Effects of the SOLVE Strategy on the Mathematical Problem Solving Skills of Secondary Students with Learning Disabilities

Science.gov (United States)

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…

Word Problem Solving of Students with Autistic Spectrum Disorders and Students with Typical Development

Science.gov (United States)

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…

The Association between Mathematical Word Problems and Reading Comprehension

Science.gov (United States)

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…

Word Problem Solving in Contemporary Math Education: A Plea for Reading Comprehension Skills Training

Science.gov (United States)

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

Word problem solving in contemporary math education: A plea for reading comprehension skills training

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.

Word Problem Solving in Contemporary Math Education: A Plea for Reading Comprehension Skills Training.

Science.gov (United States)

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.

The semantic system is involved in mathematical problem solving.

Science.gov (United States)

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.

Block Model Approach in Problem Solving: Effects on Problem Solving Performance of the Grade V Pupils in Mathematics

Science.gov (United States)

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…

The relation between early constructive play and mathematical word problem solving is mediated by spatial ability. A path analysis in sixth grade students.

NARCIS (Netherlands)

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

Language and mathematical problem solving among bilinguals.

Science.gov (United States)

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.

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.

Language and modeling word problems in mathematics among bilinguals.

Science.gov (United States)

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.

Syntactic Awareness and Arithmetic Word Problem Solving in Children with and without Learning Disabilities

Science.gov (United States)

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…

The Role of Cognitive Processes, Foundational Math Skill, and Calculation Accuracy and Fluency in Word-Problem Solving versus Pre-Algebraic Knowledge

Science.gov (United States)

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

How Can One Learn Mathematical Word Problems in a Second Language? A Cognitive Load Perspective

Science.gov (United States)

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…

The effects of using diagramming as a representational technique on high school students' achievement in solving math word problems

Science.gov (United States)

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 Model Method: Singapore Children's Tool for Representing and Solving Algebraic Word Problems

Science.gov (United States)

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…

Improvement of Word Problem Solving and Basic Mathematics Competencies in Students with Attention Deficit/Hyperactivity Disorder and Mathematical Learning Difficulties

Science.gov (United States)

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…

The Effect of Contextual and Conceptual Rewording on Mathematical Problem-Solving Performance

Science.gov (United States)

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…

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.

Secondary Teachers’ Mathematics-related Beliefs and Knowledge about Mathematical Problem-solving

Science.gov (United States)

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.

Solving applied mathematical problems with Matlab

CERN Document Server

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.

Three-M in Word Problem Solving

Science.gov (United States)

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 Effect of Dynamic and Interactive Mathematics Learning Environments (DIMLE), Supporting Multiple Representations, on Perceptions of Elementary Mathematics Pre-Service Teachers in Problem Solving Process

Science.gov (United States)

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…

Affect and mathematical problem solving a new perspective

CERN Document Server

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...

Metacognition Process of Students with High Mathematics Anxiety in Mathematics Problem-Solving

OpenAIRE

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 ...

How to solve mathematical problems

CERN Document Server

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.

Evaluation of the Effectiveness of a Tablet Computer Application (App) in Helping Students with Visual Impairments Solve Mathematics Problems

Science.gov (United States)

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…

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

Contribution of Equal-Sign Instruction beyond Word-Problem Tutoring for Third-Grade Students with Mathematics Difficulty.

Science.gov (United States)

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.

Mathematical Profiles and Problem Solving Abilities of Mathematically Promising Students

Science.gov (United States)

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…

Solving Mathematical Problems A Personal Perspective

CERN Document Server

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.

A Cognitive Analysis of Students’ Mathematical Problem Solving Ability on Geometry

Science.gov (United States)

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.

The Role of Expository Writing in Mathematical Problem Solving

Science.gov (United States)

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…

Cognitive Skills Used to Solve Mathematical Word Problems and Numerical Operations: A Study of 6- to 7-Year-Old Children

Science.gov (United States)

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…

Improving mathematical problem solving skills through visual media

Science.gov (United States)

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.

Processes involved in solving mathematical problems

Science.gov (United States)

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.

Mathematical Thinking and Creativity through Mathematical Problem Posing and Solving

Science.gov (United States)

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),…

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.

Pre-service mathematics teachers’ ability in solving well-structured problem

Science.gov (United States)

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.

It's Not a Math Lesson--We're Learning to Draw! Teachers' Use of Visual Representations in Instructing Word Problem Solving in Sixth Grade of Elementary School

Science.gov (United States)

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…

Developing Instructional Mathematical Physics Book Based on Inquiry Approach to Improve Students’ Mathematical Problem Solving Ability

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.

Effects of computer-based graphic organizers to solve one-step word problems for middle school students with mild intellectual disability: A preliminary study.

Science.gov (United States)

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.

Pre-Service Class Teacher' Ability in Solving Mathematical Problems and Skills in Solving Daily Problems

Science.gov (United States)

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…

Mathematical Problem Solving Ability of Junior High School Students through Ang’s Framework for Mathematical Modelling Instruction

Science.gov (United States)

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.

Problem solving through recreational mathematics

CERN Document Server

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

Chinese Number Words, Culture, and Mathematics Learning

Science.gov (United States)

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…

Text Comprehension and Oral Language as Predictors of Word-Problem Solving: Insights into Word-Problem Solving as a Form of Text Comprehension.

Science.gov (United States)

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.

Improving mathematical problem solving : A computerized approach

NARCIS (Netherlands)

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

A Review of the Effects of Visual-Spatial Representations and Heuristics on Word Problem Solving in Middle School Mathematics

Science.gov (United States)

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…

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.

Leveling of Critical Thinking Abilities of Students of Mathematics Education in Mathematical Problem Solving

Science.gov (United States)

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…

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 ...

Text Comprehension and Oral Language as Predictors of Word-Problem Solving: Insights into Word-Problem Solving as a Form of Text Comprehension

Science.gov (United States)

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

Effectiveness of discovery learning model on mathematical problem solving

Science.gov (United States)

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.

An Investigation of Secondary Teachers’ Understanding and Belief on Mathematical Problem Solving

Science.gov (United States)

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.

Student’s scheme in solving mathematics problems

Science.gov (United States)

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.

Scientific Approach to Improve Mathematical Problem Solving Skills Students of Grade V

Science.gov (United States)

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.

The role of problem solving method on the improvement of mathematical learning

Directory of Open Access Journals (Sweden)

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.

Is Word-Problem Solving a Form of Text Comprehension?

Science.gov (United States)

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…

Using the Wonder of Inequalities between Averages for Mathematics Problems Solving

Science.gov (United States)

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…

Teaching Elementary Mathematics through Problem Solving and Its Relationship to Mathematics Achievement

Science.gov (United States)

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…

Teaching Problem Solving to Students Receiving Tiered Interventions Using the Concrete-Representational-Abstract Sequence and Schema-Based Instruction

Science.gov (United States)

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)…

How to solve applied mathematics problems

CERN Document Server

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.

Cognitive Strategy Instruction for Teaching Word Problems to Primary-Level Struggling Students

Science.gov (United States)

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…

Analytical derivation: An epistemic game for solving mathematically based physics problems

Science.gov (United States)

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.

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.

Recent Trends in Japanese Mathematics Textbooks for Elementary Grades: Supporting Teachers to Teach Mathematics through Problem Solving

Science.gov (United States)

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…

Students’ Mathematical Problem-Solving Abilities Through The Application of Learning Models Problem Based Learning

Science.gov (United States)

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.

Exploring mathematics problem-solving and proof

CERN Document Server

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...

Investigating a Proposed Problem Solving Theory in the Context of Mathematical Problem Solving: A Multi-Case Study

Science.gov (United States)

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…

Calculus Problem Solving Behavior of Mathematic Education Students

Science.gov (United States)

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

To what extent do student teachers develop their mathematical problem solving ability by self-study?

OpenAIRE

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...

Effects of a Mathematics Fluency Program on Mathematics Performance of Students with Challenging Behaviors

Science.gov (United States)

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…

Minimalism as a Guiding Principle: Linking Mathematical Learning to Everyday Knowledge

Science.gov (United States)

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…

Applying Lakatos' Theory to the Theory of Mathematical Problem Solving.

Science.gov (United States)

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)

The Impact of Metacognitive Strategies and Self-Regulating Processes of Solving Math Word Problems

Science.gov (United States)

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.…

Young Filipino Students Making Sense of Arithmetic Word Problems in English

Science.gov (United States)

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…

Protocol Analysis of Group Problem Solving in Mathematics: A Cognitive-Metacognitive Framework for Assessment.

Science.gov (United States)

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…

Is There a Causal Relation between Mathematical Creativity and Mathematical Problem-Solving Performance?

Science.gov (United States)

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…

Methods of solving nonstandard problems

CERN Document Server

Grigorieva, Ellina

2015-01-01

This book, written by an accomplished female mathematician, is the second to explore nonstandard mathematical problems – those that are not directly solved by standard mathematical methods but instead rely on insight and the synthesis of a variety of mathematical ideas.   It promotes mental activity as well as greater mathematical skills, and is an ideal resource for successful preparation for the mathematics Olympiad. Numerous strategies and techniques are presented that can be used to solve intriguing and challenging problems of the type often found in competitions.  The author uses a friendly, non-intimidating approach to emphasize connections between different fields of mathematics and often proposes several different ways to attack the same problem.  Topics covered include functions and their properties, polynomials, trigonometric and transcendental equations and inequalities, optimization, differential equations, nonlinear systems, and word problems.   Over 360 problems are included with hints, ...

Comparison of mathematical problem solving strategies of primary school pupils

OpenAIRE

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...

The effect of Missouri mathematics project learning model on students’ mathematical problem solving ability

Science.gov (United States)

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.

Is Word-Problem Solving a Form of Text Comprehension?

Science.gov (United States)

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

Students Use Graphic Organizers to Improve Mathematical Problem-Solving Communications

Science.gov (United States)

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…

Model Drawing Strategy for Fraction Word Problem Solving of Fourth-Grade Students with Learning Disabilities

Science.gov (United States)

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…

Empowering Educationally Disadvantaged Mathematics Students through a Strategies-Based Problem Solving Approach

Science.gov (United States)

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…

The Place of Problem Solving in Contemporary Mathematics Curriculum Documents

Science.gov (United States)

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…

Mathematics Literacy of Secondary Students in Solving Simultanenous Linear Equations

Science.gov (United States)

Sitompul, R. S. I.; Budayasa, I. K.; Masriyah

2018-01-01

This study examines the profile of secondary students’ mathematical literacy in solving simultanenous linear equations problems in terms of cognitive style of visualizer and verbalizer. This research is a descriptive research with qualitative approach. The subjects in this research consist of one student with cognitive style of visualizer and one student with cognitive style of verbalizer. The main instrument in this research is the researcher herself and supporting instruments are cognitive style tests, mathematics skills tests, problem-solving tests and interview guidelines. Research was begun by determining the cognitive style test and mathematics skill test. The subjects chosen were given problem-solving test about simultaneous linear equations and continued with interview. To ensure the validity of the data, the researcher conducted data triangulation; the steps of data reduction, data presentation, data interpretation, and conclusion drawing. The results show that there is a similarity of visualizer and verbalizer-cognitive style in identifying and understanding the mathematical structure in the process of formulating. There are differences in how to represent problems in the process of implementing, there are differences in designing strategies and in the process of interpreting, and there are differences in explaining the logical reasons.

Robotic Toys as a Catalyst for Mathematical Problem Solving

Science.gov (United States)

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…

The impact of metacognitive strategies and self-regulating processes of solving math word problems

OpenAIRE

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 ...

Students’ Algebraic Reasonsing In Solving Mathematical Problems With Adversity Quotient

Science.gov (United States)

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.

On the Relationships between (Relatively) Advanced Mathematical Knowledge and (Relatively) Advanced Problem-Solving Behaviours

Science.gov (United States)

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…

The Influence of Cognitive Abilities on Mathematical Problem Solving Performance

Science.gov (United States)

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…

Glogs as Non-Routine Problem Solving Tools in Mathematics

Science.gov (United States)

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.…

Pre-Service Mathematics Teachers’ Problem Solving Processes with Geometer’s Sketchpad: Mirror Problem

OpenAIRE

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...

Developing a pedagogical problem solving view for mathematics teachers with two reflection programs

Directory of Open Access Journals (Sweden)

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.

African Journal of Educational Studies in Mathematics and Sciences ...

African Journals Online (AJOL)

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 ...

The enhancement of students' mathematical problem solving ability through teaching with metacognitive scaffolding approach

Science.gov (United States)

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.

Effect of Personalisation of Instruction on Students’ Motivation to learn Mathematics Word Problems in Nigeria

OpenAIRE

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...

Investigating and Developing Engineering Students' Mathematical Modelling and Problem-Solving Skills

Science.gov (United States)

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…

Using realistic mathematics education and the DAPIC problem-solving process to enhance secondary school students' mathematical literacy

Directory of Open Access Journals (Sweden)

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.

Improving of Junior High School Visual Thinking Representation Ability in Mathematical Problem Solving by CTL

Directory of Open Access Journals (Sweden)

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

Are Middle School Mathematics Teachers Able to Solve Word Problems without Using Variable?

Science.gov (United States)

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…

Assessing the Internal Dynamics of Mathematical Problem Solving in Small Groups.

Science.gov (United States)

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…

Profile of male-field dependent (FD) prospective teacher's reflective thinking in solving contextual mathematical problem

Science.gov (United States)

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.

Mathematical Abstraction in the Solving of Ill-Structured Problems by Elementary School Students in Korea

Science.gov (United States)

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…

Working Memory Components and Problem-Solving Accuracy: Are There Multiple Pathways?

Science.gov (United States)

Swanson, H. Lee; Fung, Wenson

2016-01-01

This study determined the working memory (WM) components (executive, phonological short-term memory [STM], and visual-spatial sketchpad) that best predicted mathematical word problem-solving accuracy in elementary schoolchildren (N = 392). The battery of tests administered to assess mediators between WM and problem-solving included measures of…

INVESTIGATING AND COMMUNICATING TECHNOLOGY MATHEMATICS PROBLEM SOLVING EXPERIENCE OF TWO PRESERVICE TEACHERS

Directory of Open Access Journals (Sweden)

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.

Problem solving as a challenge for mathematics education in The Netherlands

NARCIS (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

The Investigation of Elementary Mathematics Teacher Candidates' Problem Solving Skills According to Various Variables

Science.gov (United States)

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…

Why Do Disadvantaged Filipino Children Find Word Problems in English Difficult?

Science.gov (United States)

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…

MONTO: A Machine-Readable Ontology for Teaching Word Problems in Mathematics

Science.gov (United States)

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…

Flexibility in Mathematics Problem Solving Based on Adversity Quotient

Science.gov (United States)

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.

Using Video Prompting to Teach Mathematical Problem Solving of Real-World Video-Simulation Problems

Science.gov (United States)

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-Solving: Scaling the "Brick Wall"

Science.gov (United States)

Benson, Dave

2011-01-01

Across the primary and secondary phases, pupils are encouraged to use and apply their knowledge, skills, and understanding of mathematics to solve problems in a variety of forms, ranging from single-stage word problems to the challenge of extended rich tasks. Amongst many others, Cockcroft (1982) emphasised the importance and relevance of…

Promoting students’ mathematical problem-solving skills through 7e learning cycle and hypnoteaching model

Science.gov (United States)

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).

Incorporating the Common Core's Problem Solving Standard for Mathematical Practice into an Early Elementary Inclusive Classroom

Science.gov (United States)

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…

An Evaluation of Grades 9 and 10 Mathematics Textbooks Vis-À-Vis ...

African Journals Online (AJOL)

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 ...

Development of syntax of intuition-based learning model in solving mathematics problems

Science.gov (United States)

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

Towards efficient measurement of metacognition in mathematical problem solving

NARCIS (Netherlands)

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.

Enhancing Arithmetic and Word-Problem Solving Skills Efficiently by Individualized Computer-Assisted Practice

Science.gov (United States)

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…

Visual Representations in Mathematics Teaching: An Experiment with Students

Science.gov (United States)

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…

Factors Influencing Filipino Children's Solutions to Addition and Subtraction Word Problems

Science.gov (United States)

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…

Strategy Instruction in Mathematics.

Science.gov (United States)

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…

Reflective thinking in solving an algebra problem: a case study of field independent-prospective teacher

Science.gov (United States)

Agustan, S.; Juniati, Dwi; Yuli Eko Siswono, Tatag

2017-10-01

Nowadays, reflective thinking is one of the important things which become a concern in learning mathematics, especially in solving a mathematical problem. The purpose of this paper is to describe how the student used reflective thinking when solved an algebra problem. The subject of this research is one female student who has field independent cognitive style. This research is a descriptive exploratory study with data analysis using qualitative approach to describe in depth reflective thinking of prospective teacher in solving an algebra problem. Four main categories are used to analyse the reflective thinking in solving an algebra problem: (1) formulation and synthesis of experience, (2) orderliness of experience, (3) evaluating the experience and (4) testing the selected solution based on the experience. The results showed that the subject described the problem by using another word and the subject also found the difficulties in making mathematical modelling. The subject analysed two concepts used in solving problem. For instance, geometry related to point and line while algebra is related to algebra arithmetic operation. The subject stated that solution must have four aspect to get effective solution, specifically the ability to (a) understand the meaning of every words; (b) make mathematical modelling; (c) calculate mathematically; (d) interpret solution obtained logically. To test the internal consistency or error in solution, the subject checked and looked back related procedures and operations used. Moreover, the subject tried to resolve the problem in a different way to compare the answers which had been obtained before. The findings supported the assertion that reflective thinking provides an opportunity for the students in improving their weakness in mathematical problem solving. It can make a grow accuracy and concentration in solving a mathematical problem. Consequently, the students will get the right and logic answer by reflective thinking.

Obstacles Related to Structuring for Mathematization Encountered by Students when Solving Physics Problems

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...

Working memory components that predict word problem solving: Is it merely a function of reading, calculation, and fluid intelligence?

Science.gov (United States)

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.

Refractive Thinking Profile In Solving Mathematical Problem Reviewed from Students Math Capability

Science.gov (United States)

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.

The impact of metacognitive strategies and self-regulating processes of solving math word problems

Directory of Open Access Journals (Sweden)

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.

To what extent do student teachers develop their mathematical problem solving ability by self-study?

NARCIS (Netherlands)

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

Algebraic Reasoning in Solving Mathematical Problem Based on Learning Style

Science.gov (United States)

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.

Students’ Self-Monitoring on Mathematics Ability: Cube and Cuboid Problem Solving

Science.gov (United States)

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.

Assessing the Relation between Seventh-Grade Students' Engagement and Mathematical Problem Solving Performance

Science.gov (United States)

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…

Elementary Students' Spontaneous Metacognitive Functions in Different Types of Mathematical Problems

Science.gov (United States)

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…

Improving of Junior High School Visual Thinking Representation Ability in Mathematical Problem Solving by CTL

Science.gov (United States)

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…

Analysis of mathematical problem-solving ability based on metacognition on problem-based learning

Science.gov (United States)

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.

A broad look at the literature on math word problem-solving interventions for third graders

Directory of Open Access Journals (Sweden)

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.

Problem-solving rubrics revisited: Attending to the blending of informal conceptual and formal mathematical reasoning

Science.gov (United States)

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.

Write Is Right: Using Graphic Organizers to Improve Student Mathematical Problem Solving

Science.gov (United States)

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"…

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.

Cognitive Activities in Solving Mathematical Tasks: The Role of a Cognitive Obstacle

Science.gov (United States)

Antonijevic, Radovan

2016-01-01

In the process of learning mathematics, students practice various forms of thinking activities aimed to substantially contribute to the development of their different cognitive structures. In this paper, the subject matter is a "cognitive obstacle", a phenomenon that occurs in the procedures of solving mathematical tasks. Each task in…

The Interference of Stereotype Threat with Women's Generation of Mathematical Problem-Solving Strategies.

Science.gov (United States)

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…

Strategies That Help Learning-Disabled Students Solve Verbal Mathematical Problems.

Science.gov (United States)

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)

Examination Of Gifted Students’ Probability Problem Solving Process In Terms Of Mathematical Thinking

Directory of Open Access Journals (Sweden)

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.

Investigating Mathematics Teachers Candidates' Knowledge about Problem Solving Strategies through Problem Posing

Science.gov (United States)

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…

Problem solving of student with visual impairment related to mathematical literacy problem

Science.gov (United States)

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.

Secondary School Pre-Service Mathematics Teachers' Content Knowledge of Algebraic Word Problem in Nigeria

Science.gov (United States)

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…

Critical Thinking and Problem Solving Skills in Mathematics of Grade-7 Public Secondary Students

Directory of Open Access Journals (Sweden)

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.

Exploring a Structure for Mathematics Lessons That Foster Problem Solving and Reasoning

Science.gov (United States)

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…

The Efficacy of Using Diagrams When Solving Probability Word Problems in College

Science.gov (United States)

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…

Improving mathematical problem solving ability through problem-based learning and authentic assessment for the students of Bali State Polytechnic

Science.gov (United States)

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.

How to make university students solve physics problems requiring mathematical skills: The "Adventurous Problem Solving" approach

NARCIS (Netherlands)

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

Enhancing Learners' Problem Solving Performance in Mathematics: A Cognitive Load Perspective

Science.gov (United States)

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…

Language, arithmetic word problems, and deaf students: Linguistic strategies used to solve tasks

Science.gov (United States)

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.

Interference thinking in constructing students’ knowledge to solve mathematical problems

Science.gov (United States)

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.

Mathematical enculturation from the students' perspective: shifts in problem-solving beliefs and behaviour during the bachelor programme

NARCIS (Netherlands)

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

Effectiveness of an Online Social Constructivist Mathematical Problem Solving Course for Malaysian Pre-Service Teachers

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

The development of a professional development intervention for mathematical problem-solving pedagogy in a localised context

Directory of Open Access Journals (Sweden)

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.

Students’ mathematical representations on secondary school in solving trigonometric problems

Science.gov (United States)

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.

Metacognition, Motivation, and Emotions: Contribution of Self-Regulated Learning to Solving Mathematical Problems

Science.gov (United States)

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…

Investigating Pre-service Mathematics Teachers’ Geometric Problem Solving Process in Dynamic Geometry Environment

Directory of Open Access Journals (Sweden)

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

The universe in zero words the story of mathematics as told through equations

CERN Document Server

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

The implementation of multiple intelligences based teaching model to improve mathematical problem solving ability for student of junior high school

Science.gov (United States)

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.

Mathematics Teaching as Problem Solving: A Framework for Studying Teacher Metacognition Underlying Instructional Practice in Mathematics.

Science.gov (United States)

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…

Schema-Based Instruction with Concrete and Virtual Manipulatives to Teach Problem Solving to Students with Autism

Science.gov (United States)

Root, Jenny R.; Browder, Diane M.; Saunders, Alicia F.; Lo, Ya-yu

2017-01-01

The current study evaluated the effects of modified schema-based instruction on the mathematical word problem solving skills of three elementary students with autism spectrum disorders and moderate intellectual disability. Participants learned to solve compare problem type with themes that related to their interests and daily experiences. In…

Modeling Students' Problem Solving Performance in the Computer-Based Mathematics Learning Environment

Science.gov (United States)

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…

Cognitive Backgrounds of Problem Solving: A Comparison of Open-Ended vs. Closed Mathematics Problems

Science.gov (United States)

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…

The relationship between mathematical problem-solving skills and self-regulated learning through homework behaviours, motivation, and metacognition

Science.gov (United States)

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%).

Mathematical Enculturation from the Students' Perspective: Shifts in Problem-Solving Beliefs and Behaviour during the Bachelor Programme

Science.gov (United States)

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…

Clinical and Cognitive Characteristics Associated with Mathematics Problem Solving in Adolescents with Autism Spectrum Disorder.

Science.gov (United States)

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.

Review of Street-Fighting Mathematics: The Art of Educated Guessing and Opportunistic Problem Solving by Sanjoy Mahajan

OpenAIRE

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 ...

Problem Solving Abilities and Perceptions in Alternative Certification Mathematics Teachers

Science.gov (United States)

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…

Mathematics Instructional Model Based on Realistic Mathematics Education to Promote Problem Solving Ability at Junior High School Padang

OpenAIRE

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...

The effects of presenting multidigit mathematics problems in a realistic context on sixth graders' problem solving

NARCIS (Netherlands)

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.

Improving the basic skills of teaching mathematics through learning with search-solve-create-share strategy

Science.gov (United States)

Rahayu, D. V.; Kusumah, Y. S.; Darhim

2018-05-01

This study examined to see the improvement of prospective teachers’ basic skills of teaching mathematics through search-solve-create-share learning strategy based on overall and Mathematical Prior Knowledge (MPK) and interaction of both. Quasi experiments with the design of this experimental-non-equivalent control group design involved 67 students at the mathematics program of STKIP Garut. The instrument used in this study included pre-test and post-test. The result of this study showed that: (1) The improvement and achievement of the basic skills of teaching mathematics of the prospective teachers who get the learning of search-solve-create-share strategy is better than the improvement and achievement of the prospective teachers who get the conventional learning as a whole and based on MPK; (2) There is no interaction between the learning used and MPK on improving and achieving basic skills of teaching mathematics.

A synthesis of mathematical and cognitive performances of students with mathematics learning disabilities.

Science.gov (United States)

Shin, Mikyung; Bryant, Diane Pedrotty

2015-01-01

The purpose of this study was to synthesize the findings from 23 articles that compared the mathematical and cognitive performances of students with mathematics learning disabilities (LD) to (a) students with LD in mathematics and reading, (b) age- or grade-matched students with no LD, and (c) mathematical-ability-matched younger students with no LD. Overall results revealed that students with mathematics LD exhibited higher word problem-solving abilities and no significant group differences on working memory, long-term memory, and metacognition measures compared to students with LD in mathematics and reading. Findings also revealed students with mathematics LD demonstrated significantly lower performance compared to age- or grade-matched students with no LD on both mathematical and cognitive measures. Comparison between students with mathematics LD and younger students with no LD revealed mixed outcomes on mathematical measures and generally no significant group differences on cognitive measures. © Hammill Institute on Disabilities 2013.

GeoGebra Assist Discovery Learning Model for Problem Solving Ability and Attitude toward Mathematics

Science.gov (United States)

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.

Effects of "Handep" Cooperative Learning Based on Indigenous Knowledge on Mathematical Problem Solving Skill

Science.gov (United States)

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…

Math Teachers' Attitudes towards Photo Math Application in Solving Mathematical Problem Using Mobile Camera

Science.gov (United States)

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…

Elementary school students’ mathematical intelligence based on mathematics learning using classical music of the baroque era as the backsound

Directory of Open Access Journals (Sweden)

Karlimah

2018-01-01

Full Text Available Many studies suggest that classical music can inccrease the listeners’ intelligence, including mathematical intelligence [3, 12, 2, 11]. In this research, we used the classical music of Baroque era as the backsound during math learning. The research method used was quasi experiment with nonequivalent pretest-posttest control group design to grade V SD students in Tasikmalaya city. The results show that the use of classical music of Baroque era during the learning of mathematics gave a high contribution to the mathematical intelligence of fifth grade elementary school students. The student's mathematical intelligence can be seen in the cognitive abilities which were at the high level in the knowledge up to analysis, and at the low level in the synthesis and evaluation. Low mathematical intelligence was shown by students in calculating amount and difference of time, and projecting word problem into the form of mathematical problems. High mathematical intelligence arose in reading and writing integers in words and numbers. Thus, the mathematical intelligence of fifth grade Elementary School students will be better if classical music of Baroque era is used as the backsound in mathematics learning about solving math problems.

Mathematical expeditions chronicles by the explorers

CERN Document Server

Laubenbacher, Reinhard

1999-01-01

This book contains the stories of five mathematical journeys into new realms, told through the writings of the explorers themselves. Some were guided by mere curiosity and the thrill of adventure, while others had more practical motives. In each case the outcome was a vast expansion of the known mathematical world and the realization that still greater vistas remained to be explored. The authors tell these stories by guiding the reader through the very words of the mathematicians at the heart of these events, and thereby provide insight into the art of approaching mathematical problems. The book can be used in a variety of ways. The five chapters are completely independent, each with varying levels of mathematical sophistication. The book will be enticing to students, to instructors, and to the intellectually curious reader. By working through some of the original sources and supplemental exercises, which discuss and solve - or attempt to solve - a great problem, this book helps the reader discover the roots ...

Mathematics Instructional Model Based on Realistic Mathematics Education to Promote Problem Solving Ability at Junior High School Padang

Directory of Open Access Journals (Sweden)

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.

Academic Motivation Maintenance for Students While Solving Mathematical Problems in the Middle School

OpenAIRE

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.

The Prevalent Rate of Problem-Solving Approach in Teaching Mathematics in Ghanaian Basic Schools

Science.gov (United States)

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…

Creativity in Unique Problem-Solving in Mathematics and Its Influence on Motivation for Learning

Science.gov (United States)

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…

Investigating and developing engineering students' mathematical modelling and problem-solving skills

Science.gov (United States)

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.

Errors of Students Learning With React Strategy in Solving the Problems of Mathematical Representation Ability

Directory of Open Access Journals (Sweden)

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.

Working Memory, Attention, and Mathematical Problem Solving: A Longitudinal Study of Elementary School Children

Science.gov (United States)

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…

Learning to Solve Addition and Subtraction Word Problems in English as an Imported Language

Science.gov (United States)

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…

Exploring the Learning of Mathematics Word Problems by African Immigrant Early Learners

Science.gov (United States)

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…

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

Mathematics for the liberal arts

CERN Document Server

Brown, Jason I

2014-01-01

The Math in Your Life Health, Safety, and Mathematics Found in Translation The Essentials of Conversion Making Sense of Your World with Statistics Summarizing Data with a Few Good Numbers Estimating Unknowns Leading You Down the Garden Path with Statistics Visualizing with Mathematics Seeing Data A Graph Is Worth a Thousand Words Money and Risk Money - Now or Later Risk Taking and Probability The Life in Your Math! Deciding to Make the Best Decisions Making the Right Choices for You Game Theory - Coming Out on Top Making Joint Decisions Art Imitating Math The Math that Makes the Art Believing What You See (or Not) The Mathematics of Sound (and the Sound of Mathematics) The Mathematics of Listening The Mathematics of Composing Solving Musical Mysteries with MSI (Math Scene Investigations) Late Night Mathematics - Humor and Philosophy Laughing with Mathematics The Limits of Mathematics Bibliography Index Review questions appear at the end of each chapter.

The Transitory Phase to the Attainment of Self-Regulatory Skill in Mathematical Problem Solving

Science.gov (United States)

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…

Gender differences in algebraic thinking ability to solve mathematics problems

Science.gov (United States)

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.

A Further Study of Productive Failure in Mathematical Problem Solving: Unpacking the Design Components

Science.gov (United States)

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)…

A Metacognitive Profile of Vocational High School Student’s Field Independent in Mathematical Problem Solving

Science.gov (United States)

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.

Reflective Learning and Prospective Teachers' Conceptual Understanding, Critical Thinking, Problem Solving, and Mathematical Communication Skills

Science.gov (United States)

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…

Does chess instruction improve mathematical problem-solving ability? Two experimental studies with an active control group.

Science.gov (United States)

Sala, Giovanni; Gobet, Fernand

2017-12-01

It has been proposed that playing chess enables children to improve their ability in mathematics. These claims have been recently evaluated in a meta-analysis (Sala & Gobet, 2016, Educational Research Review, 18, 46-57), which indicated a significant effect in favor of the groups playing chess. However, the meta-analysis also showed that most of the reviewed studies used a poor experimental design (in particular, they lacked an active control group). We ran two experiments that used a three-group design including both an active and a passive control group, with a focus on mathematical ability. In the first experiment (N = 233), a group of third and fourth graders was taught chess for 25 hours and tested on mathematical problem-solving tasks. Participants also filled in a questionnaire assessing their meta-cognitive ability for mathematics problems. The group playing chess was compared to an active control group (playing checkers) and a passive control group. The three groups showed no statistically significant difference in mathematical problem-solving or metacognitive abilities in the posttest. The second experiment (N = 52) broadly used the same design, but the Oriental game of Go replaced checkers in the active control group. While the chess-treated group and the passive control group slightly outperformed the active control group with mathematical problem solving, the differences were not statistically significant. No differences were found with respect to metacognitive ability. These results suggest that the effects (if any) of chess instruction, when rigorously tested, are modest and that such interventions should not replace the traditional curriculum in mathematics.

Metacognitive experience of mathematics education students in open start problem solving based on intrapersonal intelligence

Science.gov (United States)

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.

Engineering Students' Self-Efficacy Judgment to Solve Mathematical Problems in the Classroom or Online

Science.gov (United States)

Villarreal-Treviño, Maria Guadalupe; Villarreal-Lozano, Ricardo Jesus; Morales-Martinez, Guadalupe Elizabeth; Lopez-Ramirez, Ernesto Octavio; Flores-Moreno, Norma Esthela

2017-01-01

This study explored in a sample of 560 high level education students their judgment formation to perceived self-efficacy to solve mathematical tasks. Students had to read 36 experimental vignettes describing educative scenarios to learn mathematics. Each scenario presented four manipulated pieces of information (learning modality, task difficulty,…

Teaching Mathematical Word Problem Solving: The Quality of Evidence for Strategy Instruction Priming the Problem Structure

Science.gov (United States)

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…

The Elementary School Students’ Mathematical Problem Solving Based on Reading Abilities

Science.gov (United States)

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.

Understanding and quantifying cognitive complexity level in mathematical problem solving items

Directory of Open Access Journals (Sweden)

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.

Turkish Primary School Students' Strategies in Solving a Non-Routine Mathematical Problem and Some Implications for the Curriculum Design and Implementation

Science.gov (United States)

Erdogan, Abdulkadir

2015-01-01

Turkish primary mathematics curriculum emphasizes the role of problem solving for teaching mathematics and pays particular attention to problem solving strategies. Patterns as a subject and the use of patterns as a non-routine problem solving strategy are also emphasized in the curriculum. The primary purpose of this study was to determine how…

Teaching Personal Finance Mathematical Problem Solving to Individuals with Moderate Intellectual Disability

Science.gov (United States)

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…

The profile of conceptual comprehension of pre-service teacher in the mathematical problem solving with low emotional intelligence

Science.gov (United States)

Prayitno, S. H.; Suwarsono, St.; Siswono, T. Y. E.

2018-03-01

Conceptual comprehension in this research is the ability to use the procedures that are owned by pre-service teachers to solve problems by finding the relation of the concept to another, or can be done by identifying the type of problem and associating it with a troubleshooting procedures, or connect the mathematical symbols with mathematical ideas and incorporate them into a series of logical reasoning, or by using prior knowledge that occurred directly, through its conceptual knowledge. The goal of this research is to describe the profile of conceptual comprehensin of pre-service teachers with low emotional intelligence in mathematical problems solving. Through observation and in-depth interview with the research subject the conclusion was that: pre-service teachers with low emotional intelligence pertained to the level of formal understanding in understanding the issues, relatively to the level of intuitive understanding in planning problem solving, to the level of relational understanding in implementing the relational problem solving plan, and pertained to the level of formal understanding in looking back to solve the problem.

Metacognition, Motivation and Emotions: Contribution of Self-Regulated Learning to Solving Mathematical Problems

Directory of Open Access Journals (Sweden)

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.

Understanding the Role of Linguistic Processes in the Solution of Arithmetic Word Problems.

Science.gov (United States)

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…

Assessing metacognition of grade 2 and grade 4 students using an adaptation of multi-method interview approach during mathematics problem-solving

Science.gov (United States)

Kuzle, A.

2018-06-01

The important role that metacognition plays as a predictor for student mathematical learning and for mathematical problem-solving, has been extensively documented. But only recently has attention turned to primary grades, and more research is needed at this level. The goals of this paper are threefold: (1) to present metacognitive framework during mathematics problem-solving, (2) to describe their multi-method interview approach developed to study student mathematical metacognition, and (3) to empirically evaluate the utility of their model and the adaptation of their approach in the context of grade 2 and grade 4 mathematics problem-solving. The results are discussed not only with regard to further development of the adapted multi-method interview approach, but also with regard to their theoretical and practical implications.

Enabling Metacognitive Skills for Mathematics Problem Solving: A Collective Case Study of Metacognitive Reflection and Awareness

Science.gov (United States)

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…

Using Metacognitive Strategies to Improve Reading Comprehension and Solve a Word Problem

Directory of Open Access Journals (Sweden)

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.

Solving a bi-objective mathematical programming model for bloodmobiles location routing problem

Directory of Open Access Journals (Sweden)

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.

Teaching general problem-solving skills is not a substitute for, or a viable addition to, teaching mathematics

NARCIS (Netherlands)

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.

Comparison of student's learning achievement through realistic mathematics education (RME) approach and problem solving approach on grade VII

Science.gov (United States)

Ilyas, Muhammad; Salwah

2017-02-01

The type of this research was experiment. The purpose of this study was to determine the difference and the quality of student's learning achievement between students who obtained learning through Realistic Mathematics Education (RME) approach and students who obtained learning through problem solving approach. This study was a quasi-experimental research with non-equivalent experiment group design. The population of this study was all students of grade VII in one of junior high school in Palopo, in the second semester of academic year 2015/2016. Two classes were selected purposively as sample of research that was: year VII-5 as many as 28 students were selected as experiment group I and VII-6 as many as 23 students were selected as experiment group II. Treatment that used in the experiment group I was learning by RME Approach, whereas in the experiment group II by problem solving approach. Technique of data collection in this study gave pretest and posttest to students. The analysis used in this research was an analysis of descriptive statistics and analysis of inferential statistics using t-test. Based on the analysis of descriptive statistics, it can be concluded that the average score of students' mathematics learning after taught using problem solving approach was similar to the average results of students' mathematics learning after taught using realistic mathematics education (RME) approach, which are both at the high category. In addition, It can also be concluded that; (1) there was no difference in the results of students' mathematics learning taught using realistic mathematics education (RME) approach and students who taught using problem solving approach, (2) quality of learning achievement of students who received RME approach and problem solving approach learning was same, which was at the high category.

Doing physics with scientific notebook a problem solving approach

CERN Document Server

Gallant, Joseph

2012-01-01

The goal of this book is to teach undergraduate students how to use Scientific Notebook (SNB) to solve physics problems. SNB software combines word processing and mathematics in standard notation with the power of symbolic computation. As its name implies, SNB can be used as a notebook in which students set up a math or science problem, write and solve equations, and analyze and discuss their results. Written by a physics teacher with over 20 years experience, this text includes topics that have educational value, fit within the typical physics curriculum, and show the benefits of using SNB.

Mathematical problem solving ability of sport students in the statistical study

Science.gov (United States)

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.

Solicited versus Unsolicited Metacognitive Prompts for Fostering Mathematical Problem Solving Using Multimedia

Science.gov (United States)

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…

Problem Solving Strategies of Girls and Boys in Single-Sex Mathematics Classrooms

Science.gov (United States)

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…

Problem representation and mathematical problem solving of students of varying math ability.

Science.gov (United States)

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.

COMPUTER TOOLS OF DYNAMIC MATHEMATIC SOFTWARE AND METHODICAL PROBLEMS OF THEIR USE

OpenAIRE

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 ...

The Interrelationship of Sex, Visual Spatial Abilities, and Mathematical Problem Solving Ability in Grade Seven. Parts 1, 2, and 3.

Science.gov (United States)

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…

The effect of problem posing and problem solving with realistic mathematics education approach to the conceptual understanding and adaptive reasoning

Science.gov (United States)

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.

Behaviour of mathematics and physics students in solving problem of Vector-Physics context

Science.gov (United States)

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.

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.

Teaching mathematical word problem solving: the quality of evidence for strategy instruction priming the problem structure.

Science.gov (United States)

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.

How Readability Factors Are Differentially Associated with Performance for Students of Different Backgrounds When Solving Mathematics Word Problems

Science.gov (United States)

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…

The effect of creative problem solving on students’ mathematical adaptive reasoning

Science.gov (United States)

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.

Review of Street-Fighting Mathematics: The Art of Educated Guessing and Opportunistic Problem Solving by Sanjoy Mahajan

Directory of Open Access Journals (Sweden)

Thomas J. Pfaff

2015-07-01

Full Text Available 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 that will require knowledge of Physics. At the same time, there are parts of the book that don't require this much background. While the title of the book may be misleading, as it is really street-fighting mathematics for people with a fair amount of training in the subject, there is a lot to be gained from reading this book, and calculus teachers may find it to be a useful resource.

High profile students’ growth of mathematical understanding in solving linier programing problems

Science.gov (United States)

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.

The main problem solving differences between high school and university in mathematical beliefs and professional behavior

Directory of Open Access Journals (Sweden)

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.

Personalized Computer-Assisted Mathematics Problem-Solving Program and Its Impact on Taiwanese Students

Science.gov (United States)

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.…

Problem Solving Strategies of Selected Pre-Service Secondary School Mathematics Teachers in Malaysia

Science.gov (United States)

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…

How to solve it a new aspect of mathematical method

CERN Document Server

Polya, G

2014-01-01

A perennial bestseller by eminent mathematician G. Polya, How to Solve It will show anyone in any field how to think straight. In lucid and appealing prose, Polya reveals how the mathematical method of demonstrating a proof or finding an unknown can be of help in attacking any problem that can be "reasoned" out-from building a bridge to winning a game of anagrams. Generations of readers have relished Polya's deft-indeed, brilliant-instructions on stripping away irrelevancies and going straight to the heart of the problem.

Critical Thinking Skills Of Junior High School Female Students With High Mathematical Skills In Solving Contextual And Formal Mathematical Problems

Science.gov (United States)

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.

Developing calculus textbook model that supported with GeoGebra to enhancing students’ mathematical problem solving and mathematical representation

Science.gov (United States)

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.

The Effects of Group Monitoring on Fatigue-Related Einstellung during Mathematical Problem Solving

Science.gov (United States)

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…

Examination of Gifted Students' Probability Problem Solving Process in Terms of Mathematical Thinking

Science.gov (United States)

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…

Evaluation of Students' Mathematical Problem Solving Skills in Relation to Their Reading Levels

Science.gov (United States)

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…

Does Early Algebraic Reasoning Differ as a Function of Students' Difficulty with Calculations versus Word Problems?

Science.gov (United States)

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.

Does Early Algebraic Reasoning Differ as a Function of Students’ Difficulty with Calculations versus Word Problems?

Science.gov (United States)

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

Discrete Mathematics

DEFF Research Database (Denmark)

Sørensen, John Aasted

2011-01-01

The objectives of Discrete Mathematics (IDISM2) are: The introduction of the mathematics needed for analysis, design and verification of discrete systems, including the application within programming languages for computer systems. Having passed the IDISM2 course, the student will be able...... to accomplish the following: -Understand and apply formal representations in discrete mathematics. -Understand and apply formal representations in problems within discrete mathematics. -Understand methods for solving problems in discrete mathematics. -Apply methods for solving problems in discrete mathematics......; construct a finite state machine for a given application. Apply these concepts to new problems. The teaching in Discrete Mathematics is a combination of sessions with lectures and students solving problems, either manually or by using Matlab. Furthermore a selection of projects must be solved and handed...

Application of differential transformation method for solving dengue transmission mathematical model

Science.gov (United States)

Ndii, Meksianis Z.; Anggriani, Nursanti; Supriatna, Asep K.

2018-03-01

The differential transformation method (DTM) is a semi-analytical numerical technique which depends on Taylor series and has application in many areas including Biomathematics. The aim of this paper is to employ the differential transformation method (DTM) to solve system of non-linear differential equations for dengue transmission mathematical model. Analytical and numerical solutions are determined and the results are compared to that of Runge-Kutta method. We found a good agreement between DTM and Runge-Kutta method.

The contribution of general cognitive abilities and number abilities to different aspects of mathematics in children.

Science.gov (United States)

Träff, Ulf

2013-10-01

This study examined the relative contributions of general cognitive abilities and number abilities to word problem solving, calculation, and arithmetic fact retrieval in a sample of 134 children aged 10 to 13 years. The following tasks were administered: listening span, visual matrix span, verbal fluency, color naming, Raven's Progressive Matrices, enumeration, number line estimation, and digit comparison. Hierarchical multiple regressions demonstrated that number abilities provided an independent contribution to fact retrieval and word problem solving. General cognitive abilities contributed to problem solving and calculation. All three number tasks accounted for a similar amount of variance in fact retrieval, whereas only the number line estimation task contributed unique variance in word problem solving. Verbal fluency and Raven's matrices accounted for an equal amount of variance in problem solving and calculation. The current findings demonstrate, in accordance with Fuchs and colleagues' developmental model of mathematical learning (Developmental Psychology, 2010, Vol. 46, pp. 1731-1746), that both number abilities and general cognitive abilities underlie 10- to 13-year-olds' proficiency in problem solving, whereas only number abilities underlie arithmetic fact retrieval. Thus, the amount and type of cognitive contribution to arithmetic proficiency varies between the different aspects of arithmetic. Furthermore, how closely linked a specific aspect of arithmetic is to the whole number representation systems is not the only factor determining the amount and type of cognitive contribution in 10- to 13-year-olds. In addition, the mathematical complexity of the task appears to influence the amount and type of cognitive support. Copyright © 2013 Elsevier Inc. All rights reserved.

Growing geometric reasoning in solving problems of analytical geometry through the mathematical communication problems to state Islamic university students

Science.gov (United States)

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.

INTERCULTURAL FEATURES AND THE THEME OF TRAVELLING IN BILINGUAL MATHEMATICS LESSONS

Directory of Open Access Journals (Sweden)

Zuzana Naštická

2016-08-01

Full Text Available The present qualitative research is focused on bilingual mathematics education. The research presents findings of a case study of one bilingual Slovak and English mathematics 40-minute lesson within an after school elective bilingual mathematics course running weekly since October, 2015. The lesson took place in March, 2016, and was attended by nine learners aged 12-13, eight boys and one girl. The learners are cases of successive school additive bilingual education. The elective course as a whole is a case of immerse bilingual educational programme. In terms of sociolinguistic settings, the course lessons are cases of bilingual education with external second language. The researcher designed and realized the course lessons in terms of CLIL approach, i.e. Content and Language Integrated Learning. The main aim of the case study was to examine if bilingual mathematics instruction does or does not prevent learners from solving math word problems. Secondly, the analysis of transcription of the lesson audio-record served for identification of intercultural features which might hinder the learning process. The analysis of the transcribed audio-record indicates that the bilingual context did not prevent students from solving math word problems, although each of the students worked at their individual rate. On the other hand, some students were confused by the comma as a thousands-separator in multi-digit numbers, and this actually hindered their learning and problem solving process. This fact has been identified as an intercultural difference which had to be explicitly explained to the students. In order to lessen the possible negative influences of bilingual context on mathematics education, teachers need to predict students’ responses to various intercultural differences which students are unfamiliar with.

Solving Out Loud : using discourse as a means to promote problem solving, motivation, and metacognition in a mathematics classroom

OpenAIRE

King, Megan E.

2011-01-01

Classroom communication can often be a teacher-centered discussion. Due to the teacher centered format of discussions students are not engaging in meaningful discourse in mathematics classroom, which is part of the NCTM 2000 Standards as well as a necessary component to learning. Students can only learn communication skills when discourse is a central feature from the classroom. In addition, students must explicitly learn problem-solving skills. Unfortunately, many of these features are absen...

The Effects of Schema-Based Instruction on the Mathematical Problem Solving of Students with Emotional and Behavioral Disorders

Science.gov (United States)

Peltier, Corey; Vannest, Kimberly J.

2018-01-01

The current study examines the effects of schema instruction on the problem-solving performance of four second-grade students with emotional and behavioral disorders. The existence of a functional relationship between the schema instruction intervention and problem-solving accuracy in mathematics is examined through a single case experiment using…

Schema-Based Strategy Instruction and the Mathematical Problem-Solving Performance of Two Students with Emotional or Behavioral Disorders

Science.gov (United States)

Peltier, Corey; Vannest, Kimberly J.

2016-01-01

The purpose of this study was to analyze the effects of schema instruction on the mathematical problem solving of students with emotional or behavioral disorders (EBD). The participants were two fourth-grade students identified with EBD. The intervention package consisted of schema instruction, strategy instruction on problem-solving heuristics…

Evaluation of the Effect of Mathematical Routines on the Development of Skills in Mathematical Problem Solving and School Motivation of Primary School Students in Abitibi-Témiscamingue

Science.gov (United States)

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…

Authentic assessment based showcase portfolio on learning of mathematical problem solving in senior high school

Science.gov (United States)

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.

Exploring Teachers' Process of Change in Incorporating Problem Solving into the Mathematics Classroom

Science.gov (United States)

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,…

Possibilities of mathematical models in solving flow problems in environmental protection and water architecture

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.

Critical Thinking Skills of an Eighth Grade Male Student with High Mathematical Ability in Solving Problem

Science.gov (United States)

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.

Perceptual Learning in Early Mathematics: Interacting with Problem Structure Improves Mapping, Solving and Fluency

Science.gov (United States)

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…

Gender differences in prospective teachers’ mathematical literacy: problem solving of occupational context on shipping company

Science.gov (United States)

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.

The software package for solving problems of mathematical modeling of isothermal curing process

Directory of Open Access Journals (Sweden)

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

Mathematical bridges

CERN Document Server

Andreescu, Titu; Tetiva, Marian

2017-01-01

Building bridges between classical results and contemporary nonstandard problems, Mathematical Bridges embraces important topics in analysis and algebra from a problem-solving perspective. Blending old and new techniques, tactics and strategies used in solving challenging mathematical problems, readers will discover numerous genuine mathematical gems throughout that will heighten their appreciation of the inherent beauty of mathematics. Most of the problems are original to the authors and are intertwined in a well-motivated exposition driven by representative examples. The book is structured to assist the reader in formulating and proving conjectures, as well as devising solutions to important mathematical problems by making connections between various concepts and ideas from different areas of mathematics. Instructors and educators teaching problem-solving courses or organizing mathematics clubs, as well as motivated mathematics students from high school juniors to college seniors, will find Mathematical Bri...

Gender Differences in Solving Mathematics Problems among Two-Year College Students in a Developmental Algebra Class and Related Factors.

Science.gov (United States)

Schonberger, Ann K.

A study was conducted at the University of Maine at Orono (UMO) to examine gender differences with respect to mathematical problem-solving ability, visual spatial ability, abstract reasoning ability, field independence/dependence, independent learning style, and developmental problem-solving ability (i.e., formal reasoning ability). Subjects…

The effect of Think Pair Share (TPS) using scientific approach on students’ self-confidence and mathematical problem-solving

Science.gov (United States)

Rifa’i, A.; Lestari, H. P.

2018-03-01

This study was designed to know the effects of Think Pair Share using Scientific Approach on students' self-confidence and mathematical problem-solving. Quasi-experimental with pre-test post-test non-equivalent group method was used as a basis for design this study. Self-confidence questionnaire and problem-solving test have been used for measurement of the two variables. Two classes of the first grade in religious senior high school (MAN) in Indonesia were randomly selected for this study. Teaching sequence and series from mathematics book at control group in the traditional way and at experiment group has been in TPS using scientific approach learning method. For data analysis regarding students’ problem-solving skill and self-confidence, One-Sample t-Test, Independent Sample t-Test, and Multivariate of Variance (MANOVA) were used. The results showed that (1) TPS using a scientific approach and traditional learning had positive effects (2) TPS using scientific approach learning in comparative with traditional learning had a more significant effect on students’ self-confidence and problem-solving skill.

Discrete Mathematics

DEFF Research Database (Denmark)

Sørensen, John Aasted

2011-01-01

; construct a finite state machine for a given application. Apply these concepts to new problems. The teaching in Discrete Mathematics is a combination of sessions with lectures and students solving problems, either manually or by using Matlab. Furthermore a selection of projects must be solved and handed...... to accomplish the following: -Understand and apply formal representations in discrete mathematics. -Understand and apply formal representations in problems within discrete mathematics. -Understand methods for solving problems in discrete mathematics. -Apply methods for solving problems in discrete mathematics...... to new problems. Relations and functions: Define a product set; define and apply equivalence relations; construct and apply functions. Apply these concepts to new problems. Natural numbers and induction: Define the natural numbers; apply the principle of induction to verify a selection of properties...

Errors of Students Learning with React Strategy in Solving the Problems of Mathematical Representation Ability

Science.gov (United States)

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…

Students’ Relational Thinking of Impulsive and Reflective in Solving Mathematical Problem

Science.gov (United States)

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.

Utilization of mathematics amongst healthcare students towards problem solving during their occupational safety health internship

Science.gov (United States)

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.

DIAGRAM SOLVE THE USE OF SIMULINK BLOCK DIAGRAM TO SOLVE MATHEMA THEMATICAL CONTROL EQU MATHEMATICAL MODELS AND CONTROL EQUATIONS

Directory of Open Access Journals (Sweden)

N.M. Ghasem

2003-12-01

Full Text Available In this paper, the simulink block diagram is used to solve a model consists of a set of ordinary differential and algebraic equations to control the temperature inside a simple stirred tank heater. The flexibility of simulink block diagram gives students a better understanding of the control systems. The simulink also allows solution of mathematical models and easy visualization of the system variables. A polyethylene fluidized bed reactor is considered as an industrial example and the effect of the Proportional, Integral and Derivative control policy is presented for comparison.

Do Students Trust in Mathematics or Intuition during Physics Problem Solving? An Epistemic Game Perspective

Science.gov (United States)

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…

Cognitive Profiles of Mathematical Problem Solving Learning Disability for Different Definitions of Disability

Science.gov (United States)

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

Comprehension and computation in Bayesian problem solving

Directory of Open Access Journals (Sweden)

Eric D. Johnson

2015-07-01

Full Text Available Humans have long been characterized as poor probabilistic reasoners when presented with explicit numerical information. Bayesian word problems provide a well-known example of this, where even highly educated and cognitively skilled individuals fail to adhere to mathematical norms. It is widely agreed that natural frequencies can facilitate Bayesian reasoning relative to normalized formats (e.g. probabilities, percentages, both by clarifying logical set-subset relations and by simplifying numerical calculations. Nevertheless, between-study performance on transparent Bayesian problems varies widely, and generally remains rather unimpressive. We suggest there has been an over-focus on this representational facilitator (i.e. transparent problem structures at the expense of the specific logical and numerical processing requirements and the corresponding individual abilities and skills necessary for providing Bayesian-like output given specific verbal and numerical input. We further suggest that understanding this task-individual pair could benefit from considerations from the literature on mathematical cognition, which emphasizes text comprehension and problem solving, along with contributions of online executive working memory, metacognitive regulation, and relevant stored knowledge and skills. We conclude by offering avenues for future research aimed at identifying the stages in problem solving at which correct versus incorrect reasoners depart, and how individual difference might influence this time point.

Teacher Formation in the Mathematical Thinking through Problem Solving in the Second Phase of the CCyM Network of Reading Comprehension and Mathematics

Directory of Open Access Journals (Sweden)

LUZ STELLA LÓPEZ

2008-12-01

Full Text Available This article shares the design, implementation, and evaluation of theLesson Study process used for the professional development of teachers of mathematics, through the Red de Comprensión Lectora y Matemáticas – CCyM Network, in ways to teach mathematics through problem solving. The program began with a course on the implementation of the Thinking Classroom, followed by the semi-presencial Lesson Study process. An analysis of teacher interactions during the Lesson Study process yielded these categories of study: Group Collective Thinking, Mathematical Pedagogical Content Knowledge, Subject Matter Knowledge, Knowledge about Technology, and Expert Support. The analysis reflected variations in group interactions, in the command of concepts, in reflective practice, in the ability to make arguments and to propose changes in practice, and in the ability to self-regulate.

Encouraging Sixth-Grade Students' Problem-Solving Performance by Teaching through Problem Solving

Science.gov (United States)

Bostic, Jonathan D.; Pape, Stephen J.; Jacobbe, Tim

2016-01-01

This teaching experiment provided students with continuous engagement in a problem-solving based instructional approach during one mathematics unit. Three sections of sixth-grade mathematics were sampled from a school in Florida, U.S.A. and one section was randomly assigned to experience teaching through problem solving. Students' problem-solving…

Pupils' Visual Representations in Standard and Problematic Problem Solving in Mathematics: Their Role in the Breach of the Didactical Contract

Science.gov (United States)

Deliyianni, Eleni; Monoyiou, Annita; Elia, Iliada; Georgiou, Chryso; Zannettou, Eleni

2009-01-01

This study investigated the modes of representations generated by kindergarteners and first graders while solving standard and problematic problems in mathematics. Furthermore, it examined the influence of pupils' visual representations on the breach of the didactical contract rules in problem solving. The sample of the study consisted of 38…

Profile of Secondary School Students with High Mathematics Ability in Solving Shape and Space Problem

Science.gov (United States)

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…

High School Teachers' Problem Solving Activities to Review and Extend Their Mathematical and Didactical Knowledge

Science.gov (United States)

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…

Electromagnetic Problems Solving by Conformal Mapping: A Mathematical Operator for Optimization

Directory of Open Access Journals (Sweden)

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.

Find the Dimensions: Students Solving a Tiling Problem

Science.gov (United States)

Obara, Samuel

2018-01-01

Students learn mathematics by solving problems. Mathematics textbooks are full of problems, and mathematics teachers use these problems to test students' understanding of mathematical concepts. This paper discusses how problem-solving skills can be fostered with a geometric tiling problem.

THE DEVELOPMENT OF ELECTRONIC TEACHING MATERIALS BY FLIPBOOK ASSISTANCE BASED PROBLEM SOLVING SKILL WITH CTL APPROACH ON LEARNING MATHEMATICS CLASS V

Directory of Open Access Journals (Sweden)

RUSNILAWATI Eva Gustiana RUSNILAWATI

2018-01-01

Full Text Available The purpose of this research is to produce Flipbook-based Electronic Teaching Materials (BAE based on problem solving skills with CTL Approach on Vocational School Class V learning valid, practical, and effective. This type of research is development research (Development Research. This research developed Flipbook-assisted Electronic Teaching Materials (BAE on the mathematics learning of Class V Primary School by using the 4-D development model developed by Thiagarajan, Semmel, and Semmel. The validation results show that the developed Teaching Materials are worthy of use with a good minimum category. The results of the experiments show that Electronic Materials developed are practical and effective. Completed learning in the classical has reached the minimum criteria of 75% that is for problem-solving test reached 86%. Based on a questionnaire of attitudes toward mathematics, 88% of students showed an increase in attitude scores on mathematics, and 85% of students showed attitudes toward mathematics with a good minimum category.

Investigating a Link between Pre-Calculus Students' Uses of Graphing Calculators and Their Understanding of Mathematical Symbols

Science.gov (United States)

Kenney, Rachael H.

2014-01-01

This study examined ways in which students make use of a graphing calculator and how use relates to comfort and understanding with mathematical symbols. Analysis involved examining students' words and actions in problem solving to identify evidence of algebraic insight. Findings suggest that some symbols and symbolic structures had strong…

[The application of new technologies to solving maths problems for students with learning disabilities: the 'underwater school'].

Science.gov (United States)

Miranda-Casas, A; Marco-Taverner, R; Soriano-Ferrer, M; Melià de Alba, A; Simó-Casañ, P

2008-01-01

Different procedures have demonstrated efficacy to teach cognitive and metacognitive strategies to problem solving in mathematics. Some studies have used computer-based problem solving instructional programs. To analyze in students with learning disabilities the efficacy of a cognitive strategies training for problem solving, with three instructional delivery formats: a teacher-directed program (T-D), a computer-assisted instructional (CAI) program, and a combined program (T-D + CAI). Forty-four children with mathematics learning disabilities, between 8 and 10 years old participated in this study. The children were randomly assigned to one of the three instructional formats and a control group without cognitive strategies training. In the three instructional conditions which were compared all the students learnt problems solving linguistic and visual cognitive strategies trough the self-instructional procedure. Several types of measurements were used for analysing the possible differential efficacy of the three instructional methods implemented: solving problems tests, marks in mathematics, internal achievement responsibility scale, and school behaviours teacher ratings. Our findings show that the T-D training group and the T-D + CAI group improved significantly on math word problem solving and on marks in Maths from pre- to post-testing. In addition, the results indicated that the students of the T-D + CAI group solved more real-life problems and developed more internal attributions compared to both control and CAI groups. Finally, with regard to school behaviours, improvements in school adjustment and learning problems were observed in the students of the group with a combined instructional format (T-D + CAI).

Analysis of students’ creative thinking level in problem solving based on national council of teachers of mathematics

Science.gov (United States)

Hobri; Suharto; Rifqi Naja, Ahmad

2018-04-01

This research aims to determine students’ creative thinking level in problem solving based on NCTM in function subject. The research type is descriptive with qualitative approach. Data collection methods which were used are test and interview. Creative thinking level in problem solving based on NCTM indicators consists of (1) Make mathematical model from a contextual problem and solve the problem, (2) Solve problem using various possible alternatives, (3) Find new alternative(s) to solve the problem, (4) Determine the most efficient and effective alternative for that problem, (5) Review and correct mistake(s) on the process of problem solving. Result of the research showed that 10 students categorized in very satisfying level, 23 students categorized in satisfying level and 1 students categorized in less satisfying level. Students in very satisfying level meet all indicators, students in satisfying level meet first, second, fourth, and fifth indicator, while students in less satisfying level only meet first and fifth indicator.

Students’ thinking preferences in solving mathematics problems based on learning styles: a comparison of paper-pencil and geogebra

Science.gov (United States)

Farihah, Umi

2018-04-01

The purpose of this study was to analyze students’ thinking preferences in solving mathematics problems using paper pencil comparing to geogebra based on their learning styles. This research employed a qualitative descriptive study. The subjects of this research was six of eighth grade students of Madrasah Tsanawiyah Negeri 2 Trenggalek, East Java Indonesia academic year 2015-2016 with their difference learning styles; two visual students, two auditory students, and two kinesthetic students.. During the interview, the students presented the Paper and Pencil-based Task (PBTs) and the Geogebra-based Task (GBTs). By investigating students’ solution methods and the representation in solving the problems, the researcher compared their visual and non-visual thinking preferences in solving mathematics problems while they were using Geogebra and without Geogebra. Based on the result of research analysis, it was shown that the comparison between students’ PBTs and GBTs solution either visual, auditory, or kinesthetic represented how Geogebra can influence their solution method. By using Geogebra, they prefer using visual method while presenting GBTs to using non-visual method.

Learning by Preparing to Teach: Fostering Self-Regulatory Processes and Achievement during Complex Mathematics Problem Solving

Science.gov (United States)

Muis, Krista R.; Psaradellis, Cynthia; Chevrier, Marianne; Di Leo, Ivana; Lajoie, Susanne P.

2016-01-01

We developed an intervention based on the learning by teaching paradigm to foster self-regulatory processes and better learning outcomes during complex mathematics problem solving in a technology-rich learning environment. Seventy-eight elementary students were randomly assigned to 1 of 2 conditions: learning by preparing to teach, or learning for…

Mathematics Prerequisites for Introductory Geoscience Courses: Using Technology to Help Solve the Problem

Science.gov (United States)

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

Description of Student’s Metacognitive Ability in Understanding and Solving Mathematics Problem

Science.gov (United States)

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.

The Effect of Learning Environments Based on Problem Solving on Students' Achievements of Problem Solving

Science.gov (United States)

Karatas, Ilhan; Baki, Adnan

2013-01-01

Problem solving is recognized as an important life skill involving a range of processes including analyzing, interpreting, reasoning, predicting, evaluating and reflecting. For that reason educating students as efficient problem solvers is an important role of mathematics education. Problem solving skill is the centre of mathematics curriculum.…

Strategic competence of senior secondary school students in solving mathematics problem based on cognitive style

Science.gov (United States)

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

Students’ Mathematical Literacy in Solving PISA Problems Based on Keirsey Personality Theory

Science.gov (United States)

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

Revisiting Mathematical Problem Solving and Posing in the Digital Era: Toward Pedagogically Sound Uses of Modern Technology

Science.gov (United States)

Abramovich, S.

2014-01-01

The availability of sophisticated computer programs such as "Wolfram Alpha" has made many problems found in the secondary mathematics curriculum somewhat obsolete for they can be easily solved by the software. Against this background, an interplay between the power of a modern tool of technology and educational constraints it presents is…

Investigating Plane Geometry Problem-Solving Strategies of Prospective Mathematics Teachers in Technology and Paper-and-Pencil Environments

Science.gov (United States)

Koyuncu, Ilhan; Akyuz, Didem; Cakiroglu, Erdinc

2015-01-01

This study aims to investigate plane geometry problem-solving strategies of prospective mathematics teachers using dynamic geometry software (DGS) and paper-and-pencil (PPB) environments after receiving an instruction with GeoGebra (GGB). Four plane geometry problems were used in a multiple case study design to understand the solution strategies…

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.

Counting to 20: Online Implementation of a Face-to-Face, Elementary Mathematics Methods Problem-Solving Activity

Science.gov (United States)

Schwartz, Catherine Stein

2012-01-01

This study describes implementation of the same problem-solving activity in both online and face-to-face environments. The activity, done in the first class period or first module of a K-2 mathematics methods course, was initially used in a face-to-face class and then adapted later for use in an online class. While the task was originally designed…

Don’t words come easy?A psychophysical exploration of word superiority

Directory of Open Access Journals (Sweden)

Randi eStarrfelt

2013-09-01

Full Text Available Words are made of letters, and yet sometimes it is easier to identify a word than a single letter. This word superiority effect (WSE has been observed when written stimuli are presented very briefly or degraded by visual noise. We compare performance with letters and words in three experiments, to explore the extents and limits of the WSE. Using a carefully controlled list of three letter words, we show that a word superiority effect can be revealed in vocal reaction times even to undegraded stimuli. With a novel combination of psychophysics and mathematical modelling, we further show that the typical WSE is specifically reflected in perceptual processing speed: single words are simply processed faster than single letters. Intriguingly, when multiple stimuli are presented simultaneously, letters are perceived more easily than words, and this is reflected both in perceptual processing speed and visual short term memory capacity. So, even if single words come easy, there is a limit to the word superiority effect.

Hands-On Mathematics: Two Cases from Ancient Chinese Mathematics

Science.gov (United States)

Wang, Youjun

2009-01-01

In modern mathematical teaching, it has become increasingly emphasized that mathematical knowledge should be taught by problem-solving, hands-on activities, and interactive learning experiences. Comparing the ideas of modern mathematical education with the development of ancient Chinese mathematics, we find that the history of mathematics in…

Mathematical problem solving in primary school

NARCIS (Netherlands)

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

The social essentials of learning: an experimental investigation of collaborative problem solving and knowledge construction in mathematics classrooms in Australia and China

Science.gov (United States)

Chan, Man Ching Esther; Clarke, David; Cao, Yiming

2018-03-01

Interactive problem solving and learning are priorities in contemporary education, but these complex processes have proved difficult to research. This project addresses the question "How do we optimise social interaction for the promotion of learning in a mathematics classroom?" Employing the logic of multi-theoretic research design, this project uses the newly built Science of Learning Research Classroom (ARC-SR120300015) at The University of Melbourne and equivalent facilities in China to investigate classroom learning and social interactions, focusing on collaborative small group problem solving as a way to make the social aspects of learning visible. In Australia and China, intact classes of local year 7 students with their usual teacher will be brought into the research classroom facilities with built-in video cameras and audio recording equipment to participate in purposefully designed activities in mathematics. The students will undertake a sequence of tasks in the social units of individual, pair, small group (typically four students) and whole class. The conditions for student collaborative problem solving and learning will be manipulated so that student and teacher contributions to that learning process can be distinguished. Parallel and comparative analyses will identify culture-specific interactive patterns and provide the basis for hypotheses about the learning characteristics underlying collaborative problem solving performance documented in the research classrooms in each country. The ultimate goals of the project are to generate, develop and test more sophisticated hypotheses for the optimisation of social interaction in the mathematics classroom in the interest of improving learning and, particularly, student collaborative problem solving.

Pengaruh Pembelajaran Inquiry dan Problem Solving terhadap Motivasi dan Prestasi Belajar Matematika

Directory of Open Access Journals (Sweden)

Henri Rianto

2014-06-01

This study aimed to describe the difference effect of inquiry approach and problem solving approach on motivations to learn mathematics and student mathematics achievement and the better  effect of inquiry approach and problem solving approach on motivations to learn mathematics and student mathematics achievement. This research was a quasi-experimental using nonrandomized control group, pretest-posttest design. The data were collected through non-test and test. The data were analyzed using the MANOVA test and independent sample t-test with significance level of 0,05. The results of the study show  the inquiry approach and problem solving approach was not effective to increase the student mathematics achievement, the inquiry approach and problem solving approach was not effective to increase the motivation to learn mathematics, and there is no difference effect between the inquiry approach and the problem solving approach on learning motivations and the student mathematics achievement. Keywords: inquiry approach, problem solving approach, motivations to learn mathematics, student mathematics achievement

Cognitive mechanisms underlying third graders' arithmetic skills: Expanding the pathways to mathematics model.

Science.gov (United States)

Träff, Ulf; Olsson, Linda; Skagerlund, Kenny; Östergren, Rickard

2018-03-01

A modified pathways to mathematics model was used to examine the cognitive mechanisms underlying arithmetic skills in third graders. A total of 269 children were assessed on tasks tapping the four pathways and arithmetic skills. A path analysis showed that symbolic number processing was directly supported by the linguistic and approximate quantitative pathways. The direct contribution from the four pathways to arithmetic proficiency varied; the linguistic pathway supported single-digit arithmetic and word problem solving, whereas the approximate quantitative pathway supported only multi-digit calculation. The spatial processing and verbal working memory pathways supported only arithmetic word problem solving. The notion of hierarchical levels of arithmetic was supported by the results, and the different levels were supported by different constellations of pathways. However, the strongest support to the hierarchical levels of arithmetic were provided by the proximal arithmetic skills. Copyright © 2017 Elsevier Inc. All rights reserved.

The Problem-Solving Approach in the Teaching of Number Theory

Science.gov (United States)

Toh, Pee Choon; Leong, Yew Hoong; Toh, Tin Lam; Dindyal, Jaguthsing; Quek, Khiok Seng; Tay, Eng Guan; Ho, Foo Him

2014-01-01

Mathematical problem solving is the mainstay of the mathematics curriculum for Singapore schools. In the preparation of prospective mathematics teachers, the authors, who are mathematics teacher educators, deem it important that pre-service mathematics teachers experience non-routine problem solving and acquire an attitude that predisposes them to…

The Comparison of the Effectiveness of Cognitive and Cognitive-Metacognitive Strategies based on Mathematical Problem-Solving Skills on 9th Grade Girl Students with Intellectual Disability

Directory of Open Access Journals (Sweden)

Seyyedeh Somayyeh Jalil-Abkenar

2012-01-01

Full Text Available Objective: The purpose of present research was the comparison of the effectiveness of cognitive & cognitive-metacognitive strategies based on mathematical problem-solving skills on 9th grade girl students with intellectual disability in Tehran Province. Materials & Methods: The research is an experimental, comparing pre-test and post-test data. The participants were chosen by cluster sampling from three schools three districts of Tehran Province (Gharchak, Shahrerey and Shahryar. Fifteen female students with Intellectual disability were assigned from each school and they were divided into three, one control and two experiment groups. For experimental groups students cognitive & cognitive-metacognitive strategies were taught in the 15 instructional sessions, but the control group students did not receive none of strategies in the same sessions. The instruments consist of Wechsler intelligence test was used for matching the groups in terms of IQ, a teacher performed the tests for mathematical problem-solving and instructional pakage of cognitive and cognitive-metacognitive strategies. The data analysis was done by using descriptive statistics (mean, standard deviation and frequency table and ANCOVA. Results: The findings of this research showed that there was significant increasing in mathematical problem-solving skills in the group receiving cognitive-metacognitive strategies in comparison with the cognitive group (P<0.005 and control group (P<0.001. Beside, the mean difference of the cognitive group was significantly more than the control group (P<0.003. Conclusion: The mathematical problem-solving skill of the students have been improved through cognitive-metacognitive and cognitive strategies. Also, the instruction of cognitive-metacognitive strategies, in compared with cognitive strategy caused more improvement on the performance of mathematical problem-solving skills.

Embedding Number-Combinations Practice Within Word-Problem Tutoring

Science.gov (United States)

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

Finite Mathematics and Discrete Mathematics: Is There a Difference?

Science.gov (United States)

Johnson, Marvin L.

Discrete mathematics and finite mathematics differ in a number of ways. First, finite mathematics has a longer history and is therefore more stable in terms of course content. Finite mathematics courses emphasize certain particular mathematical tools which are useful in solving the problems of business and the social sciences. Discrete mathematics…

Some Applications of Algebraic System Solving

Science.gov (United States)

Roanes-Lozano, Eugenio

2011-01-01

Technology and, in particular, computer algebra systems, allows us to change both the way we teach mathematics and the mathematical curriculum. Curiously enough, unlike what happens with linear system solving, algebraic system solving is not widely known. The aim of this paper is to show that, although the theory lying behind the "exact…

Scientific word, Version 1.0

Directory of Open Access Journals (Sweden)

Semen Köksal

1993-01-01

Full Text Available Scientific Word is the first fully integrated mathematical word processor in the Windows 3.1 environment, which uses the TEX typesetting language for output. It runs as a Microsoft Windows application program and has two-way interface to TEX. The Scientific Word is an object-oriented WYSIWYG word processor for virtually all users who need typesetting scientific books, manuals and papers. It includes automatic equation numbering, spell checking, and LATEX and DVI previewer.

Analysis Critical Thinking Stage of Eighth Grade in PBL-Scaffolding Setting To Solve Mathematical Problems

OpenAIRE

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...

Tangram solved? Prefrontal cortex activation analysis during geometric problem solving.

Science.gov (United States)

Ayaz, Hasan; Shewokis, Patricia A; Izzetoğlu, Meltem; Çakır, Murat P; Onaral, Banu

2012-01-01

Recent neuroimaging studies have implicated prefrontal and parietal cortices for mathematical problem solving. Mental arithmetic tasks have been used extensively to study neural correlates of mathematical reasoning. In the present study we used geometric problem sets (tangram tasks) that require executive planning and visuospatial reasoning without any linguistic representation interference. We used portable optical brain imaging (functional near infrared spectroscopy--fNIR) to monitor hemodynamic changes within anterior prefrontal cortex during tangram tasks. Twelve healthy subjects were asked to solve a series of computerized tangram puzzles and control tasks that required same geometric shape manipulation without problem solving. Total hemoglobin (HbT) concentration changes indicated a significant increase during tangram problem solving in the right hemisphere. Moreover, HbT changes during failed trials (when no solution found) were significantly higher compared to successful trials. These preliminary results suggest that fNIR can be used to assess cortical activation changes induced by geometric problem solving. Since fNIR is safe, wearable and can be used in ecologically valid environments such as classrooms, this neuroimaging tool may help to improve and optimize learning in educational settings.

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

Strategies to Support Students' Mathematical Modeling

Science.gov (United States)

Jung, Hyunyi

2015-01-01

An important question for mathematics teachers is this: "How can we help students learn mathematics to solve everyday problems, rather than teaching them only to memorize rules and practice mathematical procedures?" Teaching students using modeling activities can help them learn mathematics in real-world problem-solving situations that…

A Play on Words: Using Cognitive Computing as a Basis for AI Solvers in Word Puzzles

Science.gov (United States)

Manzini, Thomas; Ellis, Simon; Hendler, James

2015-12-01

In this paper we offer a model, drawing inspiration from human cognition and based upon the pipeline developed for IBM's Watson, which solves clues in a type of word puzzle called syllacrostics. We briefly discuss its situation with respect to the greater field of artificial general intelligence (AGI) and how this process and model might be applied to other types of word puzzles. We present an overview of a system that has been developed to solve syllacrostics.

The Language Factor in Elementary Mathematics Assessments: Computational Skills and Applied Problem Solving in a Multidimensional IRT Framework

Science.gov (United States)

Hickendorff, Marian

2013-01-01

The results of an exploratory study into measurement of elementary mathematics ability are presented. The focus is on the abilities involved in solving standard computation problems on the one hand and problems presented in a realistic context on the other. The objectives were to assess to what extent these abilities are shared or distinct, and…

Error Patterns in Problem Solving.

Science.gov (United States)

Babbitt, Beatrice C.

Although many common problem-solving errors within the realm of school mathematics have been previously identified, a compilation of such errors is not readily available within learning disabilities textbooks, mathematics education texts, or teacher's manuals for school mathematics texts. Using data on error frequencies drawn from both the Fourth…

The role of mathematical models in understanding pattern formation in developmental biology.

Science.gov (United States)

Umulis, David M; Othmer, Hans G

2015-05-01

In a Wall Street Journal article published on April 5, 2013, E. O. Wilson attempted to make the case that biologists do not really need to learn any mathematics-whenever they run into difficulty with numerical issues, they can find a technician (aka mathematician) to help them out of their difficulty. He formalizes this in Wilsons Principle No. 1: "It is far easier for scientists to acquire needed collaboration from mathematicians and statisticians than it is for mathematicians and statisticians to find scientists able to make use of their equations." This reflects a complete misunderstanding of the role of mathematics in all sciences throughout history. To Wilson, mathematics is mere number crunching, but as Galileo said long ago, "The laws of Nature are written in the language of mathematics[Formula: see text] the symbols are triangles, circles and other geometrical figures, without whose help it is impossible to comprehend a single word." Mathematics has moved beyond the geometry-based model of Galileo's time, and in a rebuttal to Wilson, E. Frenkel has pointed out the role of mathematics in synthesizing the general principles in science (Both point and counter-point are available in Wilson and Frenkel in Notices Am Math Soc 60(7):837-838, 2013). We will take this a step further and show how mathematics has been used to make new and experimentally verified discoveries in developmental biology and how mathematics is essential for understanding a problem that has puzzled experimentalists for decades-that of how organisms can scale in size. Mathematical analysis alone cannot "solve" these problems since the validation lies at the molecular level, but conversely, a growing number of questions in biology cannot be solved without mathematical analysis and modeling. Herein, we discuss a few examples of the productive intercourse between mathematics and biology.

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...

Exploring Primary Student’s Problem-Solving Ability by Doing Tasks Like PISA's Question

Directory of Open Access Journals (Sweden)

Rita Novita

2012-07-01

Full Text Available Problem solving plays an important role in mathematics and should have a prominent role in the mathematics education. The term “problem solving” refers to mathematics tasks that have the potential to provide intellectual challenges for enhancing students’ mathematical understanding and development. In addition, the contextual problem that requires students to connect their mathematical knowledge in solving mathematical situational problem is believed to be an impact on the development students’ problem-solving ability. The tasks that have been developed by PISA meet both of these criteria. As stated by the NCTM, that problem-solving skill and ability should be developed to students when they were in primary school (K5-8, therefore, it is important to do an effort to guide students in developing problem-solving ability from primary school such as accustom students to do some mathematical solving-problem tasks. Thus, in this research we tried to investigate how to develop mathematical problem-solving tasks like PISA’s question that have potential effect toward students’ mathematical problem-solving abilities?. We used a  formative evaluation type of development research as an mean  to achieve this research goal. This type of research is conducted in two steps, namely preliminary stage and formative evaluation stage covering self evaluation, prototyping (expert reviews, one-to-one, and small group, and  field test. This research involve four primary schools in Palembang, there are SD Muhammadiyah 6 Palembang, MIN 1 & MIN 2 Palembang, and SDN 179 Palembang. The result of this research showed that the mathematical problem-solving tasks  that have been developed have potential effect in exploring mathematical problem-solving ability of the primary school students. It  is shown from their work in solving problem where all of the indicators of problem solving competency have emerged quite well category. In addition, based on interview

Solving for Irrational Zeros: Whiteness in Mathematics Teacher Education

Science.gov (United States)

Warburton, Trevor Thayne

2015-01-01

For many, mathematics and social justice are perceived as incompatible. Several mathematics education researchers have noted resistance to social justice among mathematics teachers. However, mathematics education has a consistently negative impact on the education of students of color. This study seeks to better understand the nature of this…

Dimensional analysis and qualitative methods in problem solving: II

International Nuclear Information System (INIS)

Pescetti, D

2009-01-01

We show that the underlying mathematical structure of dimensional analysis (DA), in the qualitative methods in problem-solving context, is the algebra of the affine spaces. In particular, we show that the qualitative problem-solving procedure based on the parallel decomposition of a problem into simple special cases yields the new original mathematical concepts of special points and special representations of affine spaces. A qualitative problem-solving algorithm piloted by the mathematics of DA is illustrated by a set of examples.

Problem solving and problem strategies in the teaching and learning ...

African Journals Online (AJOL)

Perennial poor performance recorded annually in both internal and external examinations in Mathematics has been a great concern for the Mathematics Educators in Nigeria. This paper discusses problem-solving and influence of problem-solving strategies on students' performance in mathematics. The concept of ...

Best Known Problem Solving Strategies in "High-Stakes" Assessments

Science.gov (United States)

Hong, Dae S.

2011-01-01

In its mathematics standards, National Council of Teachers of Mathematics (NCTM) states that problem solving is an integral part of all mathematics learning and exposure to problem solving strategies should be embedded across the curriculum. Furthermore, by high school, students should be able to use, decide and invent a wide range of strategies.…

Application of Learning Engineering Techniques Thinking Aloud Pair Problem Solving in Learning Mathematics Students Class VII SMPN 15 Padang

Science.gov (United States)

Widuri, S. Y. S.; Almash, L.; Zuzano, F.

2018-04-01

The students activity and responsible in studying mathematic is still lack. It gives an effect for the bad result in studying mathematic. There is one of learning technic to increase students activity in the classroom and the result of studying mathematic with applying a learning technic. It is “Thinking Aloud Pair Problem Solving (TAPPS)”. The purpose of this research is to recognize the developing of students activity in mathematic subject during applying that technic “TAPPS” in seven grade at SMPN 15 Padang and compare the students proportion in learning mathematic with TAPPS between learning process without it in seven grade at SMPN 15 Padang. Students activity for indicators 1, 2, 3, 4, 5, 6 at each meeting is likely to increase and students activity for indicator 7 at each meeting is likely to decrease. The finding of this research is χ 2 = 9,42 and the value of p is 0,0005 < p < 0,005. Therefore p < 0,05 has means H 0 was rejected and H 1 was accepted. Thus, it was concluded that the activities and result in studying mathematic increased after applying learning technic the TAPPS.

Pose and Solve Varignon Converse Problems

Science.gov (United States)

Contreras, José N.

2014-01-01

The activity of posing and solving problems can enrich learners' mathematical experiences because it fosters a spirit of inquisitiveness, cultivates their mathematical curiosity, and deepens their views of what it means to do mathematics. To achieve these goals, a mathematical problem needs to be at the appropriate level of difficulty,…

Strategy Choice in Solving Arithmetic Word Problems: Are There Differences between Students with Learning Disabilities, G-V Poor Performance, and Typical Achievement Students?

Science.gov (United States)

Gonzalez, Juan E. Jimenez; Espinel, Ana Isabel Garcia

2002-01-01

A study was designed to test whether there are differences between Spanish children (ages 7-9) with arithmetic learning disabilities (n=60), garden-variety (G-V) poor performance (n=44), and typical children (n=44) in strategy choice when solving arithmetic word problems. No significant differences were found between children with dyscalculia and…

Exploring Effects of High School Students' Mathematical Processing Skills and Conceptual Understanding of Chemical Concepts on Algorithmic Problem Solving

Science.gov (United States)

Gultepe, Nejla; Yalcin Celik, Ayse; Kilic, Ziya

2013-01-01

The purpose of the study was to examine the effects of students' conceptual understanding of chemical concepts and mathematical processing skills on algorithmic problem-solving skills. The sample (N = 554) included grades 9, 10, and 11 students in Turkey. Data were collected using the instrument "MPC Test" and with interviews. The MPC…

The Effects of Computer Programming on High School Students' Reasoning Skills and Mathematical Self-Efficacy and Problem Solving

Science.gov (United States)

Psycharis, Sarantos; Kallia, Maria

2017-01-01

In this paper we investigate whether computer programming has an impact on high school student's reasoning skills, problem solving and self-efficacy in Mathematics. The quasi-experimental design was adopted to implement the study. The sample of the research comprised 66 high school students separated into two groups, the experimental and the…

An Analysis of Students Error In Solving PISA 2012 And Its Scaffolding

Directory of Open Access Journals (Sweden)

Yurizka Melia Sari

2017-08-01

Full Text Available Based on PISA survey in 2012, Indonesia was only placed on 64 out of 65 participating countries. The survey suggest that the students’ ability of reasoning, spatial orientation, and problem solving are lower compare with other participants countries, especially in Shouth East Asia. Nevertheless, the result of PISA does not elicit clearly on the students’ inability in solving PISA problem such as the location and the types of student’s errors. Therefore, analyzing students’ error in solving PISA problem would be essential countermeasure to help the students in solving mathematics problems and to develop scaffolding. Based on the data analysis, it is found that there are 5 types of error which is made by the subject. They consist of reading error, comprehension error, transformation error, process skill error, and encoding error. The most common mistake that subject do is encoding error with a percentage of 26%. While reading is the fewest errors made by the subjects that is only 12%. The types of given scaffolding was explaining the problem carefully and making a summary of new words and find the meaning of them, restructuring problem-solving strategies and reviewing the results of the completion of the problem.

The Different Patterns of Gesture between Genders in Mathematical Problem Solving of Geometry

Science.gov (United States)

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.

Selective Spatial Working Memory Impairment in a Group of Children with Mathematics Learning Disabilities and Poor Problem-Solving Skills

Science.gov (United States)

Passolunghi, Maria Chiara; Mammarella, Irene Cristina

2012-01-01

This study examines visual and spatial working memory skills in 35 third to fifth graders with both mathematics learning disabilities (MLD) and poor problem-solving skills and 35 of their peers with typical development (TD) on tasks involving both low and high attentional control. Results revealed that children with MLD, relative to TD children,…

Mathematical Literacy: A new literacy or a new mathematics?

Directory of Open Access Journals (Sweden)

Renuka Vithal

2006-10-01

Full Text Available Mathematical Literacy is a ‘hot’ topic at present in most countries, whether it is referred to by that name, or in some cases as Numeracy, or Quantitative Literacy, or Matheracy, or as some part of Ethnomathematics, or related to Mathematics in Society. Questions continue to be asked about what is meant by mathematics in any concept of Mathematical Literacy and the use of the very word ‘Literacy’ in its association with Mathematics has been challenged. Its importance, however, lies in changing our perspective on mathematics teaching, away from the elitism so often associated with much mathematics education, and towards a more equitable, accessible and genuinely educational ideal.

Mathematics Education for Engineering Technology Students – A Bridge Too Far?

Directory of Open Access Journals (Sweden)

Noraishiyah Abdullah

2013-03-01

Full Text Available Trying to decide what is best suited for someone or something is an ever enduring task let alone trying to prepare students with the right engineering mind. So ‘how do you build an engineer?’ if that is the right word. What is the right ingredient? Mathematics has been said as the most important foundation in engineers’ life. Curriculum has been developed and reviewed over the years to meet this target. This work explores how much or lack of it has the curriculum prepares the future technologist to face the world of engineering technology as far as mathematics is concerned. Analysis of mathematics lectures, interviews of engineering technologist students and engineering technology subject lecturer is undertaken. Understand what each contributes help in understanding the picture that the current education is painting. Based on the theory of learning, APOS theory helps in explaining how students bridge their knowledge of mathematics when it comes to solving engineering technology problems. The question is, is it a bridge too far? 

Child-Level Predictors of Responsiveness to Evidence-Based Mathematics Intervention.

Science.gov (United States)

Powell, Sarah R; Cirino, Paul T; Malone, Amelia S

2017-07-01

We identified child-level predictors of responsiveness to 2 types of mathematics (calculation and word-problem) intervention among 2nd-grade children with mathematics difficulty. Participants were 250 children in 107 classrooms in 23 schools pretested on mathematics and general cognitive measures and posttested on mathematics measures. We assigned classrooms randomly assigned to calculation intervention, word-problem intervention, or business-as-usual control. Intervention lasted 17 weeks. Path analyses indicated that scores on working memory and language comprehension assessments moderated responsiveness to calculation intervention. No moderators were identified for responsiveness to word-problem intervention. Across both intervention groups and the control group, attentive behavior predicted both outcomes. Initial calculation skill predicted the calculation outcome, and initial language comprehension predicted word-problem outcomes. These results indicate that screening for calculation intervention should include a focus on working memory, language comprehension, attentive behavior, and calculations. Screening for word-problem intervention should focus on attentive behavior and word problems.

Exploring Primary Student's Problem-Solving Ability by Doing Tasks Like PISA's Question

OpenAIRE

Novita, Rita; Zulkardi, Zulkardi; Hartono, Yusuf

2012-01-01

Problem solving plays an important role in mathematics and should have a prominent role in the mathematics education. The term “problem solving” refers to mathematics tasks that have the potential to provide intellectual challenges for enhancing students’ mathematical understanding and development. In addition, the contextual problem that requires students to connect their mathematical knowledge in solving mathematical situational problem is believed to be an impact on the development student...

Word Problems: A "Meme" for Our Times.

Science.gov (United States)

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)

A mathematical approach to research problems of science and technology theoretical basis and developments in mathematical modeling

CERN Document Server

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.

The Relationship between 8th Grade Students’ Opinions about Problem Solving, Beliefs about Mathematics, Learned Hopelessness and Academics Success

OpenAIRE

Agaç, Gülay; MASAL, Ercan

2017-01-01

Related literature emphasizes that affective factors are impactful on cognitive factors. For this reason, this study aims at revealing the relationship between problem solving,  which is one of metacognitive characteristics, beliefs about mathematics and learned hopelessness, which are two affective characteristics. Therefore, addressing emotional aspects together with cognitive abilities will give rise to understanding of the students’ current situation and predicting ab...

Students’ difficulties in probabilistic problem-solving

Science.gov (United States)

Arum, D. P.; Kusmayadi, T. A.; Pramudya, I.

2018-03-01

There are many errors can be identified when students solving mathematics problems, particularly in solving the probabilistic problem. This present study aims to investigate students’ difficulties in solving the probabilistic problem. It focuses on analyzing and describing students errors during solving the problem. This research used the qualitative method with case study strategy. The subjects in this research involve ten students of 9th grade that were selected by purposive sampling. Data in this research involve students’ probabilistic problem-solving result and recorded interview regarding students’ difficulties in solving the problem. Those data were analyzed descriptively using Miles and Huberman steps. The results show that students have difficulties in solving the probabilistic problem and can be divided into three categories. First difficulties relate to students’ difficulties in understanding the probabilistic problem. Second, students’ difficulties in choosing and using appropriate strategies for solving the problem. Third, students’ difficulties with the computational process in solving the problem. Based on the result seems that students still have difficulties in solving the probabilistic problem. It means that students have not able to use their knowledge and ability for responding probabilistic problem yet. Therefore, it is important for mathematics teachers to plan probabilistic learning which could optimize students probabilistic thinking ability.

Authenticity of Mathematical Modeling

Science.gov (United States)

Tran, Dung; Dougherty, Barbara J.

2014-01-01

Some students leave high school never quite sure of the relevancy of the mathematics they have learned. They fail to see links between school mathematics and the mathematics of everyday life that requires thoughtful decision making and often complex problem solving. Is it possible to bridge the gap between school mathematics and the mathematics in…

Analysis of junior high school students' attempt to solve a linear inequality problem

Science.gov (United States)

Taqiyuddin, Muhammad; Sumiaty, Encum; Jupri, Al

2017-08-01

Linear inequality is one of fundamental subjects within junior high school mathematics curricula. Several studies have been conducted to asses students' perform on linear inequality. However, it can hardly be found that linear inequality problems are in the form of "ax + b condition leads to the research questions concerning students' attempt on solving a simple linear inequality problem in this form. In order to do so, the written test was administered to 58 students from two schools in Bandung followed by interviews. The other sources of the data are from teachers' interview and mathematics books used by students. After that, the constant comparative method was used to analyse the data. The result shows that the majority approached the question by doing algebraic operations. Interestingly, most of them did it incorrectly. In contrast, algebraic operations were correctly used by some of them. Moreover, the others performed expected-numbers solution, rewriting the question, translating the inequality into words, and blank answer. Furthermore, we found that there is no one who was conscious of the existence of all-numbers solution. It was found that this condition is reasonably due to how little the learning components concern about why a procedure of solving a linear inequality works and possibilities of linear inequality solution.

Mathematical mechanic using physical reasoning to solve problems

CERN Document Server

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

Mathematical tapas

CERN Document Server

Hiriart-Urruty, Jean-Baptiste

This book contains a collection of exercises (called “tapas”) at undergraduate level, mainly from the fields of real analysis, calculus, matrices, convexity, and optimization. Most of the problems presented here are non-standard and some require broad knowledge of different mathematical subjects in order to be solved. The author provides some hints and (partial) answers and also puts these carefully chosen exercises into context, presents information on their origins, and comments on possible extensions. With stars marking the levels of difficulty, these tapas show or prove something interesting, challenge the reader to solve and learn, and may have surprising results. This first volume of Mathematical Tapas will appeal to mathematicians, motivated undergraduate students from science-based areas, and those generally interested in mathematics.

Mathematical writing

CERN Document Server

Vivaldi, Franco

2014-01-01

This book teaches the art of writing mathematics, an essential -and difficult- skill for any mathematics student.   The book begins with an informal introduction on basic writing principles and a review of the essential dictionary for mathematics. Writing techniques are developed gradually, from the small to the large: words, phrases, sentences, paragraphs, to end with short compositions. These may represent the introduction of a concept, the abstract of a presentation or the proof of a theorem. Along the way the student will learn how to establish a coherent notation, mix words and symbols effectively, write neat formulae, and structure a definition.   Some elements of logic and all common methods of proofs are featured, including various versions of induction and existence proofs. The book concludes with advice on specific aspects of thesis writing (choosing of a title, composing an abstract, compiling a bibliography) illustrated by large number of real-life examples. Many exercises are included; over 150...

Classification of SBS Mathematics Questions between 2008-2013 years with Respect to PISA Competency Levels

Directory of Open Access Journals (Sweden)

Tuğba Aydoğdu İskenderoğlu

2013-11-01

Full Text Available One of the main objectives of the education is students are ready to make the conditions of the age in which they live. From this perspective approach of mathematics education changed in our age looking for answers to the question as instead of "what we teach them?", "How they use our teaching which their life?". In other words, the main purpose of education is our students collected under the mathematical literacy. Then teach them which students' knowledge which use in everyday life, to make logical inferences, interpret and solve problems related to the various situations. The purpose of this study was implemented in our country between the years of 2008-2013 SBS questions examined and categorized according to the scale which PISA mathematics proficiency. In this study, data was collected using qualitative research techniques, document analysis methods of data collection. The results of the study, the questions examined in this study all levels of math exams in 2008-2013 SBS was not appropriate questions. Questions in general 2, 3 and 4 levels of which they are located, exams include just one question which is the highest level of 5 and there have not been any questions level 6. SBS administered by the Ministry of National Education thought-provoking the absence of the upper levels questions. For this reason, math questions of SBS should be every level and be prepared questions reconsideration measurement is recommended.Key Words: PISA, Mathematics competency levels, Mathematics competency scale, Mathematics problems of SBS

PROBLEM SOLVING IN SCHOOL MATHEMATICS BASED ON HEURISTIC STRATEGIES

Directory of Open Access Journals (Sweden)

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.

The SQUARE ONE TV Interview: Children's Reactions to the Series--Volume IV. Children's Problem-Solving Behavior and Their Attitudes toward Mathematics: A Study of the Effects of SQUARE ONE TV.

Science.gov (United States)

Hall, Eve R.; And Others

The current period in mathematics education can be characterized as one of reform. Many feel that children in the United States are not learning enough appropriate mathematics; these critics are concerned with the specific areas of problem solving and children's conceptions of the nature and uses of mathematics. A pretest/posttest experimental…

Students’ difficulties in solving linear equation problems

Science.gov (United States)

Wati, S.; Fitriana, L.; Mardiyana

2018-03-01

A linear equation is an algebra material that exists in junior high school to university. It is a very important material for students in order to learn more advanced mathematics topics. Therefore, linear equation material is essential to be mastered. However, the result of 2016 national examination in Indonesia showed that students’ achievement in solving linear equation problem was low. This fact became a background to investigate students’ difficulties in solving linear equation problems. This study used qualitative descriptive method. An individual written test on linear equation tasks was administered, followed by interviews. Twenty-one sample students of grade VIII of SMPIT Insan Kamil Karanganyar did the written test, and 6 of them were interviewed afterward. The result showed that students with high mathematics achievement donot have difficulties, students with medium mathematics achievement have factual difficulties, and students with low mathematics achievement have factual, conceptual, operational, and principle difficulties. Based on the result there is a need of meaningfulness teaching strategy to help students to overcome difficulties in solving linear equation problems.

Comparing different kinds of words and word-word relations to test an habituation model of priming.

Science.gov (United States)

Rieth, Cory A; Huber, David E

2017-06-01

Huber and O'Reilly (2003) proposed that neural habituation exists to solve a temporal parsing problem, minimizing blending between one word and the next when words are visually presented in rapid succession. They developed a neural dynamics habituation model, explaining the finding that short duration primes produce positive priming whereas long duration primes produce negative repetition priming. The model contains three layers of processing, including a visual input layer, an orthographic layer, and a lexical-semantic layer. The predicted effect of prime duration depends both on this assumed representational hierarchy and the assumption that synaptic depression underlies habituation. The current study tested these assumptions by comparing different kinds of words (e.g., words versus non-words) and different kinds of word-word relations (e.g., associative versus repetition). For each experiment, the predictions of the original model were compared to an alternative model with different representational assumptions. Experiment 1 confirmed the prediction that non-words and inverted words require longer prime durations to eliminate positive repetition priming (i.e., a slower transition from positive to negative priming). Experiment 2 confirmed the prediction that associative priming increases and then decreases with increasing prime duration, but remains positive even with long duration primes. Experiment 3 replicated the effects of repetition and associative priming using a within-subjects design and combined these effects by examining target words that were expected to repeat (e.g., viewing the target word 'BACK' after the prime phrase 'back to'). These results support the originally assumed representational hierarchy and more generally the role of habituation in temporal parsing and priming. Copyright © 2017 Elsevier Inc. All rights reserved.

Helping Children Learn Mathematics through Multiple Intelligences and Standards for School Mathematics.

Science.gov (United States)

Adams, Thomasenia Lott

2001-01-01

Focuses on the National Council of Teachers of Mathematics 2000 process-oriented standards of problem solving, reasoning and proof, communication, connections, and representation as providing a framework for using the multiple intelligences that children bring to mathematics learning. Presents ideas for mathematics lessons and activities to…

A Mathematics Software Database Update.

Science.gov (United States)

Cunningham, R. S.; Smith, David A.

1987-01-01

Contains an update of an earlier listing of software for mathematics instruction at the college level. Topics are: advanced mathematics, algebra, calculus, differential equations, discrete mathematics, equation solving, general mathematics, geometry, linear and matrix algebra, logic, statistics and probability, and trigonometry. (PK)

Mathematical visualization process of junior high school students in solving a contextual problem based on cognitive style

Science.gov (United States)

Utomo, Edy Setiyo; Juniati, Dwi; Siswono, Tatag Yuli Eko

2017-08-01

The aim of this research was to describe the mathematical visualization process of Junior High School students in solving contextual problems based on cognitive style. Mathematical visualization process in this research was seen from aspects of image generation, image inspection, image scanning, and image transformation. The research subject was the students in the eighth grade based on GEFT test (Group Embedded Figures Test) adopted from Within to determining the category of cognitive style owned by the students namely field independent or field dependent and communicative. The data collection was through visualization test in contextual problem and interview. The validity was seen through time triangulation. The data analysis referred to the aspect of mathematical visualization through steps of categorization, reduction, discussion, and conclusion. The results showed that field-independent and field-dependent subjects were difference in responding to contextual problems. The field-independent subject presented in the form of 2D and 3D, while the field-dependent subject presented in the form of 3D. Both of the subjects had different perception to see the swimming pool. The field-independent subject saw from the top, while the field-dependent subject from the side. The field-independent subject chose to use partition-object strategy, while the field-dependent subject chose to use general-object strategy. Both the subjects did transformation in an object rotation to get the solution. This research is reference to mathematical curriculum developers of Junior High School in Indonesia. Besides, teacher could develop the students' mathematical visualization by using technology media or software, such as geogebra, portable cabri in learning.

Doing words together

DEFF Research Database (Denmark)

Fusaroli, Riccardo; Østergaard, Svend; Raczaszek-Leonardi, Joanna

In this paper we test the effects of social interactions in embodied problem solving by employing a Scrabble-like setting. 28 pairs of participants had to generate as many words as possible from 2 balanced sets of 7 letters, which they could manipulate, either individually or collectively...

Enhancing learners’ problem solving performance in mathematics: A cognitive load perspective - See more at: http://www.lectitopublishing.nl/Article/List/88/11/15#sthash.gmkglGIQ.dpuf

Directory of Open Access Journals (Sweden)

Joseph J. Dhlamini

2016-03-01

Full Text Available 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 in relation to learners’ problem solving performance. In this paper CBPSI refers to a teaching approach in which everyday problem solving knowledge and practices are uncovered when learners are exposed to tasks that give meaning to their everyday experiences. Given that the design of a pilot study lacked the inclusion of a control group, it is reasonable to conclude that the current design embraced elements of a pre-experimental research approach in which a one-group pre-test post-test design was followed. Participants consisted of a convenient sample of 57 Grade 10 learners who performed poorly in mathematics problem solving. The results of the study informed various conceptual and methodological revisions to strengthen the design of the main study, however, this paper reports only the effect of CBPSI on participants’ problem solving performance. The post-intervention achievement test suggested that CBPSI was effective in substantially accelerating learners’ problem solving performance (p<0.05. Using a cognitive load theory, it is possible to explain aspects of growth in learners’ problem solving performance in relation to the conceptual notion of human cognitive architecture.

The Enhancement of Junior High School Students' Abilities in Mathematical Problem Solving Using Soft Skill-based Metacognitive Learning

OpenAIRE

Murni, Atma; Sabandar, Jozua; S. Kusumah, Yaya; Kartasamita, Bana Goerbana

2013-01-01

The aim of this study is to know the differences of enhancement in mathematical problem solving ability (MPSA) between the students who received soft skill- based metacognitive learning (SSML) with the students who got conventional learning (CL). This research is a quasi experimental design with pretest-postest control group. The population in this study is the students of Junior High School in Pekanbaru city. The sample consist of 135 students, 68 of them are from the high-level...

Multiple Paths to Mathematics Practice in Al-Kashi's Key to Arithmetic

Science.gov (United States)

Taani, Osama

2014-01-01

In this paper, I discuss one of the most distinguishing features of Jamshid al-Kashi's pedagogy from his Key to Arithmetic, a well-known Arabic mathematics textbook from the fifteenth century. This feature is the multiple paths that he includes to find a desired result. In the first section light is shed on al-Kashi's life and his contributions to mathematics and astronomy. Section 2 starts with a brief discussion of the contents and pedagogy of the Key to Arithmetic. Al-Kashi's multiple approaches are discussed through four different examples of his versatility in presenting a topic from multiple perspectives. These examples are multiple definitions, multiple algorithms, multiple formulas, and multiple methods for solving word problems. Section 3 is devoted to some benefits that can be gained by implementing al-Kashi's multiple paths approach in modern curricula. For this discussion, examples from two teaching modules taken from the Key to Arithmetic and implemented in Pre-Calculus and mathematics courses for preservice teachers are discussed. Also, the conclusions are supported by some aspects of these modules. This paper is an attempt to help mathematics educators explore more benefits from reading from original sources.

Schema Knowledge for Solving Arithmetic Story Problems: Some Affective Components.

Science.gov (United States)

Marshall, Sandra P.

This report discusses the role of affect in cognitive processing. The importance of affect in processing mathematical information is described in the context of solving arithmetic story problems. Some ideas are offered about the way affective responses to mathematical problem solving situations influence the development, maintenance, and retrieval…

Longitudinal mediators of achievement in mathematics and reading in typical and atypical development.

Science.gov (United States)

Barnes, Marcia A; Raghubar, Kimberly P; English, Lianne; Williams, Jeffrey M; Taylor, Heather; Landry, Susan

2014-03-01

Longitudinal studies of neurodevelopmental disorders that are diagnosed at or before birth and are associated with specific learning difficulties at school-age provide one method for investigating developmental precursors of later-emerging academic disabilities. Spina bifida myelomeningocele (SBM) is a neurodevelopmental disorder associated with particular problems in mathematics, in contrast to well-developed word reading. Children with SBM (n=30) and typically developing children (n=35) were used to determine whether cognitive abilities measured at 36 and 60 months of age mediated the effect of group on mathematical and reading achievement outcomes at 8.5 and 9.5 years of age. A series of multiple mediator models showed that: visual-spatial working memory at 36 months and phonological awareness at 60 months partially mediated the effect of group on math calculations, phonological awareness partially mediated the effect of group on small addition and subtraction problems on a test of math fluency, and visual-spatial working memory mediated the effect of group on a test of math problem solving. Groups did not differ on word reading, and phonological awareness was the only mediator for reading fluency and reading comprehension. The findings are discussed with reference to theories of mathematical development and disability and with respect to both common and differing cognitive correlates of math and reading. Copyright © 2013 Elsevier Inc. All rights reserved.

The Relationship between Students' Performance on Conventional Standardized Mathematics Assessments and Complex Mathematical Modeling Problems

Science.gov (United States)

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…

Cognitive Strategies, Working Memory, and Growth in Word Problem Solving in Children With Math Difficulties.

Science.gov (United States)

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.

The Social Essentials of Learning: An Experimental Investigation of Collaborative Problem Solving and Knowledge Construction in Mathematics Classrooms in Australia and China

Science.gov (United States)

Chan, Man Ching Esther; Clarke, David; Cao, Yiming

2018-01-01

Interactive problem solving and learning are priorities in contemporary education, but these complex processes have proved difficult to research. This project addresses the question "How do we optimise social interaction for the promotion of learning in a mathematics classroom?" Employing the logic of multi-theoretic research design,…

Introductory discrete mathematics

CERN Document Server

Balakrishnan, V K

2010-01-01

This concise text offers an introduction to discrete mathematics for undergraduate students in computer science and mathematics. Mathematics educators consider it vital that their students be exposed to a course in discrete methods that introduces them to combinatorial mathematics and to algebraic and logical structures focusing on the interplay between computer science and mathematics. The present volume emphasizes combinatorics, graph theory with applications to some stand network optimization problems, and algorithms to solve these problems.Chapters 0-3 cover fundamental operations involv

PEMBELAJARAN KONTEKSTUAL OPEN ENDED PROBLEM SOLVING DENGAN KOMIK MATEMATIKA UNTUK MENINGKATKAN KETERAMPILAN PEMECAHAN MASALAH

Directory of Open Access Journals (Sweden)

Lenny Kurniati

2017-01-01

ABSTRACT The aim of this research to develop a mathematics learning instrument using contextual open ended problem solving with mathematic comic to increase the problem solving skill which valid, practical and effective. The type of research used in this study is development research using modification of Plomp model. Learning instrumen that have been develop are: syllabus, Lesson plan, worksheet, mathematics comic, and problem solving ability test. The results showed: (1 device developed valid; (2 practical learning is characterized by the positive response of students and good teachers ability, (3 Effectiveness characterized by (a problem solving ability score of the experimental class higher than minimum completeness criterion, (b learn interest and problem solving skill, both affected the problem solving ability positively,  (c problem solving ability of the experimental class score is higher than the control class, (d problem solving skill of the experimental class is increasing by 31%, the problem solving ability of the experimental class higher than the control class.. Because of the learning instrument develope are valid, practice and effective, it is shows that the research has ben reach out. Keywords: contextual teaching and learning, open ended problem solving, mathematics comic, problem solving.

The Magic of Mathematics Discovering the Spell of Mathematics

CERN Document Server

Pappas, Theoni

2011-01-01

Delves into the world of ideas, explores the spell mathematics casts on our lives, and helps you discover mathematics where you least expect it. Be spellbound by the mathematical designs found in nature. Learn how knots may untie the mysteries of life. Be mesmerized by the computer revolution. Discover how the hidden forces of mathematics hold architectural structures together connect your telephone calls help airplanes get off the ground solve the mysteries of the living cell. See how some artists use a mathematical palette in their works and how many writers draw upon the wealth of its ideas

Capturing Problem-Solving Processes Using Critical Rationalism

Science.gov (United States)

Chitpin, Stephanie; Simon, Marielle

2012-01-01

The examination of problem-solving processes continues to be a current research topic in education. Knowing how to solve problems is not only a key aspect of learning mathematics but is also at the heart of cognitive theories, linguistics, artificial intelligence, and computers sciences. Problem solving is a multistep, higher-order cognitive task…

Mathematical logic as a mean of solving the problems of power supply for buildings and constructions

Science.gov (United States)

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.

Does Solving Insight-Based Problems Differ from Solving Learning-Based Problems? Some Evidence from an ERP Study

Science.gov (United States)

Leikin, Roza; Waisman, Ilana; Leikin, Mark

2016-01-01

We asked: "What are the similarities and differences in mathematical processing associated with solving learning-based and insight-based problems?" To answer this question, the ERP research procedure was employed with 69 male adolescent subjects who solved specially designed insight-based and learning-based tests. Solutions of…

Struggling Students' Use of Representation When Developing Number Sense and Problem Solving Abilities

OpenAIRE

Roxburgh, Allison L.

2016-01-01

Through my experience I have found students often rely on concrete or pictorial strategies to solve mathematical problems. These strategies are great to build an understanding in mathematical concepts. However, using these strategies becomes a tedious task when working with multi-digit numbers to solve problems involving mathematical operations. For example, a student who relies on drawing base ten blocks to solve three-digit addition problems may experience fatigue, as this is not the most e...

Mathematical methods for physicists

CERN Document Server

Arfken, George B

2005-01-01

This best-selling title provides in one handy volume the essential mathematical tools and techniques used to solve problems in physics. It is a vital addition to the bookshelf of any serious student of physics or research professional in the field. The authors have put considerable effort into revamping this new edition.* Updates the leading graduate-level text in mathematical physics* Provides comprehensive coverage of the mathematics necessary for advanced study in physics and engineering* Focuses on problem-solving skills and offers a vast array of exercises * Clearly illustrates and proves mathematical relationsNew in the Sixth Edition:* Updated content throughout, based on users'' feedback * More advanced sections, including differential forms and the elegant forms of Maxwell''s equations* A new chapter on probability and statistics* More elementary sections have been deleted

WordPress 3 Cookbook

CERN Document Server

Shreves, Ric

2011-01-01

This is a Packt Cookbook, which means it contains step-by-step instructions to achieve a particular goal or solve a particular problem. There are plenty of screenshots and explained practical tasks to make comprehension quick and easy. This book is not specifically for developers or programmers; rather it can be used by anyone who wants to get more out of their WordPress blog by following step-by-step instructions. A basic knowledge of PHP/XHTML/CSS/WordPress is desirable but not necessary.

The effects of cumulative practice on mathematics problem solving.

Science.gov (United States)

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.

Connecting Mathematics in Primary Science Inquiry Projects

Science.gov (United States)

So, Winnie Wing-mui

2013-01-01

Science as inquiry and mathematics as problem solving are conjoined fraternal twins attached by their similarities but with distinct differences. Inquiry and problem solving are promoted in contemporary science and mathematics education reforms as a critical attribute of the nature of disciplines, teaching methods, and learning outcomes involving…

Forms of Understanding in Mathematical Problem Solving.

Science.gov (United States)

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

Math in plain english literacy strategies for the mathematics classroom

CERN Document Server

Benjamin, Amy

2013-01-01

Do word problems and math vocabulary confuse students in your mathematics classes? Do simple keywords like ""value"" and ""portion"" seem to mislead them? Many words that students already know can have a different meaning in mathematics. To grasp that difference, students need to connect English literacy skills to math. Successful students speak, read, write, and listen to each other so they can understand, retain, and apply mathematics concepts. This book explains how to use 10 classroom-ready literacy strategies in concert with your mathematics instruction. You'll learn how to develop stude

Mathematical Graphic Organizers

Science.gov (United States)

Zollman, Alan

2009-01-01

As part of a math-science partnership, a university mathematics educator and ten elementary school teachers developed a novel approach to mathematical problem solving derived from research on reading and writing pedagogy. Specifically, research indicates that students who use graphic organizers to arrange their ideas improve their comprehension…

Mathematical physics applied mathematics for scientists and engineers

CERN Document Server

Kusse, Bruce R

2006-01-01

What sets this volume apart from other mathematics texts is its emphasis on mathematical tools commonly used by scientists and engineers to solve real-world problems. Using a unique approach, it covers intermediate and advanced material in a manner appropriate for undergraduate students. Based on author Bruce Kusse's course at the Department of Applied and Engineering Physics at Cornell University, Mathematical Physics begins with essentials such as vector and tensor algebra, curvilinear coordinate systems, complex variables, Fourier series, Fourier and Laplace transforms, differential and integral equations, and solutions to Laplace's equations

Mathematical learning disabilities and attention deficit and/or hyperactivity disorder: A study of the cognitive processes involved in arithmetic problem solving.

Science.gov (United States)

Iglesias-Sarmiento, Valentín; Deaño, Manuel; Alfonso, Sonia; Conde, Ángeles

2017-02-01

The purpose of this study was to examine the contribution of cognitive functioning to arithmetic problem solving and to explore the cognitive profiles of children with attention deficit and/or hyperactivity disorder (ADHD) and with mathematical learning disabilities (MLD). The sample was made up of a total of 90 students of 4th, 5th, and 6th grade organized in three: ADHD (n=30), MLD (n=30) and typically achieving control (TA; n=30) group. Assessment was conducted in two sessions in which the PASS processes and arithmetic problem solving were evaluated. The ADHD group's performance in planning and attention was worse than that of the control group. Children with MLD obtained poorer results than the control group in planning and simultaneous and successive processing. Executive processes predicted arithmetic problem solving in the ADHD group whereas simultaneous processing was the unique predictor in the MLD sample. Children with ADHD and with MLD showed characteristic cognitive profiles. Groups' problem-solving performance can be predicted from their cognitive functioning. Copyright © 2016 Elsevier Ltd. All rights reserved.

STEM Gives Meaning to Mathematics

Science.gov (United States)

Hefty, Lukas J.

2015-01-01

The National Council of Teachers of Mathematics' (NCTM's) "Principles and Standards for School Mathematics" (2000) outlines fi ve Process Standards that are essential for developing deep understanding of mathematics: (1) Problem Solving; (2) Reasoning and Proof; (3) Communication; (4) Connections; and (5) Representation. The Common Core…

Conceptual Problem Solving in High School Physics

Science.gov (United States)

Docktor, Jennifer L.; Strand, Natalie E.; Mestre, José P.; Ross, Brian H.

2015-01-01

Problem solving is a critical element of learning physics. However, traditional instruction often emphasizes the quantitative aspects of problem solving such as equations and mathematical procedures rather than qualitative analysis for selecting appropriate concepts and principles. This study describes the development and evaluation of an…

Mathematics for computer graphics

CERN Document Server

Vince, John

2006-01-01

Helps you understand the mathematical ideas used in computer animation, virtual reality, CAD, and other areas of computer graphics. This work also helps you to rediscover the mathematical techniques required to solve problems and design computer programs for computer graphic applications

Semantic Contamination and Mathematical Proof: Can a Non-Proof Prove?

Science.gov (United States)

Mejia-Ramos, Juan Pablo; Inglis, Matthew

2011-01-01

The way words are used in natural language can influence how the same words are understood by students in formal educational contexts. Here we argue that this so-called semantic contamination effect plays a role in determining how students engage with mathematical proof, a fundamental aspect of learning mathematics. Analyses of responses to…

Spoken Word Recognition and Serial Recall of Words from Components in the Phonological Network

Science.gov (United States)

Siew, Cynthia S. Q.; Vitevitch, Michael S.

2016-01-01

Network science uses mathematical techniques to study complex systems such as the phonological lexicon (Vitevitch, 2008). The phonological network consists of a "giant component" (the largest connected component of the network) and "lexical islands" (smaller groups of words that are connected to each other, but not to the giant…

Spreadsheet-Enhanced Problem Solving in Context as Modeling

Directory of Open Access Journals (Sweden)

Sergei Abramovich

2003-07-01

development through situated mathematical problem solving. Modeling activities described in this paper support the epistemological position regarding the interplay that exists between the development of mathematical concepts and available methods of calculation. The spreadsheet used is Microsoft Excel 2001

Study on solitary word based on HMM model and Baum-Welch algorithm

Directory of Open Access Journals (Sweden)

Junxia CHEN

Full Text Available This paper introduces the principle of Hidden Markov Model, which is used to describe the Markov process with unknown parameters, is a probability model to describe the statistical properties of the random process. On this basis, designed a solitary word detection experiment based on HMM model, by optimizing the experimental model, Using Baum-Welch algorithm for training the problem of solving the HMM model, HMM model to estimate the parameters of the λ value is found, in this view of mathematics equivalent to other linear prediction coefficient. This experiment in reducing unnecessary HMM training at the same time, reduced the algorithm complexity. In order to test the effectiveness of the Baum-Welch algorithm, The simulation of experimental data, the results show that the algorithm is effective.

Conceptual problem solving in high school physics

OpenAIRE

Jennifer L. Docktor; Natalie E. Strand; José P. Mestre; Brian H. Ross

2015-01-01

Problem solving is a critical element of learning physics. However, traditional instruction often emphasizes the quantitative aspects of problem solving such as equations and mathematical procedures rather than qualitative analysis for selecting appropriate concepts and principles. This study describes the development and evaluation of an instructional approach called Conceptual Problem Solving (CPS) which guides students to identify principles, justify their use, and plan their solution in w...

Why does placing the question before an arithmetic word problem improve performance? A situation model account.

Science.gov (United States)

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.

Vacuum engineering, calculations, formulas, and solved exercises

CERN Document Server

Berman, Armand

1992-01-01

This book was written with two main objectives in mind-to summarize and organize the vast material of vacuum technology in sets of useful formulas, and to provide a collection of worked out exercises showing how to use these formulas for solving technological problems. It is an ideal reference source for those with little time to devote to a full mathematical treatment of the many problems issued in vacuum practice, but who have a working knowledge of the essentials of vacuum technology, elementary physics, and mathematics. This time saving book employs a problem-solving approach throughout, p

A Primer for Mathematical Modeling

Science.gov (United States)

Sole, Marla

2013-01-01

With the implementation of the National Council of Teachers of Mathematics recommendations and the adoption of the Common Core State Standards for Mathematics, modeling has moved to the forefront of K-12 education. Modeling activities not only reinforce purposeful problem-solving skills, they also connect the mathematics students learn in school…

How students process equations in solving quantitative synthesis problems? Role of mathematical complexity in students’ mathematical performance

Directory of Open Access Journals (Sweden)

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.

Schema building profiles among elementary school students in solving problems related to operations of addition to fractions on the basis of mathematic abilities

Science.gov (United States)

Gembong, S.; Suwarsono, S. T.; Prabowo

2018-03-01

Schema in the current study refers to a set of action, process, object and other schemas already possessed to build an individual’s ways of thinking to solve a given problem. The current study aims to investigate the schemas built among elementary school students in solving problems related to operations of addition to fractions. The analyses of the schema building were done qualitatively on the basis of the analytical framework of the APOS theory (Action, Process, Object, and Schema). Findings show that the schemas built on students of high and middle ability indicate the following. In the action stage, students were able to add two fractions by way of drawing a picture or procedural way. In the Stage of process, they could add two and three fractions. In the stage of object, they could explain the steps of adding two fractions and change a fraction into addition of fractions. In the last stage, schema, they could add fractions by relating them to another schema they have possessed i.e. the least common multiple. Those of high and middle mathematic abilities showed that their schema building in solving problems related to operations odd addition to fractions worked in line with the framework of the APOS theory. Those of low mathematic ability, however, showed that their schema on each stage did not work properly.

How Mathematics Teachers Develop Their Pupils' Self-Regulated Learning Skills

Science.gov (United States)

Marchis, Iuliana

2011-01-01

Self-regulated learning skills are important in mathematical problem solving. The aim of the paper is to present a research on how mathematics teachers guide their pupils' mathematical problem-solving activities in order to increase self-regulation. 62 teachers have filled in a questionnaire developed for this research. The results are show that…

Using Mathematics and Engineering to Solve Problems in Secondary Level Biology

Science.gov (United States)

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'…

Formal languages, automata and numeration systems introduction to combinatorics on words

CERN Document Server

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

Fielding an After-School Mathematics Lab

Science.gov (United States)

Punches-Guntsch, Christina M.; Kenney, Erin N.

2012-01-01

Many students will need remedial work in mathematics during their high school years. Some sort of help will be needed to fulfill the National Council of Teachers of Mathematics' (NCTM's) (2000) vision of a mathematics classroom that involves students having access to mathematically rich problems and being engaged in solving them. The high school…

Pattern of mathematic representation ability in magnetic electricity problem

Science.gov (United States)

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.

Factors involved in making post-performance judgments in mathematics problem-solving.

Science.gov (United States)

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.

Analysis of difficulties in mathematics problem solving based on revised Bloom’s Taxonomy viewed from high self-efficacy

Science.gov (United States)

Prismana, R. D. E.; Kusmayadi, T. A.; Pramudya, I.

2018-04-01

The ability of solving problem is a part of the mathematic curriculum that is very important. Problem solving prefers the process and strategy that is done by students in solving a problem rather than the result. This learning concept in accordance with the stages on the revised bloom’s taxonomy. The revised Bloom’s Taxonomy has two dimensions, namely the dimension of cognitive process and the dimension of knowledge. Dimension of knowledge has four categories, but this study only restricted on two knowledge, conceptual knowledge and procedural knowledge. Dimensions of cognitive processes are categorized into six kinds, namely remembering, understanding, applying, analyzing, evaluating, and creating. Implementation of learning more emphasis on the role of students. Students must have their own belief in completing tasks called self-efficacy. This research is a qualitative research. This research aims to know the site of the students’ difficulty based on revised Bloom’s Taxonomy viewed from high self-efficacy. The results of the study stated the students with high self efficacy have difficulties site. They are evaluating conceptual knowledge, evaluating procedural knowledge, creating conceptual knowledge, and creating procedural knowledge. It could be the consideration of teachers in the teaching, so as to reduce the difficulties of learning in students.

Discrete Mathematics Re "Tooled."

Science.gov (United States)

Grassl, Richard M.; Mingus, Tabitha T. Y.

1999-01-01

Indicates the importance of teaching discrete mathematics. Describes how the use of technology can enhance the teaching and learning of discrete mathematics. Explorations using Excel, Derive, and the TI-92 proved how preservice and inservice teachers experienced a new dimension in problem solving and discovery. (ASK)

Problem Solving Reasoning and Problem Based Instruction in Geometry Learning

Science.gov (United States)

Sulistyowati, F.; Budiyono, B.; Slamet, I.

2017-09-01

This research aims to analyze the comparison Problem Solving Reasoning (PSR) and Problem Based Instruction (PBI) on problem solving and mathematical communication abilities viewed from Self-Regulated Learning (SRL). Learning was given to grade 8th junior high school students. This research uses quasi experimental method, and then with descriptive analysis. Data were analyzed using two-ways multivariate analysis of variance (MANOVA) and one-way analysis of variance (ANOVA) with different cells. The result of data analysis were learning model gives different effect, level of SRL gives the same effect, and there is no interaction between the learning model with the SRL on the problem solving and mathematical communication abilities. The t-test statistic was used to find out more effective learning model. Based on the test, regardless of the level of SRL, PSR is more effective than PBI for problemsolving ability. The result of descriptive analysis was PSR had the advantage in creating learning that optimizing the ability of learners in reasoning to solve a mathematical problem. Consequently, the PSR is the right learning model to be applied in the classroom to improve problem solving ability of learners.

Mathematical thinking styles of undergraduate students and their achievement in mathematics

Science.gov (United States)

Risnanosanti

2017-08-01

The main purpose of this study is to analyze the role of mathematical thinking styles in students' achievement in mathematics. On the basis of this study, it is also to generate recommendation for classroom instruction. The two specific aims are; first to observe students' mathematical thinking styles during problem solving, the second to asses students' achievement in mathematics. The data were collected by using Mathematical Thinking Styles questionnaires and test of students' achievement in mathematics. The subject in this study was 35 students from third year at mathematics study program of Muhammadiyah University of Bengkulu in academic year 2016/2017. The result of this study was that the students have three mathematical thinking styles (analytic, visual, and integrated), and the students who have analytic styles have better achievement than those who have visual styles in mathematics.

An Examination of the Relationship between Computation, Problem Solving, and Reading

Science.gov (United States)

Cormier, Damien C.; Yeo, Seungsoo; Christ, Theodore J.; Offrey, Laura D.; Pratt, Katherine

2016-01-01

The purpose of this study is to evaluate the relationship of mathematics calculation rate (curriculum-based measurement of mathematics; CBM-M), reading rate (curriculum-based measurement of reading; CBM-R), and mathematics application and problem solving skills (mathematics screener) among students at four levels of proficiency on a statewide…

Modern mathematics made simple

CERN Document Server

Murphy, Patrick

1982-01-01

Modern Mathematics: Made Simple presents topics in modern mathematics, from elementary mathematical logic and switching circuits to multibase arithmetic and finite systems. Sets and relations, vectors and matrices, tesselations, and linear programming are also discussed.Comprised of 12 chapters, this book begins with an introduction to sets and basic operations on sets, as well as solving problems with Venn diagrams. The discussion then turns to elementary mathematical logic, with emphasis on inductive and deductive reasoning; conjunctions and disjunctions; compound statements and conditional

Working Together to Improve the Quality of Mathematics Education ...

African Journals Online (AJOL)

Prof

Key words: Parents; mathematics education; perception; school climate; .... elementary school children, established that parents with higher college degrees ..... International Journal of Mathematical Education in Science and Technology,.

Strategy Keys as Tools for Problem Solving

Science.gov (United States)

Herold-Blasius, Raja

2017-01-01

Problem solving is one of the main competences we seek to teach students at school for use in their future lives. However, when dealing with mathematical problems, teachers encounter a wide variety of difficulties. To foster students' problem-solving skills, the authors developed "strategy keys." Strategy keys can serve as material to…

Teaching Mathematical Problem Solving to Students with Limited English Proficiency.

Science.gov (United States)

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…

Preservice Agricultural Education Teachers' Mathematics Ability

Science.gov (United States)

Stripling, Christopher T.; Roberts, T. Grady

2012-01-01

The purpose of this study was to examine the mathematics ability of the nation's preservice agricultural education teachers. Based on the results of this study, preservice teachers were not proficient in solving agricultural mathematics problems, and agricultural teacher education programs require basic and intermediate mathematics as their…

On Solving Linear Recurrences

Science.gov (United States)

Dobbs, David E.

2013-01-01

A direct method is given for solving first-order linear recurrences with constant coefficients. The limiting value of that solution is studied as "n to infinity." This classroom note could serve as enrichment material for the typical introductory course on discrete mathematics that follows a calculus course.

Ratio Analysis: Where Investments Meet Mathematics.

Science.gov (United States)

Barton, Susan D.; Woodbury, Denise

2002-01-01

Discusses ratio analysis by which investments may be evaluated. Requires the use of fundamental mathematics, problem solving, and a comparison of the mathematical results within the framework of industry. (Author/NB)

Soundoff: Mathematics Is Getting Easier.

Science.gov (United States)

Usiskin, Zalman

1984-01-01

Teaching mathematics in hard ways, rather than using easier methods or technology, is described. Employing the most efficient means possible to solve a problem is the essence of good mathematics, rather than wasting time in practicing obsolete skills. (MNS)

Anticipation Guides: Reading for Mathematics Understanding

Science.gov (United States)

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…

Using CAS to Solve Classical Mathematics Problems

Science.gov (United States)

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…

Applying Cooperative Techniques in Teaching Problem Solving

Directory of Open Access Journals (Sweden)

Krisztina Barczi

2013-12-01

Full Text Available Teaching how to solve problems – from solving simple equations to solving difficult competition tasks – has been one of the greatest challenges for mathematics education for many years. Trying to find an effective method is an important educational task. Among others, the question arises as to whether a method in which students help each other might be useful. The present article describes part of an experiment that was designed to determine the effects of cooperative teaching techniques on the development of problem-solving skills.

Error Analysis for Arithmetic Word Problems--A Case Study of Primary Three Students in One Singapore School