The Development Of Multiplicative Reasoning In The Learning Of Mathematics
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The Development Of Multiplicative Reasoning In The Learning Of Mathematics
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Author : Guershon Harel
language : en
Publisher: SUNY Press
Release Date : 1994-01-01
The Development Of Multiplicative Reasoning In The Learning Of Mathematics written by Guershon Harel and has been published by SUNY Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-01-01 with Education categories.
Two of the most important concepts children develop progressively throughout their mathematics education years are additivity and multiplicativity. Additivity is associated with situations that involve adding, joining, affixing, subtracting, separating and removing. Multiplicativity is associated with situations that involve duplicating, shrinking, stressing, sharing equally, multiplying, dividing, and exponentiating. This book presents multiplicativity in terms of a multiplicative conceptual field (MCF), not as individual concepts. It is presented in terms of interrelations and dependencies within, between, and among multiplicative concepts. The authors share the view that research on the mathematical, cognitive, and instructional aspects of multiplicative concepts must be situated in an MCF framework.
A Focus On Multiplication And Division
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Author : Elizabeth T. Hulbert
language : en
Publisher: Taylor & Francis
Release Date : 2023-07-04
A Focus On Multiplication And Division written by Elizabeth T. Hulbert and has been published by Taylor & Francis this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-07-04 with Education categories.
The second edition of this book offers a unique approach to making mathematics education research on the teaching and learning of multiplication and division concepts readily accessible and understandable to preservice and in-service K-6 mathematics teachers. Revealing students’ thought processes with extensive annotated samples of student work and vignettes characteristic of classroom teachers’ experience, this book provides teachers a research-based lens to interpret evidence of student thinking, inform instruction, and ultimately improve student learning. Based on research gathered in the Ongoing Assessment Project (OGAP) and updated throughout, this engaging and easy-to-use resource also features the following: New chapters on the OGAP Multiplicative Reasoning Framework and Learning Progressions and Using the OGAP Multiplicative Progression to inform instruction and support student learning In-chapter sections on how Common Core State Standards for Math are supported by math education research Case Studies focusing on a core mathematical idea and different types of instructional responses to illustrate how teachers can elicit evidence of student thinking and use that information to inform instruction Big Ideas frame the chapters and provide a platform for meaningful exploration of the teaching of multiplication and division Looking Back Questions at the end of each chapter allow teachers to analyze student thinking and to consider instructional strategies for their own students Instructional Links to help teachers relate concepts from each chapter to their own instructional materials and programs Accompanying online Support Material that includes an answer key to Looking Back questions, as well as a copy of the OGAP Fraction Framework and Progression A Focus on Multiplication and Division is part of the popular A Focus on . . . collection, designed to aid the professional development of preservice and in-service mathematics teachers. As with the other volumes on addition and subtraction, ratios and proportions, and fractions, this updated new edition bridges the gap between what math education researchers know and what teachers need to know to better understand evidence in student work and make effective instructional decisions.
Providing A Foundation For Teaching Mathematics In The Middle Grades
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Author : Judith T. Sowder
language : en
Publisher: SUNY Press
Release Date : 1995-01-01
Providing A Foundation For Teaching Mathematics In The Middle Grades written by Judith T. Sowder and has been published by SUNY Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-01-01 with Mathematics categories.
This book provides middle school teachers with a firm pedagogical foundation based on the manner in which students learn the mathematics being taught.
The Origins Of Mathematical Knowledge In Childhood
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Author : Catherine Sophian
language : en
Publisher: Routledge
Release Date : 2017-09-25
The Origins Of Mathematical Knowledge In Childhood written by Catherine Sophian and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-09-25 with Education categories.
This book examines the origins and development of children's mathematical knowledge. It contrasts the widely held view that counting is the starting point for mathematical development with an alternative comparison-of-quantities position. According to the comparison-of-quantities position, the concept of number builds upon more basic concepts of equality, inequality, and less-than and greater-than relations, which derive from comparisons between unenumerated quantities such as lengths. The concept of number combines these basic comparative concepts with the concept of a unit of measure, which allows one quantity to be described as a multiple of another. Sophian examines these alternative accounts of children's developing mathematical knowledge in the light of research: on children's counting; on their reasoning about continuous quantities such as length and area; on the development of the concept of unit; on additive and multiplicative reasoning; and on knowledge about fractions. In the closing chapters, Sophian draws out the developmental and the educational implications of the research and theory presented. Developmentally, the comparison-of-quantities position undermines the idea that numerical knowledge develops through domain-specific learning mechanisms in that it links numerical development both to physical knowledge about objects, which is the starting point for the concept of unit, and to the acquisition of linguistic number terms. Instructionally, the comparison-of-quantities perspective diverges from the counting-first perspective in that it underscores the continuity between whole-number arithmetic and fraction learning that stems from the importance of the concept of unit for both. Building on this idea, Sophian advances three instructional recommendations: First, instruction about numbers should always be grounded in thinking about quantities and how numbers represent the relations between them; second, instruction in the early years should always be guided by a long-term perspective in which current objectives are shaped by an understanding of their role in the overall course of mathematics learning; and third, instruction should be directly toward promoting the acquisition of the most general mathematical knowledge possible. The Origins of Mathematical Knowledge in Childhood is intended for researchers, professionals, and graduate students in developmental psychology, educational psychology, and mathematics education, and as a supplementary text for advanced undergraduate courses in cognitive development, educational psychology, and mathematics education.
A Focus On Multiplication And Division
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Author : Elizabeth T. Hulbert
language : en
Publisher: Taylor & Francis
Release Date : 2017-06-26
A Focus On Multiplication And Division written by Elizabeth T. Hulbert and has been published by Taylor & Francis this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-06-26 with Education categories.
A Focus on Multiplication and Division is a groundbreaking effort to make mathematics education research readily accessible and understandable to pre- and in-service K–6 mathematics educators. Revealing students’ thought processes with extensive annotated samples of student work and vignettes characteristic of teachers’ experiences, this book is sure to equip educators with the knowledge and tools needed to modify their lessons and to improve student learning of multiplication and division. Special Features: Looking Back Questions at the end of each chapter allow teachers to analyze student thinking and to consider instructional strategies for their own students. Instructional Links help teachers relate concepts from each chapter to their own instructional materials and programs. Big Ideas frame the chapters and provide a platform for meaningful exploration of the teaching of multiplication and division. Answer Key posted online offers extensive explanations of in-chapter questions. Each chapter includes sections on the Common Core State Standards for Mathematics and integrates the Ongoing Assessment Project (OGAP) Multiplicative Reasoning Progression for formative assessment purposes. Centered on the question of how students develop their understanding of mathematical concepts, this innovative book places math teachers in the mode of ongoing action researchers.
Researching And Using Progressions Trajectories In Mathematics Education
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Author :
language : en
Publisher: BRILL
Release Date : 2019-02-04
Researching And Using Progressions Trajectories In Mathematics Education written by and has been published by BRILL this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-02-04 with Education categories.
This book presents a contemporary focus on significant issues in STEM teaching, learning and research that are valuable in preparing students for a digital 21st century. The book chapters cover a wide spectrum of issues and topics using a wealth of research methodologies and methods.
A Study Of Proportional Reasoning As It Relates To The Development Of Multiplication Concepts
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Author : Judith Flowers
language : en
Publisher:
Release Date : 1998
A Study Of Proportional Reasoning As It Relates To The Development Of Multiplication Concepts written by Judith Flowers and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with categories.
Acquisition Of Mathematics Concepts And Processes
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Author : Richard A. Lesh
language : en
Publisher:
Release Date : 1983
Acquisition Of Mathematics Concepts And Processes written by Richard A. Lesh and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983 with Mathematics categories.
Using Mathematics To Understand The World
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Author : Terezinha Nunes
language : en
Publisher: Routledge
Release Date : 2021-08-05
Using Mathematics To Understand The World written by Terezinha Nunes and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-08-05 with Psychology categories.
Using Mathematics to Understand the World: How Culture Promotes Children's Mathematics offers fundamental insight into how mathematics permeates our lives as a way of representing and thinking about the world. Internationally renowned experts Terezinha Nunes and Peter Bryant examine research into children’s mathematical development to show why it is important to distinguish between quantities, relations and numbers. Using Mathematics to Understand the World presents a theory about the development of children’s quantitative reasoning and reveals why and how teaching about quantitative reasoning can be used to improve children’s mathematical attainment in school. It describes how learning about the analytical meaning of numbers is established as part of mathematics at school but quantitative reasoning is emphasized less even though it is increasingly acclaimed as essential for thinking mathematically and for using mathematics to understand the world. This essential text is for all students of mathematics education, developmental psychology and cognitive psychology. By including activities for parents and professionals to try themselves, it may help you to recognize your own quantitative reasoning.
Mathematical Reasoning Of Children And Adults
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Author : Alina Galvão Spinillo
language : en
Publisher: Springer Nature
Release Date : 2021-05-24
Mathematical Reasoning Of Children And Adults written by Alina Galvão Spinillo and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-05-24 with Education categories.
This book adopts an interdisciplinary approach to investigate the development of mathematical reasoning in both children and adults and to show how understanding the learner’s cognitive processes can help teachers develop better strategies to teach mathematics. This contributed volume departs from the interdisciplinary field of psychology of mathematics education and brings together contributions by researchers from different fields and disciplines, such as cognitive psychology, neuroscience and mathematics education. The chapters are presented in the light of the three instances that permeate the entire book: the learner, the teacher, and the teaching and learning process. Some of the chapters analyse the didactic challenges that teachers face in the classroom, such as how to interpret students' reasoning, the use of digital technologies, and their knowledge about mathematics. Other chapters examine students' opinions about mathematics, and others analyse the ways in which students solve situations that involve basic and complex mathematical concepts. The approaches adopted in the description and interpretation of the data obtained in the studies documented in this book point out the limits, the development, and the possibilities of students' thinking, and present didactic and cognitive perspectives to the learning scenarios in different school settings. Mathematical Reasoning of Children and Adults: Teaching and Learning from an Interdisciplinary Perspective will be a valuable resource for both mathematics teachers and researchers studying the development of mathematical reasoning in different fields, such as mathematics education, educational psychology, cognitive psychology, and developmental psychology.