students in each intrapersonal intelligence category. The research instruments were questionnaire, open start problem solving task, and interview guidelines. Data validity used time triangulation. Data analyses were done through data collection, data reduction, data presentation, and drawing conclusion. Based on findings, subjects with strong intrapersonal intelligence had high self confidence that they were able to solve problem correctly, able to do planning steps and able to solve the problem appropriately. Subjects with average intrapersonal intelligence had high self-assessment that they were able to solve the problem, able to do planning steps appropriately but they had not maximized in carrying out the plan so that it resulted incorrectness answer. Subjects with weak intrapersonal intelligence had high self confidence in capability of solving math problem, lack of precision in taking plans so their task results incorrectness answer.
Eloy Guerrero Seide
2004-01-01
This article summarizes the results obtained in an exploratory and comparative study of two ways of structuring the mathematical content of a B.S. program in Agronomic Engineering at Guantanamo University, Cuba: the formal systematization of the presentation of the knowledge, and an organization through problems. The sign test is used in the proof of the hypothesis. In a preliminary form, at least, it was demonstrated that the variant of systemic structuring of knowledge through proble...
Nur Aisyah Isti; Arief Agoestanto; Ary Woro Kurniasih
2017-01-01
The purpose of this research was described critical thinking stage of students grade VIII in setting PBL and scaffolding to solve mathematics problems. Critical thinking stage consists of clarification, assesment, inference, and strategy/tactics. The subject were teo students in the level of capacity to think critical (uncritical, less critical, quite critical, and critical). So that this research subject was 8 students in VIII A One State Junior High School of Temanggung. The result showed a...
Domaratzki, Michael; Rampersad, Narad
2011-01-01
We investigate Abelian primitive words, which are words that are not Abelian powers. We show that unlike classical primitive words, the set of Abelian primitive words is not context-free. We can determine whether a word is Abelian primitive in linear time. Also different from classical primitive words, we find that a word may have more than one Abelian root. We also consider enumeration problems and the relation to the theory of codes. Peer reviewed
Behaviour of mathematics and physics students in solving problem of Vector-Physics context
Sardi; Rizal, M.; Mansyur, J.
2018-04-01
This research aimed to describe behaviors of mathematics and physics students in solving problem of the vector concept in physics context. The subjects of the research were students who enrolled in Mathematics Education Study Program and Physics Education Study Program of FKIP Universitas Tadulako. The selected participants were students who received the highest score in vector fundamental concept test in each study program. The data were collected through thinking-aloud activity followed by an interview. The steps of data analysis included data reduction, display, and conclusion drawing. The credibility of the data was tested using a triangulation method. Based on the data analysis, it can be concluded that the two groups of students did not show fundamental differences in problem-solving behavior, especially in the steps of understanding the problem (identifying, collecting and analyzing facts and information), planning (looking for alternative strategies) and conducting the alternative strategy. The two groups were differ only in the evaluation aspect. In contrast to Physics students who evaluated their answer, mathematics students did not conducted an evaluation activity on their work. However, the difference was not caused by the differences in background knowledge.
Nugraheni, L.; Budayasa, I. K.; Suwarsono, S. T.
2018-01-01
The study was designed to discover examine the profile of metacognition of vocational high school student of the Machine Technology program that had high ability and field independent cognitive style in mathematical problem solving. The design of this study was exploratory research with a qualitative approach. This research was conducted at the Machine Technology program of the vocational senior high school. The result revealed that the high-ability student with field independent cognitive style conducted metacognition practices well. That involved the three types of metacognition activities, consisting of planning, monitoring, and evaluating at metacognition level 2 or aware use, 3 or strategic use, 4 or reflective use in mathematical problem solving. The applicability of the metacognition practices conducted by the subject was never at metacognition level 1 or tacit use. This indicated that the participant were already aware, capable of choosing strategies, and able to reflect on their own thinking before, after, or during the process at the time of solving mathematical problems.That was very necessary for the vocational high school student of Machine Technology program.
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Meirav Tzohar-Rozen
2014-11-01
Full Text Available Mathematical problem solving is among the most valuable aspects of mathematics education. It is also the hardest for elementary school students (Verschaffel, Greer & De Corte, 2000. Students experience cognitive and metacognitive difficulties in this area and develop negative emotions and poor motivation which hamper their efforts (Kramarski, Weiss, & Kololshi-Minsker, 2010. 9–11 seems the critical stage for developing attitudes and emotional reactions towards mathematics (Artino, 2009. These metacognitive and motivational-emotional factors are fundamental components of Self-Regulated Learning (SRL, a non-innate process requiring systematic, explicit student training (Pintrich, 2000; Zimmerman, 2000. Most self-regulation studies relating to problem-solving focus on metacognition. Few explore the motivational-emotional component. This study aimed to develop, examine, and compare two SRL interventions dealing with two additional components of self-regulation: metacognitive regulation (MC and motivational-emotional regulation (ME. It also sought to examine the significance of these components and their contribution to learners' problem-solving achievements and self-regulation. The study examined 118 fifth grade students, randomly assigned to two groups. Pre- and post-intervention, the two groups completed self-regulation questionnaires relating to metacognition, motivation, and emotion. They also solved arithmetic series problems presented in two ways (verbal form and numeric form. After intervention we also examined a novel transfer problem. The intervention consisted of 10 hours for 5 weeks. Following the intervention the groups exhibited similar improvements across all the problems. The MC group performed best in metacognitive self-regulation and the ME group performed best in certain motivational-emotional aspects of self-regulation. Research implications are discussed.
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Eloy Guerrero Seide
2004-11-01
Full Text Available This article summarizes the results obtained in an exploratory and comparative study of two ways of structuring the mathematical content of a B.S. program in Agronomic Engineering at Guantanamo University, Cuba: the formal systematization of the presentation of the knowledge, and an organization through problems. The sign test is used in the proof of the hypothesis. In a preliminary form, at least, it was demonstrated that the variant of systemic structuring of knowledge through problems is more conducive to the efficiency of the knowledge acquired by students than the structure presented by means of the logical exposition of achieved knowledge.
Mathematical problem solving ability of sport students in the statistical study
Sari, E. F. P.; Zulkardi; Putri, R. I. I.
2017-12-01
This study aims to determine the problem-solving ability of sport students of PGRI Palembang semester V in the statistics course. Subjects in this study were sport students of PGRI Palembang semester V which amounted to 31 people. The research method used is quasi experiment type one case shoot study. Data collection techniques in this study use the test and data analysis used is quantitative descriptive statistics. The conclusion of this study shown that the mathematical problem solving ability of PGRI Palembang sport students of V semester in the statistical course is categorized well with the average of the final test score of 80.3.
International Nuclear Information System (INIS)
1994-01-01
Traditional International Conference on programming and mathematical methods for solution of physical problems took place in Dubna in Jun, 14-19, 1993. More than 160 scientists from 14 countries participated in the Conference. They presented about 120 reports, the range of problems including computerized information complexes, experimental data acquisition and processing systems, mathematical simulation and calculation experiment in physics, analytical and numerical methods for solution of physical problems
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Rahmah Johar
2017-06-01
Full Text Available The lack of Indonesian students achievement in the international assessment is due to several factors. Students are not familiar with the problems requiring reasoning, in particular the proportional reasoning. This research aims to identify the distribution and the Level of Cognitive Demands (LCD of the proportional reasoning problems found in the Year 7 and Year 8 mathematics textbooks based on the 2013 curriculum (revised edition 2014. The data collection was conducted by identifying the proportional reasoning problems found in the whole chapters of the textbooks which are then analysed and classified using the Smiths and Stein’s criteria of LCD (1998. The results reveal that the proportional reasoning problems were only found in the three of 17 chapters namely ratio and proportion, rectangle and triangle, and Pythagorean Theorem, which represent different LCD including Lower-LCD (Low-M and Low-P and Higher-LCD (High-P. Out of 69 proportional reasoning problem found in the textbooks, the percentage of higher-LCD problems (n=29 ; 42.03% is less than lower-LCD (n=40;57.97%. In addition, the higher-LCD problems found were only the high-P type. None was found to meet the requirement of High-DM demanding students to conduct ‘doing mathematics’, complex approach and self-monitoring or self regulation of students’ cognitive process. It is recommended that the proportional reasoning problems, including some High-DM problems, should be provided in each topic in Indonesian mathematics textbooks.
Improving attitudes toward mathematics learning with problem posing in class VIII
Vionita, Alfha; Purboningsih, Dyah
2017-08-01
This research is classroom action research which is collaborated to improve student's behavior toward math and mathematics learning at class VIII by using problem posing approach. The subject of research is all of students grade VIIIA which consist of 32 students. This research has been held on two period, first period is about 3 times meeting, and second period is about 4 times meeting. The instrument of this research is implementation of learning observation's guidance by using problem posing approach. Cycle test has been used to measure cognitive competence, and questionnaire to measure the students' behavior in mathematics learning process. The result of research shows the students' behavior has been improving after using problem posing approach. It is showed by the behavior's criteria of students that has increasing result from the average in first period to high in second period. Furthermore, the percentage of test result is also improve from 68,75% in first period to 78,13% in second period. On the other hand, the implementation of learning observation by using problem posing approach has also improving and it is showed by the average percentage of teacher's achievement in first period is 89,2% and student's achievement 85,8%. These results get increase in second period for both teacher and students' achievement which are 94,4% and 91,11%. As a result, students' behavior toward math learning process in class VIII has been improving by using problem posing approach.
Jafari, Hamed; Salmasi, Nasser
2015-09-01
The nurse scheduling problem (NSP) has received a great amount of attention in recent years. In the NSP, the goal is to assign shifts to the nurses in order to satisfy the hospital's demand during the planning horizon by considering different objective functions. In this research, we focus on maximizing the nurses' preferences for working shifts and weekends off by considering several important factors such as hospital's policies, labor laws, governmental regulations, and the status of nurses at the end of the previous planning horizon in one of the largest hospitals in Iran i.e., Milad Hospital. Due to the shortage of available nurses, at first, the minimum total number of required nurses is determined. Then, a mathematical programming model is proposed to solve the problem optimally. Since the proposed research problem is NP-hard, a meta-heuristic algorithm based on simulated annealing (SA) is applied to heuristically solve the problem in a reasonable time. An initial feasible solution generator and several novel neighborhood structures are applied to enhance performance of the SA algorithm. Inspired from our observations in Milad hospital, random test problems are generated to evaluate the performance of the SA algorithm. The results of computational experiments indicate that the applied SA algorithm provides solutions with average percentage gap of 5.49 % compared to the upper bounds obtained from the mathematical model. Moreover, the applied SA algorithm provides significantly better solutions in a reasonable time than the schedules provided by the head nurses.
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A.O. Fatade
2014-02-01
Full Text Available The study investigated the effect of problem-based learning (PBL on senior secondary school students' beliefs about Further Mathematics in Nigeria within the blueprint of pre-test-post-test non-equivalent control group quasi-experimental design. Intact classes were used and in all, 96 students participated in the study (42 in the experimental group taught with the PBL and 54 in the control group taught using the Traditional Method (TM. One research instrument tagged Beliefs about Further Mathematics Questionnaire (BFMQ, Cronbach alpha (α=.86 was developed and used for the study and data collected were analysed using the descriptive statistics of mean and standard deviation which served as precursor to testing the null hypothesis for the study using an independent samples t-test and analysis of variance. Results showed that participants held strong beliefs about further mathematics and there was a statistically significant difference in the mean post-treatment scores on BFMQ (t=-6.22, p=.000 for t-test and (F(1,95=38.49; p<.001 for ANOVA between students exposed to the PBL and those exposed to the TM, in favour of the PBL group. Based on the results, the study recommended that PBL should be adopted as an instructional strategy for promoting meaningful learning in and enhancing beliefs about further mathematics and efforts should be made to integrate the philosophy of PBL into the preservice teachers' curriculum at the teacher-preparation institutions in Nigeria.
New Mathematical Model and Algorithm for Economic Lot Scheduling Problem in Flexible Flow Shop
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H. Zohali
2018-03-01
Full Text Available This paper addresses the lot sizing and scheduling problem for a number of products in flexible flow shop with identical parallel machines. The production stages are in series, while separated by finite intermediate buffers. The objective is to minimize the sum of setup and inventory holding costs per unit of time. The available mathematical model of this problem in the literature suffers from huge complexity in terms of size and computation. In this paper, a new mixed integer linear program is developed for delay with the huge dimentions of the problem. Also, a new meta heuristic algorithm is developed for the problem. The results of the numerical experiments represent a significant advantage of the proposed model and algorithm compared with the available models and algorithms in the literature.
Arnellis, A.; Jamaan, E. Z.; Amalita, N.
2018-04-01
The goal to analyse a improvement of teacher competence after being trained in preparing high-order math olympicad based on high order thinking skills in junior high school teachers in Pesisir Selatan Regency. The sample of these activities are teachers at the MGMP junior high school in Pesisir Selatan District. Evaluation of the implementation is done by giving a pre test and post test, which will measure the success rate of the implementation of this activities. The existence of the devotion activities is expected to understand the enrichment of mathematics olympiad material and training in the preparation of math olympiad questions for the teachers of South Pesisir district junior high school, motivating and raising the interest of the participants in order to follow the mathematics olympiad with the enrichment of mathematics materials and the training of problem solving about mathematics olympiad for junior high school teachers, the participants gain experience and gain insight, as well as the ins and outs of junior mathematics olympiad and implement to teachers and students in olympic competitions. The result of that the post-test is better than the result of pretest in the training of mathematics teacher competence improvement in composing the mathematics olympiad problem based on high order thinking skills of junior high school (SMP) in Pesisir Selatan District, West Sumatra, Indonesia.
Tolar, Tammy D.; Fuchs, Lynn; Fletcher, Jack M.; Fuchs, Douglas; Hamlett, Carol L.
2014-01-01
Three cohorts of third-grade students (N = 813) were evaluated on achievement, cognitive abilities, and behavioral attention according to contrasting research traditions in defining math learning disability (LD) status: low achievement versus extremely low achievement and IQ-achievement discrepant versus strictly low-achieving LD. We use methods from these two traditions to form math problem solving LD groups. To evaluate group differences, we used MANOVA-based profile and canonical analyses to control for relations among the outcomes and regression to control for group definition variables. Results suggest that basic arithmetic is the key distinguishing characteristic that separates low-achieving problem solvers (including LD, regardless of definition) from typically achieving students. Word problem solving is the key distinguishing characteristic that separates IQ-achievement-discrepant from strictly low-achieving LD students, favoring the IQ-achievement-discrepant students. PMID:24939971
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Nevin ORHUN
2013-07-01
Full Text Available Open and distance education plays an important role in the actualization of cultural goals as well as in societal developments. This is an independent teaching and learning method for mathematics which forms the dynamic of scientific thinking. Distance education is an important alternative to traditional teaching applications. These contributions brought by technology enable students to participate actively in having access to information and questioning it. Such an application increases students’ motivation and teaches how mathematics can be used in daily life. Derivative is a mathematical concept which can be used in many areas of daily life. The aim of this study is to enable the concept of derivatives to be understood well by using the derivative function in the solution of various problems. It also aims at interpreting difficulties theoretically in the solution of problems and determining mistakes in terms of teaching methods. In this study, how various aspects of derivatives are understood is emphasized. These aspects concern the explanation of concepts and process, and also their application to certain concepts in physics. Students’ depth of understanding of derivatives was analyzed based on two aspects of understanding; theoretical analysis and contextual application. Follow-up interviews were conducted with five students. The results show that the students preferred to apply an algebraic symbolic aspect instead of using logical meanings of function and its derivative. In addition, in relation to how the graph of the derivative function affects the aspect of function, it was determined that the students displayed low performance.
de Araujo, Zandra; Orrill, Chandra Hawley; Jacobson, Erik
2018-04-01
While there is considerable scholarship describing principles for effective professional development, there have been few attempts to examine these principles in practice. In this paper, we identify and examine the particular design features of a mathematics professional development experience provided for middle grades teachers over 14 weeks. The professional development was grounded in a set of mathematical tasks that each had one right answer, but multiple solution paths. The facilitator engaged participants in problem solving and encouraged participants to work collaboratively to explore different solution paths. Through analysis of this collaborative learning environment, we identified five design features for supporting teacher learning of important mathematics and pedagogy in a problem-solving setting. We discuss these design features in depth and illustrate them by presenting an elaborated example from the professional development. This study extends the existing guidance for the design of professional development by examining and operationalizing the relationships among research-based features of effective professional development and the enacted features of a particular design.
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Rogaieh Mohammadi
2009-10-01
Full Text Available Objectives: Dyscalculia is specific learning disabilities affecting the acquisition of mathematic skills in an otherwise normal child. The aim of this study was investigation of occupational therapy interventions effect on mathematical problems in students with special learning disorders. Methods: 40 students with dyscalculia (2-5 grades were selected and divided through randomized permuted blocks method into two groups 20 persons as intervention group and the others as the control group. Initially both of groups were administered by the "Iran Key math Test". Then intervention group received occupational therapy interventions for 20 sessions individually and two groups were administered by the Test again. Data was analyzed by using Paired and Independent t-tests. Results: By the paired sample t-test the mean of total marks of Iran Key math Test demonstrated statistically significant difference in both of groups (P<0.05, but the measure of difference in intervention group was more than control group. The mean of marks of Basic Concepts, Operations and Applications demonstrated statistically significant difference at intervention group. Discussion: Occupational therapy interventions had clinical effect on mathematical problems in students with special learning disorders.
Stein, Sherman K
2010-01-01
Anyone can appreciate the beauty, depth, and vitality of mathematics with the help of this highly readable text, specially developed from a college course designed to appeal to students in a variety of fields. Readers with little mathematical background are exposed to a broad range of subjects chosen from number theory, topology, set theory, geometry, algebra, and analysis. Starting with a survey of questions on weight, the text discusses the primes, the fundamental theorem of arithmetic, rationals and irrationals, tiling, tiling and electricity, probability, infinite sets, and many other topi
Mathematical and numerical analysis of PN models for photons transport problems
International Nuclear Information System (INIS)
Valentin, Xavier
2015-01-01
Computational costs for direct numerical simulations of photon transport problems are very high in terms of CPU time and memory. One way to tackle this issue is to develop reduced models that a cheaper to solve numerically. There exists number of these models: moments models, discrete ordinates models (S N ), diffusion-like models... In this thesis, we focus on P N models in which the transport operator is approached by mean of a truncated development on the spherical harmonics basis. These models are arbitrary accurate in the angular dimension and are rotationally invariants (in multiple space dimensions). The latter point is fundamental when one wants to simulate inertial confinement fusion (ICF) experiments where the spherical symmetry plays an important part in the accuracy of the numerical solutions. We study the mathematical structure of the PN models and construct a new numerical method in the special case of a one dimensional space dimension with spherical symmetry photon transport problems. We first focus on a linear transport problem in the vacuum. Even in this simple case, it appears in the P N equations geometrical source terms that are stiff in the neighborhood of r = 0 and thus hard to discretize. Existing numerical methods are not satisfactory for multiple reasons: (1) inaccuracy in the neighborhood of r = 0 ('flux-dip'), (2) do not capture steady states (well-balanced scheme), (3) no stability proof. Following recent works, we develop a new well-balanced scheme for which we show the L 2 stability. We then extend the scheme for photon transport problems within a no moving media, the linear Boltzmann equation, and interest ourselves on its behavior in the diffusion limit (asymptotic-preserving property). In a second part, we consider radiation hydrodynamics problems. Since modelization of these problems is still under discussion in the literature, we compare a set of existing models by mean of mathematical analysis and establish a hierarchy
Directory of Open Access Journals (Sweden)
Sunxin Wang
2014-01-01
Full Text Available This paper presents a combination of variable neighbourhood search and mathematical programming to minimize the sum of earliness and tardiness penalty costs of all operations for just-in-time job-shop scheduling problem (JITJSSP. Unlike classical E/T scheduling problem with each job having its earliness or tardiness penalty cost, each operation in this paper has its earliness and tardiness penalties, which are paid if the operation is completed before or after its due date. Our hybrid algorithm combines (i a variable neighbourhood search procedure to explore the huge feasible solution spaces efficiently by alternating the swap and insertion neighbourhood structures and (ii a mathematical programming model to optimize the completion times of the operations for a given solution in each iteration procedure. Additionally, a threshold accepting mechanism is proposed to diversify the local search of variable neighbourhood search. Computational results on the 72 benchmark instances show that our algorithm can obtain the best known solution for 40 problems, and the best known solutions for 33 problems are updated.
Using mathematics to solve real world problems: the role of enablers
Geiger, Vincent; Stillman, Gloria; Brown, Jill; Galbriath, Peter; Niss, Mogens
2018-03-01
The purpose of this article is to report on a newly funded research project in which we will investigate how secondary students apply mathematical modelling to effectively address real world situations. Through this study, we will identify factors, mathematical, cognitive, social and environmental that "enable" year 10/11 students to successfully begin the modelling process, that is, formulate and mathematise a real world problem. The 3-year study will take a design research approach in working intensively with six schools across two educational jurisdictions. It is anticipated that this research will generate new theoretical and practical insights into the role of "enablers" within the process of mathematisation, leading to the development of principles for the design and implementation for tasks that support students' development as modellers.
Utilizing geogebra in financial mathematics problems: didactic experiment in vocational college
Ghozi, Saiful; Yuniarti, Suci
2017-12-01
GeoGebra application offers users to solve real problems in geometry, statistics, and algebra fields. This studydeterminesthe effect of utilizing Geogebra on students understanding skill in the field of financial mathematics. This didactic experiment study used pre-test-post-test control group design. Population of this study were vocational college students in Banking and Finance Program of Balikpapan State Polytechnic. Two classes in the first semester were chosen using cluster random sampling technique, one class as experiment group and one class as control group. Data were analysed used independent sample t-test. The result of data analysis showed that students understanding skill with learning by utilizing GeoGeobra is better than students understanding skill with conventional learning. This result supported that utilizing GeoGebra in learning can assist the students to enhance their ability and depth understanding on mathematics subject.
International Nuclear Information System (INIS)
Sushkevich, T.A.
2011-01-01
This review is to remind scientists of the older generation of some memorable historical pages and of many famous researchers, teachers and colleagues. For the younger researchers and foreign colleagues it will be useful to get to know about pioneer advancements of the Soviet scientists in the field of information and mathematical supply for cosmonautic problems on the eve of the space era. Main attention is paid to the scientific experiments conducted on the piloted space vehicles and the research teams who created the information and mathematical tools for the first space projects. The role of Mstislav Vsevolodovich Keldysh, the Major Theoretician of cosmonautics, is particularly emphasized. He determined for the most part the basic directions of development of space research and remote sensing of the Earth and planets that are shortly called remote sensing
Use of open-ended problems as the basis for the mathematical creativity growth disclosure of student
Suyitno, A.; Suyitno, H.; Rochmad; Dwijanto
2018-03-01
Mathematical creativity is the essence of learning in mathematics. However, mathematical creativity had not yet grown among students. Means there was a gap between needs and reality. This gap must be bridged through by scientific studies, and there were novelty findings, namely the discovery of stages to cultivate of Mathematical Creativity. The problem formulation: How to use of open-ended problems as the basis for the mathematical creativity growth disclosure of student? The goal was to use of open issues as the basis for the mathematical creativity growth disclosure of student. Research method with a qualitative approach. After data was collected then activity in data analysis, include data reduction, data presentation, data interpretation, and conclusion/verification. The results of the research: After the learning by applying the modification of RTTW learning model, then the students were trained to do the open-ended problems and by looking at the UTS and UAS values then qualitatively the results: (1) There was a significant increase of the student's final score. (2) The category of the growth of mathematical creativity of students, the Very Good there were three students, the Good there were six students, There were 17 students, and there were six students. The validation of these results was reinforced by interviews and triangulation. (3) Stage to cultivate mathematical creativity: lecturers should need to provide inputs on student work; Apply an appropriate learning model, and train students to work on the continuing problems.
Widyatiningtyas, Reviandari; Kusumah, Yaya S.; Sumarmo, Utari; Sabandar, Jozua
2015-01-01
The study reported the findings of an only post-test control group research design and aims to analyze the influence of problem-based learning approach, school level, and students' prior mathematical ability to student's mathematics critical thinking ability. The research subjects were 140 grade ten senior high school students coming from…
Zetriuslita; Wahyudin; Jarnawi
2017-01-01
This research aims to describe and analyze result of applying Problem-Based Learning and Cognitive Conflict Strategy (PBLCCS) in increasing students' Mathematical Critical Thinking (MCT) ability and Mathematical Curiosity Attitude (MCA). Adopting a quasi-experimental method with pretest-posttest control group design and using mixed method with…
Seeley, Cathy L.
2016-01-01
In "Making Sense of Math," Cathy L. Seeley, former president of the National Council of Teachers of Mathematics, shares her insight into how to turn your students into flexible mathematical thinkers and problem solvers. This practical volume concentrates on the following areas: (1) Making sense of math by fostering habits of mind that…
International Nuclear Information System (INIS)
Demazure, M.
1988-01-01
The 1988 progress report of the Mathematics center (Polytechnic School, France), is presented. The Center is composed of different research teams: analysis, Riemann geometry, group theory, formal calculus and algorithm geometry, dynamical systems, topology and singularity. For each team, the members, the research topics, the national and international cooperations, are given. The papers concerning the investigations carried out in 1988, are listed [fr
Mathematical models for a batch scheduling problem to minimize earliness and tardiness
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Basar Ogun
2018-05-01
Full Text Available Purpose: Today’s manufacturing facilities are challenged by highly customized products and just in time manufacturing and delivery of these products. In this study, a batch scheduling problem is addressed to provide on-time completion of customer orders in the environment of lean manufacturing. The problem is to optimize partitioning of product components into batches and scheduling of the resulting batches where each customer order is received as a set of products made of various components. Design/methodology/approach: Three different mathematical models for minimization of total earliness and tardiness of customer orders are developed to provide on-time completion of customer orders and also, to avoid from inventory of final products. The first model is a non-linear integer programming model while the second is a linearized version of the first. Finally, to solve larger sized instances of the problem, an alternative linear integer model is presented. Findings: Computational study using a suit set of test instances showed that the alternative linear integer model is able to solve all test instances in varying sizes within quite shorter computer times comparing to the other two models. It was also showed that the alternative model can solve moderate sized real-world problems. Originality/value: The problem under study differentiates from existing batch scheduling problems in the literature since it includes new circumstances which may arise in real-world applications. This research, also, contributes the literature of batch scheduling problem by presenting new optimization models.
Solving a bi-objective mathematical programming model for bloodmobiles location routing problem
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Masoud Rabbani
2017-01-01
Full Text Available Perishability of platelets, uncertainty of donors’ arrival and conflicting views in platelet supply chain have made platelet supply chain planning a problematic issue. In this paper, mobile blood collection system for platelet production is investigated. Two mathematical models are presented to cover the bloodmobile collection planning problem. The first model is a multi-objective fuzzy mathematical programming in which the bloodmobiles locations are considered with the aim of maximizing potential amount of blood collection and minimizing the operational cost. The second model is a vehicle routing problem with time windows which studies the shuttles routing problem. To tackle the first model, it is reformulated as a crisp multi objective linear programming model and then solved through a fuzzy multi objective programming approach. Several sensitivity analysis are conducted on important parameters to demonstrate the applicability of the proposed model. The proposed model is then solved by using a tailored Simulated Annealing (SA algorithm. The numerical results demonstrate promising efficiency of the proposed solution method.
Electromagnetic Problems Solving by Conformal Mapping: A Mathematical Operator for Optimization
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Wesley Pacheco Calixto
2010-01-01
Full Text Available Having the property to modify only the geometry of a polygonal structure, preserving its physical magnitudes, the Conformal Mapping is an exceptional tool to solve electromagnetism problems with known boundary conditions. This work aims to introduce a new developed mathematical operator, based on polynomial extrapolation. This operator has the capacity to accelerate an optimization method applied in conformal mappings, to determinate the equipotential lines, the field lines, the capacitance, and the permeance of some polygonal geometry electrical devices with an inner dielectric of permittivity ε. The results obtained in this work are compared with other simulations performed by the software of finite elements method, Flux 2D.
DEFF Research Database (Denmark)
Friesel, Anna
2013-01-01
This paper presents the contents and the teaching methods used in the fourth semester course - REG4E - an important subject in engineering, namely Control Theory and Dynamical Systems. Control Theory courses in engineering education are usually related to exercises in the laboratory or to projects....... However, in order to understand complexity of control systems, the students need to possess an analytical understanding of abstract mathematical problems. Our main goal is to illustrate the theory through the robot project, but at the same time we force our students to train their analytical skills...
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Hossein Asefi
2015-09-01
Full Text Available Municipal solid waste management is one of the challenging issues in mega cities due to various interrelated factors such as operational costs and environmental concerns. Cost as one of the most significant constraints of municipal solid waste management can be effectively economized by efficient planning approaches. Considering diverse waste types in an integrated municipal solid waste system, a mathematical model of the location-routing problem is formulated and solved in this study in order to minimize the total cost of transportation and facility establishment.
Çiğdem Özcan, Zeynep
2016-04-01
Studies highlight that using appropriate strategies during problem solving is important to improve problem-solving skills and draw attention to the fact that using these skills is an important part of students' self-regulated learning ability. Studies on this matter view the self-regulated learning ability as key to improving problem-solving skills. The aim of this study is to investigate the relationship between mathematical problem-solving skills and the three dimensions of self-regulated learning (motivation, metacognition, and behaviour), and whether this relationship is of a predictive nature. The sample of this study consists of 323 students from two public secondary schools in Istanbul. In this study, the mathematics homework behaviour scale was administered to measure students' homework behaviours. For metacognition measurements, the mathematics metacognition skills test for students was administered to measure offline mathematical metacognitive skills, and the metacognitive experience scale was used to measure the online mathematical metacognitive experience. The internal and external motivational scales used in the Programme for International Student Assessment (PISA) test were administered to measure motivation. A hierarchic regression analysis was conducted to determine the relationship between the dependent and independent variables in the study. Based on the findings, a model was formed in which 24% of the total variance in students' mathematical problem-solving skills is explained by the three sub-dimensions of the self-regulated learning model: internal motivation (13%), willingness to do homework (7%), and post-problem retrospective metacognitive experience (4%).
Goodwin, Amanda P.
2016-01-01
This study explores the effectiveness of integrating morphological instruction within comprehension strategy instruction. Participants were 203 students (N = 117 fifth-grade; 86 sixth-grade) from four urban schools who were randomly assigned to the intervention (N = 110; morphological problem-solving within comprehension strategy instruction) or…
Students’ Relational Thinking of Impulsive and Reflective in Solving Mathematical Problem
Satriawan, M. A.; Budiarto, M. T.; Siswono, T. Y. E.
2018-01-01
This is a descriptive research which qualitatively investigates students’ relational thinking of impulsive and reflective cognitive style in solving mathematical problem. The method used in this research are test and interview. The data analyzed by reducing, presenting and concluding the data. The results of research show that the students’ reflective cognitive style can possibly help to find out important elements in understanding a problem. Reading more than one is useful to identify what is being questioned and write the information which is known, building relation in every element and connecting information with arithmetic operation, connecting between what is being questioned with known information, making equation model to find out the value by using substitution, and building a connection on re-checking, re-reading, and re-counting. The impulsive students’ cognitive style supports important elements in understanding problems, building a connection in every element, connecting information with arithmetic operation, building a relation about a problem comprehensively by connecting between what is being questioned with known information, finding out the unknown value by using arithmetic operation without making any equation model. The result of re-checking problem solving, impulsive student was only reading at glance without re-counting the result of problem solving.
The Elementary School Students’ Mathematical Problem Solving Based on Reading Abilities
Wulandari, R. D.; Lukito, A.; Khabibah, S.
2018-01-01
The aim of this research is to describe the third grade of elementary school students’ mathematical problem in solving skills based on their reading abilities. This research is a descriptive research with qualitative approach. This research was conducted at elementary school Kebraon II Surabaya in second semester of 2016-2017 academic years. The participants of this research consist of third grade students with different reading abilities that are independent level, instructional level and frustration level. The participants of this research were selected with purposive sampling technique. The data of this study were collected using reading the narration texts, the Ekwall and Shanker Informal Reading Inventory, problem solving task and interview guidelines. The collected data were evaluated using a descriptive analysis method. Once the study had been completed, it was concluded that problem solving skills varied according to reading abilities, student with independent level and instructional level can solve the problem and students with frustration level can’t solve the problem because they can’t interpret the problem well.
The software package for solving problems of mathematical modeling of isothermal curing process
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S. G. Tikhomirov
2016-01-01
Full Text Available Summary. On the basis of the general laws of sulfur vulcanization diene rubbers the principles of the effective cross-linking using a multi-component agents was discussed. It is noted that the description of the mechanism of action of the complex cross-linking systems are complicated by the diversity of interactions of components and the influence of each of them on the curing kinetics, leading to a variety technological complications of real technology and affects on the quality and technical and economic indicators of the production of rubber goods. Based on the known theoretical approaches the system analysis of isothermal curing process was performed. It included the integration of different techniques and methods into a single set of. During the analysis of the kinetics of vulcanization it was found that the formation of the spatial grid parameters vulcanizates depend on many factors, to assess which requires special mathematical and algorithmic support. As a result of the stratification of the object were identified the following major subsystems. A software package for solving direct and inverse kinetic problems isothermal curing process was developed. Information support “Isothermal vulcanization” is a set of applications of mathematical modeling of isothermal curing. It is intended for direct and inverse kinetic problems. When solving the problem of clarifying the general scheme of chemical transformations used universal mechanism including secondary chemical reactions. Functional minimization algorithm with constraints on the unknown parameters was used for solving the inverse kinetic problem. Shows a flowchart of the program. An example of solving the inverse kinetic problem with the program was introduced. Dataware was implemented in the programming language C ++. Universal dependence to determine the initial concentration of the curing agent was applied . It allowing the use of a model with different properties of multicomponent
Swanson, H Lee
2015-01-01
This study investigated the role of strategy instruction and working memory capacity (WMC) on problem solving solution accuracy in children with and without math disabilities (MD). Children in grade 3 (N = 204) with and without MD subdivided into high and low WMC were randomly assigned to 1 of 4 conditions: verbal strategies (e.g., underlining question sentence), visual strategies (e.g., correctly placing numbers in diagrams), verbal + visual strategies, and an untreated control. The dependent measures for training were problem solving accuracy and two working memory transfer measures (operation span and visual-spatial span). Three major findings emerged: (1) strategy instruction facilitated solution accuracy but the effects of strategy instruction were moderated by WMC, (2) some strategies yielded higher post-test scores than others, but these findings were qualified as to whether children were at risk for MD, and (3) strategy training on problem solving measures facilitated transfer to working memory measures. The main findings were that children with MD, but high WM spans, were more likely to benefit from strategy conditions on target and transfer measures than children with lower WMC. The results suggest that WMC moderates the influence of cognitive strategies on both the targeted and non-targeted measures.
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Brantina Chirinda
2017-06-01
Full Text Available This article reports on the design and findings of the first iteration of a classroom-based design research project which endeavours to design a professional development intervention for teachers’ mathematical problem-solving pedagogy. The major outcome of this study is the generation of design principles that can be used by other researchers developing a professional development (PD intervention for mathematical problem-solving pedagogy. This study contributes to the mathematical problem-solving pedagogy and PD body of knowledge by working with teachers in an under-researched environment (an informal settlement in Gauteng, South Africa. In this iteration, two experienced Grade 9 mathematics teachers and their learners at a public secondary school in Gauteng, South Africa, participated in a 6-month intervention. Findings from the data are discussed in light of their implications for the next cycle and other PD studies.
Description of Student’s Metacognitive Ability in Understanding and Solving Mathematics Problem
Ahmad, Herlina; Febryanti, Fatimah; Febryanti, Fatimah; Muthmainnah
2018-01-01
This research was conducted qualitative which was aim to describe metacognitive ability to understand and solve the problems of mathematics. The subject of the research was the first year students at computer and networking department of SMK Mega Link Majene. The sample was taken by purposive sampling technique. The data obtained used the research instrument based on the form of students achievements were collected by using test of student’s achievement and interview guidance. The technique of collecting data researcher had observation to ascertain the model that used by teacher was teaching model of developing metacognitive. The technique of data analysis in this research was reduction data, presentation and conclusion. Based on the whole findings in this study it was shown that student’s metacognitive ability generally not develops optimally. It was because of limited scope of the materials, and cognitive teaching strategy handled by verbal presentation and trained continuously in facing cognitive tasks, such as understanding and solving problem.
Mathematical modelling and numerical resolution of multi-phase compressible fluid flows problems
International Nuclear Information System (INIS)
Lagoutiere, Frederic
2000-01-01
This work deals with Eulerian compressible multi-species fluid dynamics, the species being either mixed or separated (with interfaces). The document is composed of three parts. The first parts devoted to the numerical resolution of model problems: advection equation, Burgers equation, and Euler equations, in dimensions one and two. The goal is to find a precise method, especially for discontinuous initial conditions, and we develop non dissipative algorithms. They are based on a downwind finite-volume discretization under some stability constraints. The second part treats of the mathematical modelling of fluids mixtures. We construct and analyse a set of multi-temperature and multi-pressure models that are entropy, symmetrizable, hyperbolic, not ever conservative. In the third part, we apply the ideas developed in the first part (downwind discretization) to the numerical resolution of the partial differential problems we have constructed for fluids mixtures in the second part. We present some numerical results in dimensions one and two. (author) [fr
The Mathematical Basis of the Inverse Scattering Problem for Cracks from Near-Field Data
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Yao Mao
2015-01-01
Full Text Available We consider the acoustic scattering problem from a crack which has Dirichlet boundary condition on one side and impedance boundary condition on the other side. The inverse scattering problem in this paper tries to determine the shape of the crack and the surface impedance coefficient from the near-field measurements of the scattered waves, while the source point is placed on a closed curve. We firstly establish a near-field operator and focus on the operator’s mathematical analysis. Secondly, we obtain a uniqueness theorem for the shape and surface impedance. Finally, by using the operator’s properties and modified linear sampling method, we reconstruct the shape and surface impedance.
Mathematical Model and Algorithm for the Reefer Mechanic Scheduling Problem at Seaports
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Jiantong Zhang
2017-01-01
Full Text Available With the development of seaborne logistics, the international trade of goods transported in refrigerated containers is growing fast. Refrigerated containers, also known as reefers, are used in transportation of temperature sensitive cargo, such as perishable fruits. This trend brings new challenges to terminal managers, that is, how to efficiently arrange mechanics to plug and unplug power for the reefers (i.e., tasks at yards. This work investigates the reefer mechanics scheduling problem at container ports. To minimize the sum of the total tardiness of all tasks and the total working distance of all mechanics, we formulate a mathematical model. For the resolution of this problem, we propose a DE algorithm which is combined with efficient heuristics, local search strategies, and parameter adaption scheme. The proposed algorithm is tested and validated through numerical experiments. Computational results demonstrate the effectiveness and efficiency of the proposed algorithm.
Mathematical and numerical study of nonlinear boundary problems related to plasma physics
International Nuclear Information System (INIS)
Sermange, M.
1982-06-01
After the study of some equations based on the Hodgkin-Huxley model, the work presented here is concerned with nonlinear boundary problems in MHD. They are gathered in two subjects: equilibrium equations and stability equations. The axisymmetric MHD equilibrium equations with free boundary have been studied by different authors, particularly the existence, regularity, unicity and non-unicity. Here, bifurcation, convergence of calculation methods existence of solutions in a discontinuous frame are studied. MHD stability can be determined by the principle of Bernstein et al; the mathematical work concerned here bears on the equivalence, in the case of two-dimensional or axisymmetric stability, between this model and a scalar eigenvalue problem which is introduced. At last, modules for computing MHD equilibrium for the simulation of plasma confinement in a tokamak are described [fr
Development of problem-based learning material for physics mathematics and its implementation
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Pujayanto Pujayanto
2017-02-01
Full Text Available The research aims to develop Problem Based Learning material teaching of Mathematics Physics and to know the effect on the cognitive capability of undergraduate students. The research uses development method of Borg and Gall. There are ten steps such as data collection, planning, product drafting, pretest, pretest revise 1, main test, main test revise 2, posttest, final revision, and dissemination and implementation. The data collection uses questionnaire and cognitive test which will support the qualitative data. The result shows that the criterion of developing problem-based learning teaching materials is 5 level category when 43.33% respondents rate 5 level category and the others give 4 level category. Furthermore, students which use the materials increased and the most of the students have acquired cognitive value exceeds the value of minimum completeness criteria.
Sukmawati, Zuhairoh, Faihatuz
2017-05-01
The purpose of this research was to develop authentic assessment model based on showcase portfolio on learning of mathematical problem solving. This research used research and development Method (R & D) which consists of four stages of development that: Phase I, conducting a preliminary study. Phase II, determining the purpose of developing and preparing the initial model. Phase III, trial test of instrument for the initial draft model and the initial product. The respondents of this research are the students of SMAN 8 and SMAN 20 Makassar. The collection of data was through observation, interviews, documentation, student questionnaire, and instrument tests mathematical solving abilities. The data were analyzed with descriptive and inferential statistics. The results of this research are authentic assessment model design based on showcase portfolio which involves: 1) Steps in implementing the authentic assessment based Showcase, assessment rubric of cognitive aspects, assessment rubric of affective aspects, and assessment rubric of skill aspect. 2) The average ability of the students' problem solving which is scored by using authentic assessment based on showcase portfolio was in high category and the students' response in good category.
High profile students’ growth of mathematical understanding in solving linier programing problems
Utomo; Kusmayadi, TA; Pramudya, I.
2018-04-01
Linear program has an important role in human’s life. This linear program is learned in senior high school and college levels. This material is applied in economy, transportation, military and others. Therefore, mastering linear program is useful for provision of life. This research describes a growth of mathematical understanding in solving linear programming problems based on the growth of understanding by the Piere-Kieren model. Thus, this research used qualitative approach. The subjects were students of grade XI in Salatiga city. The subjects of this study were two students who had high profiles. The researcher generally chose the subjects based on the growth of understanding from a test result in the classroom; the mark from the prerequisite material was ≥ 75. Both of the subjects were interviewed by the researcher to know the students’ growth of mathematical understanding in solving linear programming problems. The finding of this research showed that the subjects often folding back to the primitive knowing level to go forward to the next level. It happened because the subjects’ primitive understanding was not comprehensive.
Mathematical logic as a mean of solving the problems of power supply for buildings and constructions
Pryadko, Igor; Nozdrina, Ekaterina; Boltaevsky, Andrey
2017-10-01
The article analyzes the questions of application of mathematical logic in engineering design associated with machinery and construction. The aim of the work is to study the logical working-out of Russian electrical engineer V.I. Shestakov. These elaborations are considered in connection with the problem of analysis and synthesis of relay contact circuits of the degenerate (A) class which the scientist solved. The article proposes to use Shestakov’s elaborations for optimization of buildings and constructions of modern high-tech. In the second part of the article the events are actualized in association with the development of problems of application of mathematical logic in the analysis and synthesis of electric circuits, relay and bridging. The arguments in favor of the priority of the authorship of the elaborations of Russian electrical engineer V. I. Shestakov, K. Shannon - one of the founders of computer science, and Japanese engineer A. Nakashima are discussed. The issue of contradiction between V. I. Shestakov and representatives of the school of M. A. Gavrilov is touched on.
Understanding and quantifying cognitive complexity level in mathematical problem solving items
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SUSAN E. EMBRETSON
2008-09-01
Full Text Available The linear logistic test model (LLTM; Fischer, 1973 has been applied to a wide variety of new tests. When the LLTM application involves item complexity variables that are both theoretically interesting and empirically supported, several advantages can result. These advantages include elaborating construct validity at the item level, defining variables for test design, predicting parameters of new items, item banking by sources of complexity and providing a basis for item design and item generation. However, despite the many advantages of applying LLTM to test items, it has been applied less often to understand the sources of complexity for large-scale operational test items. Instead, previously calibrated item parameters are modeled using regression techniques because raw item response data often cannot be made available. In the current study, both LLTM and regression modeling are applied to mathematical problem solving items from a widely used test. The findings from the two methods are compared and contrasted for their implications for continued development of ability and achievement tests based on mathematical problem solving items.
Diagnosing and alleviating the impact of performance pressure on mathematical problem solving.
DeCaro, Marci S; Rotar, Kristin E; Kendra, Matthew S; Beilock, Sian L
2010-08-01
High-pressure academic testing situations can lead people to perform below their actual ability levels by co-opting working memory (WM) resources needed for the task at hand (Beilock, 2008). In the current work we examine how performance pressure impacts WM and design an intervention to alleviate pressure's negative impact. Specifically, we explore the hypothesis that high-pressure situations trigger distracting thoughts and worries that rely heavily on verbal WM. Individuals performed verbally based and spatially based mathematics problems in a low-pressure or high-pressure testing situation. Results demonstrated that performance on problems that rely heavily on verbal WM resources was less accurate under high-pressure than under low-pressure tests. Performance on spatially based problems that do not rely heavily on verbal WM was not affected by pressure. Moreover, the more people reported worrying during test performance, the worse they performed on the verbally based (but not spatially based) maths problems. Asking some individuals to focus on the problem steps by talking aloud helped to keep pressure-induced worries at bay and eliminated pressure's negative impact on performance.
Julie, Hongki; Sanjaya, Febi; Anggoro, Ant. Yudhi
2017-08-01
One of purposes of this study was to describe the solution profile of the junior high school students for the PISA adaptation test. The procedures conducted by researchers to achieve this objective were (1) adapting the PISA test, (2) validating the adapting PISA test, (3) asking junior high school students to do the adapting PISA test, and (4) making the students' solution profile. The PISA problems for mathematics could be classified into four areas, namely quantity, space and shape, change and relationship, and uncertainty. The research results that would be presented in this paper were the result test for uncertainty problems. In the adapting PISA test, there were fifteen questions. Subjects in this study were 18 students from 11 junior high schools in Yogyakarta, Central Java, and Banten. The type of research that used by the researchers was a qualitative research. For the first uncertainty problem in the adapting test, 66.67% of students reached level 3. For the second uncertainty problem in the adapting test, 44.44% of students achieved level 4, and 33.33% of students reached level 3. For the third uncertainty problem in the adapting test n, 38.89% of students achieved level 5, 11.11% of students reached level 4, and 5.56% of students achieved level 3. For the part a of the fourth uncertainty problem in the adapting test, 72.22% of students reached level 4 and for the part b of the fourth uncertainty problem in the adapting test, 83.33% students achieved level 4.
The Different Patterns of Gesture between Genders in Mathematical Problem Solving of Geometry
Harisman, Y.; Noto, M. S.; Bakar, M. T.; Amam, A.
2017-02-01
This article discusses about students’ gesture between genders in answering problems of geometry. Gesture aims to check students’ understanding which is undefined from their writings. This study is a qualitative research, there were seven questions given to two students of eight grade Junior High School who had the equal ability. The data of this study were collected from mathematical problem solving test, videoing students’ presentation, and interviewing students by asking questions to check their understandings in geometry problems, in this case the researchers would observe the students’ gesture. The result of this study revealed that there were patterns of gesture through students’ conversation and prosodic cues, such as tones, intonation, speech rate and pause. Female students tended to give indecisive gestures, for instance bowing, hesitating, embarrassing, nodding many times in shifting cognitive comprehension, forwarding their body and asking questions to the interviewer when they found tough questions. However, male students acted some gestures such as playing their fingers, focusing on questions, taking longer time to answer hard questions, staying calm in shifting cognitive comprehension. We suggest to observe more sample and focus on students’ gesture consistency in showing their understanding to solve the given problems.
Stochastic time-dependent vehicle routing problem: Mathematical models and ant colony algorithm
Directory of Open Access Journals (Sweden)
Zhengyu Duan
2015-11-01
Full Text Available This article addresses the stochastic time-dependent vehicle routing problem. Two mathematical models named robust optimal schedule time model and minimum expected schedule time model are proposed for stochastic time-dependent vehicle routing problem, which can guarantee delivery within the time windows of customers. The robust optimal schedule time model only requires the variation range of link travel time, which can be conveniently derived from historical traffic data. In addition, the robust optimal schedule time model based on robust optimization method can be converted into a time-dependent vehicle routing problem. Moreover, an ant colony optimization algorithm is designed to solve stochastic time-dependent vehicle routing problem. As the improvements in initial solution and transition probability, ant colony optimization algorithm has a good performance in convergence. Through computational instances and Monte Carlo simulation tests, robust optimal schedule time model is proved to be better than minimum expected schedule time model in computational efficiency and coping with the travel time fluctuations. Therefore, robust optimal schedule time model is applicable in real road network.
Walkington, Candace; Clinton, Virginia; Ritter, Steven N.; Nathan, Mitchell J.
2015-01-01
Solving mathematics story problems requires text comprehension skills. However, previous studies have found few connections between traditional measures of text readability and performance on story problems. We hypothesized that recently developed measures of readability and topic incidence measured by text-mining tools may illuminate associations…