Mathematics as Problem Solving.
Soifer, Alexander
This book contains about 200 problems. It is suggested that it be used by students, teachers or anyone interested in exploring mathematics. In addition to a general discussion on problem solving, there are problems concerned with number theory, algebra, geometry, and combinatorics. (PK)
How to solve mathematical problems
Wickelgren, Wayne A
1995-01-01
Seven problem-solving techniques include inference, classification of action sequences, subgoals, contradiction, working backward, relations between problems, and mathematical representation. Also, problems from mathematics, science, and engineering with complete solutions.
Problem solving through recreational mathematics
Averbach, Bonnie
1999-01-01
Historically, many of the most important mathematical concepts arose from problems that were recreational in origin. This book takes advantage of that fact, using recreational mathematics - problems, puzzles and games - to teach students how to think critically. Encouraging active participation rather than just observation, the book focuses less on mathematical results than on how these results can be applied to thinking about problems and solving them. Each chapter contains a diverse array of problems in such areas as logic, number and graph theory, two-player games of strategy, solitaire ga
Journey toward Teaching Mathematics through Problem Solving
Sakshaug, Lynae E.; Wohlhuter, Kay A.
2010-01-01
Teaching mathematics through problem solving is a challenge for teachers who learned mathematics by doing exercises. How do teachers develop their own problem solving abilities as well as their abilities to teach mathematics through problem solving? A group of teachers began the journey of learning to teach through problem solving while taking a…
Mathematical problem solving by analogy.
Novick, L R; Holyoak, K J
1991-05-01
We report the results of 2 experiments and a verbal protocol study examining the component processes of solving mathematical word problems by analogy. College students first studied a problem and its solution, which provided a potential source for analogical transfer. Then they attempted to solve several analogous problems. For some problems, subjects received one of a variety of hints designed to reduce or eliminate the difficulty of some of the major processes hypothesized to be involved in analogical transfer. Our studies yielded 4 major findings. First, the process of mapping the features of the source and target problems and the process of adapting the source solution procedure for use in solving the target problem were clearly distinguished: (a) Successful mapping was found to be insufficient for successful transfer and (b) adaptation was found to be a major source of transfer difficulty. Second, we obtained direct evidence that schema induction is a natural consequence of analogical transfer. The schema was found to co-exist with the problems from which it was induced, and both the schema and the individual problems facilitated later transfer. Third, for our multiple-solution problems, the relation between analogical transfer and solution accuracy was mediated by the degree of time pressure exerted for the test problems. Finally, mathematical expertise was a significant predictor of analogical transfer, but general analogical reasoning ability was not. The implications of the results for models of analogical transfer and for instruction were considered.
Improving mathematical problem solving : A computerized approach
Harskamp, EG; Suhre, CJM
Mathematics teachers often experience difficulties in teaching students to become skilled problem solvers. This paper evaluates the effectiveness of two interactive computer programs for high school mathematics problem solving. Both programs present students with problems accompanied by instruction
Improving mathematical problem solving : A computerized approach
Harskamp, EG; Suhre, CJM
2006-01-01
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
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.
Mathematical Problem Solving through Sequential Process Analysis
Codina, A.; Cañadas, M. C.; Castro, E.
2015-01-01
Introduction: The macroscopic perspective is one of the frameworks for research on problem solving in mathematics education. Coming from this perspective, our study addresses the stages of thought in mathematical problem solving, offering an innovative approach because we apply sequential relations and global interrelations between the different…
Students' Metaphors for Mathematical Problem Solving
Yee, Sean P.
2012-01-01
The purpose of this study was to determine the metaphors used by students to describe mathematical problem solving. This study focused on identifying how students interpret and perceive mathematical problem solving via conceptual metaphors (Lakoff and Johnson, 2003). These perceptions and interpretations were coded and analyzed qualitatively and…
Mathematics Teachers Circle around Problem Solving
Fernandes, Anthony; Koehler, Jacob; Reiter, Harold
2011-01-01
Making problem solving a central part of teaching may be challenging to teachers who have limited experiences in learning and teaching mathematics in this way. Math Teachers' Circles were developed with the aim of establishing a "culture of problem solving" among middle school mathematics teachers. This culture could then be carried back into…
Collis-Romberg Mathematical Problem Solving Profiles.
Collis, K. F.; Romberg, T. A.
Problem solving has become a focus of mathematics programs in Australia in recent years, necessitating the assessment of students' problem-solving abilities. This manual provides a problem-solving assessment and teaching resource package containing four elements: (1) profiles assessment items; (2) profiles diagnostic forms for recording individual…
Mathematical Thinking and Creativity through Mathematical Problem Posing and Solving
Ayllón, María F.; Gómez, Isabel A.; Ballesta-Claver, Julio
2016-01-01
This work shows the relationship between the development of mathematical thinking and creativity with mathematical problem posing and solving. Creativity and mathematics are disciplines that do not usually appear together. Both concepts constitute complex processes sharing elements, such as fluency (number of ideas), flexibility (range of ideas),…
How to solve applied mathematics problems
Moiseiwitsch, B L
2011-01-01
This workbook bridges the gap between lectures and practical applications, offering students of mathematics, engineering, and physics the chance to practice solving problems from a wide variety of fields. 2011 edition.
Chamberlin, Scott A.; Powers, Robert A.
2013-01-01
The focus of the article is the validation of an instrument to assess gifted students' affect after mathematical problem solving tasks. Participants were 225 students identified by their district as gifted in grades four to six. The Chamberlin Affective Instrument for Mathematical Problem Solving was used to assess feelings, emotions, and…
On Teaching Problem Solving in School Mathematics
Directory of Open Access Journals (Sweden)
Erkki Pehkonen
2013-12-01
Full Text Available The article begins with a brief overview of the situation throughout the world regarding problem solving. The activities of the ProMath group are then described, as the purpose of this international research group is to improve mathematics teaching in school. One mathematics teaching method that seems to be functioning in school is the use of open problems (i.e., problem fields. Next we discuss the objectives of the Finnish curriculum that are connected with problem solving. Some examples and research results are taken from a Finnish–Chilean research project that monitors the development of problem-solving skills in third grade pupils. Finally, some ideas on “teacher change” are put forward. It is not possible to change teachers, but only to provide hints for possible change routes: the teachers themselves should work out the ideas and their implementation.
Learning via problem solving in mathematics education
Directory of Open Access Journals (Sweden)
Piet Human
2009-09-01
Full Text Available Three forms of mathematics education at school level are distinguished: direct expository teaching with an emphasis on procedures, with the expectation that learners will at some later stage make logical and functional sense of what they have learnt and practised (the prevalent form, mathematically rigorous teaching in terms of fundamental mathematical concepts, as in the so-called “modern mathematics” programmes of the sixties, teaching and learning in the context of engaging with meaningful problems and focused both on learning to become good problem solvers (teaching for problem solving andutilising problems as vehicles for the development of mathematical knowledge andproﬁciency by learners (problem-centred learning, in conjunction with substantialteacher-led social interaction and mathematical discourse in classrooms.Direct expository teaching of mathematical procedures dominated in school systems after World War II, and was augmented by the “modern mathematics” movement in the period 1960-1970. The latter was experienced as a major failure, and was soon abandoned. Persistent poor outcomes of direct expository procedural teaching of mathematics for the majority of learners, as are still being experienced in South Africa, triggered a world-wide movement promoting teaching mathematics for and via problem solving in the seventies and eighties of the previous century. This movement took the form of a variety of curriculum experiments in which problem solving was the dominant classroom activity, mainly in the USA, Netherlands, France and South Africa. While initially focusing on basic arithmetic (computation with whole numbers and elementary calculus, the problem-solving movement started to address other mathematical topics (for example, elementary statistics, algebra, differential equations around the turn of the century. The movement also spread rapidly to other countries, including Japan, Singapore and Australia. Parallel with the
Applying Lakatos' Theory to the Theory of Mathematical Problem Solving.
Nunokawa, Kazuhiko
1996-01-01
The relation between Lakatos' theory and issues in mathematics education, especially mathematical problem solving, is investigated by examining Lakatos' methodology of a scientific research program. (AIM)
Affect and mathematical problem solving a new perspective
Adams, Verna
1989-01-01
Research on cognitive aspects of mathematical problem solving has made great progress in recent years, but the relationship of affective factors to problem-solving performance has been a neglected research area. The purpose of Affect and Mathematical Problem Solving: A New Perspective is to show how the theories and methods of cognitive science can be extended to include the role of affect in mathematical problem solving. The book presents Mandler's theory of emotion and explores its implications for the learning and teaching of mathematical problem solving. Also, leading researchers from mathematics, education, and psychology report how they have integrated affect into their own cognitive research. The studies focus on metacognitive processes, aesthetic influences on expert problem solvers, teacher decision-making, technology and teaching problem solving, and beliefs about mathematics. The results suggest how emotional factors like anxiety, frustration, joy, and satisfaction can help or hinder performance in...
Assessing Mathematics 4. Problem Solving: The APU Approach.
Foxman, Derek; And Others
1984-01-01
Presented are examples of problem-solving items from practical and written mathematics tests. These tests are part of an English survey designed to assess the mathematics achievement of students aged 11 and 15. (JN)
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…
INVESTIGATION OF MATHEMATICS TEACHERS’ VIEWS ABOUT IMPROVING PROBLEM SOLVING SKILLS
YILDIZ, Cemalettin
2016-01-01
Since problem solving skills playa central role in middle and secondary school mathematics curricula, this made mathematicseducators give importance to this subject. Improving problem solving skills ofstudents is one of the primary aims of education so it is very important tomake students gain problem solving skills. Thus, the aim of this research is toinvestigate views of middle and secondary school mathematics teachers relatedto improvement of students’ problem solving skills. Qualitative r...
Mathematical knowledge for teaching probem solving: lessons from lesson study
Foster, Colin; Wake, Geoff; Swan, Malcolm
2014-01-01
Although the importance of mathematical problem solving is now widely recognised, relatively little attention has been given to the conceptualisation of mathematical processes such as representing, analysing, interpreting and communicating. The construct of Mathematical Knowledge for Teaching (Hill, Ball & Schilling, 2008) is generally interpreted in terms of mathematical content, and in this paper we describe our initial attempts to broaden MKT to include mathematical process knowledge (MPK)...
Problem Solving in the Borderland between Mathematics and Physics
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 focuses on solving so-called unformalized problems,…
Graphic Organizer in Action: Solving Secondary Mathematics Word Problems
Directory of Open Access Journals (Sweden)
Khoo Jia Sian
2016-09-01
Full Text Available Mathematics word problems are one of the most challenging topics to learn and teach in secondary schools. This is especially the case in countries where English is not the first language for the majority of the people, such as in Brunei Darussalam. Researchers proclaimed that limited language proficiency and limited Mathematics strategies are the possible causes to this problem. However, whatever the reason is behind difficulties students face in solving Mathematical word problems, it is perhaps the teaching and learning of the Mathematics that need to be modified. For example, the use of four-square-and-a-diamond graphic organizer that infuses model drawing skill; and Polya’s problem solving principles, to solve Mathematical word problems may be some of the strategies that can help in improving students’ word problem solving skills. This study, through quantitative analysis found that the use of graphic organizer improved students’ performance in terms of Mathematical knowledge, Mathematical strategy and Mathematical explanation in solving word problems. Further qualitative analysis revealed that the use of graphic organizer boosted students’ confidence level and positive attitudes towards solving word problems.Keywords: Word Problems, Graphic Organizer, Algebra, Action Research, Secondary School Mathematics DOI: http://dx.doi.org/10.22342/jme.7.2.3546.83-90
Learning via problem solving in mathematics education
Piet Human
2009-01-01
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 meaningfu...
The Influence of Cognitive Abilities on Mathematical Problem Solving Performance
Bahar, Abdulkadir
2013-01-01
Problem solving has been a core theme in education for several decades. Educators and policy makers agree on the importance of the role of problem solving skills for school and real life success. A primary purpose of this study was to investigate the influence of cognitive abilities on mathematical problem solving performance of students. The…
Thinking Process of Naive Problem Solvers to Solve Mathematical Problems
Mairing, Jackson Pasini
2017-01-01
Solving problems is not only a goal of mathematical learning. Students acquire ways of thinking, habits of persistence and curiosity, and confidence in unfamiliar situations by learning to solve problems. In fact, there were students who had difficulty in solving problems. The students were naive problem solvers. This research aimed to describe…
Teaching Problem Solving in Secondary School Mathematics Classrooms
Lam, Toh Tin; Guan, Tay Eng; Seng, Quek Khiok; Hoong, Leong Yew; Choon, Toh Pee; Him, Ho Foo; Jaguthsing, Dindyal
2014-01-01
This paper reports an innovative approach to teaching problem solving in secondary school mathematics classrooms based on a specifically designed problem-solving module.This approach adopts the science practical paradigm and rides on the works of Polya and Schoenfeld in order to give greater emphasis to the problem solving processes. We report the…
Problem solving in the borderland between mathematics and physics
DEFF Research Database (Denmark)
Jensen, Jens Højgaard; Niss, Martin; Jankvist, Uffe Thomas
2017-01-01
, if it focuses on solving so-called unformalized problems, where a major challenge is to formalize the problems in mathematics and physics terms. We analyse four concrete examples of unformalized problems for which the formalization involves different order of mathematization and applying physics to the problem......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......, but all require mathematization. The analysis leads to the formulation of a model by which we attempt to capture the important steps of the process of solving unformalized problems by means of mathematization and physicalization....
Mathematical problem solving in primary school
Kolovou, A.|info:eu-repo/dai/nl/313715947
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
Mathematical problem solving in primary school
Kolovou, A.
2011-01-01
A student is engaged in (non-routine) problem solving when there is no clear pathway to the solution. In contrast to routine problems, non-routine ones cannot be solved through the direct application of a standard procedure. Consider the following problem: In a quiz you get two points for each corre
Yinghui Lai; Xiaoshuang Zhu; Yinghe Chen; Yanjun Li
2015-01-01
Mathematics is one of the most objective, logical, and practical academic disciplines. Yet, in addition to cognitive skills, mathematical problem solving also involves affective factors. In the current study, we first investigated effects of mathematics anxiety (MA) and mathematical metacognition on word problem solving (WPS). We tested 224 children (116 boys, M = 10.15 years old, SD = 0.56) with the Mathematics Anxiety Scale for Children, the Chinese Revised-edition Questionnaire of Pupil's ...
Genetic Algorithm for Solving Simple Mathematical Equality Problem
Hermawanto, Denny
2013-01-01
This paper explains genetic algorithm for novice in this field. Basic philosophy of genetic algorithm and its flowchart are described. Step by step numerical computation of genetic algorithm for solving simple mathematical equality problem will be briefly explained
Exploring Relationship between Scientific Reasoning Skills and Mathematics Problem Solving
Tajudin, Nor'ain Mohd; Chinnappan, Mohan
2015-01-01
Reasoning is considered to be an important proficiency in national mathematics curricula both in Australia (ACARA, 2014) and Malaysia (MOE, 2013). However, the nature of reasoning that supports learning and problem solving in mathematics is an area that requires further study (Schoenfeld, 2013). In this study we explored the link between…
A Working Memory Model Applied to Mathematical Word Problem Solving
Alamolhodaei, Hassan
2009-01-01
The main objective of this study is (a) to explore the relationship among cognitive style (field dependence/independence), working memory, and mathematics anxiety and (b) to examine their effects on students' mathematics problem solving. A sample of 161 school girls (13-14 years old) were tested on (1) the Witkin's cognitive style (Group Embedded…
Robotic Toys as a Catalyst for Mathematical Problem Solving
Highfield, Kate
2010-01-01
Robotic toys present unique opportunities for teachers of young children to integrate mathematics learning with engaging problem-solving tasks. This article describes a series of tasks using Bee-bots and Pro-bots, developed as part a larger project examining young children's use of robotic toys as tools in developing mathematical and metacognitive…
Mathematical problem solving in primary school
Kolovou, A
2011-01-01
A student is engaged in (non-routine) problem solving when there is no clear pathway to the solution. In contrast to routine problems, non-routine ones cannot be solved through the direct application of a standard procedure. Consider the following problem: In a quiz you get two points for each correct answer. If a question is not answered or the answer is wrong, one point is subtracted from your score. The quiz contains 10 questions. Tina received 8 points in total. How many questions did Tin...
Students' Reasoning in Mathematics Textbook Task-Solving
Sidenvall, Johan; Lithner, Johan; Jäder, Jonas
2015-01-01
This study reports on an analysis of students' textbook task-solving in Swedish upper secondary school. The relation between types of mathematical reasoning required, used, and the rate of correct task solutions were studied. Rote learning and superficial reasoning were common, and 80% of all attempted tasks were correctly solved using such…
Improving Mathematical Problem Solving Skills: The Journey to Success
Rousseau, Donna
2009-01-01
The purpose of this study was to determine if problem solving skills can be improved through the use of an interdisciplinary program incorporating reading, music, and mathematics. The study was conducted in seven fifth grade classrooms, and addresses the need to teach problem solving strategies in elementary school and the importance of problem…
Glogs as Non-Routine Problem Solving Tools in Mathematics
Devine, Matthew T.
2013-01-01
In mathematical problem solving, American students are falling behind their global peers because of a lack of foundational and reasoning skills. A specific area of difficulty with problem solving is working non-routine, heuristic-based problems. Many students are not provided with effective instruction and often grow frustrated and dislike math.…
Problem Solving Frameworks for Mathematics and Software Development
McMaster, Kirby; Sambasivam, Samuel; Blake, Ashley
2012-01-01
In this research, we examine how problem solving frameworks differ between Mathematics and Software Development. Our methodology is based on the assumption that the words used frequently in a book indicate the mental framework of the author. We compared word frequencies in a sample of 139 books that discuss problem solving. The books were grouped…
Using CAS to Solve Classical Mathematics Problems
Burke, Maurice J.; Burroughs, Elizabeth A.
2009-01-01
Historically, calculus has displaced many algebraic methods for solving classical problems. This article illustrates an algebraic method for finding the zeros of polynomial functions that is closely related to Newton's method (devised in 1669, published in 1711), which is encountered in calculus. By exploring this problem, precalculus students…
Using CAS to Solve Classical Mathematics Problems
Burke, Maurice J.; Burroughs, Elizabeth A.
2009-01-01
Historically, calculus has displaced many algebraic methods for solving classical problems. This article illustrates an algebraic method for finding the zeros of polynomial functions that is closely related to Newton's method (devised in 1669, published in 1711), which is encountered in calculus. By exploring this problem, precalculus students…
Spooner, Fred; Saunders, Alicia; Root, Jenny; Brosh, Chelsi
2017-01-01
There is a need to teach the pivotal skill of mathematical problem solving to students with severe disabilities, moving beyond basic skills like computation to higher level thinking skills. Problem solving is emphasized as a Standard for Mathematical Practice in the Common Core State Standards across grade levels. This article describes a…
Secondary Teachers’ Mathematics-related Beliefs and Knowledge about Mathematical Problem-solving
E Siswono, T. Y.; Kohar, A. W.; Hartono, S.
2017-02-01
This study investigates secondary teachers’ belief about the three mathematics-related beliefs, i.e. nature of mathematics, teaching mathematics, learning mathematics, and knowledge about mathematical problem solving. Data were gathered through a set of task-based semi-structured interviews of three selected teachers with different philosophical views of teaching mathematics, i.e. instrumental, platonist, and problem solving. Those teachers were selected from an interview using a belief-related task from purposively selected teachers in Surabaya and Sidoarjo. While the interviews about knowledge examine teachers’ problem solving content and pedagogical knowledge, the interviews about beliefs examine their views on several cases extracted from each of such mathematics-related beliefs. Analysis included the categorization and comparison on each of beliefs and knowledge as well as their interaction. Results indicate that all the teachers did not show a high consistency in responding views of their mathematics-related beliefs, while they showed weaknesses primarily on problem solving content knowledge. Findings also point out that teachers’ beliefs have a strong relationship with teachers’ knowledge about problem solving. In particular, the instrumental teacher’s beliefs were consistent with his insufficient knowledge about problem-solving, while both platonist and problem-solving teacher’s beliefs were consistent with their sufficient knowledge of either content or pedagogical problem solving.
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…
Bukova-Guzel, Esra
2011-01-01
This study examines the approaches displayed by pre-service mathematics teachers in their experiences of constructing mathematical modelling problems and the extent to which they perform the modelling process when solving the problems they construct. This case study was carried out with 35 pre-service teachers taking the Mathematical Modelling…
Cognitive functioning in mathematical problem solving during early adolescence
Collis, Kevin F.; Watson, Jane M.; Campbell, K. Jennifer
1993-12-01
Problem-solving in school mathematics has traditionally been considered as belonging only to the concrete symbolic mode of thinking, the mode which is concerned with making logical, analytical deductions. Little attention has been given to the place of the intuitive processes of the ikonic mode. The present study was designed to explore the interface between logical and intuitive processes in the context of mathematical problem solving. Sixteen Year 9 and 10 students from advanced mathematics classes were individually assessed while they solved five mathematics problems. Each student's problem-solving path, for each problem, was mapped according to the type of strategies used. Strategies were broadly classified into Ikonic (IK) or Concrete Symbolic (CS) categories. Students were given two types of problems to solve: (i) those most likely to attract a concrete symbolic approach; and (ii) problems with a significant imaging or intuitive component. Students were also assessed as to the vividness and controllability of their imaging ability, and their creativity. Results indicated that the nature of the problem is a basic factor in determining the type of strategy used for its solution. Students consistently applied CS strategies to CS problems, and IK strategies to IK problems. In addition, students tended to change modes significantly more often when solving CS-type problems than when solving IK-type problems. A switch to IK functioning appeared to be particularly helpful in breaking an unproductive set when solving a CS-type problem. Individual differences in strategy use were also found, with students high on vividness of imagery using IK strategies more frequently than students who were low on vividness. No relationship was found between IK strategy use and either students' degree of controllability of imagery or their level of creativity. The instructional implications of the results are discussed.
Lai, Yinghui; Zhu, Xiaoshuang; Chen, Yinghe; Li, Yanjun
2015-01-01
Mathematics is one of the most objective, logical, and practical academic disciplines. Yet, in addition to cognitive skills, mathematical problem solving also involves affective factors. In the current study, we first investigated effects of mathematics anxiety (MA) and mathematical metacognition on word problem solving (WPS). We tested 224 children (116 boys, M = 10.15 years old, SD = 0.56) with the Mathematics Anxiety Scale for Children, the Chinese Revised-edition Questionnaire of Pupil’s Metacognitive Ability in Mathematics, and WPS tasks. The results indicated that mathematical metacognition mediated the effect of MA on WPS after controlling for IQ. Second, we divided the children into four mathematics achievement groups including high achieving (HA), typical achieving (TA), low achieving (LA), and mathematical learning difficulty (MLD). Because mathematical metacognition and MA predicted mathematics achievement, we compared group differences in metacognition and MA with IQ partialled out. The results showed that children with MLD scored lower in self-image and higher in learning mathematics anxiety (LMA) than the TA and HA children, but not in mathematical evaluation anxiety (MEA). MLD children’s LMA was also higher than that of their LA counterparts. These results provide insight into factors that may mediate poor WPS performance which emerges under pressure in mathematics. These results also suggest that the anxiety during learning mathematics should be taken into account in mathematical learning difficulty interventions. PMID:26090806
Directory of Open Access Journals (Sweden)
Yinghui Lai
Full Text Available Mathematics is one of the most objective, logical, and practical academic disciplines. Yet, in addition to cognitive skills, mathematical problem solving also involves affective factors. In the current study, we first investigated effects of mathematics anxiety (MA and mathematical metacognition on word problem solving (WPS. We tested 224 children (116 boys, M = 10.15 years old, SD = 0.56 with the Mathematics Anxiety Scale for Children, the Chinese Revised-edition Questionnaire of Pupil's Metacognitive Ability in Mathematics, and WPS tasks. The results indicated that mathematical metacognition mediated the effect of MA on WPS after controlling for IQ. Second, we divided the children into four mathematics achievement groups including high achieving (HA, typical achieving (TA, low achieving (LA, and mathematical learning difficulty (MLD. Because mathematical metacognition and MA predicted mathematics achievement, we compared group differences in metacognition and MA with IQ partialled out. The results showed that children with MLD scored lower in self-image and higher in learning mathematics anxiety (LMA than the TA and HA children, but not in mathematical evaluation anxiety (MEA. MLD children's LMA was also higher than that of their LA counterparts. These results provide insight into factors that may mediate poor WPS performance which emerges under pressure in mathematics. These results also suggest that the anxiety during learning mathematics should be taken into account in mathematical learning difficulty interventions.
Lai, Yinghui; Zhu, Xiaoshuang; Chen, Yinghe; Li, Yanjun
2015-01-01
Mathematics is one of the most objective, logical, and practical academic disciplines. Yet, in addition to cognitive skills, mathematical problem solving also involves affective factors. In the current study, we first investigated effects of mathematics anxiety (MA) and mathematical metacognition on word problem solving (WPS). We tested 224 children (116 boys, M = 10.15 years old, SD = 0.56) with the Mathematics Anxiety Scale for Children, the Chinese Revised-edition Questionnaire of Pupil's Metacognitive Ability in Mathematics, and WPS tasks. The results indicated that mathematical metacognition mediated the effect of MA on WPS after controlling for IQ. Second, we divided the children into four mathematics achievement groups including high achieving (HA), typical achieving (TA), low achieving (LA), and mathematical learning difficulty (MLD). Because mathematical metacognition and MA predicted mathematics achievement, we compared group differences in metacognition and MA with IQ partialled out. The results showed that children with MLD scored lower in self-image and higher in learning mathematics anxiety (LMA) than the TA and HA children, but not in mathematical evaluation anxiety (MEA). MLD children's LMA was also higher than that of their LA counterparts. These results provide insight into factors that may mediate poor WPS performance which emerges under pressure in mathematics. These results also suggest that the anxiety during learning mathematics should be taken into account in mathematical learning difficulty interventions.
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…
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…
A mathematical model of a computational problem solving system
Aris, Teh Noranis Mohd; Nazeer, Shahrin Azuan
2015-05-01
This paper presents a mathematical model based on fuzzy logic for a computational problem solving system. The fuzzy logic uses truth degrees as a mathematical model to represent vague algorithm. The fuzzy logic mathematical model consists of fuzzy solution and fuzzy optimization modules. The algorithm is evaluated based on a software metrics calculation that produces the fuzzy set membership. The fuzzy solution mathematical model is integrated in the fuzzy inference engine that predicts various solutions to computational problems. The solution is extracted from a fuzzy rule base. Then, the solutions are evaluated based on a software metrics calculation that produces the level of fuzzy set membership. The fuzzy optimization mathematical model is integrated in the recommendation generation engine that generate the optimize solution.
Towards efficient measurement of metacognition in mathematical problem solving
Jacobse, Annemieke E.; Harskamp, Egbert G.
Metacognitive monitoring and regulation play an essential role in mathematical problem solving. Therefore, it is important for researchers and practitioners to assess students' metacognition. One proven valid, but time consuming, method to assess metacognition is by using think-aloud protocols.
Using Drawings and Generating Information in Mathematical Problem Solving Processes
Nunokawa, Kazuhiko
2006-01-01
The purpose of this paper is to investigate how drawings can contribute to generating new information when solvers use drawings in solving mathematical problems. For this purpose, two episodes, in which drawings enabled a solver to find ideas useful for his solutions, were qualitatively and closely analyzed, especially focusing on what roles…
Problem Solving Abilities and Perceptions in Alternative Certification Mathematics Teachers
Evans, Brian R.
2012-01-01
It is important for teacher educators to understand new alternative certification middle and high school teachers' mathematical problem solving abilities and perceptions. Teachers in an alternative certification program in New York were enrolled in a proof-based algebra course. At the beginning and end of a semester participants were given a…
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…
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
Problem-solving strategies for teaching mathematics to deaf students.
Mousley, K; Kelly, R R
1998-10-01
Three teaching and learning strategies for problem solving were implemented with first- and second-year deaf college students enrolled in mathematics courses at the National Technical Institute for the Deaf (NTID), Rochester Institute of Technology. These strategies involved the students in (a) giving an explanation to a peer observer in sign language, after which they would put their understanding of a problem and its solution in writing; (b) visualizing the problem-solving process prior to starting to solve a problem; and (c) observing their teacher modeling the analytical process step by step for a sample problem prior to solving math word problems. The students were asked to solve two types of problems: typical word problems, and a visual/manipulative puzzle that would provide a problem-solving experience that would contrast with the experience of solving a problem presented in text format. The results showed that these kinds of instructional strategies can enhance the problem-solving performance of deaf and hard of hearing college students.
Calculus Problem Solving Behavior of Mathematic Education Students
Rizal, M.; Mansyur, J.
2017-04-01
The purpose of this study is to obtain a description of the problem-solving behaviour of mathematics education students. The attainment of the purpose consisted of several stages: (1) to gain the subject from the mathematic education of first semester students, each of them who has a high, medium, and low competence of mathematic case. (2) To give two mathematical problems with different characteristics. The first problem (M1), the statement does not lead to a resolution. The second problem (M2), a statement leads to problem-solving. (3) To explore the behaviour of problem-solving based on the step of Polya (Rizal, 2011) by way of thinking aloud and in-depth interviews. The obtained data are analysed as suggested by Miles and Huberman (1994) but at first, time triangulation is done or data’s credibility by providing equivalent problem contexts and at different times. The results show that the behavioral problem solvers (mathematic education students) who are capable of high mathematic competency (ST). In understanding M1, ST is more likely to pay attention to an image first, read the texts piecemeal and repeatedly, then as a whole and more focus to the sentences that contain equations, numbers or symbols. As a result, not all information can be received well. When understanding the M2, ST can link the information from a problem that is stored in the working memory to the information on the long-term memory. ST makes planning to the solution of M1 and M2 by using a formula based on similar experiences which have been ever received before. Another case when implementing the troubleshooting plans, ST complete the M1 according to the plan, but not all can be resolved correctly. In contrast to the implementation of the solving plan of M2, ST can solve the problem according to plan quickly and correctly. According to the solving result of M1 and M2, ST conducts by reading the job based on an algorithm and reasonability. Furthermore, when SS and SR understand the
Mathematical modeling/problem solving in global oxygen transport.
Farrell, Kevin; Hill, Andrew; Dent, Leon; Nguyen, Minh Ly
2009-08-01
A simplified approach to mathematical modeling/problem solving in global oxygen transport is presented. In addition to standard oxygen transport formulae, it uses the S-Factor and a mathematical relationship relating SvO(2) to the ratio DO(2)/VO(2). This method allows the determination or specification of SvO(2), PvO(2), P(50), and systemic shunting in the context of this simplified approach. Heretofore this has not been possible. With this approach, essentially all clinical problems in global oxygen transport can be dealt with. This is illustrated by the broad scope of the five problems presented.
Mathematical problem solving, modelling, applications, and links to other subjects
Blum, Werner; Niss, Mogens
1989-01-01
The paper will consist of three parts. In part I we shall present some background considerations which are necessary as a basis for what follows. We shall try to clarify some basic concepts and notions, and we shall collect the most important arguments (and related goals) in favour of problem solving, modelling and applications to other subjects in mathematics instruction. In the main part II we shall review the present state, recent trends, and prospective lines of developm...
Developing a model for problem-solving in a Grade 4 mathematics classroom
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Susan Nieuwoudt
2015-11-01
Full Text Available The teaching of problem-solving through the development of a problem-solving model was investigated in a Grade 4 mathematics classroom. Learners completed a questionnaire regarding their knowledge of mathematical problem-solving, their attitudes towards problem-solving, as well as their experiences in solving problems. Learners’ responses revealed overall negative beliefs towards problem-solving as well as a lack of knowledge about what problem-solving in mathematics entails. The teacher then involved the learners in a structured learning programme where they worked in cooperative groups of six on different kinds of mathematical problems to solve. The groups regularly engaged in discussions about the different strategies they were using to solve a specific problem and eventually succeeded in formulating a generic problem-solving model they could call their own. The model was effectively used by the learners to solve various mathematical problems, reflecting their levels of cognitive development to a certain extent.
How to solve it a new aspect of mathematical method
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.
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…
LEVELING STUDENTS’ CREATIVE THINKING IN SOLVING AND POSING MATHEMATICAL PROBLEM
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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
The Strategies of Mathematics Teachers When Solving Number Sense Problems
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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.
Tyagi, Tarun Kumar
2016-04-01
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 eighth-grade students were analysed using a cross-lagged panel correlation (CLPC) design. CLPC attempts to rule out plausible alternative explanation of a causal effect. The result suggests that significant predominant causal relationship was found between MC and MP. It indicates that MP was found to be a cause of MC than the converse.
Factors Influencing Mathematic Problem-Solving Ability of Sixth Grade Students
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Sakorn Pimta
2009-01-01
Full Text Available Problem statement: This study aims to investigate factors influencing mathematic problem-solving ability of sixth grade students. One thousand and twenty eight of sixth grade students, studying in the second semester of academic year 2007 were sampled by stratified random sampling technique. Approach: The research instruments used in the study included mathematic problem-solving ability test and questionnaires. Data was analyzed by Path Analysis. Results: Factors influencing mathematic problem-solving ability were represented as following: (1 direct factors influencing mathematic problem-solving ability were described that direct and indirect factors influencing mathematic problem-solving ability were attitude towards mathematics, self-esteem and teachers teaching behavior. Indirect factors influencing mathematic problem-solving ability were motivation and self-efficacy (2 factor models influencing mathematic problem-solving ability of sixth grade students was associated with visual data (3 The developed model could describe variance of skill in mathematic problem-solving at 63.00 % (R2 = 0.63. Conclusion: Teachers behaviors took both direct and indirect effects on the students mathematic problem solving. The teachers are supposed to study the methods to develop this ability deeply and then bring them to manage the activities in class that encourage students to be enthusiastic to learn and have good attitude toward mathematic learning or to get students concentration.
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…
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…
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…
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…
Students’ Perceptions on Practical Problem Solving in Mathematics in E-environment
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Anda Zeidmane
2014-03-01
Full Text Available Study process in mathematics faces two major problems. First, engineers do not apply directly the problem solving skills of higher mathematics. Second, studying higher mathematics, students get an insufficient idea of its usability. The authors of the paper have worked out frameworks for practical problem solving in mathematics on the basis of didactic ontology in the Moodle computerized learning system (CMS. To determine students' perceptions on practical problem solving in mathematics in e-environment, more than 300 students from the specialties of engineering at the LUA participated in the survey. The survey results showed many students lack basic knowledge in mathematics, therefore they consume a lot of time to learn the basics in higher mathematics and to acquire the skills of practical problem solving in mathematics are less important.
Critical Mathematics Education: Recognizing the Ethical Dimension of Problem Solving
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Elizabeth de Freitas
2008-07-01
Full Text Available In this paper, I examine the notion of ‘real life’ mathematical applications as possible sites for ethical reflection in school mathematics. I discuss problems with the ‘real’ in mathematics education, and show how these problems are often based on faulty cognitive theories of knowledge transfer. I then consider alternative visions of mathematical application and suggest that attention to classroom discourse and the craft of mathematics offer ways of introducing the ethical into school mathematics.
An Investigation of Secondary Teachers’ Understanding and Belief on Mathematical Problem Solving
Yuli Eko Siswono, Tatag; Wachidul Kohar, Ahmad; Kurniasari, Ika; Puji Astuti, Yuliani
2016-02-01
Weaknesses on problem solving of Indonesian students as reported by recent international surveys give rise to questions on how Indonesian teachers bring out idea of problem solving in mathematics lesson. An explorative study was undertaken to investigate how secondary teachers who teach mathematics at junior high school level understand and show belief toward mathematical problem solving. Participants were teachers from four cities in East Java province comprising 45 state teachers and 25 private teachers. Data was obtained through questionnaires and written test. The results of this study point out that the teachers understand pedagogical problem solving knowledge well as indicated by high score of observed teachers‘ responses showing understanding on problem solving as instruction as well as implementation of problem solving in teaching practice. However, they less understand on problem solving content knowledge such as problem solving strategies and meaning of problem itself. Regarding teacher's difficulties, teachers admitted to most frequently fail in (1) determining a precise mathematical model or strategies when carrying out problem solving steps which is supported by data of test result that revealed transformation error as the most frequently observed errors in teachers’ work and (2) choosing suitable real situation when designing context-based problem solving task. Meanwhile, analysis of teacher's beliefs on problem solving shows that teachers tend to view both mathematics and how students should learn mathematics as body static perspective, while they tend to believe to apply idea of problem solving as dynamic approach when teaching mathematics.
Solving for Irrational Zeros: Whiteness in Mathematics Teacher Education
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…
A Strategy for Improving US Middle School Student Mathematics Word Problem Solving Performance
Thomas, Valerie L.
2004-01-01
U.S. middle school students have difficulty understanding and solving mathematics word problems. Their mathematics performance on the Third International Mathematics and Science Study (TIMMS) is far below their international peers, and minority students are less likely than high socioeconomic status (SES) White/Asian students to be exposed to higher-level mathematics concepts. Research literature also indicates that when students use both In-School and Out-of-School knowledge and experiences to create authentic mathematics word problems, student achievement improves. This researcher developed a Strategy for improving mathematics problem solving performance and a Professional Development Model (PDM) to effectively implement the Strategy.
Mathematical Problem Solving: A Review of the Literature.
Funkhouser, Charles
The major perspectives on problem solving of the twentieth century are reviewed--associationism, Gestalt psychology, and cognitive science. The results of the review on teaching problem solving and the uses of computers to teach problem solving are included. Four major issues related to the teaching of problem solving are discussed: (1)…
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…
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…
Huang, Tzu-Hua; Liu, Yuan-Chen; Chang, Hsiu-Chen
2012-01-01
This study developed a computer-assisted mathematical problem-solving system in the form of a network instruction website to help low-achieving second- and third-graders in mathematics with word-based addition and subtraction questions in Taiwan. According to Polya's problem-solving model, the system is designed to guide these low-achievers…
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…
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…
Good, Jennifer M.; Halpin, Glennelle; Halpin, Gerald
2002-01-01
Examined the outcomes of academic support programs designed to enhance mathematical and scientific problem solving skills among African American pre-engineering college students. Interventions included weekly scientific reasoning and mathematical critical thinking and problem solving workshops, mentoring by upper-class students, and an interactive…
Second-Graders' Mathematical Practices for Solving Fraction Tasks
Moyer-Packenham, Patricia S.; Bolyard, Johnna J.; Tucker, Stephen I.
2014-01-01
Recently, over 40 states in the United States adopted the Common Core State Standards for Mathematics (CCSSM) which include standards for content and eight standards for mathematical practices. The purpose of this study was to better understand the nature of young children's mathematical practices through an exploratory examination of the…
Learners' Approaches to Solving Mathematical Tasks: Does Specialisation Matter?
Machaba, France; Mwakapenda, Willy
2016-01-01
This article emerged from an analysis of learners' responses to a task presented to learners studying Mathematics and Mathematical Literacy (ML) in Gauteng, South Africa. Officially, Mathematics and ML are two separate learning areas. Learners from Grade 10 onwards are supposed to take either one or the other, but not both. This means that by…
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…
Investigating and Developing Engineering Students' Mathematical Modelling and Problem-Solving Skills
Wedelin, Dag; Adawi, Tom; Jahan, Tabassum; Andersson, Sven
2015-01-01
How do engineering students approach mathematical modelling problems and how can they learn to deal with such problems? In the context of a course in mathematical modelling and problem solving, and using a qualitative case study approach, we found that the students had little prior experience of mathematical modelling. They were also inexperienced…
Analytical derivation: An epistemic game for solving mathematically based physics problems
Bajracharya, Rabindra R.; Thompson, John R.
2016-06-01
Problem solving, which often involves multiple steps, is an integral part of physics learning and teaching. Using the perspective of the epistemic game, we documented a specific game that is commonly pursued by students while solving mathematically based physics problems: the analytical derivation game. This game involves deriving an equation through symbolic manipulations and routine mathematical operations, usually without any physical interpretation of the processes. This game often creates cognitive obstacles in students, preventing them from using alternative resources or better approaches during problem solving. We conducted hour-long, semi-structured, individual interviews with fourteen introductory physics students. Students were asked to solve four "pseudophysics" problems containing algebraic and graphical representations. The problems required the application of the fundamental theorem of calculus (FTC), which is one of the most frequently used mathematical concepts in physics problem solving. We show that the analytical derivation game is necessary, but not sufficient, to solve mathematically based physics problems, specifically those involving graphical representations.
Cognitive Backgrounds of Problem Solving: A Comparison of Open-Ended vs. Closed Mathematics Problems
Bahar, Abdulkadir; Maker, C. June
2015-01-01
Problem solving has been a core theme in education for several decades. Educators and policy makers agree on the importance of the role of problem solving skills for school and real life success. A primary purpose of this study was to investigate the influence of cognitive abilities on mathematical problem solving performance of elementary…
Iiskala, Tuike; Vauras, Marja; Lehtinen, Erno; Salonen, Pekka
2011-01-01
This study investigated how metacognition appears as a socially shared phenomenon within collaborative mathematical word-problem solving processes of dyads of high-achieving pupils. Four dyads solved problems of different difficulty levels. The pupils were 10 years old. The problem-solving activities were videotaped and transcribed in terms of…
Increasing Mathematical Problem-Solving Performance through Relaxation Training.
Sharp, Conni; Coltharp, Hazel; Hurford, David; Cole, AmyKay
2000-01-01
Studies two intact classes of 30 undergraduate students enrolled in a mathematics course; however, one group received relaxation training during an initial class meeting and during the first 5-7 minutes of each subsequent class. The group which received the relaxation training had significantly lower mathematics anxiety and significantly higher…
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Hamsa Venkat
2009-09-01
Full Text Available In this paper we consider the ways in which the Mathematical Literacy (ML assessment taxonomy provides spaces for the problem solving and reasoning identified as critical to mathematical literacy competence. We do this through an analysis of the taxonomy structure within which Mathematical Literacy competences are assessed. We argue that shortcomings in this structure in relation to the support and development of reasoning and problem solving feed through into the kinds of questions that are asked within the assessment of Mathematical Literacy. Some of these shortcomings are exemplified through the questions that appeared in the 2008 Mathematical Literacy examinations. We conclude the paper with a brief discussion of the implications of this taxonomy structure the development of the reasoning and problem–solving competences that align with curricular aims. This paper refers to the assessment taxonomy in the Mathematical Literacy Curriculum Statement (Deparment of Education (DOE, 2007.
PROBLEM SOLVING IN SCHOOL MATHEMATICS BASED ON HEURISTIC STRATEGIES
Novotná, Jarmila; EISENMANN. Petr; PŘIBYL, Jiří; ONDRUŠOVÁ, Jiřina; BŘEHOVSKÝ, Jiří
2014-01-01
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-te...
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.
Özcan, Zeynep Çigdem; Imamoglu, Yesim; Katmer Bayrakli, Vildan
2017-01-01
Problem solving is highlighted in many mathematics curricula and has recently become one of the most investigated topics in the field of mathematics education. Extensive studies report that developing students' problem solving skills enhances their understanding of mathematics. Therefore, there is a focus on investigating problem solving processes…
Developing a pedagogical problem solving view for mathematics teachers with two reflection programs
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Bracha KRAMARSKI
2009-10-01
Full Text Available The study investigated the effects of two reflection support programs on elementary school mathematics teachers’ pedagogical problem solving view. Sixty-two teachers participated in a professional development program. Thirty teachers were assigned to the self-questioning (S_Q training and thirty two teachers were assigned to the reflection discourse (R_D training. The S_Q program was based on the IMPROVE self-questioning approach which emphasizes systematic discussion along the phases of mathematical or pedagogical problem solving as student and teacher. The R_D program emphasized discussion of standard based teaching and learning principles. Findings indicated that systematic reflection support (S_Q is effective for developing mathematics PCK, and strengthening metacognitive knowledge of mathematics teachers, more than reflection discourse (R_D. No differences were found between the groups in developing beliefs about teaching mathematics in using problem solving view.
Mathematical mechanic using physical reasoning to solve problems
Levi, Mark
2009-01-01
Everybody knows that mathematics is indispensable to physics--imagine where we'd be today if Einstein and Newton didn't have the math to back up their ideas. But how many people realize that physics can be used to produce many astonishing and strikingly elegant solutions in mathematics? Mark Levi shows how in this delightful book, treating readers to a host of entertaining problems and mind-bending puzzlers that will amuse and inspire their inner physicist. Levi turns math and physics upside down, revealing how physics can simplify proofs and lead to quicker solutions and new theorems, and how physical solutions can illustrate why results are true in ways lengthy mathematical calculations never can
Mathematical Modelling as Problem Solving for Children in the Singapore Mathematics Classrooms
Eric, Chan Chun Ming
2009-01-01
The newly revised mathematics curriculum in Singapore has recently factored Applications and Modelling to be part of the teaching and learning of mathematics. Its implication is that even children should now be involved in works of mathematical modelling. However, to be able to implement modelling activities in the primary mathematics classroom,…
Schuchardt, Anita M.; Schunn, Christian D.
2016-01-01
Amid calls for integrating science, technology, engineering, and mathematics (iSTEM) in K-12 education, there is a pressing need to uncover productive methods of integration. Prior research has shown that increasing contextual linkages between science and mathematics is associated with student problem solving and conceptual understanding. However,…
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…
Problem solving as a challenge for mathematics education in The Netherlands
Doorman, M.; Drijvers, P.; Dekker, T.; Heuvel-Panhuizen, T. van; Lange, J. de; Wijers, M.
2007-01-01
This paper deals with the challenge to establish problem solving as a living domain in mathematics education in The Netherlands. While serious attempts are made to implement a problem-oriented curriculum based on principles of realistic mathematics education with room for modelling and with integrat
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…
Cognitive Activities in Solving Mathematical Tasks: The Role of a Cognitive Obstacle
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…
Marchis, Iuliana
2013-01-01
Developing the problem solving competency is one of the main goals of school education, as it is a very important competency in someone's everyday life and career as well. Mathematics is highly appropriate for developing this competence. This research studies future Primary and Preschool Pedagogy specialization students' mathematical problem…
Stylianou, Despina A.
2013-01-01
Representation and justification are two central "mathematical practices". In the past, each has been examined to gain insights in the functions that they have in students' mathematical problem solving. Here, we examine the ways that representation and justification interact and influence the development of one another. We focus on the…
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…
Write Is Right: Using Graphic Organizers to Improve Student Mathematical Problem Solving
Zollman, Alan
2012-01-01
Teachers have used graphic organizers successfully in teaching the writing process. This paper describes graphic organizers and their potential mathematics benefits for both students and teachers, elucidates a specific graphic organizer adaptation for mathematical problem solving, and discusses results using the "four-corners-and-a-diamond"…
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…
Ikons for Mathematics, Part I. Problem Solving and Strategy Games.
Melrose, Jean; Rowe, Susan
1989-01-01
Described are some designs in the playground of an infant school, and indicated are some mathematical activities that resulted from their use. Games included are Schlegel diagram of Dodecahedron, Pong Hau K'i, Ko No, Achi, Draughts, and Star with their diagrams. (YP)
Cognitive Style and Competence in Mathematics Problem Solving.
Clark, Henry T., III; And Others
Fifty-five college students participated in a study investigating the effect of field dependence and time limitations on the solution of mathematics word problems and visual interpretation problems. Field-independent (n=25) and field-dependent (n=30) subjects represented the upper and lower thirds on the Hidden Figures Test. Field-independent…
Field-Dependence-Independence and Mathematics Problem-Solving.
Vaidya, Sheila; And Others
Presented is a discussion of the nature of individual differences in the learning of mathematics, which leads to a review of field-dependent and field-independent cognitive styles. Field-dependence-independence is noted as an important variable in school learning and a study is cited that investigated the relationship between pupil success at…
Leveling Students' Creative Thinking in Solving and Posing Mathematical Problem
Siswono, Tatag Yuli Eko
2010-01-01
Many researchers assume that people are creative, but their degree of creativity is different. The notion of creative thinking level has been discussed .by experts. The perspective of mathematics creative thinking refers to a combination of logical and divergent thinking which is based on intuition but has a conscious aim. The divergent thinking…
The effects of cumulative practice on mathematics problem solving.
Mayfield, Kristin H; Chase, Philip N
2002-01-01
This study compared three different methods of teaching five basic algebra rules to college students. All methods used the same procedures to teach the rules and included four 50-question review sessions interspersed among the training of the individual rules. The differences among methods involved the kinds of practice provided during the four review sessions. Participants who received cumulative practice answered 50 questions covering a mix of the rules learned prior to each review session. Participants who received a simple review answered 50 questions on one previously trained rule. Participants who received extra practice answered 50 extra questions on the rule they had just learned. Tests administered after each review included new questions for applying each rule (application items) and problems that required novel combinations of the rules (problem-solving items). On the final test, the cumulative group outscored the other groups on application and problem-solving items. In addition, the cumulative group solved the problem-solving items significantly faster than the other groups. These results suggest that cumulative practice of component skills is an effective method of training problem solving.
Analytical Derivation: An Epistemic Game for Solving Mathematically Based Physics Problems
Bajracharya, Rabindra R.; Thompson, John R.
2016-01-01
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…
Embedding Game-Based Problem-Solving Phase into Problem-Posing System for Mathematics Learning
Chang, Kuo-En; Wu, Lin-Jung; Weng, Sheng-En; Sung, Yao-Ting
2012-01-01
A problem-posing system is developed with four phases including posing problem, planning, solving problem, and looking back, in which the "solving problem" phase is implemented by game-scenarios. The system supports elementary students in the process of problem-posing, allowing them to fully engage in mathematical activities. In total, 92 fifth…
Serafino, Kathleen; Cicchelli, Terry
2003-01-01
Tested the effects of prior knowledge and two instructional models--structured problem solving and guided generation (GG)--on mathematical problem solving and transfer to an analogous task. Data on students with high and low prior knowledge highlighted significant main effects for prior knowledge, significant differences on transfer to analogous…
Middle School Students' Perceptions, Persistence, and Performance in Mathematical Problem Solving.
Montague, Marjorie; Applegate, Brooks
2000-01-01
A study explored middle school students' (N=54) perceptions of problem difficulty, persistence, and knowledge, and use of problem-solving strategies in solving mathematical word problems. Students with learning disabilities rated problems as significantly more difficult and had a significantly lower total word problem score than both average and…
Directory of Open Access Journals (Sweden)
Deniz KAYA
2013-03-01
Full Text Available 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 University in the fall term of 2012-2013. As a result of analyses, there was not a significant difference between male and female candidates’ perceptions of their problem solving skills. There was a significant difference on their problem solving skills and impulsive approach to problem solving according to grades. Additionally, there was not a significant difference between their problem solving skills and their level of family income, settlement and region where they were lived before coming to the university and leisure activities. It was suggested to give weight to achievement that will leave a positive lasting impact on students’ attitudes like metacognitive skills, for the reason that students’ impulsive approach to the problems.
Emergence of Abductive Reasoning in Mathematical Problem Solving.
Cifarelli, Victor
This paper examines the novel problem solving actions of a pair of college students. The analysis highlights the role of the solvers' inferential processes including abductions, deductions, and inductions as structuring resources that contribute to both their understanding of the problems they face and the emerging novelty that constitutes their…
Koichu, Boris
2010-03-01
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 between mathematical knowledge and problem-solving behaviours are analysed in the contexts of solving an insight geometry problem, posing algebraic problems and calculus exploration. A particularly knowledgeable and skilled university student was involved in all the episodes. The presented examples substantiate the claim that advanced mathematical knowledge and advanced problem-solving behaviours do not always support each other. More advanced behaviours were observed when the student worked within her conceptual-embodied mathematical world, and less advanced ones when she worked within her symbolic and formal-axiomatic worlds. Alternative explanations of the findings are discussed. It seems that the most comprehensive explanation is in terms of the Principle of Intellectual Parsimony. Implications for further research are drawn.
Inductive-Deductive Approach to Improve Mathematical Problem Solving for Junior High School
Rahmah, Mariam Ar
2017-02-01
This research is experimental quantitative about quasi experiment that emphasize on improve mathematical understanding and problem solving for Junior High School students by inductive-deductive implementation. The population of this research are all of students at IX degree students in Subang 2012/2013. Two of nine classes were chosen as sample for this research. The topic which used is probability including random occurrence, basics of chance, relative frequency, calculation of probability, determining the value of probability, the expected frequency and the combined odds of two events. The instrument that was used are test and non-test. Mathematical understanding and problem solving were used as a test methods. Meanwhile questionnaire, and observation sheet were used as non-test methods. The data was analyzed by Mann-Whitney and t-test. According to whole analyze in this research, can be concluded: 1) the student improvement of mathematical understanding by using inductive-deductive approach is in middle quality, 2) there is no significant difference at improvement mathematical understanding between experimental class and control class, 3) the improvement of student’s ability in mathematical problem solving that use inductive-deductive approach has a low quality, 4) there is no significant difference at mathematical problem solving between experimental class and control class, 5) most of students has positive responses to mathematic learning by inductive-deductive approach, although the students have many problems when learning takes place.
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...
Fuchs, Lynn S; Fuchs, Douglas; Hamlett, Carol L; Lambert, Warren; Stuebing, Karla; Fletcher, Jack M
2008-02-01
The purpose of this study was to explore patterns of difficulty in 2 domains of mathematical cognition: computation and problem solving. Third graders (n = 924; 47.3% male) were representatively sampled from 89 classrooms; assessed on computation and problem solving; classified as having difficulty with computation, problem solving, both domains, or neither domain; and measured on 9 cognitive dimensions. Difficulty occurred across domains with the same prevalence as difficulty with a single domain; specific difficulty was distributed similarly across domains. Multivariate profile analysis on cognitive dimensions and chi-square tests on demographics showed that specific computational difficulty was associated with strength in language and weaknesses in attentive behavior and processing speed; problem-solving difficulty was associated with deficient language as well as race and poverty. Implications for understanding mathematics competence and for the identification and treatment of mathematics difficulties are discussed.
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Svetlana N. Dvoryatkina
2017-03-01
Full Text Available Introduction: the article is concerned with the topical problem of the humanitarian and mathematical knowledge synergy in the context of solving important crosscutting issues. Since the authors have given a theoretical justification of mathematical integration of humanitarian and information knowledge and its implementation in the educational activities of universities. There is a description of the genesis and the main aspects of synergy. It is shown that the synergy of mathematical and humanitarian knowledge with using information technology is the complex educational environment dominant approach to many inter¬disciplinary problems. Materials and Methods: the synergetic approach is a conceptual framework for solving cross-cutting problems. The initial, exploratory and training options of the experimental research method are used to identify synergies problems of humanitarian and mathematical knowledge; mathematical modeling method is applied in solving professional problems for the development of a probabilistic model of analysis and comparison of styles of text works. Results: the complex of pedagogical conditions is defined, substantiated and tested, taking into account the dominant synergy of humanitarian and mathematical knowledge through the developed integrative course. The draft of the integrative course “Mathematical Methods in Linguistics” is presented; the optimum modular structure of the course is defined (“Formation of Modern Mathematics as a New Cultural Paradigm”, “Basic Mathematical Concepts in Linguistics”, “Mathematical Methods in Linguistics”; the essential elements of every mathematical module are practice-oriented tasks of philol ogical contents. Discussion and Conclusions: the synergy of mathematics and humanities is highly productive thing in scientific and research activities of students and in the learning process. The submitted materials can be included in lectures, practical exercises, integrative
Hodnik Cadež, Tatjana; Manfreda Kolar, Vida
2015-01-01
A cognitive schema is a mechanism which allows an individual to organize her/his experiences in such a way that a new similar experience can easily be recognised and dealt with successfully. Well-structured schemas provide for the knowledge base for subsequent mathematical activities. A new experience can be assimilated into a previously existing…
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Ana Kuzle
2012-04-01
Full Text Available In this paper, I report on preservice teachers’ reflections and perceptions on theirproblem-solving process in a technological context. The purpose of the study was to to investigatehow preservice teachers experience working individually in a dynamic geometry environment andhow these experiences affect their own mathematical activity when integrating content (nonroutineproblems and context (technology environment. Careful analysis of participants’ perceptionsregarding their thinking while engaged in problem solving, provided an opportunity to explorehow they explain the emergence of problem solving when working in a dynamic geometryenvironment. The two participants communicated their experience both through the lenses ofthemselves as problem solvers and as future mathematics educators. Moreover, the results of thestudy indicated that problem solving in a technology environment does not necessarily allow focuson decision-making, reflection, and problem solving processes as reported by previous research.
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.
A good diagram is valuable despite the choice of a mathematical approach to problem solving
Maries, Alexandru
2016-01-01
Drawing appropriate diagrams is a useful problem solving heuristic that can transform a problem into a representation that is easier to exploit for solving the problem. A major focus while helping introductory physics students learn problem solving is to help them appreciate that drawing diagrams facilitates problem solution. We conducted an investigation in which 118 students in an algebra-based introductory physics course were subjected to two different interventions during the problem solving in recitation quizzes throughout the semester. Here, we discuss the problem solving performance of students in different intervention groups for two problems involving standing waves in tubes, one which was given in a quiz and the other in a midterm exam. These problems can be solved using two different methods, one involving a diagrammatic representation and the other involving mostly mathematical manipulation of equations. In the quiz, students were either (1) asked to solve the problem in which a partial diagram wa...
Morin, Lisa L.; Watson, Silvana M. R.; Hester, Peggy; Raver, Sharon
2017-01-01
For students with mathematics difficulties (MD), math word problem solving is especially challenging. The purpose of this study was to examine the effects of a problem-solving strategy, bar model drawing, on the mathematical problem-solving skills of students with MD. The study extended previous research that suggested that schematic-based…
The development of cognitive skills by solving mathematical problems.
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Gustavo José Defaz Cruz
2017-03-01
Full Text Available The present investigation work has as main objective to determine the procedures mechanical memoristics in the resolution of mathematical problems and its incidence in the development of abilities cognitive a focus decrease that has limited its didactics to the memorization and mechanization of processes, the lack of understanding of the transversally of the concepts that allows the student to flow among the different systems without breaking into fragments the curriculum, the lack of relationship of these contents with the student’s environment, the reproduction of mechanical processes that favor the memorization and limit the development of the thought, the contributions of the investigation for the solution of the problem and of the proposal it is given in the systematic organization of the resolution of problems where the students put at stake the acquired knowledge and find roads so that they can imagine conjectures or hypothesis, to argue, to explain and to justify the used procedures, to communicate conclusions, discoveries or produced solutions and of course, the use of the abilities cognitive.
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.
Grizzle-Martin, Tamieka
2014-01-01
Children who struggle in mathematics may also lack cognitive awareness in mathematical problem solving. The cognitively-driven program IMPROVE, a multidimensional method for teaching mathematics, has been shown to be helpful for students with mathematical learning difficulties (MLD). Guided by cognitive theory, the purpose of this…
Costner, Kelly Mitchell
This study developed and piloted the Problem-Solving Approach to program evaluation, which involves the direct application of the problem-solving process as a metaphor for program evaluation. A rationale for a mathematics-specific approach is presented, and relevant literature in both program evaluation and mathematics education is reviewed. The Problem-Solving Approach was piloted with a high-school level integrated course in mathematics and science that used graphing calculators and data collection devices with the goal of helping students to gain better understanding of relationships between mathematics and science. Twelve students participated in the course, which was co-taught by a mathematics teacher and a science teacher. Data collection for the evaluation included observations, a pre- and posttest, student questionnaires, student interviews, teacher interviews, principal interviews, and a focus group that involved both students and their teachers. Results of the evaluation of the course are presented as an evaluation report. Students showed improvement in their understandings of mathematics-science relationships, but also showed growth in terms of self-confidence, independence, and various social factors that were not expected outcomes. The teachers experienced a unique form of professional development by learning and relearning concepts in each other's respective fields and by gaining insights into each other's teaching strengths. Both the results of the evaluation and the evaluation process itself are discussed in light of the proposed problem-solving approach. The use of problem solving and of specific problem-solving strategies was found to be prevalent among the students and the teachers, as well as in the activities of the evaluator. Specific problem-solving strategies are highlighted for their potential value in program evaluation situations. The resulting Problem-Solving Approach, revised through the pilot application, employs problem solving as a
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.
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.
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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.
Visual spatial representation in mathematical problem solving by deaf and hearing students.
Blatto-Vallee, Gary; Kelly, Ronald R; Gaustad, Martha G; Porter, Jeffrey; Fonzi, Judith
2007-01-01
This research examined the use of visual-spatial representation by deaf and hearing students while solving mathematical problems. The connection between spatial skills and success in mathematics performance has long been established in the literature. This study examined the distinction between visual-spatial "schematic" representations that encode the spatial relations described in a problem versus visual-spatial "pictorial" representations that encode only the visual appearance of the objects described in a problem. A total of 305 hearing (n = 156) and deaf (n = 149) participants from middle school, high school, and college participated in this study. At all educational levels, the hearing students performed significantly better in solving the mathematical problems compared to their deaf peers. Although the deaf baccalaureate students exhibited the highest performance of all the deaf participants, they only performed as well as the hearing middle school students who were the lowest scoring hearing group. Deaf students remained flat in their performance on the mathematical problem-solving task from middle school through the college associate degree level. The analysis of the students' problem representations showed that the hearing participants utilized visual-spatial schematic representation to a greater extent than did the deaf participants. However, the use of visual-spatial schematic representations was a stronger positive predictor of mathematical problem-solving performance for the deaf students. When deaf students' problem representation focused simply on the visual-spatial pictorial or iconic aspects of the mathematical problems, there was a negative predictive relationship with their problem-solving performance. On two measures of visual-spatial abilities, the hearing students in high school and college performed significantly better than their deaf peers.
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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
Improving Mathematical Problem-Solving Skills in the Middle Grades. A Staff Training Manual.
Weiland, Linnea; And Others
This manual was written to help district curriculum leaders in New Jersey improve instruction in mathematical problem solving in middle and junior high schools. Four training modules contain the material and information needed to conduct a staff development course. The manual was designed to accompany turn-key training sessions to prepare the…
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…
Xenofontos, Constantinos; Andrews, Paul
2014-01-01
This paper presents a comparative analysis of prospective elementary teachers' mathematical problem solving-related beliefs in Cyprus and England. Twenty-four participants, twelve from a well-regarded university in each country, were interviewed qualitatively at the exit point of their undergraduate teacher education studies. Analyses…
Coughlin, Judy; Montague, Marjorie
2011-01-01
This study investigated the effects of cognitive strategy instruction on the mathematical problem solving of three adolescents with spina bifida. Conditions of the multiple-baseline across-individuals design included baseline, two levels of treatment, posttesting, and maintenance. Treatment 1 focused on one-step math problems, and Treatment 2…
Björn, Piia Maria; Aunola, Kaisa; Nurmi, Jari-Erik
2016-01-01
This longitudinal study aimed to investigate the extent to which primary school text comprehension predicts mathematical word problem-solving skills in secondary school among Finnish students. The participants were 224 fourth graders (9-10 years old at the baseline). The children's text-reading fluency, text comprehension and basic calculation…
Evaluation of Students' Mathematical Problem Solving Skills in Relation to Their Reading Levels
Özsoy, Gökhan; Kuruyer, Hayriye Gül; Çakiroglu, Ahmet
2015-01-01
The purpose of the current study is to investigate the correlation between students' reading levels and mathematical problem solving skills. The present study was conducted in line with a qualitative research method, i.e., the phenomenological method. The study group of the current research is composed of six third grade students with different…
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…
Train Students to Solve the Practical Problem by Building Mathematics Models
Institute of Scientific and Technical Information of China (English)
ZHANG Lian-zhong
2005-01-01
It focuses on that students must be developed the ability to solve the practical problem by building the mathematics models and the ability to combine the theory with the practice. It also states that students must be improved the learning interests and practical experience.
Coughlin, Judy; Montague, Marjorie
2011-01-01
This study investigated the effects of cognitive strategy instruction on the mathematical problem solving of three adolescents with spina bifida. Conditions of the multiple-baseline across-individuals design included baseline, two levels of treatment, posttesting, and maintenance. Treatment 1 focused on one-step math problems, and Treatment 2…
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…
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…
Xenofontos, Constantinos; Andrews, Paul
2014-01-01
This paper presents a comparative analysis of prospective elementary teachers' mathematical problem solving-related beliefs in Cyprus and England. Twenty-four participants, twelve from a well-regarded university in each country, were interviewed qualitatively at the exit point of their undergraduate teacher education studies. Analyses revealed…
Students' Mathematics Word Problem-Solving Achievement in a Computer-Based Story
Gunbas, N.
2015-01-01
The purpose of this study was to investigate the effect of a computer-based story, which was designed in anchored instruction framework, on sixth-grade students' mathematics word problem-solving achievement. Problems were embedded in a story presented on a computer as computer story, and then compared with the paper-based version of the same story…
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…
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…
A Naturalistic Study of Executive Function and Mathematical Problem-Solving
Kotsopoulos, Donna; Lee, Joanne
2012-01-01
Our goal in this research was to understand the specific challenges middle-school students face when engaging in mathematical problem-solving by using executive function (i.e., shifting, updating, and inhibiting) of working memory as a functional construct for the analysis. Using modified talk-aloud protocols, real-time naturalistic analysis of…
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…
A Naturalistic Study of Executive Function and Mathematical Problem-Solving
Kotsopoulos, Donna; Lee, Joanne
2012-01-01
Our goal in this research was to understand the specific challenges middle-school students face when engaging in mathematical problem-solving by using executive function (i.e., shifting, updating, and inhibiting) of working memory as a functional construct for the analysis. Using modified talk-aloud protocols, real-time naturalistic analysis of…
Difficulties in solving context-based PISA mathematics tasks : An analysis of students' errors
Wijaya, Ariyadi; van den Heuvel-Panhuizen, Marja; Doorman, Michiel; Robitzsch, Alexander
2014-01-01
The intention of this study was to clarify students' difficulties in solving context-based mathematics tasks as used in the Programme for International Student Assessment (PISA). The study was carried out with 362 Indonesian ninth- and tenth-grade students. In the study we used 34 released PISA math
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…
More on the Fragility of Performance: Choking Under Pressure in Mathematical Problem Solving
Beilock, Sian L.; Kulp, Catherine A.; Holt, Lauren E.; Carr, Thomas H.
2004-01-01
In 3 experiments, the authors examined mathematical problem solving performance under pressure. In Experiment 1, pressure harmed performance on only unpracticed problems with heavy working memory demands. In Experiment 2, such high-demand problems were practiced until their answers were directly retrieved from memory. This eliminated choking under…
Björn, Piia Maria; Aunola, Kaisa; Nurmi, Jari-Erik
2016-01-01
This longitudinal study aimed to investigate the extent to which primary school text comprehension predicts mathematical word problem-solving skills in secondary school among Finnish students. The participants were 224 fourth graders (9-10 years old at the baseline). The children's text-reading fluency, text comprehension and basic calculation…
An Appropriate Prompts System Based on the Polya Method for Mathematical Problem-Solving
Lee, Chien I.
2017-01-01
Current mathematics education emphasizes techniques, formulas, and procedures, neglecting the importance of understanding, presentation, and reasoning. This turns students into passive listeners that are well-practiced only in using formulas that they do not understand. We therefore adopted the Polya problem-solving method to provide students with…
Problem Solving Strategies of Selected Pre-Service Secondary School Mathematics Teachers in Malaysia
Yew, Wun Theam; Zamri, Sharifah Norul Akmar Syed
2016-01-01
Problem solving strategies of eight pre-service secondary school mathematics teachers (PSSMTs) were examined in this study. A case study research design was employed and clinical interview technique was used to collect the data. Materials collected for analysis consisted of audiotapes and videotapes of clinical interviews, subjects' notes and…
Adapting a Problem-Solving Approach to Teaching Mathematics to Students with Mild Disabilities.
Salend, Spencer J.; Hofstetter, Elaine
1996-01-01
Guidelines for implementing a problem-solving approach to teaching mathematics concepts and skills to students with mild disabilities include: establish connections to daily life; use visual presentations; use manipulatives; use peer-mediated instruction; provide models, cues, and prompts; teach self-management techniques and learning strategies;…
The Effects of Different Modes of Representation on Mathematical Problem Solving
Gagatsis, Athanasios; Elia, Iliada
2004-01-01
The main objective of this study is to investigate the role of four different modes of representation in mathematical problem solving (MPS), and more specifically to develop a model, which provides information about the effects of these representations in the solution procedures of one-step problems of additive structures. Data were collected from…
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Edwin Musdi
2016-02-01
Full Text Available This research aims to develop a mathematics instructional model based realistic mathematics education (RME to promote students' problem-solving abilities. The design research used Plomp models, which consists of preliminary phase, development or proto-typing phase and assessment phase. At this study, only the first two phases conducted. The first phase, a preliminary investigation, carried out with a literature study to examine the theory-based instructional learning RME model, characteristics of learners, learning management descriptions by junior high school mathematics teacher and relevant research. The development phase is done by developing a draft model (an early prototype model that consists of the syntax, the social system, the principle of reaction, support systems, and the impact and effects of instructional support. Early prototype model contain a draft model, lesson plans, worksheets, and assessments. Tesssmer formative evaluation model used to revise the model. In this study only phase of one to one evaluation conducted. In the ppreliminary phase has produced a theory-based learning RME model, a description of the characteristics of learners in grade VIII Junior High School Padang and the description of teacher teaching in the classroom. The result showed that most students were still not be able to solve the non-routine problem. Teachers did not optimally facilitate students to develop problem-solving skills of students. It was recommended that the model can be applied in the classroom.
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.
Hoffman, Bobby
2010-01-01
This study investigated the role of self-efficacy beliefs, mathematics anxiety, and working memory capacity in problem-solving accuracy, response time, and efficiency (the ratio of problem-solving accuracy to response time). Pre-service teachers completed a mathematics anxiety inventory measuring cognitive and affective dispositions for…
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Güney HACIÖMEROGLU
2013-04-01
Full Text Available This present study aimed to adapt the Mathematical Processing Instrument (MPI developed by Suwarsono (1982 to Turkish and determine elementary pre-service teachers’ problem solving preferences. Results of the study revealed that the MPI is a valid and reliable instrument that can be used to measure students’ preference for visual or analytic problem solving strategies. The Cronbach’s alpha coefficients were calculated as 0.72 and 0.78 for the Mathematical Processing Instrument-Tests I and II, respectively. The Cronbach’s alpha coefficient for the overall instrument was found as 0.86. The difficulty of tasks and grade level had a significant impact on pre-service teachers’ problem solving preferences.
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Deniz Özen
2013-03-01
Full Text Available The aim of this study is to investigate pre-service elementary mathematics teachers’ open geometric problem solving process in a Dynamic Geometry Environment. With its qualitative inquiry based research design employed, the participants of the study are three pre-service teachers from 4th graders of the Department of Elementary Mathematics Teaching. In this study, clinical interviews, screencaptures of the problem solving process in the Cabri Geomery Environment, and worksheets included 2 open geometry problems have been used to collect the data. It has been investigated that all the participants passed through similar recursive phases as construction, exploration, conjecture, validate, and justification in the problem solving process. It has been thought that this study provide a new point of view to curriculum developers, teachers and researchers
Kinsella, John J.
1970-01-01
Discussed are the nature of a mathematical problem, problem solving in the traditional and modern mathematics programs, problem solving and psychology, research related to problem solving, and teaching problem solving in algebra and geometry. (CT)
Investigating and developing engineering students' mathematical modelling and problem-solving skills
Wedelin, Dag; Adawi, Tom; Jahan, Tabassum; Andersson, Sven
2015-09-01
How do engineering students approach mathematical modelling problems and how can they learn to deal with such problems? In the context of a course in mathematical modelling and problem solving, and using a qualitative case study approach, we found that the students had little prior experience of mathematical modelling. They were also inexperienced problem solvers, unaware of the importance of understanding the problem and exploring alternatives, and impeded by inappropriate beliefs, attitudes and expectations. Important impacts of the course belong to the metacognitive domain. The nature of the problems, the supervision and the follow-up lectures were emphasised as contributing to the impacts of the course, where students show major development. We discuss these empirical results in relation to a framework for mathematical thinking and the notion of cognitive apprenticeship. Based on the results, we argue that this kind of teaching should be considered in the education of all engineers.
Bernardo, Allan B. I.; Calleja, Marissa O.
2005-01-01
Researchers have suggested that among bilinguals, solving word problems in mathematics is influenced by linguistic factors (K. Durkin & B. Shire, 1991; L. Verschaffel, B. Greer, & E. De Corte, 2000). Others have suggested that students exhibit a strong tendency to exclude real-world constraints in solving mathematics word problems (L. Verschaffel,…
Hwang, Jiwon; Riccomini, Paul J.
2016-01-01
Requirements for reasoning, explaining, and generalizing mathematical concepts increase as students advance through the educational system; hence, improving overall mathematical proficiency is critical. Mathematical proficiency requires students to interpret quantities and their corresponding relationships during problem-solving tasks as well as…
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.
Bender, Carl
2017-01-01
The theory of complex variables is extremely useful because it helps to explain the mathematical behavior of functions of a real variable. Complex variable theory also provides insight into the nature of physical theories. For example, it provides a simple and beautiful picture of quantization and it explains the underlying reason for the divergence of perturbation theory. By using complex-variable methods one can generalize conventional Hermitian quantum theories into the complex domain. The result is a new class of parity-time-symmetric (PT-symmetric) theories whose remarkable physical properties have been studied and verified in many recent laboratory experiments.
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.
A protocol-analytic study of metacognition in mathematical problem solving
Cai, Jinfa
1994-12-01
The metacognitive behaviours of two subjects having a high level of mathematical experience and two subjects having a low level of mathematical experience were compared within each of the four cognitive processes of mathematical problem solving: orientation, organisation, execution, and verification. The results showed that the high-experience subjects engaged in self-regulation during the problem-solving process and that the low-experience subjects did not. Also, the high-experience subjects had stronger awareness about what they knew and how they should use this knowledge, and were able to sequentially monitor their goal-changing and decision-making activities in order to implement their goal. Another important finding was that the high-experience subjects spent the majority of their time on orientation and organisation rather than on execution, while low-experience subjects spent the majority of their time on execution rather than on orientation and organisation. Finally, the high-experience subjects accurately evaluated their strategies, actions and intermediate results. The results suggest that individual differences between the high- and low-experience subjects are unlikely to emerge either from the subjects' selection of solution strategies or from the level of mathematical knowledge required for solving the problem. Therefore, the results from this study support the argument that metacognitive behaviours have important influences on subjects' problem-solving success. This study also suggests that a complex, difficult, or novel task appears to function well as a task for examining metacognitive behaviours because such a task results in the subjects being unable to arrive at closure quickly.
Applied mathematical problem solving, modelling, applications, and links to other subjects
Blum, Werner; Niss, Mogens
1991-01-01
The paper will consist of three parts. In part I we shall present some background considerations which are necessary as a basis for what follows. We shall try to clarify some basic concepts and notions, and we shall collect the most important arguments (and related goals) in favour of problem solving, modelling and applications to other subjects in mathematics instruction. In the main part II we shall review the present state, recent trends, and prospective lines of development, both...
THE USE OF SIMULINK BLOCK DIAGRAM TO SOLVE MATHEMATICAL MODELS AND CONTROL EQUATIONS
Ghasem, N. M.; Departamento de Biología Facultad de Ciencias Pontificia Universidad Javeriana; Hussain, M. A.; Department of Chemical Engineering University of Malaya, 50603 Kuala Lumpur, Malaysia, School of Engineering, Design and Technology, University of Bradford, Bradford BD7 1DP, UK; Mujtaba, I. M.; Department of Chemical Engineering University of Malaya, 50603 Kuala Lumpur, Malaysia, School of Engineering, Design and Technology, University of Bradford, Bradford BD7 1DP, UK
2003-01-01
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 alsoallows 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 ...
Rosales, Javier; Vicente, Santiago; Chamoso, Jose M.; Munez, David; Orrantia, Josetxu
2012-01-01
Word problem solving involves the construction of two different mental representations, namely, mathematical and situational. Although educational research in word problem solving has documented different kinds of instruction at these levels, less is known about how both representational levels are evoked during word problem solving in day-to-day…
What Teachers Say About Student Difficulties Solving Mathematical Word Problems in Grades 2-5
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Daniel L. Pearce, Faye Bruun, Kimberly Skinner, & Claricia Lopez-Mohler
2013-02-01
Full Text Available Close This study investigated teachers' perspectives of difficulties students have solving mathematical word problems and causes of those difficulties. Classroom practices and strategies teachers used in their attempts to foster student problem solving success were also studied. Participants were 70 second-fifth grade teachers from 42 different schools in a south central region of the United States. Data included analyses of interview transcriptions of teachers' responses. Findings from teachers' responses showed students' abilities to read and understand the problem was the most frequently cited difficulty; standardized testing and text difficulties were the most cited causes of those difficulties. Examination of teachers' responses to practices and strategies used in the classroom revealed the most cited practice was working the problem independently and the most cited strategy taught to students was to identify key words. This study revealed the significant role reading plays in teachers' perspectives of students' difficulties solving mathematical word problems and provided insight into practices and strategies teachers reported using to teach word problems. With attention to teacher-reported causes of difficulties and importance of this ability for students, this study also showed the impact state mandated testing has on instruction of mathematical word problems
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Serdal BALTACI
2016-10-01
Full Text Available It is a widely known fact that gifted students have different skills compared to their peers. However, to what extent gifted students use mathematical thinking skills during probability problem solving process emerges as a significant question. Thence, the main aim of the present study is to examine 8th grade gifted students’ probability problem-solving process related to daily life in terms of mathematical thinking skills. In this regard, a case study was used in the study. The participants of the study were six students at 8th grade (four girls and two boys from the Science and Art Center. One of the purposeful sampling methods, maximum variation sampling was used for selecting the participants. Clinical interview and problems were used as a data collection tool. As a results of the study, it was determined that gifted students use reasoning and strategies skill, which is one of the mathematical thinking skills, mostly on the process of probability problem solving, and communication skills at least.
Warming up for PBL: a course in mathematical modelling and problem solving for engineering students
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Dag Wedelin
2015-06-01
Full Text Available The step from traditional teaching to PBL is considerable and it has previously been proposed that students should be skilled at problem solving before entering a PBL course. In this paper, we first discuss some key ideas behind the design of a successful course in mathematical modelling and problem solving for engineering students. A central aim of the course is to help the students to understand the power of learning by exploration, a missing key component in the students’ ability to solve problems. We then discuss how this kind of course can serve as an intermediate step in a progression towards more self-directed project-based and problem-based learning.
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Meirav Tzohar-Rozen
2014-11-01
Full Text Available Mathematical problem solving is among the most valuable aspects of mathematics education. It is also the hardest for elementary school students (Verschaffel, Greer & De Corte, 2000. Students experience cognitive and metacognitive difficulties in this area and develop negative emotions and poor motivation which hamper their efforts (Kramarski, Weiss, & Kololshi-Minsker, 2010. 9–11 seems the critical stage for developing attitudes and emotional reactions towards mathematics (Artino, 2009. These metacognitive and motivational-emotional factors are fundamental components of Self-Regulated Learning (SRL, a non-innate process requiring systematic, explicit student training (Pintrich, 2000; Zimmerman, 2000. Most self-regulation studies relating to problem-solving focus on metacognition. Few explore the motivational-emotional component. This study aimed to develop, examine, and compare two SRL interventions dealing with two additional components of self-regulation: metacognitive regulation (MC and motivational-emotional regulation (ME. It also sought to examine the significance of these components and their contribution to learners' problem-solving achievements and self-regulation. The study examined 118 fifth grade students, randomly assigned to two groups. Pre- and post-intervention, the two groups completed self-regulation questionnaires relating to metacognition, motivation, and emotion. They also solved arithmetic series problems presented in two ways (verbal form and numeric form. After intervention we also examined a novel transfer problem. The intervention consisted of 10 hours for 5 weeks. Following the intervention the groups exhibited similar improvements across all the problems. The MC group performed best in metacognitive self-regulation and the ME group performed best in certain motivational-emotional aspects of self-regulation. Research implications are discussed.
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
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…
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…
Jitendra, Asha K.; Dupuis, Danielle N.; Zaslofsky, Anne F.
2014-01-01
This purpose of this study was to examine the reliability and validity of a curriculum-based measure of word problem solving (CBM-WPS) as an indicator of performance and progress in a sample of 136 third-grade students at risk for mathematics difficulties (MDs) instructed in a standards-based mathematics curriculum. Students completed the CBM-WPS…
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.
Bal, Ayten Pinar
2015-01-01
The aim of this study is to examine the mathematical problem-solving beliefs and problem-solving success levels of primary school teacher candidates through the variables of academic success and gender. The research was designed according to the mixed methods technique in which qualitative and quantitative methods are used together. The working…
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…
Electromagnetic Problems Solving by Conformal Mapping: A Mathematical Operator for Optimization
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Wesley Pacheco Calixto
2010-01-01
Full Text Available Having the property to modify only the geometry of a polygonal structure, preserving its physical magnitudes, the Conformal Mapping is an exceptional tool to solve electromagnetism problems with known boundary conditions. This work aims to introduce a new developed mathematical operator, based on polynomial extrapolation. This operator has the capacity to accelerate an optimization method applied in conformal mappings, to determinate the equipotential lines, the field lines, the capacitance, and the permeance of some polygonal geometry electrical devices with an inner dielectric of permittivity ε. The results obtained in this work are compared with other simulations performed by the software of finite elements method, Flux 2D.
Capraro, Mary Margaret; An, Song A.; Ma, Tingting; Rangel-Chavez, A. Fabiola; Harbaugh, Adam
2012-01-01
Open-ended problems have been regarded as powerful tools for teaching mathematics. This study examined the problem solving of eight mathematics/science middle-school teachers. A semi-structured interview was conducted with (PTs) after completing an open-ended triangle task with four unique solutions. Of particular emphasis was how the PTs used a…
Murata, Aki; Kattubadi, Sailaja
2012-01-01
In considering mathematics problem solving as a model-eliciting activity (Lesh & Doerr, 2003; Lesh & Harel, 2003; Lesh & Zawojewski, 2008), it is important to know "what" students are modeling for the problems: situations or solutions. This study investigated Grade 3 students' mathematization process by examining how they modeled different…
Nelson, Laura Lynn
2012-01-01
Over the past decade, research has shown that problem solving skills and students' achievement in mathematics have been a primary focus for mathematics instruction at all grade levels. Despite this persistent focus on cognitive development and children's thinking processes, some teachers fail to help students use these cognitive…
An Evaluation of Grades 9 and 10 Mathematics Textbooks vis-a-vis Fostering Problem Solving Skills
Buishaw, Alemayehu; Ayalew, Assaye
2013-01-01
This study sought to evaluate the adequacy of integration of problematic situations and general problem-solving strategies (heuristics) in grades 9 and 10 mathematics textbooks. Grade 9 and grade 10 mathematics textbooks were used for analysis. Document analysis and interview were used as data gathering instruments. Document analysis was carried…
The effects of group monitoring on fatigue-related einstellung during mathematical problem solving.
Frings, Daniel
2011-12-01
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 fatigue and problem solving also involve people working in teams. However, little research has considered the role of social processes in managing the effects of fatigue. Research into the group monitoring hypothesis suggests that membership in a team can offset the effects of impairing factors such as fatigue upon performance. Thus, the present study also aimed to test whether group membership exacerbates or ameliorates the negative effects of fatigue. During the course of a weekend military training exercise, participants (N = 171) attempted to solve a series of problems either alone or in a team, and while either reasonably alert (nonfatigued) or fatigued through sleep deficit. Fatigued problem solvers working alone showed increased Einstellung. In contrast, and in line with the group monitoring hypothesis, teams of fatigued problem solvers did not experience increased Einstellung. The present study also showed that teams with a group member who was relatively less fatigued experienced less Einstellung than other groups. These effects persisted even once participants were cued toward more direct strategies. These findings highlight the risk of Einstellung when fatigued and also the importance of team membership with reference to problem solving in an occupational context.
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…
de Kock, Willem D.; Harskamp, Egbert G.
2014-01-01
Teachers in primary education experience difficulties in teaching word problem solving in their mathematics classes. However, during controlled experiments with a metacognitive computer programme, students' problem-solving skills improved. Also without the supervision of researchers, metacognitive computer programmes can be beneficial in a natural…
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…
Abdullah, Nasarudin; Halim, Lilia; Zakaria, Effandi
2014-01-01
This study aimed to determine the impact of strategic thinking and visual representation approaches (VStops) on the achievement, conceptual knowledge, metacognitive awareness, awareness of problem-solving strategies, and student attitudes toward mathematical word problem solving among primary school students. The experimental group (N = 96)…
Meli, Kalliopi; Zacharos, Konstantinos; Koliopoulos, Dimitrios
2016-01-01
This article presents a case study that examines the level of integration of mathematical knowledge in physics problem solving among first grade students of upper secondary school. We explore the ways in which two specific students utilize their knowledge and we attempt to identify the epistemological framings they refer to while solving a physics…
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…
Meli, Kalliopi; Zacharos, Konstantinos; Koliopoulos, Dimitrios
2016-01-01
This article presents a case study that examines the level of integration of mathematical knowledge in physics problem solving among first grade students of upper secondary school. We explore the ways in which two specific students utilize their knowledge and we attempt to identify the epistemological framings they refer to while solving a physics…
Understanding and quantifying cognitive complexity level in mathematical problem solving items
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SUSAN E. EMBRETSON
2008-09-01
Full Text Available The linear logistic test model (LLTM; Fischer, 1973 has been applied to a wide variety of new tests. When the LLTM application involves item complexity variables that are both theoretically interesting and empirically supported, several advantages can result. These advantages include elaborating construct validity at the item level, defining variables for test design, predicting parameters of new items, item banking by sources of complexity and providing a basis for item design and item generation. However, despite the many advantages of applying LLTM to test items, it has been applied less often to understand the sources of complexity for large-scale operational test items. Instead, previously calibrated item parameters are modeled using regression techniques because raw item response data often cannot be made available. In the current study, both LLTM and regression modeling are applied to mathematical problem solving items from a widely used test. The findings from the two methods are compared and contrasted for their implications for continued development of ability and achievement tests based on mathematical problem solving items.
Self-Efficacy Beliefs and Mathematical Problem-Solving of Gifted Students
Pajares
1996-10-01
Path analysis was used to test the predictive and mediational role that self-efficacy beliefs play in the mathematical problem-solving of middle school gifted students (n = 66) mainstreamed with regular education students (n = 232) in algebra classes. Self-efficacy of gifted students made an independent contribution to the prediction of problem-solving in a model that controlled for the effects of math anxiety, cognitive ability, mathematics GPA, self-efficacy for self-regulated learning, and sex. Gifted girls surpassed gifted boys in performance but did not differ in self-efficacy. Gifted students reported higher math self-efficacy and self-efficacy for self-regulated learning as well as lower math anxiety than did regular education students. Although most students were overconfident about their capabilities, gifted students had more accurate self-perceptions and gifted girls were biased toward underconfidence. Results support the hypothesized role of self-efficacy in A. Bandura's (1986) social cognitive theory.
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%).
Teacher’s Stimulus Helps Students Achieve Mathematics Reasoning and Problem Solving Competences
Hidayah, Isti; Pujiastuti, Emi; Chrisna, Jeanet Eva
2017-04-01
The students’ problem-solving ability in mathematics learning still becomes a challenge for teachers, especially in primary education. The scientific approach, with its activities including observing, asking, collecting information/experimenting/trying, associating/analysing information/reasoning, communicating/presenting/ networking is expected to be able to help students to achieve their competence of reasoning and problem-solving. The Missouri Mathematics Project learning by using student worksheet and manipulative (classical and group) have helped students achieved problem-solving competence. The implementation of scientific approach in the activities of observing, experimenting, and communicating are good. However, the questioning and associating activities are still less promoted. The result of observation towards four meetings of learning by using teaching aids shows that the expected activity which did not emerge during the learning is “students ask questions from the factual thing to hypothetical thing, starting with guidance from teacher until they can do by themselves”. The result of analysis towards theoretical background and research result conclude that the students’ asking and thinking abilities can be developed gradually by delivering stimuli in the form of tasks which have been designed by the teacher. The task could be a problem or a clue; then the students determine things such as: “what the question?”, “facts from pictures/text/graphs/tables”, “find the hidden question”, what’s extra?”, “what’s missing?”, “what’s wrong?”, alternatively, “make up the problem.
Anderson, John R; Betts, Shawn; Ferris, Jennifer L; Fincham, Jon M
2011-03-01
Students were taught an algorithm for solving a new class of mathematical problems. Occasionally in the sequence of problems, they encountered exception problems that required that they extend the algorithm. Regular and exception problems were associated with different patterns of brain activation. Some regions showed a Cognitive pattern of being active only until the problem was solved and no difference between regular or exception problems. Other regions showed a Metacognitive pattern of greater activity for exception problems and activity that extended into the post-solution period, particularly when an error was made. The Cognitive regions included some of parietal and prefrontal regions associated with the triple-code theory of (Dehaene, S., Piazza, M., Pinel, P., & Cohen, L. (2003). Three parietal circuits for number processing. Cognitive Neuropsychology, 20, 487-506) and associated with algebra equation solving in the ACT-R theory (Anderson, J. R. (2005). Human symbol manipulation within an 911 integrated cognitive architecture. Cognitive science, 29, 313-342. Metacognitive regions included the superior prefrontal gyrus, the angular gyrus of the triple-code theory, and frontopolar regions.
Cranfield, Corvell
2013-01-01
The construct of mathematical identity has recently been widely used in mathematics education with the intention to understand how students relate to and engage (or disengage) with mathematics. Grootenboer and Zevenbergen (2008) define mathematical identity as the students' knowledge, abilities, skills, beliefs, dispositions, attitudes and…
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Von Anthony Gayas Torio
2015-02-01
Full Text Available The field of Mathematics requires a lot of critical thinking and problem solving. These skills are honed as early as the basic education years of the students. Teacher training institutions should make it a necessity that they are able to cater to pre-service teachers who will be able to meet the demands of mathematics education. This paper aimed to construct, validate and determine the Differential Item Functioning (DIF of a problem solving test for pre-service mathematics teachers. This test will later be used as a basis for designing interventions to improve the mathematical aptitude of pre-service teachers. Two universities were chosen with 100 third year students taking Bachelor of Science in Secondary Education major in Mathematics. The tests were constructed and validated by experts before administration to the participants. The participants took the examination and the test was improved based on the results of the item analysis. Differential Item Functioning was also tested using the Standardization Method. The study led to the development of a 60-item validated test on problem solving. After subjecting to DIF analysis, it was found that the two groups tested performed with no significant difference between individuals of similar abilities. The test yielded norm values per sub-skill of the test which will help gauge pre-service mathematics teachers’ problem-solving skills.
Bernardo, Allan B I; Calleja, Marissa O
2005-03-01
Researchers have suggested that among bilinguals, solving word problems in mathematics is influenced by linguistic factors (K. Durkin & B. Shire, 1991; L. Verschaffel, B. Greer, & E. De Corte, 2000). Others have suggested that students exhibit a strong tendency to exclude real-world constraints in solving mathematics word problems (L. Verschaffel, E. De Corte, & S. Lasure, 1994). In the present study, the authors explored the effects of stating word problems in either Filipino or English on how Filipino-English bilingual students solved word problems in which the solution required the application of real-world knowledge. The authors asked bilingual students to solve word problems in either their first or second language. For some of the word problems, real-life constraints prevented straightforward application of mathematical procedures. The authors analyzed the students' solutions to determine whether the language of the word problems affected the tendency to apply real-life constraints in the solution. Results showed that the bilingual students (a) rarely considered real-life constraints in their solutions, (b) were more successful in understanding and solving word problems that were stated in their first language, and (c) were more likely to experience failure in finding a solution to problems stated in their second language. The results are discussed in terms of the relationship between linguistic and mathematical problem-solving processes among bilinguals.
Jitendra, Asha K; Harwell, Michael R; Dupuis, Danielle N; Karl, Stacy R
This article reports results from a study investigating the efficacy of a proportional problem-solving intervention, schema-based instruction (SBI), in seventh grade. Participants included 806 students with mathematical difficulties in problem solving (MD-PS) from an initial pool of 1,999 seventh grade students in a larger study. Teachers and their students in the larger study were randomly assigned to an SBI or control condition and teachers in both conditions then provided instruction on the topics of ratio, proportion, and percent. We found that students with MD-PS in SBI classrooms scored on average higher than their counterparts in control classrooms on a posttest and delayed posttest administered 9 weeks later. Given students' difficulties with proportional problem-solving and the consequences of these difficulties, an important contribution of this research is the finding that when provided with appropriate instruction, students with MD-PS are capable of enhanced proportional problem-solving performance.
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…
Chen, Peggy P
2006-06-01
The study examined the judgments made by four seventh-grade mathematics teachers of their 107 students' competence in solving mathematics problems. Simultaneously, the 107 students made self-efficacy judgments about their capability in solving mathematics problems. The two sets of judgments were tested for predicting students' mathematics performance. Also, students' prior mathematics achievement was studied for its influence on both teachers' and students' judgments and students' mathematics performance. Teachers were asked to make judgments of each student for every mathematics problem solved. Results were consistent with prior research indicating that students' mathematics self-efficacy beliefs were highly predictive of their performance. Path analysis indicated that the mathematics teachers' judgments were also highly predictive of students' performance and self-efficacy. In turn, these variables predicted students' postperformance judgments. Combining students' self-efficacy judgments and teachers' judgments of students increased predictiveness for students' mathematics performance. Educational implications were also discussed.
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.
The Different Patterns of Gesture between Genders in Mathematical Problem Solving of Geometry
Harisman, Y.; Noto, M. S.; Bakar, M. T.; Amam, A.
2017-02-01
This article discusses about students’ gesture between genders in answering problems of geometry. Gesture aims to check students’ understanding which is undefined from their writings. This study is a qualitative research, there were seven questions given to two students of eight grade Junior High School who had the equal ability. The data of this study were collected from mathematical problem solving test, videoing students’ presentation, and interviewing students by asking questions to check their understandings in geometry problems, in this case the researchers would observe the students’ gesture. The result of this study revealed that there were patterns of gesture through students’ conversation and prosodic cues, such as tones, intonation, speech rate and pause. Female students tended to give indecisive gestures, for instance bowing, hesitating, embarrassing, nodding many times in shifting cognitive comprehension, forwarding their body and asking questions to the interviewer when they found tough questions. However, male students acted some gestures such as playing their fingers, focusing on questions, taking longer time to answer hard questions, staying calm in shifting cognitive comprehension. We suggest to observe more sample and focus on students’ gesture consistency in showing their understanding to solve the given problems.
Leh, Jayne M.; Jitendra, Asha K.; Caskie, Grace I. L.; Griffin, Cynthia C.
2007-01-01
The purpose of this study was to examine the tenability of a curriculum-based mathematical word problem-solving (WPS) measure as a progress-monitoring tool to index students' rate of growth or slope of achievement over time. Participants consisted of 58 third-grade students, who were assessed repeatedly over 16 school weeks. Students were measured…
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.
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,…
Chen, I-Ching; Hu, Shueh-Cheng
2013-01-01
The capability of solving fundamental mathematical problems is essential to elementary school students; however instruction based on ordinary narration usually perplexes students. Concept mapping is well known for its effectiveness on assimilating and organizing knowledge, which is essential to meaningful learning. A variety of concept map-based…
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…
Miller, Tiffany Leigh
2010-01-01
Kirschner, Sweller and Clark (2006) suggest that minimally guided instructional methods are not as successful or efficient as guided instructional approaches. The goal of the current study was to address both the issue of learner performance and knowledge transfer when problem solving in anchored instruction was used for mathematical instruction…
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…
Badru, Ademola K.
2015-01-01
This study examined the prediction of academic success of Junior secondary school mathematics students using their cognitive style and problem solving technique. A descriptive survey of correlation type was adopted for this study. A purposive sampling procedure was used to select five Public Junior secondary schools in Ijebu-Ode local government…
One More Time: The Need for More Mathematical Problem Solving and What the Research Says about It
Woodward, John
2013-01-01
This article reviews recent research in math problem solving for students with learning disabilities. Two recently published syntheses of research on mathematics by the Institute of Education Sciences (IES) are used as frameworks for interpreting this body of work. A significant amount of the work in special education over the last decade is…
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…
Alberta Dept. of Education, Edmonton.
This document is designed to assist teachers in helping students in further development of problem-solving skills. It consists of: a statement of purpose; an introduction (noting the place of problem-solving in junior high school mathematics curricula); a definition of problem-solving; a four-stage general framework for solving problems (which…
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.
Sala, Giovanni; Gobet, Fernand
2017-06-23
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.
Mathematics Student Teachers' Modelling Approaches While Solving the Designed Esme Rug Problem
Hidiroglu, Çaglar Naci; Dede, Ayse Tekin; Ünver, Semiha Kula; Güzel, Esra Bukova
2017-01-01
The purpose of the study is to analyze the mathematics student teachers' solutions on the Esme Rug Problem through 7-stage mathematical modelling process. This problem was designed by the researchers by considering the modelling problems' main properties. The study was conducted with twenty one secondary mathematics student teachers. The data were…
Using Mathematics and Engineering to Solve Problems in Secondary Level Biology
Cox, Charles; Reynolds, Birdy; Schunn, Christian; Schuchardt, Anita
2016-01-01
There are strong classroom ties between mathematics and the sciences of physics and chemistry, but those ties seem weaker between mathematics and biology. Practicing biologists realize both that there are interesting mathematics problems in biology, and that viewing classroom biology in the context of another discipline could support students'…
Mathematics Student Teachers' Modelling Approaches While Solving the Designed Esme Rug Problem
Hidiroglu, Çaglar Naci; Dede, Ayse Tekin; Ünver, Semiha Kula; Güzel, Esra Bukova
2017-01-01
The purpose of the study is to analyze the mathematics student teachers' solutions on the Esme Rug Problem through 7-stage mathematical modelling process. This problem was designed by the researchers by considering the modelling problems' main properties. The study was conducted with twenty one secondary mathematics student teachers. The data were…
Ryzhikov, I. S.; Semenkin, E. S.
2017-02-01
This study is focused on solving an inverse mathematical modelling problem for dynamical systems based on observation data and control inputs. The mathematical model is being searched in the form of a linear differential equation, which determines the system with multiple inputs and a single output, and a vector of the initial point coordinates. The described problem is complex and multimodal and for this reason the proposed evolutionary-based optimization technique, which is oriented on a dynamical system identification problem, was applied. To improve its performance an algorithm restart operator was implemented.
Hull, Michael M.; Kuo, Eric; Gupta, Ayush; Elby, Andrew
2013-01-01
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…
Using Coaching to Improve the Teaching of Problem Solving to Year 8 Students in Mathematics
Kargas, Christine Anestis; Stephens, Max
2014-01-01
This study investigated how to improve the teaching of problem solving in a large Melbourne secondary school. Coaching was used to support and equip five teachers, some with limited experiences in teaching problem solving, with knowledge and strategies to build up students' problem solving and reasoning skills. The results showed increased…
Hull, Michael M.; Kuo, Eric; Gupta, Ayush; Elby, Andrew
2013-01-01
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…
Chamberlin, Scott A; Moore, Alan D; Parks, Kelly
2017-09-01
Student affect plays a considerable role in mathematical problem solving performance, yet is rarely formally assessed. In this manuscript, an instrument and its properties are discussed to enable educational psychologists the opportunity to assess student affect. The study was conducted to norm the CAIMPS (instrument) with gifted students. In so doing, educational psychologists are informed of the process and the instrument's properties. The sample was comprised of 160 middle-grade (7 and 8) students, identified as gifted, in the United States. After completing one of four model-eliciting activities (MEAs), all participants completed the CAIMPS (Chamberlin Affective Instrument for Mathematical Problem Solving). Data were analysed using confirmatory factor analysis to ascertain the number of factors in the instrument. The normed fit index (0.6939), non-normed fit index (0.8072), and root mean square error approximation (.076) were at or near the acceptable levels. Alpha levels for factors were also robust (.637-.923). Data suggest that the instrument was a good fit for use with mathematics students in middle grades when solving problems. Perhaps the most impressive characteristic of the instrument was that the four factors (AVI: anxiety, value, and interest), SS (self-efficacy and self-esteem), ASP (aspiration), and ANX (anxiety) did not correlate highly with one another, which defies previous hypotheses in educational psychology. © 2017 The British Psychological Society.
Xin, Ziqiang; Zhang, Li
2009-01-01
The present study explored whether first and second order cognitive holding power perceived by children in mathematical classrooms, fluid intelligence, and mathematical achievement predicted their performance on standard problems, and especially realistic problems. A sample of 119 Chinese 4-6th graders were administered the word problem test, the…
Xin, Ziqiang; Zhang, Li
2009-01-01
The present study explored whether first and second order cognitive holding power perceived by children in mathematical classrooms, fluid intelligence, and mathematical achievement predicted their performance on standard problems, and especially realistic problems. A sample of 119 Chinese 4-6th graders were administered the word problem test, the…
Moving beyond Solving for "x": Teaching Abstract Algebra in a Liberal Arts Mathematics Course
Cook, John Paul
2015-01-01
This paper details an inquiry-based approach for teaching the basic notions of rings and fields to liberal arts mathematics students. The task sequence seeks to encourage students to identify and comprehend core concepts of introductory abstract algebra by thinking like mathematicians; that is, by investigating an open-ended mathematical context,…
Moving beyond Solving for "x": Teaching Abstract Algebra in a Liberal Arts Mathematics Course
Cook, John Paul
2015-01-01
This paper details an inquiry-based approach for teaching the basic notions of rings and fields to liberal arts mathematics students. The task sequence seeks to encourage students to identify and comprehend core concepts of introductory abstract algebra by thinking like mathematicians; that is, by investigating an open-ended mathematical context,…
Blum, Werner; Niss, Mogens
1991-01-01
This paper reviews the present state, recent trends, and prospective lines of development concerning applied problem solving, modeling, and their respective applications. Four major trends are scrutinized with respect to curriculum inclusion: a widened spectrum of arguments, an increased universality, an increased consolidation, and an extended…
Constructing squares as a mathematical problem solving process in pre-school
Directory of Open Access Journals (Sweden)
MARIA ANGELA SHIAKALLI
2014-06-01
Full Text Available Could problem solving be the object of teaching in early education? Could children’s engagement in problem solving processes lead to skills and conceptual understanding development? Could appropriate teaching interventions scaffold children’s efforts? The sample consisted of 25 children attending public pre-school in Cyprus. The children were asked to construct different sized squares. Findings show that children responded positively to the problem and were successful in solving it. During the problem solving process children demonstrated development of skills and conceptual understanding. Teacher-children and children-children interactions played an important role in the positive outcome of the activity.
Identification of Strategies Used by Fifth Graders To Solve Mathematics Word Problems.
Palomares, Julio Cesar Arteaga; Hernandez, Jose Guzman
When students confront arithmetic or algebraic word problems, they develop ideas and notations during the processes of solving them by using various arithmetic strategies. Those ideas and notations are the basis for solving that type of problems. Is it possible to aid the development of students' algebraic thinking during their transition from…
Kingsdorf, Sheri; Krawec, Jennifer
2014-01-01
Solving word problems is a common area of struggle for students with learning disabilities (LD). In order for instruction to be effective, we first need to have a clear understanding of the specific errors exhibited by students with LD during problem solving. Error analysis has proven to be an effective tool in other areas of math but has had…
Content Effects in Mathematics Problem Solving. A Possible Source of Test Bias?
1991-04-15
it is usually in tests or subtests of mathematics word problems (Chipman & Thomas, 1985; Chipman, 1988; Hyde, Fennema & Lamon, 1990). The diversity and...8217- Content Effects 2 males or females (Chipman, 1988). For example, one study may report that females do worse on geometry items ( Fennema & 4Carpenter...in mathematics anxiety/confidence (Chipman & Wilson, 1985; Hyde, Fennema , Ryan, Frost & Hopp, 1990) may make females more prone to omit problems that
Factors involved in making post-performance judgments in mathematics problem-solving.
García Fernández, Trinidad; Kroesbergen, Evelyn; Rodríguez Pérez, Celestino; González-Castro, Paloma; González-Pienda, Julio A
2015-01-01
This study examines the impact of executive functions, affective-motivational variables related to mathematics, mathematics achievement and task characteristics on fifth and sixth graders’ calibration accuracy after completing two mathematical problems. A sample of 188 students took part in the study. They were divided into two groups as function of their judgment accuracy after completing the two tasks (accurate= 79, inaccurate= 109). Differences between these groups were examined. The discriminative value of these variables to predict group membership was analyzed, as well as the effect of age, gender, and grade level. The results indicated that accurate students showed better levels of executive functioning, and more positive feelings, beliefs, and motivation related to mathematics. They also spent more time on the tasks. Mathematics achievement, perceived usefulness of mathematics, and time spent on Task 1 significantly predicted group membership, classifying 71.3% of the sample correctly. These results support the relationship between academic achievement and calibration accuracy, suggesting the need to consider a wide range of factors when explaining performance judgments.
Scene matching based on non-linear pre-processing on reference image and sensed image
Institute of Scientific and Technical Information of China (English)
Zhong Sheng; Zhang Tianxu; Sang Nong
2005-01-01
To solve the heterogeneous image scene matching problem, a non-linear pre-processing method for the original images before intensity-based correlation is proposed. The result shows that the proper matching probability is raised greatly. Especially for the low S/N image pairs, the effect is more remarkable.
Archambeault, Betty
1993-01-01
Holistic math focuses on problem solving with numbers and concepts. Whole math activities for adults include shopping for groceries, eating in restaurants, buying gas, taking medicine, measuring a room, estimating servings, and compiling a family cookbook. (SK)
The Examining Mathematical Word Problems Solving Ability under Efficient Representation Aspect
Directory of Open Access Journals (Sweden)
Maryam Sajadi
2013-02-01
Full Text Available Word problem solving is complex process for students. Efficient instruction of word problem solving needed to efficient strategies. One of these strategies is using representation. Some students apply key words or numbers only but when they face complex word problems then they cannot apply the keywords. Therefore teachers have to teach efficient strategy such as representation. In this research is tried whether using efficient representation can lead to efficient solution. Through cluster sampling method, forty one students are selected at girly elementary school. Through math exam, their solutions are studied. Through Spearman test, results indicate that there is significant relation between efficient representation and efficient word problem solving ability. At second grade, students have used of representation, have gotten to high means and inverse, students have not used of representation, have not gotten to high means. Therefore there is significant and direct relation between efficient representation and efficient word problem solving ability.
DEFF Research Database (Denmark)
Friesel, Anna
2013-01-01
. However, in order to understand complexity of control systems, the students need to possess an analytical understanding of abstract mathematical problems. Our main goal is to illustrate the theory through the robot project, but at the same time we force our students to train their analytical skills...... by mandatory exercises including problems of abstract mathematics. This paper describes our effort to motivate students to work with the theory. We conclude with our and students' own opinion on their work during the semester. Ideas for future development of this course are presented....
Pre-processing Tasks in Indonesian Twitter Messages
Hidayatullah, A. F.; Ma’arif, M. R.
2017-01-01
Twitter text messages are very noisy. Moreover, tweet data are unstructured and complicated enough. The focus of this work is to investigate pre-processing technique for Twitter messages in Bahasa Indonesia. The main goal of this experiment is to clean the tweet data for further analysis. Thus, the objectives of this pre-processing task is simply removing all meaningless character and left valuable words. In this research, we divide our proposed pre-processing experiments into two parts. The first part is common pre-processing task. The second part is a specific pre-processing task for tweet data. From the experimental result we can conclude that by employing a specific pre-processing task related to tweet data characteristic we obtained more valuable result. The result obtained is better in terms of less meaningful word occurrence which is not significant in number comparing to the result obtained by just running common pre-processing tasks.
Comparing Binaural Pre-processing Strategies II
Directory of Open Access Journals (Sweden)
Regina M. Baumgärtel
2015-12-01
Full Text Available Several binaural audio signal enhancement algorithms were evaluated with respect to their potential to improve speech intelligibility in noise for users of bilateral cochlear implants (CIs. 50% speech reception thresholds (SRT50 were assessed using an adaptive procedure in three distinct, realistic noise scenarios. All scenarios were highly nonstationary, complex, and included a significant amount of reverberation. Other aspects, such as the perfectly frontal target position, were idealized laboratory settings, allowing the algorithms to perform better than in corresponding real-world conditions. Eight bilaterally implanted CI users, wearing devices from three manufacturers, participated in the study. In all noise conditions, a substantial improvement in SRT50 compared to the unprocessed signal was observed for most of the algorithms tested, with the largest improvements generally provided by binaural minimum variance distortionless response (MVDR beamforming algorithms. The largest overall improvement in speech intelligibility was achieved by an adaptive binaural MVDR in a spatially separated, single competing talker noise scenario. A no-pre-processing condition and adaptive differential microphones without a binaural link served as the two baseline conditions. SRT50 improvements provided by the binaural MVDR beamformers surpassed the performance of the adaptive differential microphones in most cases. Speech intelligibility improvements predicted by instrumental measures were shown to account for some but not all aspects of the perceptually obtained SRT50 improvements measured in bilaterally implanted CI users.
Csikos, Csaba; Szitanyi, Judit; Kelemen, Rita
2012-01-01
The present study aims to investigate the effects of a design experiment developed for third-grade students in the field of mathematics word problems. The main focus of the program was developing students' knowledge about word problem solving strategies with an emphasis on the role of visual representations in mathematical modeling. The experiment…
Gazit, Avikam
2012-01-01
The objective of this case study was to investigate the ability of 10th graders and pre-service teachers to solve logical-mathematical thinking challenges. The challenges do not require mathematical knowledge beyond that of primary school but rather an informed use of the problem representation. The percentage of correct answers given by the 10th…
Open-Start Mathematics Problems: An Approach to Assessing Problem Solving
Monaghan, John; Pool, Peter; Roper, Tom; Threlfall, John
2009-01-01
This article describes one type of mathematical problem, open-start problems, and discusses their potential for use in assessment. In open-start problems how one starts to address the problem can vary but they have a correct answer. We argue that the use of open-start problems in assessment could positively influence classroom mathematics…
Directory of Open Access Journals (Sweden)
E. M. E. Zayed
2014-01-01
Full Text Available We apply the generalized projective Riccati equations method to find the exact traveling wave solutions of some nonlinear evolution equations with any-order nonlinear terms, namely, the nonlinear Pochhammer-Chree equation, the nonlinear Burgers equation and the generalized, nonlinear Zakharov-Kuznetsov equation. This method presents wider applicability for handling many other nonlinear evolution equations in mathematical physics.
Skoumpourdi, Chrysanthi
2010-01-01
The aim of this paper is to investigate the role that auxiliary means (manipulatives such as cubes and representations such as number line) play for kindergartners in working out mathematical tasks. Our assumption was that manipulatives such as cubes would be used by kindergartners easily and successfully whereas the number line would be used by…
Mathematics Problem Solving: A More Advanced Skill for Chapter 1. Workshop Leader's Guide.
Advanced Technology, Inc., Indianapolis, IN.
This guide is designed to assist inservice providers in conducting successful workshops for teachers, administrators, and others associated with Chapter 1 mathematics programs. It contains step-by-step procedures for preparing, organizing, and presenting the workshop. Included in this guide are: (1) an advanced planner, which includes a detailed…
Teacher Actions That Encourage Students to Persist in Solving Challenging Mathematical Tasks
Ingram, Naomi; Linsell, Chris; Holmes, Marilyn; Livy, Sharyn; Sullivan, Peter
2016-01-01
As part of a project exploring the use of challenging mathematical tasks, data from New Zealand teachers and their students were analysed to explore teachers' actions that encouraged students to persist. Rather than rescuing the students when they needed help, the teachers' actions included arranging for and encouraging students to work…
Solving the empty space problem in robot path planning by mathematical morphology
Roerdink, J.B.T.M.
1993-01-01
In this paper we formulate a morphological approach to path planning problems, in particular with respect to the empty-space problem, that is, the question of finding the allowed states for an object, moving in a space with obstacles. Our approach is based upon a recent generalization of mathematic
Using Computers to Solve Mathematics by Junior Secondary School Students in Edo State Nigeria
Olusi, F. I.
2008-01-01
The purpose of this study was to determine the effect of computer aided instruction and traditional method of instruction on the junior secondary school students achievement in mathematics. Four research questions and hypotheses were stated and tested in the study. The design of the study was the pre-test post-test control group experimental…
Langer-Osuna, Jennifer M.
2016-01-01
This article describes a study of how students construct relations of authority during dyadic mathematical work and how teachers' interactions with students during small group conferences affect subsequent student dynamics. Drawing on the influence framework (Engle, Langer-Osuna, & McKinney de Royston, 2014), I examined interactions when…
The benefits of computer-generated feedback for mathematics problem solving.
Fyfe, Emily R; Rittle-Johnson, Bethany
2016-07-01
The goal of the current research was to better understand when and why feedback has positive effects on learning and to identify features of feedback that may improve its efficacy. In a randomized experiment, second-grade children received instruction on a correct problem-solving strategy and then solved a set of relevant problems. Children were assigned to receive no feedback, immediate feedback, or summative feedback from the computer. On a posttest the following day, feedback resulted in higher scores relative to no feedback for children who started with low prior knowledge. Immediate feedback was particularly effective, facilitating mastery of the material for children with both low and high prior knowledge. Results suggest that minimal computer-generated feedback can be a powerful form of guidance during problem solving.
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.
Lee, Chun-Yi; Chen, Ming-Puu.
2009-01-01
The purpose of this study was to investigate the effects of type of question prompt and level of prior knowledge on non-routine mathematical problem solving. A computer game was blended within the pattern reasoning tasks, along with question prompts, in order to demonstrate and enhance the connections between viable problem-solving strategies and…
Predicting Development of Mathematical Word Problem Solving across the Intermediate Grades
Tolar, Tammy D.; Fuchs, Lynn; Cirino, Paul T.; Fuchs, Douglas; Hamlett, Carol L.; Fletcher, Jack M.
2012-01-01
This study addressed predictors of the development of word problem solving (WPS) across the intermediate grades. At beginning of 3rd grade, 4 cohorts of students (N = 261) were measured on computation, language, nonverbal reasoning skills, and attentive behavior and were assessed 4 times from beginning of 3rd through end of 5th grade on 2 measures…
Using mathematics to solve real world problems: the role of enablers
Geiger, Vincent; Stillman, Gloria; Brown, Jill; Galbriath, Peter; Niss, Mogens
2017-06-01
The purpose of this article is to report on a newly funded research project in which we will investigate how secondary students apply mathematical modelling to effectively address real world situations. Through this study, we will identify factors, mathematical, cognitive, social and environmental that "enable" year 10/11 students to successfully begin the modelling process, that is, formulate and mathematise a real world problem. The 3-year study will take a design research approach in working intensively with six schools across two educational jurisdictions. It is anticipated that this research will generate new theoretical and practical insights into the role of "enablers" within the process of mathematisation, leading to the development of principles for the design and implementation for tasks that support students' development as modellers.
Directory of Open Access Journals (Sweden)
Elsayed Mohamed Elsayed ZAYED
2014-07-01
Full Text Available In this article, many new exact solutions of the (2+1-dimensional nonlinear Boussinesq-Kadomtsev-Petviashvili equation and the (1+1-dimensional nonlinear heat conduction equation are constructed using the Riccati equation mapping method. By means of this method, many new exact solutions are successfully obtained. This method can be applied to many other nonlinear evolution equations in mathematical physics.doi:10.14456/WJST.2014.14
Leh, Jayne
2011-01-01
Substantial evidence indicates that teacher-delivered schema-based instruction (SBI) facilitates significant increases in mathematics word problem solving (WPS) skills for diverse students; however research is unclear whether technology affordances facilitate superior gains in computer-mediated (CM) instruction in mathematics WPS when compared to…
Directory of Open Access Journals (Sweden)
Nevin ORHUN
2013-07-01
Full Text Available Open and distance education plays an important role in the actualization of cultural goals as well as in societal developments. This is an independent teaching and learning method for mathematics which forms the dynamic of scientific thinking. Distance education is an important alternative to traditional teaching applications. These contributions brought by technology enable students to participate actively in having access to information and questioning it. Such an application increases students’ motivation and teaches how mathematics can be used in daily life. Derivative is a mathematical concept which can be used in many areas of daily life. The aim of this study is to enable the concept of derivatives to be understood well by using the derivative function in the solution of various problems. It also aims at interpreting difficulties theoretically in the solution of problems and determining mistakes in terms of teaching methods. In this study, how various aspects of derivatives are understood is emphasized. These aspects concern the explanation of concepts and process, and also their application to certain concepts in physics. Students’ depth of understanding of derivatives was analyzed based on two aspects of understanding; theoretical analysis and contextual application. Follow-up interviews were conducted with five students. The results show that the students preferred to apply an algebraic symbolic aspect instead of using logical meanings of function and its derivative. In addition, in relation to how the graph of the derivative function affects the aspect of function, it was determined that the students displayed low performance.
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Hande Çamlı
2009-09-01
Full Text Available This paper aims to determine the effect of computer aided instruction on students’ academic performance in solving Lowest Common Multiple and Greatest Common Factor problems and multiplicative structures. The study was held in the second semester of 2008 for five weeks with a total number of 102 sixth grade students. The research was carried out experimentally and a post test control group design method was used in this experimental study. An academic level test was used at the beginning of the study to compare the existing knowledge of experimental and control groups; and a post test and software developed by the researchers about the topic were used as data collection instruments in this study. The means of scores received in academic success test and post test were analyzed using t-test technique. The results of the study show that the use of computer support in teaching and learning Lowest Common Multiple and Greatest Common Factor problems and multiplicative structures in mathematics lesson may increase students academic success.
Tolar, Tammy D; Fuchs, Lynn; Fletcher, Jack M; Fuchs, Douglas; Hamlett, Carol L
2016-01-01
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.
A Comparative Study of Three Different Mathematical Methods for Solving the Unit Commitment Problem
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Mehmet Kurban
2009-01-01
Full Text Available The unit commitment (UC problem which is an important subject in power system engineering is solved by using Lagragian relaxation (LR, penalty function (PF, and augmented Lagrangian penalty function (ALPF methods due to their higher solution quality and faster computational time than metaheuristic approaches. This problem is considered to be a nonlinear programming-(NP- hard problem because it is nonlinear, mixed-integer, and nonconvex. These three methods used for solving the problem are based on dual optimization techniques. ALPF method which combines the algorithmic aspects of both LR and PF methods is firstly used for solving the UC problem. These methods are compared to each other based on feasible schedule for each stage, feasible cost, dual cost, duality gap, duration time, and number of iterations. The numerical results show that the ALPF method gives the best duality gap, feasible and dual cost instead of worse duration time and the number of iterations. The four-unit Tuncbilek thermal plant which is located in Kutahya region in Turkey is chosen as a test system in this study. The programs used for all the analyses are coded and implemented using general algebraic modeling system (GAMS.
Fuchs, Lynn S; Seethaler, Pamela M; Powell, Sarah R; Fuchs, Douglas; Hamlett, Carol L; Fletcher, Jack M
2008-01-01
This study assessed the effects of preventative tutoring on the math problem solving of third-grade students with math and reading difficulties. Students (n = 35) were assigned randomly to continue in their general education math program or to receive secondary preventative tutoring 3 times per week, 30 min per session, for 12 weeks. Schema-broadening tutoring taught students to (a) focus on the mathematical structure of 3 problem types; (b) recognize problems as belonging to those 3 problem-type schemas; (c) solve the 3 word-problem types; and (d) transfer solution methods to problems that include irrelevant information, 2-digit operands, missing information in the first or second positions in the algebraic equation, or relevant information in charts, graphs, and pictures. Also, students were taught to perform the calculation and algebraic skills foundational for problem solving. Analyses of variance revealed statistically significant effects on a wide range of word problems, with large effect sizes. Findings support the efficacy of the tutoring protocol for preventing word-problem deficits among third-grade students with math and reading deficits.
A Study on Pre-processing Algorithms for Metal Parts Inspection
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Haider Sh. Hashim
2011-06-01
Full Text Available Pre-processing is very useful in a variety of situations since it helps to suppress information that is not related to the exact image processing or analysis task. Mathematical morphology is used for analysis, understanding and image processing. It is an influential method in the geometric morphological analysis and image understanding. It has befallen a new theory in the digital image processing domain. Edges detection and noise reduction are a crucial and very important pre-processing step. The classical edge detection methods and filtering are less accurate in detecting complex edge and filtering various types of noise. This paper proposed some useful mathematic morphological techniques to detect edge and to filter noise in metal parts image. The experimental result showed that the proposed algorithm helps to increase accuracy of metal parts inspection system.
Agustan, S.; Juniati, Dwi; Siswono, Tatag Yuli Eko
2017-05-01
In the last few years, reflective thinking becomes very popular term in the world of education, especially in professional education of teachers. One of goals of the educational personnel and teacher institutions create responsible prospective teachers and they are able reflective thinking. Reflective thinking is a future competence that should be taught to students to face the challenges and to respond of demands of the 21st century. Reflective thinking can be applied in mathematics becauseby reflective thinking, students can improve theircuriosity to solve mathematical problem. In solving mathematical problem is assumed that cognitive style has an impact on prospective teacher's mental activity. As a consequence, reflective thinking and cognitive style are important things in solving mathematical problem. The subject, in this research paper, isa female-prospective teacher who has fielddependent cognitive style. The purpose of this research paperis to investigate the ability of prospective teachers' reflective thinking in solving mathematical problem. This research paper is a descriptive by using qualitativeapproach. To analyze the data related to prospectiveteacher's reflective thinking in solving contextual mathematicalproblem, the researchers focus in four main categories which describe prospective teacher's activities in 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.
Berteletti, Ilaria; Prado, Jérôme; Booth, James R
2014-08-01
Greater skill in solving single-digit multiplication problems requires a progressive shift from a reliance on numerical to verbal mechanisms over development. Children with mathematical learning disability (MD), however, are thought to suffer from a specific impairment in numerical mechanisms. Here we tested the hypothesis that this impairment might prevent MD children from transitioning toward verbal mechanisms when solving single-digit multiplication problems. Brain activations during multiplication problems were compared in MD and typically developing (TD) children (3rd to 7th graders) in numerical and verbal regions which were individuated by independent localizer tasks. We used small (e.g., 2 × 3) and large (e.g., 7 × 9) problems as these problems likely differ in their reliance on verbal versus numerical mechanisms. Results indicate that MD children have reduced activations in both the verbal (i.e., left inferior frontal gyrus and left middle temporal to superior temporal gyri) and the numerical (i.e., right superior parietal lobule including intra-parietal sulcus) regions suggesting that both mechanisms are impaired. Moreover, the only reliable activation observed for MD children was in the numerical region when solving small problems. This suggests that MD children could effectively engage numerical mechanisms only for the easier problems. Conversely, TD children showed a modulation of activation with problem size in the verbal regions. This suggests that TD children were effectively engaging verbal mechanisms for the easier problems. Moreover, TD children with better language skills were more effective at engaging verbal mechanisms. In conclusion, results suggest that the numerical- and language-related processes involved in solving multiplication problems are impaired in MD children. Published by Elsevier Ltd.
Development of Finnish Elementary Pupils’ Problem-Solving Skills in Mathematics
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Anu Laine
2014-09-01
Full Text Available The purpose of this study is to determine how Finnish pupils’ problemsolving skills develop from the 3rd to 5th grade. As research data, we use one non-standard problem from pre- and post-test material from a three-year follow-up study, in the area of Helsinki, Finland. The problems in both tests consisted of four questions related to each other. The purpose of the formulation of the problem was to help the pupils to find how many solutions for a certain answer exist. The participants in the study were 348 third-graders and 356 fifth-graders. Pupils’ fluency, i.e. ability to develop different solutions, was found to correlate with their ability to solve the problem. However, the proportions of the pupils (17% of the 3rd graders and 21% of the 5th graders who answered that there were an infinite number of solutions are of the same magnitude. Thus, the pupils’ ability to solve this kind of problem does not seem to have developed from the 3rd to the 5th grade. The lack and insufficiency of pupils’ justifications reveal the importance of the teacher carefully listening to the pupils’ ideas in order to be able to promote pupils’ understanding of the concept of infinity, as well as the basic calculations.
Hong, Felix T
2013-09-01
Rosen classified sciences into two categories: formalizable and unformalizable. Whereas formalizable sciences expressed in terms of mathematical theories were highly valued by Rutherford, Hutchins pointed out that unformalizable parts of soft sciences are of genuine interest and importance. Attempts to build mathematical theories for biology in the past century was met with modest and sporadic successes, and only in simple systems. In this article, a qualitative model of humans' high creativity is presented as a starting point to consider whether the gap between soft and hard sciences is bridgeable. Simonton's chance-configuration theory, which mimics the process of evolution, was modified and improved. By treating problem solving as a process of pattern recognition, the known dichotomy of visual thinking vs. verbal thinking can be recast in terms of analog pattern recognition (non-algorithmic process) and digital pattern recognition (algorithmic process), respectively. Additional concepts commonly encountered in computer science, operations research and artificial intelligence were also invoked: heuristic searching, parallel and sequential processing. The refurbished chance-configuration model is now capable of explaining several long-standing puzzles in human cognition: a) why novel discoveries often came without prior warning, b) why some creators had no ideas about the source of inspiration even after the fact, c) why some creators were consistently luckier than others, and, last but not least, d) why it was so difficult to explain what intuition, inspiration, insight, hunch, serendipity, etc. are all about. The predictive power of the present model was tested by means of resolving Zeno's paradox of Achilles and the Tortoise after one deliberately invoked visual thinking. Additional evidence of its predictive power must await future large-scale field studies. The analysis was further generalized to constructions of scientific theories in general. This approach
Assessing age-related patterns in strategy selection on a mathematical problem-solving task.
Lamson, Nina; Rogers, Wendy A
2008-05-01
We examined age-related differences in strategy-choice behavior in 27 younger and 28 older adults. Participants solved 4 two-digit by two-digit multiplication problems. We expected them to initially calculate the answers but eventually switch to a retrieval strategy, recalling answers from memory. Three groups emerged: younger adults who met the criterion (20 consecutive, correct, retrieval trials selected and answered in time), older adults who met the criterion, and older adults who did not meet the criterion. Younger and older adults who met the criterion had similar performance patterns. Some older adults who did not meet the criterion were slower to learn, whereas others seemed to be averse to the retrieval strategy. Thus, older adult patterns in strategy choice are considerably more varied than younger adult patterns, suggesting different explanations for differences in memory performance.
Research on the basic factors and strategies for solving mathematical problems%数学问题解决的基本要素和策略研究
Institute of Scientific and Technical Information of China (English)
黄燕
2014-01-01
数学问题解决，是以思考为内涵，以问题目标为定向的心理活动及心理过程。数学问题的解决受到很多方面的影响，现就知识结构、技能因素和情感因素这三方面来谈它们对数学问题解决的影响并对其提出一些改进的策略。%The mathematical problem solving,is its connotation is thinking to problem of goal orientation,the psychological activity and psychological process.Mathematical problem solving is influenced by many aspects,the structure of knowledge, skills and emotional factors of these three aspects to discuss their influence on mathematical problem solving,and puts forward some strategies to improve on it.
Diagnosing and alleviating the impact of performance pressure on mathematical problem solving.
DeCaro, Marci S; Rotar, Kristin E; Kendra, Matthew S; Beilock, Sian L
2010-08-01
High-pressure academic testing situations can lead people to perform below their actual ability levels by co-opting working memory (WM) resources needed for the task at hand (Beilock, 2008). In the current work we examine how performance pressure impacts WM and design an intervention to alleviate pressure's negative impact. Specifically, we explore the hypothesis that high-pressure situations trigger distracting thoughts and worries that rely heavily on verbal WM. Individuals performed verbally based and spatially based mathematics problems in a low-pressure or high-pressure testing situation. Results demonstrated that performance on problems that rely heavily on verbal WM resources was less accurate under high-pressure than under low-pressure tests. Performance on spatially based problems that do not rely heavily on verbal WM was not affected by pressure. Moreover, the more people reported worrying during test performance, the worse they performed on the verbally based (but not spatially based) maths problems. Asking some individuals to focus on the problem steps by talking aloud helped to keep pressure-induced worries at bay and eliminated pressure's negative impact on performance.
Institute of Scientific and Technical Information of China (English)
麦康玲
2015-01-01
Mathematics is a highly logical and rigorous discipline, which is also indirectly embodied in the solving of mathematics problems as various mathematical methods are used in the pro-cess, so teachers and students are paying more and more attention to the learning of mathematics problem-solving skills and mathe-matical analysis thought, especially in the mathematics test of college entrance examination in recent years, the advantage of mathematical analysis thought has been significantly highlighted. This paper will mainly study the application of mathematical analysis thought in the solving of senior mathematics problems, in order to further enhance students' problem-solving efficiency.%数学是一门逻辑性和严谨性都较高的学科，而且在解题时所采用的各种数学方式也间接体现了学科本身的这种特性，所以教师和学生越来越注重数学解题技巧和数学分析思想的学习，尤其是在近些年的数学高考中，具备数学分析思想有着明显的优势，而本文也将主要研究数学分析思想在高中数学解题中的应用，以便进一步提高学生的解题效率。
Using DNA to solve mathematical problems: Multiplication and 3-colorability computation
Wu, Gang
A functional machine is not only an assembly of parts, but also an assembly of processes. The processing of each part must obey laws that respect to the property of this part. For example, building any kind of computer entails selecting appropriate components and assembling their properties to function in computation. Here, we describe computation using a DNA strand as the basic unit and we have used this unit to achieve the function of multiplication. We exploit the phenomenon of DNA hybridization, in which each strand can represent two individual units that can pair to form a single unit. We represent the numbers we multiply in binary, with different lengths representing each digit present in the number. In principle, all combinations of the numbers will be present in solution. Following hybridization, there is present a collection of duplex molecules that are tailed by single-stranded ends. These intermediates are converted to fully duplex molecules by filling in the ends with DNA polymerase. The lengths that are present represent the digits that are present, and they may be separated by denaturing PAGE. The results give a series of bands for each power of two. The number of bands in the size domain for a particular power of two is converted to binary and the sum of all present bands is then added together. Experimentally, the result of this process always yields the correct answer. The combination of DNA and enzymes has been used to produce a structure that provides the answer to a computational problem. A graph of 6 vertices and 9 edges was constructed to solve an instance of the three-colorability problem. The final construct is obtained by joining coded branched DNA junctions with sticky ends representing the colored vertices. The DNA structure corresponding to the solution of the problem was identified through its resistance to restriction endonuclease cleavage. The method uses a constant number of steps, which is independent of the size of the graph.
Lei, Ting; Belykh, Evgenii; Dru, Alexander B; Yagmurlu, Kaan; Elhadi, Ali M; Nakaji, Peter; Preul, Mark C
2016-07-01
Chen Jingrun (1933-1996), perhaps the most prodigious mathematician of his time, focused on the field of analytical number theory. His work on Waring's problem, Legendre's conjecture, and Goldbach's conjecture led to progress in analytical number theory in the form of "Chen's Theorem," which he published in 1966 and 1973. His early life was ravaged by the Second Sino-Japanese War and the Chinese Cultural Revolution. On the verge of solving Goldbach's conjecture in 1984, Chen was struck by a bicyclist while also bicycling and suffered severe brain trauma. During his hospitalization, he was also found to have Parkinson's disease. Chen suffered another serious brain concussion after a fall only a few months after recovering from the bicycle crash. With significant deficits, he remained hospitalized for several years without making progress while receiving modern Western medical therapies. In 1988 traditional Chinese medicine experts were called in to assist with his treatment. After a year of acupuncture and oxygen therapy, Chen could control his basic bowel and bladder functions, he could walk slowly, and his swallowing and speech improved. When Chen was unable to produce complex work or finish his final work on Goldbach's conjecture, his mathematical pursuits were taken up vigorously by his dedicated students. He was able to publish Youth Math, a mathematics book that became an inspiration in Chinese education. Although he died in 1996 at the age of 63 after surviving brutal political repression, being deprived of neurological function at the very peak of his genius, and having to be supported by his wife, Chen ironically became a symbol of dedication, perseverance, and motivation to his students and associates, to Chinese youth, to a nation, and to mathematicians and scientists worldwide.
Korkmaz, Özgen
2016-01-01
The aim of this study was to investigate the effect of the Scratch and Lego Mindstorms Ev3 programming activities on academic achievement with respect to computer programming, and on the problem-solving and logical-mathematical thinking skills of students. This study was a semi-experimental, pretest-posttest study with two experimental groups and…
Schaefer Whitby, Peggy J.
2009-01-01
Children with HFA/AS are outperformed by their neuro-typical peers on mathematical problem solving skills even though they have average-to-above-average intelligence (Dickerson Mayes & Calhoun, 2003b); have average-to-above-average computation skills (Chiang & Lin, 2007); and, are educated in the general education setting (Twenty Eighth…
Al-Omari, Wesal; Miqdadi, Ruba
2014-01-01
The purpose of this paper was to examine the perception pre-service teachers hold to the nature of the relationship between physics and mathematics. The study examined this relationship in reference to their performance in problem solving and strategies they used. The results of this empirical study suggested that most participants hold a naïve…
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…
Directory of Open Access Journals (Sweden)
Rahmat Arab
2014-01-01
Full Text Available In this paper a novel, bi-objective mixed-integer mathematical programming has been proposed for a distribution network problem. One objective function minimizes the total purchasing, transportation and holding costs and the another objective minimizes the total amount of delayed or before time deliveries multiplied by respective durations, named "JIT distribution". Supplying the customer demand, holding and delivering products at warehouse are the most important constraints considered in this model. This model has been designed for a three-echelon distribution network consisting multiple suppliers, wholesalers and retailers to distribute multiple products with a deterministic amount of demand through either direct or indirect channels in a planning horizon. Since real-sized problems of the resulting bi-objective mixed-integer linear programming (MILP cannot be solved with exact methods, a multi objective particle swarm algorithm (MOPSO is designed of which, quality in small-sized problems is compared with the solutions obtained by the LINGO software. The computational results show that the proposed MOPSO algorithm finds good solutions in shorter times than LINGO and has acceptable running times in large-scale problems.
Directory of Open Access Journals (Sweden)
Atma Murni
2013-07-01
Full Text Available The aim of this study is to know the differences of enhancement inmathematical problem solving ability (MPSA between the studentswho received soft skill- based metacognitive learning (SSML with thestudents who got conventional learning (CL. This research is a quasiexperimental design with pretest-postest control group. The populationin 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-levelschool, and 67 students are from the middle-level school. The instruments are mathematical prior knowledge (MPK test, MPSA test,instruction observation sheet, students journal about the lesson, and the guideline for interview. The data was analyzed using t-test and two way ANOVA. The result of data analysis indicates: (1 overall, theenhancement of students’ MPSA with SSML approach significantly ishigher than those with conventional learning (CL; (2 there is nointeraction between the learning approach (SSML and CL with theschool level (high and middle toward the enhancement of MPSA; (3there is no interaction between the learning approach (SSML and CLwith MPK (upper, middle, and low toward the enhancement of MPSA.
Clever Use of Structure Method in Mathematical Problem Solving in High School%高中数学解题中构造法的巧妙运用
Institute of Scientific and Technical Information of China (English)
卓水鑫
2014-01-01
Mathematics is a basic subject,with the increase of students’age,the difficulty of mathematics curriculum increases.The diffi-culty of solving problem is the main problem of the current high school students. In order to improve this situation, teachers should change the teaching idea and method in the process of mathematics problem solving teaching in senior high school, break through the conventional method of solving problems. In this context, construction method has been used in high school mathematics problems. By applying the method of con-structing ,we can make the abstract problem visualization and complex problem simplistic, stimulate students’ problem solving enthusiasm, en-hance problem-solving confidence, and ultimately improve the efficiency of solving the problems.%数学是基础学科，随着学生学龄的增加，数学课程的难度随之增加。解题难是当前高中学生面临的主要问题。为了有效改善这一现状，教师在高中数学解题教学过程中应转变教学观念、教学方法，突破常规解题方法。在此背景下，构造法在高中数学解题中得到有效应用。通过构造法的应用可将抽象问题形象化，复杂问题简单化，激发学生的解题热情，增强解题信心，最终提高解题效率。
浅谈高中数学的解题策略%On the problem-solving strategies of high school mathematics
Institute of Scientific and Technical Information of China (English)
徐永东
2013-01-01
高中数学对学生的要求相对比较高，因为其对解题的能力要求很高，要求学生对于解题的技巧性有一种熟悉度，但是如何才能够在教学的过程中让学生形成一种解题策略呢？文章从数学观察力对高中数学解题策略进行剖析。% The requirements of high school mathematics to students is relatively high, because of its ability of solving high demands for skills in problem solving, students are required to have a degree of familiarity, but how they can allow students to form a problem-solving strategy in the process of teaching? This paper analyzes high school mathematics problem-solving strategies from the observation of mathematics.
Image pre-processing research of coal level in underground coal pocket
Institute of Scientific and Technical Information of China (English)
WU Bing; GAO Na
2008-01-01
Mathematical morphology is widely applicated in digital image procesing. Vari-ary morphology construction and algorithm being developed are used in deferent digital image processing. The basic idea of mathematical morphology is to use construction ele-ment measure image morphology for solving understand problem. The article presented advanced cellular neural network that forms mathematical morphological cellular neural network (MMCNN) equation to be suit for mathematical morphology filter. It gave the theo-ries of MMCNN dynamic extent and stable state. It is evidenced that arrived mathematical morphology filter through steady of dynamic process in definite condition.
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…
Syahputra, Edi; Surya, Edy
2017-01-01
This paper is a summary study of team Postgraduate on 11th grade. The objective of this study is to develop a learning model based on problem solving which can construct high-order thinking on the learning mathematics in SMA/MA. The subject of dissemination consists of Students of 11th grade in SMA/MA in 3 kabupaten/kota in North Sumatera, namely:…
Pre-Processing Rules for Triangulation of Probabilistic Networks
Bodlaender, H.L.; Koster, A.M.C.A.; Eijkhof, F. van den
2003-01-01
The currently most efficient algorithm for inference with a probabilistic network builds upon a triangulation of a network’s graph. In this paper, we show that pre-processing can help in finding good triangulations for probabilistic networks, that is, triangulations with a minimal maximum clique siz
Pre-processing for Triangulation of Probabilistic Networks
Bodlaender, H.L.; Koster, A.M.C.A.; Eijkhof, F. van den; Gaag, L.C. van der
2001-01-01
The currently most efficient algorithm for inference with a probabilistic network builds upon a triangulation of a networks graph. In this paper, we show that pre-processing can help in finding good triangulations for probabilistic networks, that is, triangulations with a minimal maximum clique
Pre-processing for Triangulation of Probabilistic Networks
Bodlaender, H.L.; Koster, A.M.C.A.; Eijkhof, F. van den; Gaag, L.C. van der
2001-01-01
The currently most efficient algorithm for inference with a probabilistic network builds upon a triangulation of a networks graph. In this paper, we show that pre-processing can help in finding good triangulations for probabilistic networks, that is, triangulations with a minimal maximum clique
Gazit, Avikam
2012-12-01
The objective of this case study was to investigate the ability of 10th graders and pre-service teachers to solve logical-mathematical thinking challenges. The challenges do not require mathematical knowledge beyond that of primary school but rather an informed use of the problem representation. The percentage of correct answers given by the 10th graders was higher than that of the pre-service teachers. Unlike the 10th graders, some of whom used various strategies for representing the problem, most of the pre-service teachers' answers were based on a technical algorithm, without using control processes. The obvious conclusion drawn from the findings supports and recommends expanding and enhancing the development of logical-mathematical thinking, both in specific lessons and as an integral part of other lessons in pre-service frameworks.
Chan, Man Ching Esther; Clarke, David; Cao, Yiming
2017-06-01
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.
Pereira de Ataide, Ana Raquel; Greca, Ileana Maria
2013-01-01
The relationship between physics and mathematics is hardly ever presented with sufficient clarity to satisfy either physicists or mathematicians. It is a situation that often leads to misunderstandings that may spread quickly from teacher to student, such as the idea that mathematics is a mere instrument for the physicist. In this paper, we…
Bouck, Emily C.; Satsangi, Rajiv; Doughty, Teresa Taber; Courtney, William T.
2014-01-01
Students with autism spectrum disorder (ASD) are included in general education classes and expected to participate in general education content, such as mathematics. Yet, little research explores academically-based mathematics instruction for this population. This single subject alternating treatment design study explored the effectiveness of…
Bouck, Emily C.; Satsangi, Rajiv; Doughty, Teresa Taber; Courtney, William T.
2014-01-01
Students with autism spectrum disorder (ASD) are included in general education classes and expected to participate in general education content, such as mathematics. Yet, little research explores academically-based mathematics instruction for this population. This single subject alternating treatment design study explored the effectiveness of…
Directory of Open Access Journals (Sweden)
Jale İPEK
2013-12-01
Full Text Available The aim of research is to determine the effect of STAR strategy on 2nd grade students’ academic achievement and problem solving skills in the computer assisted mathematics instruction. 30 students who attend to 2nd grade course in a primary school in Aydın in 2010-2011 education year join the study group. The research has been taken place in 7 week. 3 types of tests have been used as means of data collecting tool, “Academic Achievement Test”, “Problem Solving Achievement Test” and “The Evaluation Form of Problem Solving Skills”. At the end of research students’ views about computer assisted mathematics instruction were evaluated. It has been examined that whether the differences between the scores of pre-test and post-test are statistically meaningful or not. According to the results, a positive increase on the academic achievement and problem solving skills has been determined at the end of the education carried out with STAR strategy.
Eringen, A Cemal
2013-01-01
Continuum Physics: Volume 1 - Mathematics is a collection of papers that discusses certain selected mathematical methods used in the study of continuum physics. Papers in this collection deal with developments in mathematics in continuum physics and its applications such as, group theory functional analysis, theory of invariants, and stochastic processes. Part I explains tensor analysis, including the geometry of subspaces and the geometry of Finsler. Part II discusses group theory, which also covers lattices, morphisms, and crystallographic groups. Part III reviews the theory of invariants th
Directory of Open Access Journals (Sweden)
Galvão, Elizangela da Silva
2013-12-01
Full Text Available Este artigo tem como tema central a análise das concepções de letramento presentes em situações problemas na Provinha Brasil de Matemática do 2º ano do Ensino Fundamental e realiza reflexões acerca da relação entre o letramento e o letramento matemático. Seu objetivo é distinguir os conceitos de alfabetização matemática e de letramento matemático presentes nas questões que envolvem a resolução de problemas. O referencial teórico adotado centra-se em autores que discorrem sobre a questão do letramento e, também, sobre o letramento matemático; sobre os conceitos de letramento autônomo e ideológico; e sobre seu paralelismo entre a alfabetização matemática e o letramento matemático. Refletimos sobre as concepções de resolução de problemas, bem como quais destas concepções adotadas pelos teóricos perpassam pela alfabetização ou pelo conceito de letramento matemático. Para realizar a análise documental, trouxemos, na íntegra, as cinco questões relacionadas à resolução de situações problemas, tal qual foram apresentadas para os alunos, e analisamos como as concepções de letramento são evidenciadas nas resoluções de problemas no documento. Os resultados apontam que o discurso presente no Plano de Desenvolvimento da Educação (PDE, 2011, sobre a resolução de problemas, não se aplica na prática, pois as questões analisadas resumem-se a atividades de alfabetização matemática, não perpassando pelo conceito de letramento. This article has as its focus the analysis of literacy conceptions present in problem-solving situations in Maths from ‘Provinha Brasil’ for the 2nd year of Secondary School and promotes reflections on the relationship between literacy and mathematics literacy. Its aim is to distinguish the concept of mathematics alphabetization and mathematics literacy in problem-solving questions. The adopted theoretical references come from authors who discuss the literacy issue and also
Özcan, Zeynep Çigdem
2016-01-01
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…
Özcan, Zeynep Çigdem
2016-01-01
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…
Teaching Mathematical Problem-Solving with the Brain in Mind: How can opening a closed problem help?
Directory of Open Access Journals (Sweden)
András Ambrus
2014-06-01
Full Text Available In the international literature, increasing numbers of articles and books are published about teaching and learning, with the brain in mind. For a long time, I have been sceptical about this question. However, seeing many unresolved issues in the teaching and learning of mathematics, I slowly started to study the relevant literature and have attempted to implement some ideas in my teaching. In this article, I will report on my experience with a selected mathematical problem in mathematics lessons and group study sessions; I will demonstrate how I modified the problem, based on my experience with the students, and I will reflect on my studies of brain-based mathematics teaching and learning.
Research on pre-processing of QR Code
Sun, Haixing; Xia, Haojie; Dong, Ning
2013-10-01
QR code encodes many kinds of information because of its advantages: large storage capacity, high reliability, full arrange of utter-high-speed reading, small printing size and high-efficient representation of Chinese characters, etc. In order to obtain the clearer binarization image from complex background, and improve the recognition rate of QR code, this paper researches on pre-processing methods of QR code (Quick Response Code), and shows algorithms and results of image pre-processing for QR code recognition. Improve the conventional method by changing the Souvola's adaptive text recognition method. Additionally, introduce the QR code Extraction which adapts to different image size, flexible image correction approach, and improve the efficiency and accuracy of QR code image processing.
Research on Digital Watermark Using Pre-Processing Technology
Institute of Scientific and Technical Information of China (English)
Ru Guo-bao; Ru Guo-bao; Niu Hui-fang; Niu Hui-fang; Yang Rui; Yang Rui; Sun Hong; Sun Hong; Shi Hong-ling; Shi Hong-ling; Huang Tian-xi; Huang Tian-xi
2003-01-01
We have realized a watermark embedding system based on audio perceptual masking and brought forward a watermark detection system using pre-processing technology.We can detect watermark from watermarked audio without original audio by using this method. The results have indicated that this embedding and detecting method is robust, on the premise of not affecting the hearing quality, it can resist those attacks such as MPEG compressing, filtering and adding white noise.
Elementary Analysis of High School Mathematics Problem-solving Error Reasons%高中数学解题出错原因浅析
Institute of Scientific and Technical Information of China (English)
杨婷
2014-01-01
高中数学解题教学过程中，学生解题出错的现象时有发生，而且是不可完全避免的，因此应当正确对待。将对当前高中数学解题过程中的主要出错原因、影响因素等进行分析，并在此基础上就如何应对这些问题，提出一些建设性建议，以期能够为高中数学教育教学事业的发展，作出一点贡献。%In the high school mathematics problem-solving teaching process,students’problem-solving error phenomenon occurs frequently, and it is not to completely avoid,so should be treated correctly.The teacher on the current high school math problem-solving in the process of the main error causes and influence factors were analyzed,and on this basis on how to deal with these problems,puts forward some constructive suggestions,in order to for the development of the cause of the high school mathematics education teaching,and make some contribution.
高考数学客观题的解法探究%A Probe into Problem-solving Methods for Objective Mathematics Questions in NMT
Institute of Scientific and Technical Information of China (English)
曾小平
2012-01-01
Objective mathematics questions in NMT are of large quantity and high scores and they emphasize the checking for basic knowledge. In order to solve these questions, students should grasp common problem-solving methods and skills besides grasping solid mathematics basis. This paper summarizes some common problem-solving methods.%高考数学客观题题量大（16小题），分值高（占80分），突出对三基（基本知识、基本技能、基本思想方法）的考查。要解好高考客观题，除要求考生具有扎实的数学基础外，还要掌握一些常见的解题方法与技巧。本文将对一些常用的解题方法进行归纳总结。
Stein, Sherman K
2010-01-01
Anyone can appreciate the beauty, depth, and vitality of mathematics with the help of this highly readable text, specially developed from a college course designed to appeal to students in a variety of fields. Readers with little mathematical background are exposed to a broad range of subjects chosen from number theory, topology, set theory, geometry, algebra, and analysis. Starting with a survey of questions on weight, the text discusses the primes, the fundamental theorem of arithmetic, rationals and irrationals, tiling, tiling and electricity, probability, infinite sets, and many other topi
The Effect of Thinking in Solving Mathematical Problems%思维定式在解决数学问题中的作用
Institute of Scientific and Technical Information of China (English)
徐书香
2014-01-01
In the process of mathematics teaching,We will find many problems associated with the mind-set,Mindset on both the active role of mathematics, but also has a negative effect.The scientific and rational use of mindset can effectively cultivate the quality of students ’ thinking,Improve the students thinking, problem analysis,problem solving skills.%在数学教学过程中，会发现许多与思维定式相关的问题，思维定式对数学既有着积极的作用，同时又有着消极作用。而科学合理地运用思维定式可有效培养学生的思维品质，提高学生思考问题、分析问题、解决问题的能力。
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...
Driver, Melissa K.; Powell, Sarah R.
2017-01-01
Word problems are prevalent on high-stakes assessments, and success on word problems has implications for grade promotion and graduation. Unfortunately, English Language Learners (ELLs) continue to perform significantly below their native English-speaking peers on mathematics assessments featuring word problems. Little is known about the…
Teaching Mathematical Problem-Solving with the Brain in Mind: How Can Opening a Closed Problem Help?
Ambrus, András
2014-01-01
In the international literature, increasing numbers of articles and books are published about teaching and learning, with the brain in mind. For a long time, I have been sceptical about this question. However, seeing many unresolved issues in the teaching and learning of mathematics, I slowly started to study the relevant literature and have…
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.
Directory of Open Access Journals (Sweden)
S. Shojaeilangari
2012-09-01
Full Text Available In recent years, an increasing number of researches have been focused on bio-inspired algorithms to solve the elaborate engineering problems. Artificial Immune System (AIS is an artificial intelligence technique which has potential of solving problems in various fields. The immune system, due to self-regulating nature, has been an inspiration source of unsupervised learning methods for pattern recognition task. The purpose of this study is to apply the AIS to pre-process the lie-detection dataset to promote the recognition of guilty and innocent subjects. A new Unsupervised AIS (UAIS was proposed in this study as a pre-processing method before classification. Then, we applied three different classifiers on pre-processed data for Event Related Potential (ERP assessment in a P300-based Guilty Knowledge Test (GKT. Experiment results showed that UAIS is a successful pre-processing method which is able to improve the classification rate. In our experiments, we observed that the classification accuracies for three different classifiers: K-Nearest Neighbourhood (KNN, Support Vector Machine (SVM and Linear Discriminant Analysis (LDA were increased after applying UAIS pre-processing. Using of scattering criterion to assessment the features before and after pre-processing proved that our proposed method was able to perform data mapping from a primary feature space to a new area where the data separability was improved significantly.
Contour extraction of echocardiographic images based on pre-processing
Energy Technology Data Exchange (ETDEWEB)
Hussein, Zinah Rajab; Rahmat, Rahmita Wirza; Abdullah, Lili Nurliyana [Department of Multimedia, Faculty of Computer Science and Information Technology, Department of Computer and Communication Systems Engineering, Faculty of Engineering University Putra Malaysia 43400 Serdang, Selangor (Malaysia); Zamrin, D M [Department of Surgery, Faculty of Medicine, National University of Malaysia, 56000 Cheras, Kuala Lumpur (Malaysia); Saripan, M Iqbal
2011-02-15
In this work we present a technique to extract the heart contours from noisy echocardiograph images. Our technique is based on improving the image before applying contours detection to reduce heavy noise and get better image quality. To perform that, we combine many pre-processing techniques (filtering, morphological operations, and contrast adjustment) to avoid unclear edges and enhance low contrast of echocardiograph images, after implementing these techniques we can get legible detection for heart boundaries and valves movement by traditional edge detection methods.
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...
Foley, Teresa E.; Parmar, Rene S.; Cawley, John F.
2003-01-01
This is the first of two papers that develop a framework and encourage discussion of research and programmatic concerns on arithmetic word problem solving. The two papers include a comprehensive framework for expanding the traditional three to five sentence word problem into a scheme that assures problems will be of a variety of structures and…
Goldston, J. W.
This unit introduces analytic solutions of ordinary differential equations. The objective is to enable the student to decide whether a given function solves a given differential equation. Examples of problems from biology and chemistry are covered. Problem sets, quizzes, and a model exam are included, and answers to all items are provided. The…
Chang'E-3 data pre-processing system based on scientific workflow
tan, xu; liu, jianjun; wang, yuanyuan; yan, wei; zhang, xiaoxia; li, chunlai
2016-04-01
The Chang'E-3(CE3) mission have obtained a huge amount of lunar scientific data. Data pre-processing is an important segment of CE3 ground research and application system. With a dramatic increase in the demand of data research and application, Chang'E-3 data pre-processing system(CEDPS) based on scientific workflow is proposed for the purpose of making scientists more flexible and productive by automating data-driven. The system should allow the planning, conduct and control of the data processing procedure with the following possibilities: • describe a data processing task, include:1)define input data/output data, 2)define the data relationship, 3)define the sequence of tasks,4)define the communication between tasks,5)define mathematical formula, 6)define the relationship between task and data. • automatic processing of tasks. Accordingly, Describing a task is the key point whether the system is flexible. We design a workflow designer which is a visual environment for capturing processes as workflows, the three-level model for the workflow designer is discussed:1) The data relationship is established through product tree.2)The process model is constructed based on directed acyclic graph(DAG). Especially, a set of process workflow constructs, including Sequence, Loop, Merge, Fork are compositional one with another.3)To reduce the modeling complexity of the mathematical formulas using DAG, semantic modeling based on MathML is approached. On top of that, we will present how processed the CE3 data with CEDPS.
用初等数论知识巧解小学数学题%Solving Primary School Mathematics Problems by Primary Number Theory
Institute of Scientific and Technical Information of China (English)
李子萍
2014-01-01
初等数论是主要研究整数性质的数学分支，它以初等方法为主要研究工具，主要研究整数的整除理论、同余理论、连分数理论和某些不定方程等。从数的整除性和同余理论两方面通过实例总结了初等数论在解小学数学题中的应用。以帮助我们在解某些小学数学题时，能发散思维、灵活运用数论知识解答。%Elementary Number Theory is a branch of mathematics studies the properties of integer .It takes the elementary method as the main research tool to research integer divisibility theory , congruence theory , the theory of continued fraction and some indeterminate equation .The paper , through examples from two aspects of the divisibility of numbers and congruence theory , summarizes the application of the elementary number theory in solving primary school mathematics problems and provides the solutions to some primary school mathematics problems , by using divergent thinking and flexibility in the use of the knowledge of number theory .
析高等数学教学中的解题技巧%On the Problem- solving Skills in the Teaching of Advanced Mathematics
Institute of Scientific and Technical Information of China (English)
邱云兰
2012-01-01
To talk about mathematical problem is one of the important forms of mathematical communication In the vocational high number of teaching that question, that can improve the students' results, interest in learning and communication skills. Teachers in the process should be presenter's protector, focusing on the mathematical activities. What it includes: the knowledge structure, the principle, the background, the mental process, the variant, the misunderstandings, and the resolution, thus reuniting the presenting and solving process together.%高等数学教学的核心任务是培养学生的思维能力，数学能力的提高在于解题质量的提高。解题找准三个点：寻找适当切入点，控制解题过程的调节点，审视解题后的反思点。教师在解题过程中，发挥例习题的榜样及培养功能，使学生真正掌握所学知识。
Institute of Scientific and Technical Information of China (English)
ZHENG Bin
2012-01-01
In this paper, the ( G'/G)-expansion method is extended to solve fractional partial differential equations in the sense of modified Riemann-Liouville derivative. Based on a nonlinear fractional complex transformation, a certain fractional partial differential equation can be turned into another ordinary differential equation of integer order. For illustrating the validity of this method, we apply it to the space-time fractional generalized Hirota-Satsuma coupled KdV equations and the time-fractional fifth-order Sawada-Kotera equation. As a result, some new exact solutions for them are successfully established.
Directory of Open Access Journals (Sweden)
Olga Vergazova
2016-04-01
Full Text Available The problem of raising the level of mathematical preparation of students of mathematical and technical specialties should be addressed to both the course of school level algebra and analysis, and the preparation to the Unified State Examination in mathematics (profile level. The example of the application of the functional-graphical method for solving trigonometric equations and inequalities in problems of high level on the use math level profile, demonstrates one of the possibilities of differentiated approach in training future first-year student of technical or mathematical University. For example, the decision of tasks demonstrates the advantages of using functional-graphical method for solving trigonometric equations and inequalities in the formation and development of skills of analysis and graphing of elementary functions. The paper is of interest to academicians, high school teachers and students wishing to enter technical or mathematical university.
Tapia, R. A.; Vanrooy, D. L.
1976-01-01
A quasi-Newton method is presented for minimizing a nonlinear function while constraining the variables to be nonnegative and sum to one. The nonnegativity constraints were eliminated by working with the squares of the variables and the resulting problem was solved using Tapia's general theory of quasi-Newton methods for constrained optimization. A user's guide for a computer program implementing this algorithm is provided.
Directory of Open Access Journals (Sweden)
N. Novianawati
2015-04-01
Full Text Available This study aims to determine students’ decision making strategy to answer TIMSS science reasoning test in cognitive reasoning domain. This research is quantitative descriptive research. The result shows that students tend to use compensatory strategy for decision making in solving multiple-choice questions and use rational category to answer essay questions. The result shows that more than half of students have been able to answer the questions TIMSS science tests correctly.
Munhoven, G.
2013-08-01
The total alkalinity-pH equation, which relates total alkalinity and pH for a given set of total concentrations of the acid-base systems that contribute to total alkalinity in a given water sample, is reviewed and its mathematical properties established. We prove that the equation function is strictly monotone and always has exactly one positive root. Different commonly used approximations are discussed and compared. An original method to derive appropriate initial values for the iterative solution of the cubic polynomial equation based upon carbonate-borate-alkalinity is presented. We then review different methods that have been used to solve the total alkalinity-pH equation, with a main focus on biogeochemical models. The shortcomings and limitations of these methods are made out and discussed. We then present two variants of a new, robust and universally convergent algorithm to solve the total alkalinity-pH equation. This algorithm does not require any a priori knowledge of the solution. SolveSAPHE (Solver Suite for Alkalinity-PH Equations) provides reference implementations of several variants of the new algorithm in Fortran 90, together with new implementations of other, previously published solvers. The new iterative procedure is shown to converge from any starting value to the physical solution. The extra computational cost for the convergence security is only 10-15% compared to the fastest algorithm in our test series.
The researches on the problem solving ability of primary mathematics%小学数学问题解决能力培养探究
Institute of Scientific and Technical Information of China (English)
孙群若
2015-01-01
As a problem-centered teaching mode,“problem solving”can give full play to the dominant position of students,raise their interests in learning math,and help them to enhance the ability of analyzing and solving problems. By chan-ging the way of students’solving problems,“problem solving”can improve teachers'teaching mode and build efficient and stra-tegic classroom. Strategic teaching will benefit for the elementary mathematical problems. It will provide a useful reference for the promotion of the students’problem-solving skills and the ability to improve application.%“问题解决”作为一种以问题为核心的教学模式，能够充分发挥学生的主体地位，提高学习数学的兴趣，有助于学生分析问题和解决问题的能力的培育。通过转变学生问题解决方式，完善教师的教学模式，可以构建高效的课堂等教学策略对小学数学问题解决影响的探讨，为促进学生问题解决能力和应用能力的提高提供有益参考。
The Pre-Processing of Images Technique for the Materia
Directory of Open Access Journals (Sweden)
Yevgeniy P. Putyatin
2016-08-01
Full Text Available The image processing analysis is one of the most powerful tool in various research fields, especially in material / polymer science. Therefore in the present article an attempt has been made for study of pre-processing of images technique of the material samples during the images taken out by Scanning Electron Microscope (SEM. First we prepared the material samples with coir fibre (natural and its polymer composite after that the image analysis has been performed by SEM technique and later on the said studies have been conducted. The results presented here were found satisfactory and also are in good agreement with our earlier work and some other worker in the same field.
Pre-Processing and Modeling Tools for Bigdata
Directory of Open Access Journals (Sweden)
Hashem Hadi
2016-09-01
Full Text Available Modeling tools and operators help the user / developer to identify the processing field on the top of the sequence and to send into the computing module only the data related to the requested result. The remaining data is not relevant and it will slow down the processing. The biggest challenge nowadays is to get high quality processing results with a reduced computing time and costs. To do so, we must review the processing sequence, by adding several modeling tools. The existing processing models do not take in consideration this aspect and focus on getting high calculation performances which will increase the computing time and costs. In this paper we provide a study of the main modeling tools for BigData and a new model based on pre-processing.
Pre-processing in AI based Prediction of QSARs
Patri, Om Prasad
2009-01-01
Machine learning, data mining and artificial intelligence (AI) based methods have been used to determine the relations between chemical structure and biological activity, called quantitative structure activity relationships (QSARs) for the compounds. Pre-processing of the dataset, which includes the mapping from a large number of molecular descriptors in the original high dimensional space to a small number of components in the lower dimensional space while retaining the features of the original data, is the first step in this process. A common practice is to use a mapping method for a dataset without prior analysis. This pre-analysis has been stressed in our work by applying it to two important classes of QSAR prediction problems: drug design (predicting anti-HIV-1 activity) and predictive toxicology (estimating hepatocarcinogenicity of chemicals). We apply one linear and two nonlinear mapping methods on each of the datasets. Based on this analysis, we conclude the nature of the inherent relationships betwee...
Digital soil mapping: strategy for data pre-processing
Directory of Open Access Journals (Sweden)
Alexandre ten Caten
2012-08-01
Full Text Available The region of greatest variability on soil maps is along the edge of their polygons, causing disagreement among pedologists about the appropriate description of soil classes at these locations. The objective of this work was to propose a strategy for data pre-processing applied to digital soil mapping (DSM. Soil polygons on a training map were shrunk by 100 and 160 m. This strategy prevented the use of covariates located near the edge of the soil classes for the Decision Tree (DT models. Three DT models derived from eight predictive covariates, related to relief and organism factors sampled on the original polygons of a soil map and on polygons shrunk by 100 and 160 m were used to predict soil classes. The DT model derived from observations 160 m away from the edge of the polygons on the original map is less complex and has a better predictive performance.
Directory of Open Access Journals (Sweden)
A. S. Diakov
2014-01-01
Full Text Available One of the main trends for development of promising military equipment is to create transport robot systems (TRS.To conduct a theoretical study of the potential properties of TRS mobility was used a software package for invariant simulation of multibody dynamics system "Euler", which allows us to solve problems regarding the "large displacements", typical for TRS.The modelling results of TRS motion dynamics when overcoming the single-stage and two stages, which are higher than the roller diameter of propeller are obtained.Analysis of modelling results of the TRS motion dynamics to overcome obstacles commensurate with its dimensions allows us to conclude that the use of wheel-legged three-roller propulsion can provide the required level of permeability and, as a result, increasing TRS mobility.
Pierce, Allan D; Thiam, Amadou G
2012-03-01
A sequence of dictums for mathematical acoustics is given representing opinions intended to be regarded as authoritative, but not necessarily universally agreed upon. The dictums are presented in the context of the detailed solution for a class of problems involving the forced vibration of a long cylinder protruding half-way into a half-space bounded by a compliant surface (impedance boundary) characterized by a spring constant. One limiting case corresponds to a cylinder vibrating within an infinite rigid baffle, and another limiting case corresponds to a vibrating cylinder on the compliant surface of an incompressible fluid. The second limiting case is identified as analogous to that of a floating half-submerged cylinder whose vibrations cause water waves to propagate over the surface. Attention is focused on vibrations at very low frequencies. Difficulties with insuring a causal solution are pointed out and dictums are given as to how one overcomes such difficulties. Various approximation techniques are described. The derivations involve application of the theory of complex variables and the method of matched asymptotic expansions, and the results include the apparent entrained mass in the near field of the cylinder and the radiation resistance per unit length experienced by the vibrating cylinder.
Institute of Scientific and Technical Information of China (English)
刘福霞
2014-01-01
It is well known that mathematical knowledge comes from life,and also applied to life. In math class,therefore,we should try to make the mathematics teaching into life,guide students to use mathematical knowledge to solve practical problems of life,and gradually improve students’ability to use mathematical knowledge to solve practical problems.%众所周知，数学知识来源于生活，同时又应用于生活。因此，在数学课堂上，教师应努力做到使数学教学走进生活，引导学生运用所学数学知识解决生活实际问题，并逐渐提高学生运用数学知识解决实际问题的能力。
Breast image pre-processing for mammographic tissue segmentation.
He, Wenda; Hogg, Peter; Juette, Arne; Denton, Erika R E; Zwiggelaar, Reyer
2015-12-01
During mammographic image acquisition, a compression paddle is used to even the breast thickness in order to obtain optimal image quality. Clinical observation has indicated that some mammograms may exhibit abrupt intensity change and low visibility of tissue structures in the breast peripheral areas. Such appearance discrepancies can affect image interpretation and may not be desirable for computer aided mammography, leading to incorrect diagnosis and/or detection which can have a negative impact on sensitivity and specificity of screening mammography. This paper describes a novel mammographic image pre-processing method to improve image quality for analysis. An image selection process is incorporated to better target problematic images. The processed images show improved mammographic appearances not only in the breast periphery but also across the mammograms. Mammographic segmentation and risk/density classification were performed to facilitate a quantitative and qualitative evaluation. When using the processed images, the results indicated more anatomically correct segmentation in tissue specific areas, and subsequently better classification accuracies were achieved. Visual assessments were conducted in a clinical environment to determine the quality of the processed images and the resultant segmentation. The developed method has shown promising results. It is expected to be useful in early breast cancer detection, risk-stratified screening, and aiding radiologists in the process of decision making prior to surgery and/or treatment.
Visualisation and pre-processing of peptide microarray data.
Reilly, Marie; Valentini, Davide
2009-01-01
The data files produced by digitising peptide microarray images contain detailed information on the location, feature, response parameters and quality of each spot on each array. In this chapter, we will describe how such peptide microarray data can be read into the R statistical package and pre-processed in preparation for subsequent comparative or predictive analysis. We illustrate how the information in the data can be visualised using images and graphical displays that highlight the main features, enabling the quality of the data to be assessed and invalid data points to be identified and excluded. The log-ratio of the foreground to background signal is used as a response index. Negative control responses serve as a reference against which "detectable" responses can be defined, and slides incubated with only buffer and secondary antibody help identify false-positive responses from peptides. For peptides that have a detectable response on at least one subarray, and no false-positive response, we use linear mixed models to remove artefacts due to the arrays and their architecture. The resulting normalized responses provide the input data for further analysis.
Institute of Scientific and Technical Information of China (English)
付洪春
2012-01-01
数学思想是对教学知识内容的一种本质认识，它是数学的灵魂，是解决数学问题的金钥匙。灵活运用各种数学思想方法是提高解题能力的根本所在。本文将从近几年来各地中考试题中归纳、分析数学思想在综合试题中应用的类型和解题技巧，旨在提高学生解题效率。%Mathematics thought is a kind of essential cognition of teaching contents and it is the soul of mathematics and the golden key to solve mathematics problems. Flexibly applying various mathematics thought methods is the decisive factor in improving problem-solving ability. This paper analyzes the applying types and problem-solving skills of mathematics thought in comprehensive test papers, hoping to improve students＇ problem- solving effect.
数学思想方法在解题教学中的作用%On the Function of Mathematics Thinking Method in Math Problem-solving Teaching
Institute of Scientific and Technical Information of China (English)
陈安宁
2015-01-01
数学思想方法是对数学本质的认识，是数学知识的精髓。新课程理念下注重数学思想方法教学是培养学生数学素养，形成良好思维品质的关键。本文通过对一道数学题的多种解法中所蕴含的数学思想方法的分析指出，在中学数学教学中，教师必须重视和加强对学生数学思想方法的渗透与培养，使得学生更加深刻地领会解题过程中所隐含的思想方法以及由此形成的数学知识体系，切实提高学生的数学素养和解题能力。%The mathematical thinking method is not only the cognitive results of nature of mathematics but also the embodiment of the essence of mathematics knowledge.The new curriculum concept considers it the key to cultivate student mathematical literacy and to develop their good traits of thinking by paying more attention to the teaching of mathematical thinking method.Through analyzing mathematical thinking methods contained in various solutions to a mathematical problem, this article points out that teachers should pay more attention to and strengthen the penetration and cultivation of students mathematics think-ing methods in middle school mathematics teaching, help students understand the connotation of these methods in the process of problem solving and the systematic mathematics knowledge created by the meth-ods themselves, and encourage students to improve their mathematics accomplishment and problem sol-ving ability.
Institute of Scientific and Technical Information of China (English)
焦潍苹
2014-01-01
Higher vocational mathematics knowledge is widely applied in solving the economic problems, training students to master the application of mathematics knowledge to solve practical problems is the basic task of higher vocational mathematics education, and the fundamental task of the mathematics education for students of Economic Management in higher vocational school is to develop the students' ability of applying the mathematics knowledge they have learned to related courses in economic. Now union Economic Management specialized characteristic, to discuss the application of higher vocational mathematics knowledge to solve economic problems through examples.%高职数学知识在经济问题的解决中应用已十分广泛，培养学生掌握应用所学数学知识解决实际问题是高职数学教育的根本任务，对高职经管专业学生数学教育的根本任务是培养学生将所学的数学知识运用到相关经济专业课学习中去的能力。现结合高职院校经济管理类的专业特点举例讨论高等数学知识在解决经济问题中的应用。
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.
Automated Pre-processing for NMR Assignments with Reduced Tedium
Energy Technology Data Exchange (ETDEWEB)
2004-05-11
An important rate-limiting step in the reasonance asignment process is accurate identification of resonance peaks in MNR spectra. NMR spectra are noisy. Hence, automatic peak-picking programs must navigate between the Scylla of reliable but incomplete picking, and the Charybdis of noisy but complete picking. Each of these extremes complicates the assignment process: incomplete peak-picking results in the loss of essential connectivities, while noisy picking conceals the true connectivities under a combinatiorial explosion of false positives. Intermediate processing can simplify the assignment process by preferentially removing false peaks from noisy peak lists. This is accomplished by requiring consensus between multiple NMR experiments, exploiting a priori information about NMR spectra, and drawing on empirical statistical distributions of chemical shift extracted from the BioMagResBank. Experienced NMR practitioners currently apply many of these techniques "by hand", which is tedious, and may appear arbitrary to the novice. To increase efficiency, we have created a systematic and automated approach to this process, known as APART. Automated pre-processing has three main advantages: reduced tedium, standardization, and pedagogy. In the hands of experienced spectroscopists, the main advantage is reduced tedium (a rapid increase in the ratio of true peaks to false peaks with minimal effort). When a project is passed from hand to hand, the main advantage is standardization. APART automatically documents the peak filtering process by archiving its original recommendations, the accompanying justifications, and whether a user accepted or overrode a given filtering recommendation. In the hands of a novice, this tool can reduce the stumbling block of learning to differentiate between real peaks and noise, by providing real-time examples of how such decisions are made.
Callejo, Maria Luz
1994-01-01
Reports, in French, an investigation on the use of graphic representations in problem-solving tasks of the type in Spanish Mathematical Olympiads. Analysis showed that the choice and interpretation of the first graphic representation played a decisive role in the discovery of the solution. (34 references) (Author/MKR)
数学解题自我监控能力培养的实践研究%Mathematics Problem-solving Ability of Serf-monitoring Research Practice
Institute of Scientific and Technical Information of China (English)
杨巧梅
2009-01-01
通过分析学生数学解题的现状,从重视学生数学解题的主动性、自觉性和主体性的角度出发,提出影响学生数学解题能力和解题质量的关键因素在于学生的自我监控能力.解题自我监控能力的培养是提高教学质量、教学生学会学习的有效途径.%By analyzing the status of students in mathematical problem solving, attention to students from the mathe-matics problem-solving initiative, consciousness and the point of view of subjectivity, the impact on students mathe-matical problem-solving abihty and problem-solving is a key factor in the quality of the self-monitoring ability of students. Problem-solving ability in self-monitoring is to improve the quality of teaching and teaching students an ef-fective way to learn how to learn.
Institute of Scientific and Technical Information of China (English)
宁兴全; 冯长焕; 王博蓉
2015-01-01
本文利用“数学问题解决中的元认知问卷量表”，对初中学生进行了抽样调查。然后对数据进行了数学问题解决中的元认知与数学成绩的相关性研究，对不同性别、不同成绩段以及不同年级学生的数学问题解决中的元认知进行了差异分析。结果表明，初中生数学问题解决中的元认知与数学成绩成显著正相关；初中生数学问题解决中的元认知在性别上差异不大，但在年级和优差生间差异较大。%Using a questionnaire about meta-cognition of mathematics problem solving , this study conducted a sample survey in junior middle school students .Analysis of the correlation between meta-cognition of mathematics problem solving and math scores , we also have analyzed the difference about meta-cognition of mathematics problem solving for different gender , math scores and grades .The following results are obtained: the meta-cognition of mathematics problem solving and math scores are of significant positive correlation on the part of junior middle school students;the meta-cognition of mathematics problem solving is little difference in gender , but there are sig-nificant differences in different grades and different math scores .
Authenticity of Mathematical Modeling
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…
Performance of Pre-processing Schemes with Imperfect Channel State Information
DEFF Research Database (Denmark)
Christensen, Søren Skovgaard; Kyritsi, Persa; De Carvalho, Elisabeth
2006-01-01
Pre-processing techniques have several benefits when the CSI is perfect. In this work we investigate three linear pre-processing filters, assuming imperfect CSI caused by noise degradation and channel temporal variation. Results indicate, that the LMMSE filter achieves the lowest BER and the high...
Institute of Scientific and Technical Information of China (English)
陈杰伟
2015-01-01
"Problem solving"teaching emphasizes allow students to experience the problem-solving process, grasp solu-tions to problems in the process, perception of mathematical thinking in order to improve the ability to solve problems suc-cessor. In this paper, the case talk about"problem solving"teaching approach allows students to experience the problem-solving process, perception of mathematical thinking:First, focus on the positioning of mathematical thinking from mul-tiple perspectives;the second is based on the exploration of mathematical thinking, allowing students to participate, ex-perience and sentiment.%"解决问题"的教学强调让学生经历问题解决的过程,在过程中掌握解决问题的方法,感悟数学思想,才能提高后继解决问题的能力.本文结合案例谈谈在"解决问题"的教学中让学生经历问题解决过程,感悟数学思想的做法:一是从多角度着眼数学思想的定位;二是基于数学思想的探究,让学生参与、体验、感悟.
Laughlin, Patrick R
2011-01-01
Experimental research by social and cognitive psychologists has established that cooperative groups solve a wide range of problems better than individuals. Cooperative problem solving groups of scientific researchers, auditors, financial analysts, air crash investigators, and forensic art experts are increasingly important in our complex and interdependent society. This comprehensive textbook--the first of its kind in decades--presents important theories and experimental research about group problem solving. The book focuses on tasks that have demonstrably correct solutions within mathematical
Ghezavati, V. R.; Beigi, M.
2016-06-01
During the last decade, the stringent pressures from environmental and social requirements have spurred an interest in designing a reverse logistics (RL) network. The success of a logistics system may depend on the decisions of the facilities locations and vehicle routings. The location-routing problem (LRP) simultaneously locates the facilities and designs the travel routes for vehicles among established facilities and existing demand points. In this paper, the location-routing problem with time window (LRPTW) and homogeneous fleet type and designing a multi-echelon, and capacitated reverse logistics network, are considered which may arise in many real-life situations in logistics management. Our proposed RL network consists of hybrid collection/inspection centers, recovery centers and disposal centers. Here, we present a new bi-objective mathematical programming (BOMP) for LRPTW in reverse logistic. Since this type of problem is NP-hard, the non-dominated sorting genetic algorithm II (NSGA-II) is proposed to obtain the Pareto frontier for the given problem. Several numerical examples are presented to illustrate the effectiveness of the proposed model and algorithm. Also, the present work is an effort to effectively implement the ɛ-constraint method in GAMS software for producing the Pareto-optimal solutions in a BOMP. The results of the proposed algorithm have been compared with the ɛ-constraint method. The computational results show that the ɛ-constraint method is able to solve small-size instances to optimality within reasonable computing times, and for medium-to-large-sized problems, the proposed NSGA-II works better than the ɛ-constraint.
Directory of Open Access Journals (Sweden)
Izaak Hendrik Wenno
2015-01-01
Full Text Available The purpose of the study is to determine the relation between interest at Physics and knowledge of Mathematics basic concepts with the ability to solve Physics problems. The populations are all students in the 7th grade at the junior high school in Ambon, Maluku, Indonesia. The used sample schools are Junior High Schools 8, 9, and 10 during 2013/2014 academic year with 44 students per school. Two independent variables and one dependent variable are studied. The independent variables are the interest at Physics (X1 and the knowledge of Mathematics basic concepts (X2, while the dependent variable is the ability to solve Physics problems (Y. Data collection technique for X1 is an interview with questionnaire instrument, while for the X2 and Y is using the test technique with test items instrument. The obtained data from the measurements were analyzed with descriptive analysis and inferential analysis. The results show that there is a positive relation between interest at Physics and knowledge of Mathematics basic concepts with students’ ability to solve Physics problems.
Institute of Scientific and Technical Information of China (English)
王成营
2012-01-01
Mathematics knowledge is communicated and transmitted by various symbols, so mathematics teaching should be aimed at developing students' ability to obtain the meaning of mathematical symbols independently. Mathematical symbols has their own systems that not only have three equivalent forms including word, symbolic language and chart, but also bear six different types of meaning including basic meaning, conversion meaning, associative meaning, etc. These characters of mathematical symbols determine that the ability to obtain mathematical symbols' meaning is diversified, hierarchical and developmental. In the teaching of mathematics problem solving, the cultivation of students' ability to obtain mathematical symbols' meaning generally includes four stages: recognition and segmentation of symbols, association and finding of symbols' meaning, integration and optimization of symbols' meaning as well as operation and representation of the symbols.%承载数学知识的数学符号是自成体系的，不仅具有文字语言、符号语言、图表语言三种等价的符号形式，而且具有基本意义、转换意义、联想意义等六种不同的符号意义。数学符号的这种特点决定了数学符号意义获得能力具有多元性、层次性、发展性。在数学问题解决教学中，培养学生的符号意义获得能力一般包括符号的识别与切分、符号意义的联想与发现、符号意义的整合与优化、符号的操作与表征四个阶段。
Directory of Open Access Journals (Sweden)
Dewi Herawaty
2016-10-01
Full Text Available This research aims at: 1 the influence of the implementation of the model of teaching mathematics realistic based on cognitive conflict students to the ability to understanding the concept and troubleshooting capabilities; 2 determine the larger capacity of the understanding of the concept through the implementation of the model of teaching mathematics realistic based on cognitive conflict junior secondary school students the City of Bengkulu. 3 determine the great improvement of the ability to solve problems through the implementation of the model of teaching mathematics realistic based on cognitive conflict SMP students Bengkulu City.To achieve the goal of this research is to apply Research Design pseudo experiments with research design Pretest-Postest Nonequivalent Control Group Design, with the test instrument the ability to understanding the concept and test the troubleshooting capabilities. The data has been analyzed using the test gains. The results of this research is 1 the ability of understanding the concept and troubleshooting class experiment the given learning with PMR is better than with the ability to understanding the concept and troubleshooting control classes assigned to conventional mathematics lesson; 2 increase the ability of the understanding of the concept through the implementation of the model of teaching mathematics based on cognitive conflict SMP students Bengkulu City is significant with the index gain of 0,755 (high-level; 3 increase the ability to solve problems through the implementation of the model of teaching mathematics based on cognitive conflict SMP students Bengkulu City is significant with the index gain of 0,500 level (is.
The Effects of Pre-processing Strategies for Pediatric Cochlear Implant Recipients
Rakszawski, Bernadette; Wright, Rose; Cadieux, Jamie H.; Davidson, Lisa S.; Brenner, Christine
2016-01-01
Background Cochlear implants (CIs) have been shown to improve children’s speech recognition over traditional amplification when severe to profound sensorineural hearing loss is present. Despite improvements, understanding speech at low-level intensities or in the presence of background noise remains difficult. In an effort to improve speech understanding in challenging environments, Cochlear Ltd. offers pre-processing strategies that apply various algorithms prior to mapping the signal to the internal array. Two of these strategies include Autosensitivity Control™ (ASC) and Adaptive Dynamic Range Optimization (ADRO®). Based on previous research, the manufacturer’s default pre-processing strategy for pediatrics’ everyday programs combines ASC+ADRO®. Purpose The purpose of this study is to compare pediatric speech perception performance across various pre-processing strategies while applying a specific programming protocol utilizing increased threshold (T) levels to ensure access to very low-level sounds. Research Design This was a prospective, cross-sectional, observational study. Participants completed speech perception tasks in four pre-processing conditions: no pre-processing, ADRO®, ASC, ASC+ADRO®. Study Sample Eleven pediatric Cochlear Ltd. cochlear implant users were recruited: six bilateral, one unilateral, and four bimodal. Intervention Four programs, with the participants’ everyday map, were loaded into the processor with different pre-processing strategies applied in each of the four positions: no pre-processing, ADRO®, ASC, and ASC+ADRO®. Data Collection and Analysis Participants repeated CNC words presented at 50 and 70 dB SPL in quiet and HINT sentences presented adaptively with competing R-Space noise at 60 and 70 dB SPL. Each measure was completed as participants listened with each of the four pre-processing strategies listed above. Test order and condition were randomized. A repeated-measures analysis of variance (ANOVA) was used to
Directory of Open Access Journals (Sweden)
GORGUNOGLU, S.
2014-05-01
Full Text Available In analysis of minutiae based fingerprint systems, fingerprints needs to be pre-processed. The pre-processing is carried out to enhance the quality of the fingerprint and to obtain more accurate minutiae points. Reducing the pre-processing time is important for identification and verification in real time systems and especially for databases holding large fingerprints information. Parallel processing and parallel CPU computing can be considered as distribution of processes over multi core processor. This is done by using parallel programming techniques. Reducing the execution time is the main objective in parallel processing. In this study, pre-processing of minutiae based fingerprint system is implemented by parallel processing on multi core computers using OpenMP and on graphics processor using CUDA to improve execution time. The execution times and speedup ratios are compared with the one that of single core processor. The results show that by using parallel processing, execution time is substantially improved. The improvement ratios obtained for different pre-processing algorithms allowed us to make suggestions on the more suitable approaches for parallelization.
Trimmer, Ronald G.
This literature review focuses on determining the psychological variables related to problem solving and presents arguments for self-correcting manipulatives as a media for teaching problem solving. Ten traits are considered: attitude, debilitating anxiety, self-concept, orderliness, set, confidence, impulsive/reflective thinking, concentration…
Murray, James D
1993-01-01
The book is a textbook (with many exercises) giving an in-depth account of the practical use of mathematical modelling in the biomedical sciences. The mathematical level required is generally not high and the emphasis is on what is required to solve the real biological problem. The subject matter is drawn, e.g. from population biology, reaction kinetics, biological oscillators and switches, Belousov-Zhabotinskii reaction, reaction-diffusion theory, biological wave phenomena, central pattern generators, neural models, spread of epidemics, mechanochemical theory of biological pattern formation and importance in evolution. Most of the models are based on real biological problems and the predictions and explanations offered as a direct result of mathematical analysis of the models are important aspects of the book. The aim is to provide a thorough training in practical mathematical biology and to show how exciting and novel mathematical challenges arise from a genuine interdisciplinary involvement with the biosci...
Mastering mathematics geometry & measures
Various
2014-01-01
Deliver outstanding lessons that build fluency, problem-solving and mathematical reasoning skills to enable sustained progress at Key Stage 3, in preparation for GCSE. Mastering Mathematics provides flexible online and print teaching and learning resources. The service focuses on strands within the curriculum to improve progression throughout Secondary Mathematics . Mastering Mathematics Student Books and Whiteboard eTextbooks are organised into progression strands in line with Mastering Mathematics Teaching and Learning Resources:. - Enable students to identify appropriate remediation or exte
Problem Solving Using Microcomputers.
Demana, Franklin; Waits, Bert
1987-01-01
It is argued that microcomputer technology has evolved to the stage that it should be routinely used by mathematics students at all levels. It is shown how the use of microcomputers can change the way problems are solved. Computer-generated graphics are highlighted. (PK)
Performance of Pre-processing Schemes with Imperfect Channel State Information
DEFF Research Database (Denmark)
Christensen, Søren Skovgaard; Kyritsi, Persa; De Carvalho, Elisabeth
2006-01-01
Pre-processing techniques have several benefits when the CSI is perfect. In this work we investigate three linear pre-processing filters, assuming imperfect CSI caused by noise degradation and channel temporal variation. Results indicate, that the LMMSE filter achieves the lowest BER and the high...... and the highest SINR when the CSI is perfect, whereas the simple matched filter may be a good choice when the CSI is imperfect. Additionally the results give insight into the inherent trade-off between robustness against CSI imperfections and spatial focusing ability....
Influence of Hemp Fibers Pre-processing on Low Density Polyethylene Matrix Composites Properties
Kukle, S.; Vidzickis, R.; Zelca, Z.; Belakova, D.; Kajaks, J.
2016-04-01
In present research with short hemp fibres reinforced LLDPE matrix composites with fibres content in a range from 30 to 50 wt% subjected to four different pre-processing technologies were produced and such their properties as tensile strength and elongation at break, tensile modulus, melt flow index, micro hardness and water absorption dynamics were investigated. Capillary viscosimetry was used for fluidity evaluation and melt flow index (MFI) evaluated for all variants. MFI of fibres of two pre-processing variants were high enough to increase hemp fibres content from 30 to 50 wt% with moderate increase of water sorption capability.
Institute of Scientific and Technical Information of China (English)
郑瑞丽
2014-01-01
Today's talent with problem solving ability more and more get the welcome of the society, based on the teaching reform, and also adapt elementary school teaching form, take active reform itself,"problem solving"as the teaching goal. In this paper, according to the teaching content of teaching material for primary school grade four top volume, according to the existing elementary school mathematics education of cultivating the ability of problem solving oriented game design should follow the design concept and strategy, has carried on the case of conceptual design in the world, and its teaching function has carried on the detailed elaboration, and explains how to implementation in elementary school mathematics education game problem solving ability.%当今具有问题解决能力的人才越来越受到社会的欢迎，基于此教学改革势在必行，而基础小学教学也随之适应形式，积极采取自身改革，将“问题解决能力”作为教学目标。本文依照小学四年级上册教材的教学内容，根据已有的面向问题解决能力培养的小学数学教育游戏设计时要遵循的设计理念与策略，进行了世界案例的概念设计，并对其教学功能进行了详细的阐述，并解释了如何在小学数学教育游戏中实现问题解决能力的培养。
Rosenzweig, Carly; Krawec, Jennifer; Montague, Marjorie
2011-01-01
The purpose of the study was to investigate the metacognitive abilities of students with LD as they engage in math problem solving and to determine processing differences between these students and their low- and average-achieving peers (n = 73). Students thought out loud as they solved three math problems of increasing difficulty. Protocols were coded and analyzed to determine frequency of cognitive verbalizations and productive and nonproductive metacognitive verbalizations. Results indicated different patterns of metacognitive activity for ability groups when type of metacognitive verbalization and problem difficulty were considered. Implications for instruction are discussed.
Fibonacci's Triangle: A Vehicle for Problem Solving.
Ouellette, Hugh
1979-01-01
A method for solving certain types of problems is illustrated by problems related to Fibonacci's triangle. The method involves pattern recognition, generalizing, algebraic manipulation, and mathematical induction. (MP)
Methods of solving nonstandard problems
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, ...
Hiriart-Urruty, Jean-Baptiste
2016-01-01
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.
Pre-processing filter design at transmitters for IBI mitigation in an OFDM system
Institute of Scientific and Technical Information of China (English)
Xia Wang; Lei Wang
2013-01-01
In order to meet the demands for high transmission rates and high service quality in broadband wireless communica-tion systems, orthogonal frequency division multiplexing (OFDM) has been adopted in some standards. However, the inter-block interference (IBI) and inter-carrier interference (ICI) in an OFDM system affect the performance. To mitigate IBI and ICI, some pre-processing approaches have been proposed based on ful channel state information (CSI), which improved the system per-formance. A pre-processing filter based on partial CSI at the trans-mitter is designed and investigated. The filter coefficient is given by the optimization processing, the symbol error rate (SER) is tested, and the computation complexity of the proposed scheme is analyzed. Computer simulation results show that the proposed pre-processing filter can effectively mitigate IBI and ICI and the performance can be improved. Compared with pre-processing approaches at the transmitter based on ful CSI, the proposed scheme has high spectral efficiency, limited CSI feedback and low computation complexity.
Directory of Open Access Journals (Sweden)
Isabel Alonso Berenguer
2012-10-01
Full Text Available This paper proposes a model of the dynamics formation process of the value of perseverance in mathematical problems solving, the one is structured in two dimensions: the cognitive-solver and the affective-solver. This model can serves as a basis for developing practical tools to intervene didactically in that dynamic and enhance the success of students in mathematical problem solving.ResumenEl presente trabajo propone un modelo de la dinámica del proceso de formación del valor de la perseverancia en la resolución de problemas matemáticos, el que se estructura en dos dimensiones: la dimensión cognitivo-resolutora y la afectivo-resolutora. Este modelo sirve de base para el desarrollo de herramientas prácticas para intervenir didácticamente en esa dinámica y mejorar el éxito de los estudiantes en la resolución de problemas matemáticos.
Institute of Scientific and Technical Information of China (English)
宋广文; 何文广; 孔伟
2011-01-01
Since 1980's systematic researches have been made on mental processes, influencing factors and psychological models of problem solving. The researches found that problem context, problem representationtypes, mental preparation, working memory, cognitive styles, and self-evaluation are the main factors for problem solving (Lu haidong, 2004; You xuqun, 2006; Chen yinghe, 2004; Beckmann et al., 2007). Some researchers pointed out that problem representation and problem solving plans are the basic inner processes (Kintch & Greeno, 1985; Greeno, 1986). Along with deeper studies, direct translation strategy and problem-model strategy (Mayer, 1996) were considered as the main representation types, and working memory as the major factor for problem representation type (Baddeley, 1992; Cornoldi, 1999; Mclean, 1999; Wang enguo, 2007; Wanyan, 2007). However, the past studies paid much attention to how verbal working memory affected problem representation, while there were few studies on how visual-spacial memory span influenced problemrepresentation in mathematics. As a hypothesis, we thought that it was the individual differences in working memory that resulted in different problem representation in mathematics, which led to different performances in mathematical assignments. Those with a high spacial working memory span, based on an overall comprehension of the problem, could construct a good problem representation, and would show superiority in high speed and accuracy in mathematical problem solving. Those with a high verbal working memory span, might display an advantage in comprehension of mathematical problems. However, compared with the high visual-spacial memory span group, they might have different problem representation. This study was especially concerned about whether there were differences in problem representation and problem solving between the two groups with different working memory.This study included four separate experiments. 104 Grade 6 pupils from
AN ENHANCED PRE-PROCESSING RESEARCH FRAMEWORK FOR WEB LOG DATA USING A LEARNING ALGORITHM
Directory of Open Access Journals (Sweden)
V.V.R. Maheswara Rao
2011-01-01
Full Text Available With the continued growth and proliferation of Web services and Web based information systems, the volumes of user data have reached astronomical proportions. Before analyzing such data using web mining techniques, the web log has to be pre processed, integrated and transformed. As the World Wide Web is continuously and rapidly growing, it is necessary for the web miners to utilize intelligent tools in order to find, extract, filter and evaluate the desired information. The data pre-processing stage is the most important phase for investigation of the web user usage behaviour. To do this one must extract the only human user accesses from weblog data which is critical and complex. The web log is incremental in nature, thus conventional data pre-processing techniques were proved to be not suitable. Hence an extensive learning algorithm is required in order to get the desired information.This paper introduces an extensive research frame work capable of pre processing web log data completely and efficiently. The learning algorithm of proposed research frame work can separates human user and search engine accesses intelligently, with less time. In order to create suitable target data, the further essential tasks of pre-processing Data Cleansing, User Identification, Sessionization and Path Completion are designed collectively. The framework reduces the error rate and improves significant learning performance of the algorithm. The work ensures the goodness of split by using popular measures like Entropy and Gini index. This framework helps to investigate the web user usage behaviour efficiently. The experimental results proving this claim are given in this paper.
Reproducible cancer biomarker discovery in SELDI-TOF MS using different pre-processing algorithms.
Directory of Open Access Journals (Sweden)
Jinfeng Zou
Full Text Available BACKGROUND: There has been much interest in differentiating diseased and normal samples using biomarkers derived from mass spectrometry (MS studies. However, biomarker identification for specific diseases has been hindered by irreproducibility. Specifically, a peak profile extracted from a dataset for biomarker identification depends on a data pre-processing algorithm. Until now, no widely accepted agreement has been reached. RESULTS: In this paper, we investigated the consistency of biomarker identification using differentially expressed (DE peaks from peak profiles produced by three widely used average spectrum-dependent pre-processing algorithms based on SELDI-TOF MS data for prostate and breast cancers. Our results revealed two important factors that affect the consistency of DE peak identification using different algorithms. One factor is that some DE peaks selected from one peak profile were not detected as peaks in other profiles, and the second factor is that the statistical power of identifying DE peaks in large peak profiles with many peaks may be low due to the large scale of the tests and small number of samples. Furthermore, we demonstrated that the DE peak detection power in large profiles could be improved by the stratified false discovery rate (FDR control approach and that the reproducibility of DE peak detection could thereby be increased. CONCLUSIONS: Comparing and evaluating pre-processing algorithms in terms of reproducibility can elucidate the relationship among different algorithms and also help in selecting a pre-processing algorithm. The DE peaks selected from small peak profiles with few peaks for a dataset tend to be reproducibly detected in large peak profiles, which suggests that a suitable pre-processing algorithm should be able to produce peaks sufficient for identifying useful and reproducible biomarkers.
Institute of Scientific and Technical Information of China (English)
张明会
2014-01-01
the development of any branch of mathematics, in addition to the basic method of permeability and transport it must create mathematical science, must also have their own ideas and methods are unique, in educa⁃tion and teaching in how these thinking methods through inside, is also an essential teaching skills. In this paper, the point of view of teaching and learning focuses on the discussion of the construction and application of reverse thinking in the teaching of higher mathematics problem solving thinking mode.%任何一门数学分支的发展，除了它必须渗透和运数学科学创造的基本方法之外，还必须有自己所具特色的思想和方法。在教育教学中如何将这些思维方法贯穿进去，也是一种必不可少的教学技能。
Institute of Scientific and Technical Information of China (English)
陈美清
2012-01-01
在初中数学解题教学中,怎样培养学生的思维品质直接影响着教学的成败。笔者认为,在初中数学解题教学中,除了让学生熟练解题的一般步骤,学会解题的一些通法与利用认知理论做解题后反思外,还应让学生不断感受数学的思维过程,学到思维方法,培养思维品质,从而学会独立探索,有所发现,有所创新,以便更好地掌握和应用知识。思维品质是衡量数学思维质量的指标,它包括思维的广阔性、敏捷性、深刻性、批判性等。%In junior middle school mathematics problem-solving teaching, how to cultivate students＇ thinking qualities directly affects the success of teaching. Besides practcing general problem-solving steps, learning common problem-sovling methods and using cognitive theory to make reflections, students should constantly feel mathematical thinking process, learn thinking methods, cultivate thinking qualities so as to learn to independently explore, discover, innovate, grasp and apply knowledge. Thinking quality is one of indicators to measure quality of mathematical thinking, which includes the extensity, agility, profundity and criticalness of thinking.
Translations toward Connected Mathematics
Applebaum, Mark; Leikin, Roza
2010-01-01
The translation principle allows students to solve problems in different branches of mathematics and thus to develop connectedness in their mathematical knowledge. Successful application of the translation principle depends on the classroom mathematical norms for the development of discussions and the comparison of different solutions to one…
Combinatorial reasoning to solve problems
Coenen, Tom; Hof, Frits; Verhoef, Nellie
2016-01-01
This study reports combinatorial reasoning to solve problems. We observed the mathematical thinking of students aged 14-16. We study the variation of the students’ solution strategies in the context of emergent modelling. The results show that the students are tempted to begin the problem solving pr
Directory of Open Access Journals (Sweden)
Michalczyk J.
2016-09-01
Full Text Available The paper presents the results of numerical studies based on a mathematical model determined by the stress-strain state examination method. Numerical computations for two steel grades, namely H40 and C45, were made at similar strain and process rate parameters. As a result of the studies, the distribution of elastic and plastic zones was obtained, while the tube hollow drawing force was verified experimentally. The distribution of longitudinal, radial and circumferential stresses and, after the drawing operation, the distribution of residual stresses in the tube cross-section were also obtained.
Directory of Open Access Journals (Sweden)
Gülhiz Pilten
2016-01-01
Full Text Available The aim of this study was to determine the effect of mathematical writing activities on 3 rd grade students' mathematical problem solving and posing skills. Therefore this study was done by using quasi-experimental model with pretest-posttest control group. Research was conducted in 2014- 2015 Education Year Spring Semester. The study group of the research consists of totally 66 3rd grade students At the experimental group, the activities of 3rd grade mathematics curriculum and 3 rd grade mathematic text book are applied. In addition to these activities, mathematical writing activities put into application to the experimental group. However to the control group only the activities of 3rd grade mathematics curriculum and 3rd grade mathematic text book are applied. All groups' applications lasted for 8 weeks. As a result of this study, it was seen that, at the end of the experimental processes, there is a meaningful statistical difference between experiment group and control group, among problem solving and problem posing skills of students in experiment’s group favour. This result is supporting the relevant literature. Özet Bu araştırmanın amacı, matematiksel yazma etkinliklerinin, ilkokul 3. sınıf öğrencilerinin matematiksel problem çözme ve kurma becerileri üzerindeki etkilerini belirlemektir. Bu yönüyle çalışmada, ön test-son test kontrol gruplu deneme modeli kullanılmıştır. Çalışma 2014-2015 bahar yarıyılında gerçekleştirilmiş olup çalışma grubunu toplam 66 3. sınıf öğrencisi oluşturmaktadır. Deney grubunda deneysel işlem sürecinde ilköğretim matematik öğretim programında ve ders kitabında ön görülen etkinliklere ek olarak matematiksel yazma etkinlikleri gerçekleştirilmiştir. Kontrol grubunda ise 3. sınıf matematik programı ve ders kitabında yer verilen etkinliklere bağlı kalınmıştır. Uygulamalar 8 hafta sürmüştür. Araştırma sonuçları, deneysel işlem s
PRE-Processing for Video Coduing with Rate-Distortion Optimization Decision
Institute of Scientific and Technical Information of China (English)
QI Yi; HUANG Yong-gui; QI Hong-gang
2006-01-01
This paper proposes an adaptive video pre-processing algorithm for video coding. This algorithm works on the original image before intra- or inter-prediction. It adopts Gaussian filter to remove noise and insignificant features existing in images of video. Detection and restoration of edges are followed to restore the edges which are excessively filtered out in filtered images. Rate-Distortion Optimization (RDO) is employed to decide adaptively whether a processed block or a unprocessed block is coded into bit-streams doe more efficient coding. Our experiment results show that the algorithm achieves good coding performances on both subjective and objective aspects. In addition, the proposed pre-processing algorithm is transparent to decoder, and thus can be compliant with any video coding standards without modifying the decoder.
Radar signal pre-processing to suppress surface bounce and multipath
Paglieroni, David W; Mast, Jeffrey E; Beer, N. Reginald
2013-12-31
A method and system for detecting the presence of subsurface objects within a medium is provided. In some embodiments, the imaging and detection system operates in a multistatic mode to collect radar return signals generated by an array of transceiver antenna pairs that is positioned across the surface and that travels down the surface. The imaging and detection system pre-processes that return signal to suppress certain undesirable effects. The imaging and detection system then generates synthetic aperture radar images from real aperture radar images generated from the pre-processed return signal. The imaging and detection system then post-processes the synthetic aperture radar images to improve detection of subsurface objects. The imaging and detection system identifies peaks in the energy levels of the post-processed image frame, which indicates the presence of a subsurface object.
The Combined Effect of Filters in ECG Signals for Pre-Processing
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Isha V. Upganlawar
2014-05-01
Full Text Available The ECG signal is abruptly changing and continuous in nature. The heart disease such as paroxysmal of heart, arrhythmia diagnosing, are related with the intelligent health care decision this ECG signal need to be pre-process accurately for further action on it such as extracting the features, wavelet decomposition, distribution of QRS complexes in ECG recordings and related information such as heart rate and RR interval, classification of the signal by using various classifiers etc. Filters plays very important role in analyzing the low frequency components in ECG signal. The biomedical signals are of low frequency, the removal of power line interference and baseline wander is a very important step at the pre-processing stage of ECG. In these paper we deal with the study of Median filtering and FIR (Finite Impulse Responsefiltering of ECG signals under noisy condition
关于高考数学选择题解题技巧的探讨%Exploration on the Problem-solving Skills of the Choices in Entrance Mathematics
Institute of Scientific and Technical Information of China (English)
林培国
2011-01-01
The main entrance mathematics multiple-choice basic knowledge test the candidate＇s understanding and grasp of the basic problem-solving skills,proficiency with the use of basic computing accuracy and speed of thinking and other aspects of comprehensive and rigorous content,so the candidates should have the necessary solution of choice problem skills,problem-solving in order to improve the accuracy and speed,make sure to obtain high scores on multiple-choice questions.This multiple-choice math college entrance examination conducted by a brief introduction,and then summed up the choice of college entrance math problem-solving skills,and over the years the college entrance examination multiple choice math questions,for example,or simulation of multiple-choice math problem-solving skills in the entrance depth in the concrete application discussed.%高考数学选择题主要考察考生基础知识的理解与掌握、基本解题技能的熟练与运用、基本计算的准确与速度、思考问题的全面与严谨等方面内容,所以,考生应掌握选择题必要的解题技巧,以此提高解题的准确性和速度,确保在选择题上取得高分。本文通过对高考数学选择题进行简要介绍,进而总结出高考数学选择的解题技巧,并以历年高考数学选择题或模拟试题为例,对解题技巧在高考数学选择题中的具体运用进行深入探讨。
Modern mathematics made simple
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
The Combined Effect of Filters in ECG Signals for Pre-Processing
Isha V. Upganlawar; Harshal Chowhan
2014-01-01
The ECG signal is abruptly changing and continuous in nature. The heart disease such as paroxysmal of heart, arrhythmia diagnosing, are related with the intelligent health care decision this ECG signal need to be pre-process accurately for further action on it such as extracting the features, wavelet decomposition, distribution of QRS complexes in ECG recordings and related information such as heart rate and RR interval, classification of the signal by using various classifiers etc. Filters p...
Pre-Processing and Re-Weighting Jet Images with Different Substructure Variables
Huynh, Lynn
2016-01-01
This work is an extension of Monte Carlo simulation based studies in tagging boosted, hadronically decaying W bosons at a center of mass energy of s = 13 TeV. Two pre-processing techniques used with jet images, translation and rotation, are first examined. The generated jet images for W signal jets and QCD background jets are then rescaled and weighted with five different substructure variables for visual comparison.
PepsNMR for the 1H-NMR metabolomic data pre-processing
Martin, Manon; Legat, Benoît; Leenders, Justine; Vanwinsberghe, Julien; Rousseau, Réjane; Boulanger, Bruno; Eilers, Paul H. C.; De Tullio, Pascal; Govaerts, Bernadette
2017-01-01
In the analysis of complex biological samples, control over experimental design and data acquisition procedures cannot ensure alone well-conditioned 1H-NMR spectra with maximal information recovery for data analysis. A third major element affects the accuracy and robustness of the results: the data pre-processing/pre-treatment for which not enough attention is usually devoted, in particular in the metabolomic studies. The usual approach is to use proprietary software provided by the analytica...
Pre-Processing Noise Cross-Correlations with Equalizing the Network Covariance Matrix Eigen-Spectrum
Seydoux, L.; de Rosny, J.; Shapiro, N.
2016-12-01
Theoretically, the extraction of Green functions from noise cross-correlation requires the ambient seismic wavefield to be generated by uncorrelated sources evenly distributed in the medium. Yet, this condition is often not verified. Strong events such as earthquakes often produce highly coherent transient signals. Also, the microseismic noise is generated at specific places on the Earth's surface with source regions often very localized in space. Different localized and persistent seismic sources may contaminate the cross-correlations of continuous records resulting in spurious arrivals or asymmetry and, finally, in biased travel-time measurements. Pre-processing techniques therefore must be applied to the seismic data in order to reduce the effect of noise anisotropy and the influence of strong localized events. Here we describe a pre-processing approach that uses the covariance matrix computed from signals recorded by a network of seismographs. We extend the widely used time and spectral equalization pre-processing to the equalization of the covariance matrix spectrum (i.e., its ordered eigenvalues). This approach can be considered as a spatial equalization. This method allows us to correct for the wavefield anisotropy in two ways: (1) the influence of strong directive sources is substantially attenuated, and (2) the weakly excited modes are reinforced, allowing to partially recover the conditions required for the Green's function retrieval. We also present an eigenvector-based spatial filter used to distinguish between surface and body waves. This last filter is used together with the equalization of the eigenvalue spectrum. We simulate two-dimensional wavefield in a heterogeneous medium with strongly dominating source. We show that our method greatly improves the travel-time measurements obtained from the inter-station cross-correlation functions. Also, we apply the developed method to the USArray data and pre-process the continuous records strongly influenced
Hyperspectral imaging in medicine: image pre-processing problems and solutions in Matlab.
Koprowski, Robert
2015-11-01
The paper presents problems and solutions related to hyperspectral image pre-processing. New methods of preliminary image analysis are proposed. The paper shows problems occurring in Matlab when trying to analyse this type of images. Moreover, new methods are discussed which provide the source code in Matlab that can be used in practice without any licensing restrictions. The proposed application and sample result of hyperspectral image analysis.
Fernandes, José Antonio
2013-02-01
A multi-species approach to fisheries management requires taking into account the interactions between species in order to improve recruitment forecasting of the fish species. Recent advances in Bayesian networks direct the learning of models with several interrelated variables to be forecasted simultaneously. These models are known as multi-dimensional Bayesian network classifiers (MDBNs). Pre-processing steps are critical for the posterior learning of the model in these kinds of domains. Therefore, in the present study, a set of \\'state-of-the-art\\' uni-dimensional pre-processing methods, within the categories of missing data imputation, feature discretization and feature subset selection, are adapted to be used with MDBNs. A framework that includes the proposed multi-dimensional supervised pre-processing methods, coupled with a MDBN classifier, is tested with synthetic datasets and the real domain of fish recruitment forecasting. The correctly forecasting of three fish species (anchovy, sardine and hake) simultaneously is doubled (from 17.3% to 29.5%) using the multi-dimensional approach in comparison to mono-species models. The probability assessments also show high improvement reducing the average error (estimated by means of Brier score) from 0.35 to 0.27. Finally, these differences are superior to the forecasting of species by pairs. © 2012 Elsevier Ltd.
Data pre-processing for web log mining: Case study of commercial bank website usage analysis
Directory of Open Access Journals (Sweden)
Jozef Kapusta
2013-01-01
Full Text Available We use data cleaning, integration, reduction and data conversion methods in the pre-processing level of data analysis. Data processing techniques improve the overall quality of the patterns mined. The paper describes using of standard pre-processing methods for preparing data of the commercial bank website in the form of the log file obtained from the web server. Data cleaning, as the simplest step of data pre-processing, is non–trivial as the analysed content is highly specific. We had to deal with the problem of frequent changes of the content and even frequent changes of the structure. Regular changes in the structure make use of the sitemap impossible. We presented approaches how to deal with this problem. We were able to create the sitemap dynamically just based on the content of the log file. In this case study, we also examined just the one part of the website over the standard analysis of an entire website, as we did not have access to all log files for the security reason. As the result, the traditional practices had to be adapted for this special case. Analysing just the small fraction of the website resulted in the short session time of regular visitors. We were not able to use recommended methods to determine the optimal value of session time. Therefore, we proposed new methods based on outliers identification for raising the accuracy of the session length in this paper.
Energy Technology Data Exchange (ETDEWEB)
Fromm, Catherine [SLAC National Accelerator Lab., Menlo Park, CA (United States)
2015-08-20
Ptychography is an advanced diffraction based imaging technique that can achieve resolution of 5nm and below. It is done by scanning a sample through a beam of focused x-rays using discrete yet overlapping scan steps. Scattering data is collected on a CCD camera, and the phase of the scattered light is reconstructed with sophisticated iterative algorithms. Because the experimental setup is similar, ptychography setups can be created by retrofitting existing STXM beam lines with new hardware. The other challenge comes in the reconstruction of the collected scattering images. Scattering data must be adjusted and packaged with experimental parameters to calibrate the reconstruction software. The necessary pre-processing of data prior to reconstruction is unique to each beamline setup, and even the optical alignments used on that particular day. Pre-processing software must be developed to be flexible and efficient in order to allow experiments appropriate control and freedom in the analysis of their hard-won data. This paper will describe the implementation of pre-processing software which successfully connects data collection steps to reconstruction steps, letting the user accomplish accurate and reliable ptychography.
Green, George
2005-01-01
An almost entirely self-taught mathematical genius, George Green (1793 -1841) is best known for Green's theorem, which is used in almost all computer codes that solve partial differential equations. He also published influential essays, or papers, in the fields of hydrodynamics, electricity, and magnetism. This collection comprises his most significant works.The first paper, ""An Essay on the Application of Mathematical Analysis to the Theories of Electricity and Magnetism,"" which is also the longest and perhaps the most Important, appeared In 1828. It introduced the term potential as desig
Some Applications of Algebraic System Solving
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…
A Mathematics Software Database Update.
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)
Kop, Reinier; Hoogendoorn, Mark; Teije, Annette Ten; Büchner, Frederike L; Slottje, Pauline; Moons, Leon M G; Numans, Mattijs E
2016-01-01
Over the past years, research utilizing routine care data extracted from Electronic Medical Records (EMRs) has increased tremendously. Yet there are no straightforward, standardized strategies for pre-processing these data. We propose a dedicated medical pre-processing pipeline aimed at taking on
Reduce Skills Teaching in the Mathematics Class.
Devlin, Keith
1999-01-01
Mathematics is much more than a collection of procedures for solving problems. Argues that the primary goal in the mathematics class is to create an awareness of the what, the how, and the why of mathematics. (ASK)
Institute of Scientific and Technical Information of China (English)
卢佳; 周丽清; 俞佳
2012-01-01
Objective: To explore the way that how children with mathematics disabilities solve arithmatic word problem- Methods: An eye movement test was administered to 32 students from fifth and sixth grade. The subjects were divided into three group: MD group, MDRD group and control group. The degree of difficulty in the teat had two level: easy and normal. Results; ①There were significant differences between easy level and normal level in both the performance of solving arithmetic word problems and eye movement indicator. ②The MD group's performance was near to the normal group and better than the MDRD group signigicantly in observation length, pupil diameter, fixation duration and fixation duration in AOL Conclusion; MD children is the lack of mathematical ability, the MDRD children is the lack of reading ability.%目的:探查数学障碍儿童解答应用题的规律.方法:采用自编数学应用题(难度分简单、一般)对小学5、6年级学生(数学障碍组、数学障碍阅读障碍共生组和平常组)进行眼动实验.结果:①无论是列式成绩还是眼动指标,不同难度差异显著.②MD儿童在观察时间、瞳孔直径、注视点持续时间和兴趣区总注视时间指标上接近平常儿童组,并显著好于MDRD儿童.结论:MD儿童主要是数学能力不足,MDRD儿童主要是阅读能力不足.
Directory of Open Access Journals (Sweden)
Jaime A Irahola
2007-01-01
Full Text Available Se presenta una aplicación para formular y resolver modelos matemáticos de sistemas de evaporación multiefecto. La aplicación permite que cualquier usuario, sin ser un experto en optimización, simulación e ingeniería química pueda simular, optimizar, hacer re-ingeniería o sintetizar un sistema de evaporación multiefecto. La información del problema se ingresa por medio de tablas o "flowsheet" y la aplicación formula el modelo y lo resuelve usando un optimizador comercial. En el modelo matemático se considera el numero de los efectos, el condensador y un calentador/enfriador del producto final. Además, el uso del software elimina la necesidad de verificar el modelo, permite modelar de manera rápida y confiable, disminuyendo considerablemente el tiempo total de análisis desde la especificación del modelo hasta obtener el resultado óptimo.An application to formulate and to solve mathematical models of multieffect evaporation systems Is presented. The application allows that any user, without being an expert in optimization, simulation and chemical engineering can simulate, optimize, make re-engineering or synthesize a multieffect evaporation system. The information of the problem is entered by means of tables or flowsheet and the application formulates the model and it solves it using a commercial optimizer. In the mathematical model the number of effects, the condenser and a heater/cooler for the final product, are considered. In addition, the use of software eliminates the necessity of verifying the model, it allows to model in a fast and reliable way, considerably reducing the time consumed in the analysis from the specification of the model until the optimal result is obtained.
高等数学几种解题思维的探究%Exploration on Several Problem solving Thinking of Advanced Mathematics
Institute of Scientific and Technical Information of China (English)
詹玉; 徐肖丽
2015-01-01
The thinking ability is useful in all aspects of math teaching.For example,the inductive thinking,analogical thinking,divergent thinking and reverse thinking can be applied and manifested in the conditions of one question with multi solutions or one question with multi variations.In this paper,certain methods of thinking ability will be described through some specific examples in advance mathematics.%思维的培养应体现在数学教学的各个方面，一题多解、一题多变是归纳思维、类比思维、发散思维、逆向思维在实际教学中的具体应用和表现形式。通过高等数学的一些基本实例，具体阐述了培养学生思维的方法与途径。
Ebrahimi, Ahmad; Kia, Reza; Komijan, Alireza Rashidi
2016-01-01
In this article, a novel integrated mixed-integer nonlinear programming model is presented for designing a cellular manufacturing system (CMS) considering machine layout and part scheduling problems simultaneously as interrelated decisions. The integrated CMS model is formulated to incorporate several design features including part due date, material handling time, operation sequence, processing time, an intra-cell layout of unequal-area facilities, and part scheduling. The objective function is to minimize makespan, tardiness penalties, and material handling costs of inter-cell and intra-cell movements. Two numerical examples are solved by the Lingo software to illustrate the results obtained by the incorporated features. In order to assess the effects and importance of integration of machine layout and part scheduling in designing a CMS, two approaches, sequentially and concurrent are investigated and the improvement resulted from a concurrent approach is revealed. Also, due to the NP-hardness of the integrated model, an efficient genetic algorithm is designed. As a consequence, computational results of this study indicate that the best solutions found by GA are better than the solutions found by B&B in much less time for both sequential and concurrent approaches. Moreover, the comparisons between the objective function values (OFVs) obtained by sequential and concurrent approaches demonstrate that the OFV improvement is averagely around 17 % by GA and 14 % by B&B.
EARLINET Single Calculus Chain - technical - Part 1: Pre-processing of raw lidar data
D'Amico, Giuseppe; Amodeo, Aldo; Mattis, Ina; Freudenthaler, Volker; Pappalardo, Gelsomina
2016-02-01
In this paper we describe an automatic tool for the pre-processing of aerosol lidar data called ELPP (EARLINET Lidar Pre-Processor). It is one of two calculus modules of the EARLINET Single Calculus Chain (SCC), the automatic tool for the analysis of EARLINET data. ELPP is an open source module that executes instrumental corrections and data handling of the raw lidar signals, making the lidar data ready to be processed by the optical retrieval algorithms. According to the specific lidar configuration, ELPP automatically performs dead-time correction, atmospheric and electronic background subtraction, gluing of lidar signals, and trigger-delay correction. Moreover, the signal-to-noise ratio of the pre-processed signals can be improved by means of configurable time integration of the raw signals and/or spatial smoothing. ELPP delivers the statistical uncertainties of the final products by means of error propagation or Monte Carlo simulations. During the development of ELPP, particular attention has been payed to make the tool flexible enough to handle all lidar configurations currently used within the EARLINET community. Moreover, it has been designed in a modular way to allow an easy extension to lidar configurations not yet implemented. The primary goal of ELPP is to enable the application of quality-assured procedures in the lidar data analysis starting from the raw lidar data. This provides the added value of full traceability of each delivered lidar product. Several tests have been performed to check the proper functioning of ELPP. The whole SCC has been tested with the same synthetic data sets, which were used for the EARLINET algorithm inter-comparison exercise. ELPP has been successfully employed for the automatic near-real-time pre-processing of the raw lidar data measured during several EARLINET inter-comparison campaigns as well as during intense field campaigns.
EARLINET Single Calculus Chain – technical – Part 1: Pre-processing of raw lidar data
Directory of Open Access Journals (Sweden)
G. D'Amico
2015-10-01
Full Text Available In this paper we describe an automatic tool for the pre-processing of lidar data called ELPP (EARLINET Lidar Pre-Processor. It is one of two calculus modules of the EARLINET Single Calculus Chain (SCC, the automatic tool for the analysis of EARLINET data. The ELPP is an open source module that executes instrumental corrections and data handling of the raw lidar signals, making the lidar data ready to be processed by the optical retrieval algorithms. According to the specific lidar configuration, the ELPP automatically performs dead-time correction, atmospheric and electronic background subtraction, gluing of lidar signals, and trigger-delay correction. Moreover, the signal-to-noise ratio of the pre-processed signals can be improved by means of configurable time integration of the raw signals and/or spatial smoothing. The ELPP delivers the statistical uncertainties of the final products by means of error propagation or Monte Carlo simulations. During the development of the ELPP module, particular attention has been payed to make the tool flexible enough to handle all lidar configurations currently used within the EARLINET community. Moreover, it has been designed in a modular way to allow an easy extension to lidar configurations not yet implemented. The primary goal of the ELPP module is to enable the application of quality-assured procedures in the lidar data analysis starting from the raw lidar data. This provides the added value of full traceability of each delivered lidar product. Several tests have been performed to check the proper functioning of the ELPP module. The whole SCC has been tested with the same synthetic data sets, which were used for the EARLINET algorithm inter-comparison exercise. The ELPP module has been successfully employed for the automatic near-real-time pre-processing of the raw lidar data measured during several EARLINET inter-comparison campaigns as well as during intense field campaigns.
A Multi-channel Pre-processing Circuit for Signals from Thermocouple/Thermister
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
In this paper,a new developed multi-channel pre-processing circuit for signals from temperature sensor was introduced in brief.This circuit was developed to collect and amplify the signals from temperature sensor.This is a universal circuit.It can be used to process the signals from thermocouples and also used to process signals from thermistors.This circuit was mounted in a standard box(440W×405D×125H mm)as an instrument.The
Applying Cooperative Techniques in Teaching Problem Solving
Barczi, Krisztina
2013-01-01
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…
Developing Creativity through Collaborative Problem Solving
Albert, Lillie R.; Kim, Rina
2013-01-01
This paper discusses an alternative approach for developing problem solving experiences for students. The major argument is that students can develop their creativity by engaging in collaborative problem solving activities in which they apply a variety of mathematical methods creatively to solve problems. The argument is supported by: considering…
Creating Games from Mathematical Problems
Pinter, Klara
2011-01-01
The emphasis on problem solving and problem solving courses has become a standard staple of most teacher preparation programs in mathematics. While opinions differ on whether problem solving should be integrated throughout the preparatory courses or teachers should also have a dedicated course for it, everybody agrees that problem solving skills…
Directory of Open Access Journals (Sweden)
Miri eMichaeli
2012-12-01
Full Text Available High throughput sequencing (HTS yields tens of thousands to millions of sequences that require a large amount of pre-processing work to clean various artifacts. Such cleaning cannot be performed manually. Existing programs are not suitable for immunoglobulin (Ig genes, which are variable and often highly mutated. This paper describes Ig-HTS-Cleaner (Ig High Throughput Sequencing Cleaner, a program containing a simple cleaning procedure that successfully deals with pre-processing of Ig sequences derived from HTS, and Ig-Indel-Identifier (Ig Insertion – Deletion Identifier, a program for identifying legitimate and artifact insertions and/or deletions (indels. Our programs were designed for analyzing Ig gene sequences obtained by 454 sequencing, but they are applicable to all types of sequences and sequencing platforms. Ig-HTS-Cleaner and Ig-Indel-Identifier have been implemented in Java and saved as executable JAR files, supported on Linux and MS Windows. No special requirements are needed in order to run the programs, except for correctly constructing the input files as explained in the text. The programs' performance has been tested and validated on real and simulated data sets.
Penggunaan Web Crawler Untuk Menghimpun Tweets dengan Metode Pre-Processing Text Mining
Directory of Open Access Journals (Sweden)
Bayu Rima Aditya
2015-11-01
Full Text Available Saat ini jumlah data di media sosial sudah terbilang sangat besar, namun jumlah data tersebut masih belum banyak dimanfaatkan atau diolah untuk menjadi sesuatu yang bernilai guna, salah satunya adalah tweets pada media sosial twitter. Paper ini menguraikan hasil penggunaan engine web crawel menggunakan metode pre-processing text mining. Penggunaan engine web crawel itu sendiri bertujuan untuk menghimpun tweets melalui API twitter sebagai data teks tidak terstruktur yang kemudian direpresentasikan kembali kedalam bentuk web. Sedangkan penggunaan metode pre-processing bertujuan untuk menyaring tweets melalui tiga tahap, yaitu cleansing, case folding, dan parsing. Aplikasi yang dirancang pada penelitian ini menggunakan metode pengembangan perangkat lunak yaitu model waterfall dan diimplementasikan dengan bahasa pemrograman PHP. Sedangkan untuk pengujiannya menggunakan black box testing untuk memeriksa apakah hasil perancangan sudah dapat berjalan sesuai dengan harapan atau belum. Hasil dari penelitian ini adalah berupa aplikasi yang dapat mengubah tweets yang telah dihimpun menjadi data yang siap diolah lebih lanjut sesuai dengan kebutuhan user berdasarkan kata kunci dan tanggal pencarian. Hal ini dilakukan karena dari beberapa penelitian terkait terlihat bahwa data pada media sosial khususnya twitter saat ini menjadi tujuan perusahaan atau instansi untuk memahami opini masyarakat
Directory of Open Access Journals (Sweden)
Sutikno Sutikno
2010-08-01
Full Text Available One of the climate models used to predict the climatic conditions is Global Circulation Models (GCM. GCM is a computer-based model that consists of different equations. It uses numerical and deterministic equation which follows the physics rules. GCM is a main tool to predict climate and weather, also it uses as primary information source to review the climate change effect. Statistical Downscaling (SD technique is used to bridge the large-scale GCM with a small scale (the study area. GCM data is spatial and temporal data most likely to occur where the spatial correlation between different data on the grid in a single domain. Multicollinearity problems require the need for pre-processing of variable data X. Continuum Regression (CR and pre-processing with Principal Component Analysis (PCA methods is an alternative to SD modelling. CR is one method which was developed by Stone and Brooks (1990. This method is a generalization from Ordinary Least Square (OLS, Principal Component Regression (PCR and Partial Least Square method (PLS methods, used to overcome multicollinearity problems. Data processing for the station in Ambon, Pontianak, Losarang, Indramayu and Yuntinyuat show that the RMSEP values and R2 predict in the domain 8x8 and 12x12 by uses CR method produces results better than by PCR and PLS.
Introductory discrete mathematics
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
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.…
Encouraging Sixth-Grade Students' Problem-Solving Performance by Teaching through Problem Solving
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…
The Problem-Solving Approach in the Teaching of Number Theory
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…
Advanced Mathematical Thinking in a Technological Workplace.
Magajna, Zlatan; Monaghan, John
2003-01-01
Examines the use of mathematics in a computer-aided design and manufacturing setting, whether this mathematics is related to school mathematics, how technicians understand this mathematics, and the role of technology in the technicians' mathematics-related problem solving activities. Focuses on technician's calculations of the interval volume of…
Best Known Problem Solving Strategies in "High-Stakes" Assessments
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.…
Solving Optimal Timing Problems Elegantly
Todorova, Tamara
2013-01-01
Few textbooks in mathematical economics cover optimal timing problems. Those which cover them do it scantly or in a rather clumsy way, making it hard for students to understand and apply the concept of optimal time in new contexts. Discussing the plentiful illustrations of optimal timing problems, we present an elegant and simple method of solving them. Whether the present value function is exponential or logarithmic, a convenient way to solve it is to convert the base to the exponential numb...
Sweller, John; Clark, Richard; Kirschner, Paul A.
2012-01-01
Sweller, J., Clark, R. E., & Kirschner, P. A. (2012). Ensinar capacidades gerais de resolução de problemas não é uma substituição, nem um complemento viável, a ensinar matemática [Teaching general problem-solving skills is not a substitute for, or a viable addition to, teaching mathematics]. Gazeta
Sweller, John; Clark, Richard; Kirschner, Paul A.
2012-01-01
Sweller, J., Clark, R. E., & Kirschner, P. A. (2012). Ensinar capacidades gerais de resolução de problemas não é uma substituição, nem um complemento viável, a ensinar matemática [Teaching general problem-solving skills is not a substitute for, or a viable addition to, teaching mathematics]. Gazeta
HEp-2 Cell Classification: The Role of Gaussian Scale Space Theory as A Pre-processing Approach
Qi, Xianbiao; Zhao, Guoying; Chen, Jie; Pietikäinen, Matti
2015-01-01
\\textit{Indirect Immunofluorescence Imaging of Human Epithelial Type 2} (HEp-2) cells is an effective way to identify the presence of Anti-Nuclear Antibody (ANA). Most existing works on HEp-2 cell classification mainly focus on feature extraction, feature encoding and classifier design. Very few efforts have been devoted to study the importance of the pre-processing techniques. In this paper, we analyze the importance of the pre-processing, and investigate the role of Gaussian Scale Space (GS...
Mathematical Graphic Organizers
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…
Discrete Mathematics Re "Tooled."
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)
Mathematics across the Curriculum.
Kleiman, Glenn M.
1991-01-01
Except for its relationship to science, mathematics is the forgotten cousin in interdisciplinary teaching and learning. In the Journeys in Mathematics project, teachers engage children in imaginative activities that inspire them to identify patterns and relationships, solve problems, and communicate accurately, using Jonathan Swift's…
Mathematical model and solving algorithm for the lot planning of slab hot rolling%板坯热轧批量计划数学模型及求解算法
Institute of Scientific and Technical Information of China (English)
杨业建; 姜泽毅; 张欣欣
2012-01-01
According to the technical demand of hot-rolling production,the lot planning of slab hot rolling was summed up as a multiple traveling salesperson problem with uncertain traveling salesman number.A production scheduling mathematical model considering the energy consumption of the heating section was proposed,with minimizing the production cost as the primary objective and optimizing the product quality as the secondary objective.A hybrid algorithm based on the genetic algorithm and the tabu search algorithm was proposed to solve the problem.Simulation results of practical data show that the mathematical model fully meets the demand of hot-rolling production.On the basis of the optimal number of rolling units,the transport time is shortened,the hot charging rate is increased and the product quality is optimized.Compared with a human-computer method,the results from the mathematical model and hybrid algorithm have a better performance of high production and energy-saving efficiency.%根据热轧工艺特点将板坯热轧批量计划编制问题归结为不确定旅行商数的多旅行商问题,建立了以生产成本最小化和产品质量最优化为主次目标且考虑加热区段能耗的生产调度数学模型,并采用遗传算法和禁忌搜索相结合的混合算法进行求解.基于实际生产数据的计算结果表明：该模型充分满足了现场热轧批量计划编制的需求,在轧制单元数最优的基础上,缩短了传搁时间,提高了热送热装率,优化了产品质量.与人机结合方式相比,本文模型的计算结果体现了更好的高产和节能效果.
Institute of Scientific and Technical Information of China (English)
吴晓超
2015-01-01
Analyzing and solving mathematical problems is the key and also difficult point in low grade mathematics learning, and learning mathematics by correcting the errors is an effective way to im—prove students, ability of analyzing and solving problems. From the perspective of mathematical problem solving cognitive mode, this article analyz the possible reasons that may lead to errors in low grade stu—dents, mathematics learning: neglecting meanings of mathematical notations and thus being unclear about the target, having difficuly in identifying hybrid concept model, interference of working memory on prob—lem solving monitoring, and lack of transfer ability in problem solving. Therefore, some strategies in teach—ing are suggested as follows: emphasizing meanings and thus help students realizing the importance of mathematical notations, usage of body movements to help identifying of concepts, improvement of stu—dents, transfer ability based on effective communication and reflection, encouraging hands_on exercises to improve monitoring in problem solving, and cultivating good habits in mathematical exercises.%分析和解决数学问题是低年级数学学习的重点和难点，通过纠正错题学习数学是提高学生分析和解决问题能力的有效途径。从数学问题解决认知模式的角度分析，可能导致低年级学生解题错误的原因有：忽略符号含义，目标状态不明确；混合概念模型识别困难；工作记忆干扰解题监控；欠缺解题迁移能力。因此，在教学中要明确符号含义，建立符号意识；以身体动作帮助概念识别；用有效交流与反思促进解题迁移；通过动手操作增强解题过程监控并培养良好的做题习惯。
Problem Solving: Polya's Heuristic Applied to Psychological Research.
Damarin, Suzanne K.
Using the "How to Solve It" list developed by Polya as a vehicle of comparison, research findings and key concepts from the psychological study of problem solving are applied to mathematical problem solving. Hypotheses concerning the interpretation of psychological phenomena for mathematical problem situations are explored. Several areas…
International Mathematical Internet Olympiad
Directory of Open Access Journals (Sweden)
Alexander Domoshnitsky
2012-10-01
Full Text Available Modern Internet technologies open new possibilities in wide spectrum of traditional methods used in mathematical education. One of the areas, where these technologies can be efficiently used, is an organization of mathematical competitions. Contestants can stay at their schools or universities and try to solve as many mathematical problems as possible and then submit their solutions through Internet. Simple Internet technologies supply audio and video connection between participants and organizers.
Directory of Open Access Journals (Sweden)
Benish Fida
2015-09-01
Full Text Available Inertial sensors are increasingly being used to recognize and classify physical activities in a variety of applications. For monitoring and fitness applications, it is crucial to develop methods able to segment each activity cycle, e.g., a gait cycle, so that the successive classification step may be more accurate. To increase detection accuracy, pre-processing is often used, with a concurrent increase in computational cost. In this paper, the effect of pre-processing operations on the detection and classification of locomotion activities was investigated, to check whether the presence of pre-processing significantly contributes to an increase in accuracy. The pre-processing stages evaluated in this study were inclination correction and de-noising. Level walking, step ascending, descending and running were monitored by using a shank-mounted inertial sensor. Raw and filtered segments, obtained from a modified version of a rule-based gait detection algorithm optimized for sequential processing, were processed to extract time and frequency-based features for physical activity classification through a support vector machine classifier. The proposed method accurately detected >99% gait cycles from raw data and produced >98% accuracy on these segmented gait cycles. Pre-processing did not substantially increase classification accuracy, thus highlighting the possibility of reducing the amount of pre-processing for real-time applications.
Ilhan KARATAS; 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 educatingstudents as efficient problem solvers is an important role of mathematics education. Problem solving skill is the centre of mathematics curriculum. Students’ gaining of that skill in school mathematics is closely related with the learning environment to beformed and the roles given to the students....
From Voids to Coma: the prevalence of pre-processing in the local Universe
Cybulski, Ryan; Fazio, Giovanni G; Gutermuth, Robert A
2014-01-01
We examine the effects of pre-processing across the Coma Supercluster, including 3505 galaxies over 500 sq deg, by quantifying the degree to which star-forming (SF) activity is quenched as a function of environment. We characterise environment using the complementary techniques of Voronoi Tessellation, to measure the density field, and the Minimal Spanning Tree, to define continuous structures, and so we measure SF activity as a function of local density and the type of environment (cluster, group, filament, and void), and quantify the degree to which environment contributes to quenching of SF activity. Our sample covers over two orders of magnitude in stellar mass (10^8.5 to 10^11 Msun), and consequently we trace the effects of environment on SF activity for dwarf and massive galaxies, distinguishing so-called "mass quenching" from "environment quenching". Environmentally-driven quenching of SF activity, measured relative to the void galaxies, occurs to progressively greater degrees in filaments, groups, and...
Rinkel, Jean; Gerfault, Laurent; Estève, François; Dinten, Jean-Marc
2006-03-01
In order to obtain accurate quantitative results, flat panel detectors require specific calibration and correction of acquisitions. Main artefacts are due to bad pixels, variations of photodiodes characteristics and inhomogeneity of X-rays sensitivity of the scintillator layer. Other limitations for quantification are the non-linearity of the detector due to charge trapping in the transistors and the scattering generated inside the detector, called detector scattering. Based on physical models of artefacts generation, this paper presents an unified framework for the calibration and correction of these artefacts. The following specific algorithms have been developed to correct them. A new method for correction of deviation to linearity is based on the comparison between experimental and simulated data. A method of detector scattering correction is performed in two steps: off-line characterization of detector scattering by considering its spatial distribution through a convolution model and on-line correction based on a deconvolution approach. Radiographic results on an anthropomorphic thorax phantom imaged with a flat panel detector, that convert X-rays into visible light using scintillator coupled to an amorphous silicon transistor frame for photons to electrons conversion, demonstrate that experimental X-rays attenuation images are significantly improved qualitatively and quantitatively by applying non-linearity correction and detector scattering correction. Results obtained on tomographic reconstructions from pre-processed acquisitions of the phantom are in very good agreement with expected attenuation coefficients values obtained with a multi-slice CT scanner. Thus, this paper demonstrates the efficiency of the proposed pre-processings to perform accurate quantification on radiographies and tomographies.
Pre-processing ambient noise cross-correlations with equalizing the covariance matrix eigenspectrum
Seydoux, Léonard; de Rosny, Julien; Shapiro, Nikolai M.
2017-09-01
Passive imaging techniques from ambient seismic noise requires a nearly isotropic distribution of the noise sources in order to ensure reliable traveltime measurements between seismic stations. However, real ambient seismic noise often partially fulfils this condition. It is generated in preferential areas (in deep ocean or near continental shores), and some highly coherent pulse-like signals may be present in the data such as those generated by earthquakes. Several pre-processing techniques have been developed in order to attenuate the directional and deterministic behaviour of this real ambient noise. Most of them are applied to individual seismograms before cross-correlation computation. The most widely used techniques are the spectral whitening and temporal smoothing of the individual seismic traces. We here propose an additional pre-processing to be used together with the classical ones, which is based on the spatial analysis of the seismic wavefield. We compute the cross-spectra between all available stations pairs in spectral domain, leading to the data covariance matrix. We apply a one-bit normalization to the covariance matrix eigenspectrum before extracting the cross-correlations in the time domain. The efficiency of the method is shown with several numerical tests. We apply the method to the data collected by the USArray, when the M8.8 Maule earthquake occurred on 2010 February 27. The method shows a clear improvement compared with the classical equalization to attenuate the highly energetic and coherent waves incoming from the earthquake, and allows to perform reliable traveltime measurement even in the presence of the earthquake.
Image pre-processing method for near-wall PIV measurements over moving curved interfaces
Jia, L. C.; Zhu, Y. D.; Jia, Y. X.; Yuan, H. J.; Lee, C. B.
2017-03-01
PIV measurements near a moving interface are always difficult. This paper presents a PIV image pre-processing method that returns high spatial resolution velocity profiles near the interface. Instead of re-shaping or re-orientating the interrogation windows, interface tracking and an image transformation are used to stretch the particle image strips near a curved interface into rectangles. Then the adaptive structured interrogation windows can be arranged at specified distances from the interface. Synthetic particles are also added into the solid region to minimize interfacial effects and to restrict particles on both sides of the interface. Since a high spatial resolution is only required in high velocity gradient region, adaptive meshing and stretching of the image strips in the normal direction is used to improve the cross-correlation signal-to-noise ratio (SN) by reducing the velocity difference and the particle image distortion within the interrogation window. A two dimensional Gaussian fit is used to compensate for the effects of stretching particle images. The working hypothesis is that fluid motion near the interface is ‘quasi-tangential flow’, which is reasonable in most fluid-structure interaction scenarios. The method was validated against the window deformation iterative multi-grid scheme (WIDIM) using synthetic image pairs with different velocity profiles. The method was tested for boundary layer measurements of a supersonic turbulent boundary layer on a flat plate, near a rotating blade and near a flexible flapping flag. This image pre-processing method provides higher spatial resolution than conventional WIDIM and good robustness for measuring velocity profiles near moving interfaces.
Directory of Open Access Journals (Sweden)
Hoefsloot Huub CJ
2009-05-01
Full Text Available Abstract Background Mass spectrometry is increasingly being used to discover proteins or protein profiles associated with disease. Experimental design of mass-spectrometry studies has come under close scrutiny and the importance of strict protocols for sample collection is now understood. However, the question of how best to process the large quantities of data generated is still unanswered. Main challenges for the analysis are the choice of proper pre-processing and classification methods. While these two issues have been investigated in isolation, we propose to use the classification of patient samples as a clinically relevant benchmark for the evaluation of pre-processing methods. Results Two in-house generated clinical SELDI-TOF MS datasets are used in this study as an example of high throughput mass-spectrometry data. We perform a systematic comparison of two commonly used pre-processing methods as implemented in Ciphergen ProteinChip Software and in the Cromwell package. With respect to reproducibility, Ciphergen and Cromwell pre-processing are largely comparable. We find that the overlap between peaks detected by either Ciphergen ProteinChip Software or Cromwell is large. This is especially the case for the more stringent peak detection settings. Moreover, similarity of the estimated intensities between matched peaks is high. We evaluate the pre-processing methods using five different classification methods. Classification is done in a double cross-validation protocol using repeated random sampling to obtain an unbiased estimate of classification accuracy. No pre-processing method significantly outperforms the other for all peak detection settings evaluated. Conclusion We use classification of patient samples as a clinically relevant benchmark for the evaluation of pre-processing methods. Both pre-processing methods lead to similar classification results on an ovarian cancer and a Gaucher disease dataset. However, the settings for pre-processing
Mathematics for the liberal arts
Bindner, Donald; Hemmeter, Joe
2014-01-01
Presents a clear bridge between mathematics and the liberal arts Mathematics for the Liberal Arts provides a comprehensible and precise introduction to modern mathematics intertwined with the history of mathematical discoveries. The book discusses mathematical ideas in the context of the unfolding story of human thought and highlights the application of mathematics in everyday life. Divided into two parts, Mathematics for the Liberal Arts first traces the history of mathematics from the ancient world to the Middle Ages, then moves on to the Renaissance and finishes with the development of modern mathematics. In the second part, the book explores major topics of calculus and number theory, including problem-solving techniques and real-world applications. This book emphasizes learning through doing, presents a practical approach, and features: A detailed explanation of why mathematical principles are true and how the mathematical processes workNumerous figures and diagrams as well as hundreds of worked example...
Mathematics, anxiety, and the brain.
Moustafa, Ahmed A; Tindle, Richard; Ansari, Zaheda; Doyle, Margery J; Hewedi, Doaa H; Eissa, Abeer
2017-02-03
Given that achievement in learning mathematics at school correlates with work and social achievements, it is important to understand the cognitive processes underlying abilities to learn mathematics efficiently as well as reasons underlying the occurrence of mathematics anxiety (i.e. feelings of tension and fear upon facing mathematical problems or numbers) among certain individuals. Over the last two decades, many studies have shown that learning mathematical and numerical concepts relies on many cognitive processes, including working memory, spatial skills, and linguistic abilities. In this review, we discuss the relationship between mathematical learning and cognitive processes as well as the neural substrates underlying successful mathematical learning and problem solving. More importantly, we also discuss the relationship between these cognitive processes, mathematics anxiety, and mathematics learning disabilities (dyscalculia). Our review shows that mathematical cognition relies on a complex brain network, and dysfunction to different segments of this network leads to varying manifestations of mathematical learning disabilities.
Quantitative Reasoning in Problem Solving
Ramful, Ajay; Ho, Siew Yin
2015-01-01
In this article, Ajay Ramful and Siew Yin Ho explain the meaning of quantitative reasoning, describing how it is used in the to solve mathematical problems. They also describe a diagrammatic approach to represent relationships among quantities and provide examples of problems and their solutions.
Common Core: Solve Math Problems
Strom, Erich
2012-01-01
The new common core standards for mathematics demand that students (and teachers!) exhibit deeper conceptual understanding. That's music to the ears of education professor John Tapper, who says teachers have overemphasized teaching procedures--and getting right answers. In his new book, "Solving for Why," he makes a powerful case for moving beyond…
Promote Problem-Solving Discourse
Bostic, Jonathan; Jacobbe, Tim
2010-01-01
Fourteen fifth-grade students gather at the front of the classroom as their summer school instructor introduces Jonathan Bostic as the mathematics teacher for the week. Before examining any math problems, Bostic sits at eye level with the students and informs them that they will solve problems over the next four days by working individually as…
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
Mathematics Anxiety and the Underprepared Student.
Godbey, Cathy
This article discusses the symptoms and causes of math anxiety, and preventative measures that teachers can use to alleviate the stress some students experience in mathematics problem solving. Mathematics anxiety is defined as "feelings of tension and anxiety that interfere with the manipulation of numbers and the solving of mathematical problems…
Directory of Open Access Journals (Sweden)
Elaine Vieira
2001-01-01
Full Text Available O presente estudo insere-se no âmbito da investigação cognitiva. Refere-se às dificuldades nas estratégias de compreensão na fase de Representação Mental (RM relacionadas com a resolução de problemas matemáticos com enunciados verbais, detectadas em professores de séries iniciais do Ensino Fundamental. São analisadas as dificuldades relacionadas com a construção da Representação Mental, mais especificamente, a fase de integração. São investigados os processos responsáveis pelas mudanças na Representação Mental inicial: codificação, combinação e comparação seletivas. Os resultados comprovam que a Intervenção Psicopedagógica centrada no monitoramento cognitivo possibilita aos professores atuarem sobre suas próprias atividades cognitivas e metacognitivas, controlando e regulando as funções cognitivas relacionadas com os processos de mudança representacional, reduzindo assim, significativamente, as dificuldades nas estratégias de resolução de problemas matemáticos.This study is included in the field of cognitive investigation. It encloses the difficulties of comprehension strategies of the Mental Representation phase regarding the solution of verbal stated mathematical problems, seen in teachers of the first years of basic education. The difficulties, related to the Mental Representation construction, were analyzed, more specifically the ones associated to the integration phase. The processes, which account for changes in the initial Mental Representation are also investigated: encoding, combination and selective comparison. The results show that psychopedagogical intervention on cognitive monitoring allowed teachers to work on their own cognitive and metacognitive activities, as well as control and regulate the cognitive functions related to processes of representational change, thus reducing significantly the difficulties in the use of strategies for solving mathematical problems
Automatic pre-processing for an object-oriented distributed hydrological model using GRASS-GIS
Sanzana, P.; Jankowfsky, S.; Branger, F.; Braud, I.; Vargas, X.; Hitschfeld, N.
2012-04-01
Landscapes are very heterogeneous, which impact the hydrological processes occurring in the catchments, especially in the modeling of peri-urban catchments. The Hydrological Response Units (HRUs), resulting from the intersection of different maps, such as land use, soil types and geology, and flow networks, allow the representation of these elements in an explicit way, preserving natural and artificial contours of the different layers. These HRUs are used as model mesh in some distributed object-oriented hydrological models, allowing the application of a topological oriented approach. The connectivity between polygons and polylines provides a detailed representation of the water balance and overland flow in these distributed hydrological models, based on irregular hydro-landscape units. When computing fluxes between these HRUs, the geometrical parameters, such as the distance between the centroid of gravity of the HRUs and the river network, and the length of the perimeter, can impact the realism of the calculated overland, sub-surface and groundwater fluxes. Therefore, it is necessary to process the original model mesh in order to avoid these numerical problems. We present an automatic pre-processing implemented in the open source GRASS-GIS software, for which several Python scripts or some algorithms already available were used, such as the Triangle software. First, some scripts were developed to improve the topology of the various elements, such as snapping of the river network to the closest contours. When data are derived with remote sensing, such as vegetation areas, their perimeter has lots of right angles that were smoothed. Second, the algorithms more particularly address bad-shaped elements of the model mesh such as polygons with narrow shapes, marked irregular contours and/or the centroid outside of the polygons. To identify these elements we used shape descriptors. The convexity index was considered the best descriptor to identify them with a threshold
Effects of Problem-Solving, Guided-Discovery and Expository ...
African Journals Online (AJOL)
Effects of Problem-Solving, Guided-Discovery and Expository Teaching ... of problem-solving, guideddiscovery, and expository methods of instruction on students performance in redox reaction, considering their mathematics ability. It was a ...
On image pre-processing for PIV of single- and two-phase flows over reflecting objects
Energy Technology Data Exchange (ETDEWEB)
Deen, Niels G.; Willems, Paul; Sint Annaland, Martin van; Kuipers, J.A.M.; Lammertink, Rob G.H.; Kemperman, Antoine J.B.; Wessling, Matthias; Meer, Walter G.J. van der [University of Twente, Faculty of Science and Technology, Institute of Mechanics, Processes and Control Twente (IMPACT), Enschede (Netherlands)
2010-08-15
A novel image pre-processing scheme for PIV of single- and two-phase flows over reflecting objects which does not require the use of additional hardware is discussed. The approach for single-phase flow consists of image normalization and intensity stretching followed by background subtraction. For two-phase flow, an additional masking step is added after the background subtraction. The effectiveness of the pre-processing scheme is shown for two examples: PIV of single-phase flow in spacer-filled channels and two-phase flow in these channels. The pre-processing scheme increased the displacement peak detectability significantly and produced high quality vector fields, without the use of additional hardware. (orig.)
Research on the Effect of Different Thinking Types in Solving Mathematics Problems%不同思维类型对数学解题的影响研究
Institute of Scientific and Technical Information of China (English)
张跃红
2015-01-01
美国学者安东尼·格里高提出了4种不同的思维类型,即具体而有序、抽象而有序、具体而随机、抽象而随机的思维.不同的思维类型对数学解题理当产生不同的影响,通过对240名学生进行的相关调查研究,获得了一些初步的结论,并由此提出了相应的发展性策略建议,即具体而有序的思维需要提高抽象概括能力,抽象而有序的思维需要提高发散思维能力,具体而随机的思维需要提高集中概括能力,抽象而随机的思维需要提高集中思维能力.%U.S. scholar Anthony Gregory has proposed four thinking types which contained Specific and Ordered (SO), Abstract and Ordered (AO), Specific and Random (SR) and Abstract and Random (AR). It is believed that different thinking types can exert different influences in mathematics problem-solving. Based on an investigation involving 240 students, this paper concluded some preliminary findings, and therefore proposed corresponding developmental strategies: students with SO thinking type should promote abstract generalization ability; students with AO thinking type should promote divergent thinking ability; students with SR thinking type should promote concentrated generalization ability and students with AR thinking type should promote concentrated thinking ability.
Logic training through algorithmic problem solving
Ferreira, João Fernando; Mendes, Alexandra; Cunha, Alcino; Baquero, Carlos; Silva, Paulo; L. S. Barbosa; Oliveira, José Nuno Fonseca
2011-01-01
Available for individual study only. Although much of mathematics is algorithmic in nature, the skills needed to formulate and solve algorithmic problems do not form an integral part of mathematics education. In particular, logic, which is central to algorithm development, is rarely taught explicitly at preuniversity level, under the justification that it is implicit in mathematics and therefore does not need to be taught as an independent topic. This paper argues in the opposite direction...
Pre-Processing of Point-Data from Contact and Optical 3D Digitization Sensors
Directory of Open Access Journals (Sweden)
Mirko Soković
2012-01-01
Full Text Available Contemporary 3D digitization systems employed by reverse engineering (RE feature ever-growing scanning speeds with the ability to generate large quantity of points in a unit of time. Although advantageous for the quality and efficiency of RE modelling, the huge number of point datas can turn into a serious practical problem, later on, when the CAD model is generated. In addition, 3D digitization processes are very often plagued by measuring errors, which can be attributed to the very nature of measuring systems, various characteristics of the digitized objects and subjective errors by the operator, which also contribute to problems in the CAD model generation process. This paper presents an integral system for the pre-processing of point data, i.e., filtering, smoothing and reduction, based on a cross-sectional RE approach. In the course of the proposed system development, major emphasis was placed on the module for point data reduction, which was designed according to a novel approach with integrated deviation analysis and fuzzy logic reasoning. The developed system was verified through its application on three case studies, on point data from objects of versatile geometries obtained by contact and laser 3D digitization systems. The obtained results demonstrate the effectiveness of the system.
Pre-processing Algorithm for Rectification of Geometric Distortions in Satellite Images
Directory of Open Access Journals (Sweden)
Narayan Panigrahi
2011-02-01
Full Text Available A number of algorithms have been reported to process and remove geometric distortions in satellite images. Ortho-correction, geometric error correction, radiometric error removal, etc are a few important examples. These algorithm require supplementary meta-information of the satellite images such as ground control points and correspondence, sensor orientation details, elevation profile of the terrain, etc to establish corresponding transformations. In this paper, a pre-processing algorithm has been proposed which removes systematic distortions of a satellite image and thereby removes the blank portion of the image. It is an input-to-output mapping of image pixels, where the transformation computes the coordinate of each output pixel corresponding to the input pixel of an image. The transformation is established by the exact amount of scaling, rotation and translation needed for each pixel in the input image so that the distortion induced during the recording stage is corrected.Defence Science Journal, 2011, 61(2, pp.174-179, DOI:http://dx.doi.org/10.14429/dsj.61.421
Data Cleaning In Data Warehouse: A Survey of Data Pre-processing Techniques and Tools
Directory of Open Access Journals (Sweden)
Anosh Fatima
2017-03-01
Full Text Available A Data Warehouse is a computer system designed for storing and analyzing an organization's historical data from day-to-day operations in Online Transaction Processing System (OLTP. Usually, an organization summarizes and copies information from its operational systems to the data warehouse on a regular schedule and management performs complex queries and analysis on the information without slowing down the operational systems. Data need to be pre-processed to improve quality of data, before storing into data warehouse. This survey paper presents data cleaning problems and the approaches in use currently for preprocessing. To determine which technique of preprocessing is best in what scenario to improve the performance of Data Warehouse is main goal of this paper. Many techniques have been analyzed for data cleansing, using certain evaluation attributes and tested on different kind of data sets. Data quality tools such as YALE, ALTERYX, and WEKA have been used for conclusive results to ready the data in data warehouse and ensure that only cleaned data populates the warehouse, thus enhancing usability of the warehouse. Results of paper can be useful in many future activities like cleansing, standardizing, correction, matching and transformation. This research can help in data auditing and pattern detection in the data.
Tactile on-chip pre-processing with techniques from artificial retinas
Maldonado-Lopez, R.; Vidal-Verdu, F.; Linan, G.; Roca, E.; Rodriguez-Vazquez, A.
2005-06-01
The interest in tactile sensors is increasing as their use in complex unstructured environments is demanded, like in telepresence, minimal invasive surgery, robotics etc. The matrix of pressure data these devices provide can be managed with many image processing algorithms to extract the required information. However, as in the case of vision chips or artificial retinas, problems arise when the array size and the computation complexity increase. Having a look to the skin, the information collected by every mechanoreceptor is not carried to the brain for its processing, but some complex pre-processing is performed to fit the limited throughput of the nervous system. This is specially important for high bandwidth demanding tasks. Experimental works report that neural response of skin mechanoreceptors encodes the change in local shape from an offset level rather than the absolute force or pressure distributions. This is also the behavior of the retina, which implements a spatio-temporal averaging. We propose the same strategy in tactile preprocessing, and we show preliminary results when it faces the detection of the slip, which involves fast real-time processing.
A new approach to pre-processing digital image for wavelet-based watermark
Agreste, Santa; Andaloro, Guido
2008-11-01
The growth of the Internet has increased the phenomenon of digital piracy, in multimedia objects, like software, image, video, audio and text. Therefore it is strategic to individualize and to develop methods and numerical algorithms, which are stable and have low computational cost, that will allow us to find a solution to these problems. We describe a digital watermarking algorithm for color image protection and authenticity: robust, not blind, and wavelet-based. The use of Discrete Wavelet Transform is motivated by good time-frequency features and a good match with Human Visual System directives. These two combined elements are important for building an invisible and robust watermark. Moreover our algorithm can work with any image, thanks to the step of pre-processing of the image that includes resize techniques that adapt to the size of the original image for Wavelet transform. The watermark signal is calculated in correlation with the image features and statistic properties. In the detection step we apply a re-synchronization between the original and watermarked image according to the Neyman-Pearson statistic criterion. Experimentation on a large set of different images has been shown to be resistant against geometric, filtering, and StirMark attacks with a low rate of false alarm.
Mastering mathematics for OCR GCSE
Lambert, Elaine
2015-01-01
Build your students' knowledge and understanding so that they can confidently reason, interpret, communicate mathematically and apply their mathematical skills to solve problems within mathematics and wider contexts; with resources developed specifically for the OCR GCSE 2015 specification by mathematics subject specialists experienced in teaching and examining GCSE. - Supports you and your students through the new specifications, with topic explanations and new. exam-style questions, written in line with the new assessment objectives. - Measure progress and assess learning throughout the cour
Institute of Scientific and Technical Information of China (English)
乔希民; 刘晓民; 李超
2015-01-01
Mathematical democratization of mathematics class is an exhibition of educational ideal,methodand reflection based on the teachers' conscience.In the process of teaching in mathematics class,mathematical democratization refers to begin from the interestingness of introducing a mathematics problem,so as to make the students' mathematics knowledge generated naturally and smoothly.In this way,they can both understand the mathematics ideas and methods,and think and explore independently,and they can form the critical spirit of rational query and reflection.In this way,the research on mathematics problem can only be broad,simple and appreciative, so as to promote the students' overall development of their correct mind.Based on the research of method of solving equation with one unknown,the democratization of mathematics classroom teaching was studied.%数学课堂数学民主化是基于教师良知的教育理想、教育方式、教育反思的实现。体现在数学课堂教学的过程中，就是从数学问题引入的趣味性着手，使学生的数学知识生成自然顺畅，既能理解数学思想方法，又能独立思考探究，更能形成理性质疑反思的批判精神。这样，才能使数学问题的研究广阔与简洁，促进学生正确心智的全面发展。基于一元方程求解方法的讨论，研究了数学课堂教学民主化问题。
Journey into Problem Solving: A Gift from Polya
Lederman, Eric
2009-01-01
In "How to Solve It", accomplished mathematician and skilled communicator George Polya describes a four-step universal solving technique designed to help students develop mathematical problem-solving skills. By providing a glimpse at the grace with which experts solve problems, Polya provides definable methods that are not exclusive to…
Journey into Problem Solving: A Gift from Polya
Lederman, Eric
2009-01-01
In "How to Solve It", accomplished mathematician and skilled communicator George Polya describes a four-step universal solving technique designed to help students develop mathematical problem-solving skills. By providing a glimpse at the grace with which experts solve problems, Polya provides definable methods that are not exclusive to…
Teaching and Learning through Problem Solving
Ollerton, Mike
2007-01-01
In this article, the author relates some problem solving work with primary schools to Department for Children, Schools, and Families (DfES) support. In four primary schools in the West Midlands, the focus was teaching mathematics through problem solving, based on materials published on the DfES "standards" website. The author noticed…
Conceptual Problem Solving in High School Physics
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…
Solving Cubic Equations by Polynomial Decomposition
Kulkarni, Raghavendra G.
2011-01-01
Several mathematicians struggled to solve cubic equations, and in 1515 Scipione del Ferro reportedly solved the cubic while participating in a local mathematical contest, but did not bother to publish his method. Then it was Cardano (1539) who first published the solution to the general cubic equation in his book "The Great Art, or, The Rules of…
The Functions of Pictures in Problem Solving
Elia, Iliada; Philippou, George
2004-01-01
In the present study, we assert that pictures serve four functions in problem solving: decorative, representational, organizational and informational. We, therefore, investigate the effects of pictures based on their functions in mathematical problem solving (MPS), by high achievement students of Grade 6 in Cyprus, in a communication setting. A…
A Mathematical Prediction of Standing Waves
Higgins, Jon
1970-01-01
Presents a problem in standing waves that provides an example of the mathematics used by theoretical physicists to generate predictions of new phenomena from fundamental background knowledge. Mathematical analysis required to solve problem is accomplished by simple graphical processes. (BR)
Ratio Analysis: Where Investments Meet Mathematics.
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)
DEFF Research Database (Denmark)
Westphael, Henning; Mogensen, Arne
2013-01-01
In this article we present the notion of Mathematical competences as a tool to describe the mathematically gifted students.......In this article we present the notion of Mathematical competences as a tool to describe the mathematically gifted students....
Upadhaya, Taman; Morvan, Yannick; Stindel, Eric; Le Reste, Pierre-Jean; Hatt, Mathieu
2016-03-01
Heterogeneity image-derived features of Glioblastoma multiforme (GBM) tumors from multimodal MRI sequences may provide higher prognostic value than standard parameters used in routine clinical practice. We previously developed a framework for automatic extraction and combination of image-derived features (also called "Radiomics") through support vector machines (SVM) for predictive model building. The results we obtained in a cohort of 40 GBM suggested these features could be used to identify patients with poorer outcome. However, extraction of these features is a delicate multi-step process and their values may therefore depend on the pre-processing of images. The original developed workflow included skull removal, bias homogeneity correction, and multimodal tumor segmentation, followed by textural features computation, and lastly ranking, selection and combination through a SVM-based classifier. The goal of the present work was to specifically investigate the potential benefit and respective impact of the addition of several MRI pre-processing steps (spatial resampling for isotropic voxels, intensities quantization and normalization) before textural features computation, on the resulting accuracy of the classifier. Eighteen patients datasets were also added for the present work (58 patients in total). A classification accuracy of 83% (sensitivity 79%, specificity 85%) was obtained using the original framework. The addition of the new pre-processing steps increased it to 93% (sensitivity 93%, specificity 93%) in identifying patients with poorer survival (below the median of 12 months). Among the three considered pre-processing steps, spatial resampling was found to have the most important impact. This shows the crucial importance of investigating appropriate image pre-processing steps to be used for methodologies based on textural features extraction in medical imaging.
Interactive problem solving using LOGO
Boecker, Heinz-Dieter; Fischer, Gerhard
2014-01-01
This book is unique in that its stress is not on the mastery of a programming language, but on the importance and value of interactive problem solving. The authors focus on several specific interest worlds: mathematics, computer science, artificial intelligence, linguistics, and games; however, their approach can serve as a model that may be applied easily to other fields as well. Those who are interested in symbolic computing will find that Interactive Problem Solving Using LOGO provides a gentle introduction from which one may move on to other, more advanced computational frameworks or more
Mathematical methods for physicists
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
Solved problems in electromagnetics
Salazar Bloise, Félix; Bayón Rojo, Ana; Gascón Latasa, Francisco
2017-01-01
This book presents the fundamental concepts of electromagnetism through problems with a brief theoretical introduction at the beginning of each chapter. The present book has a strong didactic character. It explains all the mathematical steps and the theoretical concepts connected with the development of the problem. It guides the reader to understand the employed procedures to learn to solve the exercises independently. The exercises are structured in a similar way: The chapters begin with easy problems increasing progressively in the level of difficulty. This book is written for students of physics and engineering in the framework of the new European Plans of Study for Bachelor and Master and also for tutors and lecturers. .
Reading-Enhanced Word Problem Solving: A Theoretical Model
Capraro, Robert M.; Capraro, Mary Margaret; Rupley, William H.
2012-01-01
There is a reciprocal relationship between mathematics and reading cognition. Metacognitive training within reading-enhanced problem solving should facilitate students developing an awareness of what good readers do when reading for meaning in solving mathematical problems enabling them to apply these strategies. The constructs for each cognitive…
Griesser, Sara Anne
Current mathematics education emphasizes the importance of a problem solving mindset in the classroom. Students need to know how they are going to use what they are learning in real life. The purpose of this study was to determine the effect of anchored problem solving instruction on middle school students' mathematical abilities. The researcher…
The Magic of Mathematics Discovering the Spell of Mathematics
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
Latinas and Problem Solving: What They Say and What They Do
Guerra, Paula; Lim, Woong
2014-01-01
In this article, the authors present three adolescent Latinas' perceptions of ideal mathematical competencies, their perception of their individual "abilities" in mathematics, and their work on a mathematics problem-solving task. Results indicate that these Latinas recognize flexible mathematics as the ideal mathematical competency in…
Higher engineering mathematics
John Bird
2014-01-01
A practical introduction to the core mathematics principles required at higher engineering levelJohn Bird's approach to mathematics, based on numerous worked examples and interactive problems, is ideal for vocational students that require an advanced textbook.Theory is kept to a minimum, with the emphasis firmly placed on problem-solving skills, making this a thoroughly practical introduction to the advanced mathematics engineering that students need to master. The extensive and thorough topic coverage makes this an ideal text for upper level vocational courses. Now in
Mathematical modelling techniques
Aris, Rutherford
1995-01-01
""Engaging, elegantly written."" - Applied Mathematical ModellingMathematical modelling is a highly useful methodology designed to enable mathematicians, physicists and other scientists to formulate equations from a given nonmathematical situation. In this elegantly written volume, a distinguished theoretical chemist and engineer sets down helpful rules not only for setting up models but also for solving the mathematical problems they pose and for evaluating models.The author begins with a discussion of the term ""model,"" followed by clearly presented examples of the different types of mode
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…
Advanced engineering mathematics
Jeffrey, Alan
2001-01-01
Advanced Engineering Mathematics provides comprehensive and contemporary coverage of key mathematical ideas, techniques, and their widespread applications, for students majoring in engineering, computer science, mathematics and physics. Using a wide range of examples throughout the book, Jeffrey illustrates how to construct simple mathematical models, how to apply mathematical reasoning to select a particular solution from a range of possible alternatives, and how to determine which solution has physical significance. Jeffrey includes material that is not found in works of a similar nature, such as the use of the matrix exponential when solving systems of ordinary differential equations. The text provides many detailed, worked examples following the introduction of each new idea, and large problem sets provide both routine practice, and, in many cases, greater challenge and insight for students. Most chapters end with a set of computer projects that require the use of any CAS (such as Maple or Mathematica) th...
Directory of Open Access Journals (Sweden)
Ilhan KARATAS
2013-07-01
Full Text Available 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 educatingstudents as efficient problem solvers is an important role of mathematics education. Problem solving skill is the centre of mathematics curriculum. Students’ gaining of that skill in school mathematics is closely related with the learning environment to beformed and the roles given to the students. The aim of this study is to create a problem solving based learning environment to enhance the students’ problem solving skill. Within this scope, students’practiced activities and problems that provide them to proceed in Polya (1945’s problem solving phases and throughout the study, students’ success in problem solving have been evaluated. While experimental group students received problem solving based learning environment performed, control group students have continued their present program in this quise1experimental study. Eleven problem solving activities were given to the students at the beginning, middle and end of the study and the students’ performances wereanalyzed based on problem solving phases. The findings illustrated that the experimental group students’ success in problem solving activities has increased while the control group students’ success has not changed significantly.
Seidel, Kathrin; Kahl, Johannes; Paoletti, Flavio; Birlouez, Ines; Busscher, Nicolaas; Kretzschmar, Ursula; Särkkä-Tirkkonen, Marjo; Seljåsen, Randi; Sinesio, Fiorella; Torp, Torfinn; Baiamonte, Irene
2015-02-01
The market for processed food is rapidly growing. The industry needs methods for "processing with care" leading to high quality products in order to meet consumers' expectations. Processing influences the quality of the finished product through various factors. In carrot baby food, these are the raw material, the pre-processing and storage treatments as well as the processing conditions. In this study, a quality assessment was performed on baby food made from different pre-processed raw materials. The experiments were carried out under industrial conditions using fresh, frozen and stored organic carrots as raw material. Statistically significant differences were found for sensory attributes among the three autoclaved puree samples (e.g. overall odour F = 90.72, p food.
Directory of Open Access Journals (Sweden)
Farshid eSepehrband
2015-01-01
Full Text Available We describe and evaluate a pre-processing method based on a periodic spiral sampling of diffusion gradient directions for high angular resolution diffusion magnetic resonance imaging. Our pre-processing method incorporates prior knowledge about the acquired diffusion-weighted signal, facilitating noise reduction. Periodic spiral sampling of gradient direction encodings results in an acquired signal in each voxel that is pseudo periodic with characteristics that allow separation of low-frequency signal from high frequency noise. Consequently, it enhances local reconstruction of the orientation distribution function used to define fibre tracks in the brain. Denoising with periodic spiral sampling was tested using synthetic data and in vivo human brain images. The level of improvement in signal-to-noise ratio and in the accuracy of local reconstruction of fibre tracks was significantly improved using our method.
Sepehrband, Farshid; Choupan, Jeiran; Caruyer, Emmanuel; Kurniawan, Nyoman D; Gal, Yaniv; Tieng, Quang M; McMahon, Katie L; Vegh, Viktor; Reutens, David C; Yang, Zhengyi
2014-01-01
We describe and evaluate a pre-processing method based on a periodic spiral sampling of diffusion-gradient directions for high angular resolution diffusion magnetic resonance imaging. Our pre-processing method incorporates prior knowledge about the acquired diffusion-weighted signal, facilitating noise reduction. Periodic spiral sampling of gradient direction encodings results in an acquired signal in each voxel that is pseudo-periodic with characteristics that allow separation of low-frequency signal from high frequency noise. Consequently, it enhances local reconstruction of the orientation distribution function used to define fiber tracks in the brain. Denoising with periodic spiral sampling was tested using synthetic data and in vivo human brain images. The level of improvement in signal-to-noise ratio and in the accuracy of local reconstruction of fiber tracks was significantly improved using our method.
DEFF Research Database (Denmark)
Dabrowski, Dariusz; Hashemiyan, Zahra; Adamczyk, Jan
2015-01-01
and bucket wheel excavators. In this paper, a signal pre-processing algorithm designed for condition monitoring of planetary gears working in non-stationary operation is presented. The algorithm is dedicated for hardware implementation on Field Programmable Gate Arrays (FPGAs). The purpose of the algorithm......%, it can be performed in real-time conditions and its implementation does not require many resources of FPGAs....
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.
Putting Mathematical Discourse in Writing
Lynch, Sararose D.; Bolyard, Johnna J.
2012-01-01
This article describes an action research project in which a sixth-grade teacher engaged students in writing about their problem-solving efforts. The written mathematical work provided new artifacts for examining students' metacognitive and mathematical communication skills, prompting the teacher to make instructional changes to address students'…
Mathematical Modeling and Computational Thinking
Sanford, John F.; Naidu, Jaideep T.
2017-01-01
The paper argues that mathematical modeling is the essence of computational thinking. Learning a computer language is a valuable assistance in learning logical thinking but of less assistance when learning problem-solving skills. The paper is third in a series and presents some examples of mathematical modeling using spreadsheets at an advanced…
Aspects of Children's Mathematics Anxiety.
Newstead, Karen
1998-01-01
Focuses on mathematics anxiety in 9- to 11-year-old children. Compares the mathematics anxiety of pupils taught in a traditional manner with that of pupils whose teachers adopted an alternative teaching approach that emphasizes problem solving and discussion of the pupil's own informal strategies. Concludes that pupils exposed to the traditional…
Mathematical Programming and Logical Inference
1990-12-01
solution of inference problems in propositional logic, to appear in Annals of Mathematics and Al. (271 Howard, R. A., and J. E. Matheson, Influence...1981). (281 Jeroslow, R., and J. Wang, Solving propositional satisfiability problems, to appear in Annals of Mathematics and Al. [29] Nilsson, N. J
Luther, Kenneth H.
2012-01-01
Mathematical modeling of groundwater flow is a topic at the intersection of mathematics and geohydrology and is rarely encountered in undergraduate mathematics. However, this subject is full of interesting and meaningful examples of truly "applied" mathematics accessible to undergraduates, from the pre-calculus to advanced mathematics levels. This…
Luther, Kenneth H.
2012-01-01
Mathematical modeling of groundwater flow is a topic at the intersection of mathematics and geohydrology and is rarely encountered in undergraduate mathematics. However, this subject is full of interesting and meaningful examples of truly "applied" mathematics accessible to undergraduates, from the pre-calculus to advanced mathematics levels. This…
Mastering mathematics for Edexcel GCSE
Davis, Heather; Liggett, Linda
2015-01-01
Help students to develop their knowledge, skills and understanding so that they can reason mathematically, communicate mathematical information and apply mathematical techniques in solving problems; with resources developed specifically for the Edexcel GCSE 2015 specification with leading Assessment Consultant Keith Pledger and a team of subject specialists. - Supports you and your students through the new specifications, with topic explanations and new exam-style questions, to support the new assessment objectives. - Builds understanding and measures progress throughout the course with plenty
Tugizimana, Fidele; Steenkamp, Paul A; Piater, Lizelle A; Dubery, Ian A
2016-11-03
Untargeted metabolomic studies generate information-rich, high-dimensional, and complex datasets that remain challenging to handle and fully exploit. Despite the remarkable progress in the development of tools and algorithms, the "exhaustive" extraction of information from these metabolomic datasets is still a non-trivial undertaking. A conversation on data mining strategies for a maximal information extraction from metabolomic data is needed. Using a liquid chromatography-mass spectrometry (LC-MS)-based untargeted metabolomic dataset, this study explored the influence of collection parameters in the data pre-processing step, scaling and data transformation on the statistical models generated, and feature selection, thereafter. Data obtained in positive mode generated from a LC-MS-based untargeted metabolomic study (sorghum plants responding dynamically to infection by a fungal pathogen) were used. Raw data were pre-processed with MarkerLynx(TM) software (Waters Corporation, Manchester, UK). Here, two parameters were varied: the intensity threshold (50-100 counts) and the mass tolerance (0.005-0.01 Da). After the pre-processing, the datasets were imported into SIMCA (Umetrics, Umea, Sweden) for more data cleaning and statistical modeling. In addition, different scaling (unit variance, Pareto, etc.) and data transformation (log and power) methods were explored. The results showed that the pre-processing parameters (or algorithms) influence the output dataset with regard to the number of defined features. Furthermore, the study demonstrates that the pre-treatment of data prior to statistical modeling affects the subspace approximation outcome: e.g., the amount of variation in X-data that the model can explain and predict. The pre-processing and pre-treatment steps subsequently influence the number of statistically significant extracted/selected features (variables). Thus, as informed by the results, to maximize the value of untargeted metabolomic data, understanding
Towards mathematical philosophy
Hendricks, Vincent F
2008-01-01
Logical investigations in cognitive science have successfully utilized methods and systems of belief revision, non-monotonic logic and dynamic epistemic logic. This title deals with focal issues of belief revision. It contains a collection of articles applying methods of logic or, more generally, of mathematics to solve problems.