Teaching Fractions Through Situations : A Fundamental Experiment

 

(Mathematics Education Library) 

Guy Brousseau e Virginia McShane Warfield 

Springer | 2014 | 226 páginas | rar - pdf |1,8 Mb

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This work presents one of the original and fundamental experiments of Didactique, a research program whose underlying tenet is that Mathematics Education research should be solidly based on scientific observation. Here the observations are of a series of adventures that were astonishing for both the students and the teachers: the reinvention of fractions and of decimal numbers in a sequence of lessons and situations that permitted the students to construct the concepts for themselves. The book leads the reader through the highlights of the sequence's structure and some of the reasoning behind the lesson choices. It then presents explanations of some of the principal concepts of the Theory of Situations. In the process, it offers the reader the opportunity to join a lively set of fifth graders as they experience a particularly attractive set of lessons and master a topic that baffles many of their contemporaries.

Linguistic and Cultural Influences on Learning Mathematics

(Psychology of Education and Instruction Series)

Rodney R. Cocking e Jose P. Mestre 

Routledge | 1988 | 329 páginas | rar- pdf | 16,1 Mb

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The combined impact of linguistic, cultural, educational and cognitive factors on mathematics learning is considered in this unique book. By uniting the diverse research models and perspectives of these fields, the contributors describe how language and cognitive factors can influence mathematical learning, thinking and problem solving. The authors contend that cognitive skills are heavily dependent upon linguistic skills and both are critical to the representational knowledge intimately linked to school achievement in mathematics.

Contents
Contributors/ ix
Foreword xi
Chapter 1 Introduction: Considerations of Language Mediators of Mathematics Learning
Rodney R. Cocking, Jose P. Mestre
Chapter 2 Conceptual Issues Related to Mathematics Achievement of Language Minority Children 
Rodney R. Cocking, Susan Chipman
Chapter 3 Linking Language with Mathematics Achievement: Problems and Prospects
Geoffrey B. Saxe
Chapter 4 Intention and Convention in Mathematics Instruction: Reflections on the Learning of Deaf Students 63
Joan B. Stone
Chapter 5 Why Should Developmental Psychologists Be Interested in Studying the Acquisition of Arithmetic? 73
Ellin Kofsky Scholnick
Chapter 6 Patterns of Experience and the Language of Mathematics 91
Manon P. Charbonneau, Vera John-Steiner
Chapter 7 Bilingualism, Cognitive Function, and Language Minority Group Membership 101
Edward A. De A vila
Chapter 8 the Mathematics Achievement Characteristics of Asian-American Students 123
Sau-Lim Tsang
Chapter 9 Mexican-American Women and Mathematics: Participation, Aspirations, and Achievement 137
Patricia MacCorquodale
Chapter 10 Assumptions and Strategies Guiding Mathematics Problem Solving by Ute Indian Students 161
William L. Leap
Chapter 11 Opportunity to Learn Mathematics in Eighth-Grade Classrooms in the United States: Some Findings from the Second International Mathematics Study 187
Kenneth J. Travers
Chapter 12 the Role of Language Comprehension in Mathematics and Problem Solving 201
Jose P. Mestre
Chapter 13 Linguistic Features of Mathematical Problem Solving: Insights and Applications 221
George Spanos, Nancy C. Rhodes, Theresa Corasaniti Dale, Joann Crandall
Chapter 14 Bilinguals' Logical Reasoning Aptitude: a Construct Validity Study 241
Richard P. Duran
Chapter 15 Effects of Home Language and Primary Language on Mathematics Achievement: a Model and Results for Secondary Analysis 259
David E. Myers, Ann M. Milne
A Final Note... 294
Epilogue: And Then I Went to School 295
Joseph H. Suina
Author Index 301
Subject Index 309

Investigations into Assessment in Mathematics Education: An ICMI Study

(New ICMI Study Series)

Mogens Niss

Springer |1993; edição de 2010 | 272 páginas | rar - pdf | 24,5 Mb

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This book is one of the first to attempt a systematic in-depth analysis of assessment in mathematics education in most of its important aspects: it deals with assessment in mathematics education from historical, psychological, sociological, epistmological, ideological, and political perspectives. The book is based on work presented at an invited international ICMI seminar and includes chapters by a team of outstanding and prominent scholars in the field of mathematics education. Based on the observation of an increasing mismatch between the goals and accomplishments of mathematics education and prevalent assessment modes, the book assesses assessment in mathematics education and its effects. In so doing it pays particular attention to the need for and possibilities of assessing a much wider range of abilities than before, including understanding, problem solving and posing, modelling, and creativity. The book will be of particular interest to mathematics educators who are concerned with the role of assessment in mathematics education, especially as regards innovation, and to everybody working within the field of mathematics education and related areas: in R&D, curriculum planning, assessment institutions and agencies, teacher trainers, etc. 

TABLE OF CONTENTS
MOGENS NISS
Assessment in Mathematics Education and its Effects: An Introduction 1
JEREMY KILPATRICK
The Chain and the Arrow: From the History of Mathematics Assessment 31
GEOFFREY HOWSON
The Relationship Between Assessment, Curriculum and Society 47
JIM RIDGWAY & DON PASSEY
An International View of Mathematics Assessment - Through a Class, Darkly
PETER GALBRAITH
Paradigms, Problems and Assessment: Some Ideological Implications
DAVID WHEELER
Epistemological Issues and Challenges to Assessment: What is Mathematical Knowledge?
THOMAS A. ROMBERG
How One Comes to Know:
Models and Theories of the Learning of Mathematics
ANTOINE BODIN
What Does to Assess Mean? The Case of Assessing Mathematical Knowledge
STIEG MELLIN-OLSEN
A Critical View of Assessment in Mathematics Education: Where is the Student as a Subject? 143
HERBERT P. GINSBURG & SUSAN F. JACOBS & LUZ S. LOPEZ
Assessing Mathematical Thinking and Learning Potential in Primary Grade Children 157
BENGT JOHANSSON
Diagnostic Assessment in Arithmetic 169
JOHN IZARD
Challenges to the Improvement of Assessment Practice 185
MALCOLM SWAN
Improving the Design and Balance of Mathematical Assessment 195
DEREK FOXMAN
The Assessment of Performance Unit's Monitoring Surveys 1978-1987 217
DAVID F. ROBITAILLE & J. STUART DONN
TIMSS: The Third International Mathematics and Science Study 229
GIlA HANNA
The Validity of International Performance Comparisons 245
NORMAN L. WEBB
Visualizing a Theory of the Assessment of Students' Knowledge of Mathematics 253
Index 265

Early Fraction Learning

(Recent Research in Psychology)

 Robert Hunting e  Gary Davis

Springer | 1991 | 244 páginas | pdf | 9,1 Mb

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Early Fraction learning is centrally of interest to students and researchersin mathematics education, tackling as it does one of that discipline's most vexing problems: why are fractions so difficult to learn and to teach?

Contents
Introduction
Robert P. Hunting, Gary Davis
Pre-fraction Concepts of Preschoolers
Robert P. Hunting, Christopher F. Sharpley
Dimensions of Young Children’s Conceptions of the Fraction One Half
Robert P. Hunting, Gary E. Davis
The Social Origins of Pre-fraction Knowledge in Three Year Olds
Robert P. Hunting
Higher Order Thinking in Young Children’s Engagements with a Fraction Machine
Robert P. Hunting, Gary Davis, John C. Bigelow
Fractions as Operators and as Cloning Machines
Gary Davis
Preschoolers’ Knowledge of Counting and Sharing in Discrete Quantity Settings
Kristine L. Pepper
Preschoolers’ Spontaneous Partitioning of Discrete Items
Gary Davis, Robert P. Hunting
Cognitive Issues about Dealing
Gary Davis
Sharing by Dealing as Problem Solving
Gary Davis, Kristine L. Pepper
Cognitive Research on Early Fraction Learning Applied to Classrooms: Two Experiments
Robert P. Hunting, Douglas M. Clarke, Charles Lovitt
The Interaction of Thought, Words, and Deeds in Children’s Early Fraction Learning
Robert P. Hunting
On Clinical Methods for Studying Young Children’s Mathematics
Gary Davis, Robert P. Hunting
A Fraction of Epistemology

Gary Davis

Elementary and Middle School Mathematics: Teaching Developmentally

(Teaching Student-Centered Mathematics Series)

John A. Van de Walle, Karen S. Karp e Jennifer M. Bay-Williams 

Pearson | 2012 - 8.ª edição | 575 páginas | rar - pdf | 23,4 Mb

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Written by leaders in the field, this best-selling book will guide teachers as they help all Pre-K — 8 learners make sense of math by supporting their own mathematical understanding and effective planning and instruction.

Elementary and Middle School Mathematics: Teaching Developmentallywas written to help teacher candidates and practicing teachers understand mathematics and become more confident in their ability to teach the subject to children in pre-K through eighth grade. Structured for easy reference, offering 23 chapters reflecting the latest research to consult throughout one’s teaching career, the revised edition infuses NCTM and Common Core State Standards with the benefits of problem-based mathematics instruction.
The Eighth Edition better prepares teachers to teach mathematics to all learners by including new strategies for English language learners and students with disabilities. The amount of coverage relating to mathematics in early childhood has been increased. More activities infusing technology and samples of authentic student work are introduced. Increased emphasis on formative assessment, showcased with an icon and notes throughout, guide teachers to master this difficult practice.

Contents

Section I Teaching Mathematics: Foundations and Perspectives

Chapter 1 T eaching Mathematics in the 21st Century 1

Chapter 2 Exploring What It Means to Know and Do Mathematics 13

Chapter 3 Teaching Through Problem Solving 32

Chapter 4 Planning in the Problem-Based Classroom 59

Chapter 5 Building Assessment into Instruction 78

Chapter 6 T eaching Mathematics Equitably to All Children 94

Chapter 7 Using Technological Tools to Teach Mathematics 113

Section II Development of Mathematical Concepts and Procedures

Chapter 8 Developing Early Number Concepts and Number Sense 128

Chapter 9 D eveloping Meanings for the Operations 148

Chapter 10 H elping Students Master the Basic Facts 171

Chapter 11 Developing Whole-Number Place-Value Concepts 192

Chapter 12 D eveloping Strategies for Addition and Subtraction Computation 216

Chapter 13 D eveloping Strategies for Multiplication and Division Computation 236

Chapter 14 Algebraic Thinking: Generalizations, Patterns, and Functions 258

Chapter 15 Developing Fraction Concepts 290

Chapter 16 Developing Strategies for Fraction Computation 315

Chapter 17 Developing Concepts of Decimals and Percents 338

Chapter 18 Proportional Reasoning 357

Chapter 19 Developing Measurement Concepts 375

Chapter 20 Geometric Thinking and Geometric Concepts 402

Chapter 21 Developing Concepts of Data Analysis 434

Chapter 22 Exploring Concepts of Probability 454

Chapter 23 Developing Concepts of Exponents, Integers, and Real Numbers 472

Appendix A Standards for Mathematical Practice 491

Appendix B Standards for Teaching Mathematics 493

Appendix C G uide to Blackline Masters 495

Fibonacci Numbers

(Dover Books on Mathematics)

Nikolai Nikolaevich Vorob'ev

Dover Publications |  2011 | 80 páginas | rar - epub | 1,4 Mb

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Fibonacci numbers date back to an 800-year-old problem concerning the number of offspring born in a single year to a pair of rabbits. This book offers the solution and explores the occurrence of Fibonacci numbers in number theory, continued fractions, and geometry. A discussion of the "golden section" rectangle, in which the lengths of the sides can be expressed as a ration of two successive Fibonacci numbers, draws upon attempts by ancient and medieval thinkers to base aesthetic and philosophical principles on the beauty of these figures. Recreational readers as well as students and teachers will appreciate this light and entertaining treatment of a classic puzzle.

CONTENTS
Foreword
Introduction
I.    The simplest properties of Fibonacci numbers
II.   Number-theoretic properties of Fibonacci numbers
III.  Fibonacci numbers and continued fractions
IV.  Fibonacci numbers and geometry

V.   Conclusion

Visualizing Elementary and Middle School Mathematics Methods

Joan Cohen Jones

Wiley | 2011 | 512 páginas | rar - PDF | 48,3 Mb

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The goal of Visualizing Elementary and Middle School Mathematics Methods is to teach mathematics in a way that excites and motivates readers, with an accessible format that serves as an introduction to the teaching of mathematics. This text, in partnership with National Geographic, is designed to present mathematics content and pedagogy in a fresh new way. This unique approach, while maintaining necessary rigor, provides the opportunity to set aside previous beliefs about mathematics and to learn concepts and pedagogy from a new perspective.

The structure of Visualizing Elementary and Middle School Mathematics Methods is similar to the format of other methods texts, however, it has many unique features that are designed to be engaging and make the text relevant for readers. It begins with a brief summary of the history of mathematics. Diversity is integrated into the content of every chapter, through Multicultural Perspectives in Mathematics.