Students Use Of Multiple Representations In Mathematical Problem Solving
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Students Use Of Multiple Representations In Mathematical Problem Solving
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Author : James William Ballard
language : en
Publisher:
Release Date : 2000
Students Use Of Multiple Representations In Mathematical Problem Solving written by James William Ballard and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with MSU-BZ thesis categories.
External Multiple Representations In Mathematics Teaching
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Author :
language : en
Publisher:
Release Date : 2003
External Multiple Representations In Mathematics Teaching written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with categories.
An emerging theoretical view on mathematical learning is that utilizing multiple representations in mathematical instruction will empower students during problem solving and at the same time help students develop deeper understanding of mathematical relationships and concepts. However not everyone in the mathematics education community share this view point, some researchers argue that utilizing multiple representations in mathematics instruction will impair rather than help students to develop understanding of mathematical relations and concepts. The purpose of the review was to examine and ascertain information from available studies on multiple representations and to assess whether evidence obtained from these studies supported or refuted the assertion that utilizing multiple representations in mathematics teaching enabled students develop deeper understanding of mathematical relationships and problem solving success. Findings from available research studies on multiple representations indicated that students taught with multiple representations demonstrated deeper understanding of mathematical relations and achieved superior performances during problem solving tasks.
Calculus Students Representation Use In Group Work And Individual Settings
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Author : Dov Zazkis
language : en
Publisher:
Release Date : 2013
Calculus Students Representation Use In Group Work And Individual Settings written by Dov Zazkis and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with categories.
The study of student representation use and specifically the distinction between analytic and visual representations has fueled a long line of mathematics education literature that began more than 35 years ago. This literature can be partitioned into two bodies of work, one that is primarily cognitive and one that is primarily social. In spite of the large overlap in the results and foci of these two bodies of work they have tended to not inform one another. I bridge these two bodies of work by creating and implementing an analysis tool, referred to as the VAP-model, which can be used within both group-work and individual interview settings. This model allows focusing on how students in both settings transition between representations during problem-solving and how these transitions fuel students' mathematical advancement. The VAP-model considers physical representations in addition to the analytic/visual distinction, which has driven much of the research on representation use. Physical representations are references to realistic or imaginable scenarios in mathematical problem-solving. Fluency with multiple representations has been long considered an important aspect of deep understanding of mathematics in general and calculus in particular. This study examines the representation use of three calculus students from a technologically enriched calculus course in both in-class group-work settings and individual interview settings. This analysis reveals that students incorporate representations not required by given tasks and that, in spite of their common classroom experiences, the representations used in problem-solving vary widely across students. Comparing representation usage in the two settings showed similarities in how frequently each participant transitioned between modes of representation, which modes appeared within their reasoning and the types of questions in which particular shifts between representations occurred. This analysis also highlighted cross-setting similarities in how social roles facilitated shifts in representation use and in what ways these transitions occurred. Within both settings physical representations played an important role in students' thinking and were often introduced to reason about non-physical problems. Since in past studies this type of representation use was commonly subsumed under other categories this phenomenon was often overlooked.
Multiple Representations In Physics Education
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Author : David F. Treagust
language : en
Publisher: Springer
Release Date : 2017-07-24
Multiple Representations In Physics Education written by David F. Treagust and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-07-24 with Science categories.
This volume is important because despite various external representations, such as analogies, metaphors, and visualizations being commonly used by physics teachers, educators and researchers, the notion of using the pedagogical functions of multiple representations to support teaching and learning is still a gap in physics education. The research presented in the three sections of the book is introduced by descriptions of various psychological theories that are applied in different ways for designing physics teaching and learning in classroom settings. The following chapters of the book illustrate teaching and learning with respect to applying specific physics multiple representations in different levels of the education system and in different physics topics using analogies and models, different modes, and in reasoning and representational competence. When multiple representations are used in physics for teaching, the expectation is that they should be successful. To ensure this is the case, the implementation of representations should consider design principles for using multiple representations. Investigations regarding their effect on classroom communication as well as on the learning results in all levels of schooling and for different topics of physics are reported. The book is intended for physics educators and their students at universities and for physics teachers in schools to apply multiple representations in physics in a productive way.
Problems Of Representation In The Teaching And Learning Of Mathematics
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Author : Université du Québec à Montréal. Centre interdisciplinaire de recherche sur l'apprentissage et le développement en éducation
language : en
Publisher: Hillsdale, N.J. : L. Erlbaum Associates
Release Date : 1987
Problems Of Representation In The Teaching And Learning Of Mathematics written by Université du Québec à Montréal. Centre interdisciplinaire de recherche sur l'apprentissage et le développement en éducation and has been published by Hillsdale, N.J. : L. Erlbaum Associates this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987 with Education categories.
Papers derived from a symposium organized by CIRADE of Université du Québec à Montréal.
Mathematical Problem Posing
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Author : Florence Mihaela Singer
language : en
Publisher: Springer
Release Date : 2015-06-12
Mathematical Problem Posing written by Florence Mihaela Singer and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-06-12 with Education categories.
The mathematics education community continues to contribute research-based ideas for developing and improving problem posing as an inquiry-based instructional strategy for enhancing students’ learning. A large number of studies have been conducted which have covered many research topics and methodological aspects of teaching and learning mathematics through problem posing. The Authors' groundwork has shown that many of these studies predict positive outcomes from implementing problem posing on: student knowledge, problem solving and posing skills, creativity and disposition toward mathematics. This book examines, in-depth, the contribution of a problem posing approach to teaching mathematics and discusses the impact of adopting this approach on the development of theoretical frameworks, teaching practices and research on mathematical problem posing over the last 50 years.
Handbook Of Learning From Multiple Representations And Perspectives
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Author : Peggy Van Meter
language : en
Publisher: Routledge
Release Date : 2020-03-10
Handbook Of Learning From Multiple Representations And Perspectives written by Peggy Van Meter and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-03-10 with Education categories.
In and out of formal schooling, online and off, today’s learners must consume and integrate a level of information that is exponentially larger and delivered through a wider range of formats and viewpoints than ever before. The Handbook of Learning from Multiple Representations and Perspectives provides a path for understanding the cognitive, motivational, and socioemotional processes and skills necessary for learners across educational contexts to make sense of and use information sourced from varying inputs. Uniting research and theory from education, psychology, literacy, library sciences, media and technology, and more, this forward-thinking volume explores the common concerns, shared challenges, and thematic patterns in our capacity to make meaning in an information-rich society. Chapter 16 of this book is freely available as a downloadable Open Access PDF under a Creative Commons Attribution-Non Commercial-No Derivatives 4.0 license available at http://www.taylorfrancis.com/books/e/9780429443961.
Investigating Students Use Of Mathematical Tools And Representations In Undergraduate Physics Problem Solving
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Author : Nandana Weliweriya
language : en
Publisher:
Release Date : 2019
Investigating Students Use Of Mathematical Tools And Representations In Undergraduate Physics Problem Solving written by Nandana Weliweriya and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019 with categories.
One of the major focuses in the PER community has been on understanding student learning in order to improve how we teach undergraduate physics courses. Problem-solving receives significant emphasis across the undergraduate physics curriculum, and students' ability to solve physics problems has been researched extensively. Studying student problem- solving processes in upper-division physics courses is a growing area of research. The research presented in this dissertation is done in an effort to understand student problem-solving processes at the upper-division level. In particular, we investigate students' use of mathematical tools across the undergraduate physics curriculum, in particular, at intermediate mechanics students' written homework solutions in order to better understand how students use these tools as they solve traditional mechanics problems. We use a modified version of the ACER (Activation-Construction-Execution-Reflection) framework to analyze students' solutions and to identify patterns of mathematical skill use on traditional problems. We apply techniques borrowed from network analysis and the Resources Framework to build a "fingerprint" of students' mathematical tool use. In this study, we present preliminary findings on patterns that we have identified in students' problem-solving. Then we shift our focus to investigate how students use multiple representations as they solve problems. First, we study how students translate among different representations. Data for this study is drawn from an upper-division Electromagnetism I course, where students engaged in individual oral exams. We do a moment-by-moment analysis of students' problem solving to see how they translate among durable representations (diagrams, written mathematical equations) with the help of evanescent representations (gestures, words), and how students build up durable representations where they can "stand fast" later. In this study, we present the case of Larry as an exemplary case for problem-solving. Larry starts from a durable representation (a diagram). He then builds from there, using evanescent representations (gestures and words) and standing fast on the diagram. He later translates to a different kind of durable representation (mathematics), where he reasons and answers the original problem. In our investigation to understand how students use multiple representations while solving problems, we further investigate how students construct spontaneous representations and also make connections among these representations. We use a social semiotic perspective to sketch a theoretical framework that accounts for how semiotic resources might be combined to solve problems. We identify the semiotic and conceptual resources that Larry uses, and we use a resource-graph representation to show Larry's coordination of resources in his problem- solving activity. Larry's case exemplifies coordination between multiple semiotic resources with different disciplinary affordances to build up compound representations. Our analysis of this case illustrates a novel way to think about how students use semiotic resources as they solve physics problems. After that, we revise our theoretical framework to better describe students connecting multimodal representations. The revised framework focuses on the semiotic modes and it describes how students coordinate among different semiotic resources with different modes. In this study, we use multiple cases of students solving oral-exam problems to generalize the approach.
Mathematical Problem Solving
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Author : Berinderjeet Kaur
language : en
Publisher: World Scientific
Release Date : 2009
Mathematical Problem Solving written by Berinderjeet Kaur and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Education categories.
This book is the first in the series of the yearbooks of the Association of Mathematics Educators in Singapore. It is highly unique as it addresses a focused theme of mathematics education. The chapters of the book, illustrate the immense diversity within the theme and presents research that translates into classroom pedagogies. The thirteen chapters of the book illustrate how mathematical problems may be crafted and infused in classroom teaching. Several novel pedagogies, such as learning mathematics through productive failure, problem posing and generative activities are presented in the book. The chapters are comprehensive and laden with evidence-based examples for both mathematics educators and classroom teachers of mathematics. The book is an invaluable contribution towards the already established field of research of mathematical problem solving. It is also a must read for graduate research students and mathematics educators.
Effect Of Using Multiple Representations On Student Success In Solving Rational Radical And Absolute Value Equations And Inequalities
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Author :
language : en
Publisher:
Release Date : 2006
Effect Of Using Multiple Representations On Student Success In Solving Rational Radical And Absolute Value Equations And Inequalities written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with categories.
Because of an emerging body of research and a wealth of classroom experiences, the National Council of Teachers of Mathematics adopted representation as a process standard in 2000 to add to the four previously adopted (1989) process standards - problem solving, reasoning and proof, connections, and communication. The purpose of this study was to determine the effect of using multiple representations on learning to solve equations at the grade 11 level. The sources of data included three unit test scores for two different groups over a seven-week period prior to the treatment and a test score for the two groups after the treatment. Because of small class sizes (23 and 26), the statistical results need to be verified in future studies with larger groups. However, the results of this study indicate that students benefit from a multi-representational approach to equation solving. Students in the experimental group chose the graphing method of solving equations more often than the algebraic method and had more success with graphing compared to the algebraic approach. However, on some questions, students in the experimental group scored lower with the graphical method than the algebraic method. These results indicate that teachers need to weigh the benefits of teaching mathematical concepts with more than one representation against the costs of the learning demands placed on the student.