Beyond Constructivism: Models and Modeling Perspectives on Mathematics Problem Solving, Learning, and Teaching

Richard A. Lesh, Helen M. Doerr

Lawrence Erlbaum| 2003 | 331 páginas | PDF | 30 Mb

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Referência em: MathEduc

This book has two primary goals. On the level of theory development, the book clarifies the nature of an emerging "models and modeling perspective" about teaching, learning, and problem solving in mathematics and science education. On the level of emphasizing practical problems, it clarifies the nature of some of the most important elementary-but-powerful mathematical or scientific understandings and abilities that Americans are likely to need as foundations for success in the present and future technology-based information age. Beyond Constructivism: Models and Modeling Perspectives on Mathematics Problem Solving, Learning, and Teaching features an innovative Web site housing online appendices for each chapter, designed to supplement the print chapters with digital resources that include example problems, relevant research tools and video clips, as well as transcripts and other samples of students' work: modeling/ This is an essential volume for graduate-level courses in mathematics and science education, cognition and learning, and critical and creative thinking, as well as a valuable resource for researchers and practitioners in these areas.

Table of Contents

Contents

Preface

PART I: INTRODUCTION TO A MODELS AND MODELING PERSPECTIVE

1 Foundations of a Models and Modeling Perspective on Mathematics Teaching, Learning, and Problem Solving

Richard Lesh and Helen M. Doerr

2 Model Development Sequences

Richard Lesh, Kathleen Cramer, Helen M. Doerr, Thomas Post, and Judith S. Zawojewski

3 Origins and Evolution of Model-Based Reasoning in Mathematics and Science

Richard Lehrer and Leona Schauble

4 Piagetian Conceptual Systems and Models for Mathematizing Everyday Experiences

Richard Lesh and Guadalupe Carmona

5 A Semiotic Look at Modeling Behavior

Paul E. Kehle and Frank K. Lester, Jr.

6 A Modeling Perspective on Teacher Development

Helen M. Doerr and Richard Lesh

7 A Modeling Approach for Providing Teacher Development

Roberta Y. Schorr and Richard Lesh

8 A Modeling Approach to Describe Teacher Knowledge

Karen Koellner Clark and Richard Lesh

9 Task-Analysis Cycles as Tools for Supporting Students' Mathematical Development

Kay McClain

10 Explanations Why? The Role of Explanations in Answers to (Assessment) Problems

Martin van Reeuwijk and Monica Wijers

PART HI: MODELS AND MODELING AS VIEWED BY HEAVY USERS OF MATHEMATICS

11 What Mathematical Abilities Are Needed for Success Beyond School in a Technology-Based Age of Information?

Richard Lesh, Judith S. Zawojewski, and Guadalupe Carmona

12 The EPICS Model in Engineering Education: Perspectives on Problem-Solving Abilities Needed for Success Beyond Schools

William Oakes and Anthony G. Rud, Jr.

13 The Case for Cases

Geza Kardos

14 Introduction to an Economic Problem: A Models and Modeling Perspective

Charalambos D. Aliprantis and Guadalupe Carmona

15 A Models and Modeling Perspective on Technology-Based Representational Media

Tristan Johnson and Richard Lesh

16 A Models and Modeling Perspective on Skills for the High Performance Workplace

Melissa J. Dark

PART IV: MODELS AND MODELING IN PROBLEM SOLVING AND LEARNING

17 Ends-in-View Problems

Lyn English and Richard Lesh

18 A Models and Modeling Perspective on Problem Solving

Judith S. Zawojewski and Richard Lesh

19 A Models and Modeling Perspective on the Role of Small Group Learning Activities

Judith S. Zawojewski, Richard Lesh, and Lyn English

20 Local Conceptual Development of Proof Schemes in a Cooperative Learning Setting

Guershon Harel and Richard Lesh

21 A Models and Modeling Perspective on Metacognitive Functioning in Everyday Situations Where Problem Solvers Develop Mathematical Constructs

Richard Lesh, Frank K. Lester, Jr., and Margret Hjalmarson

22 Interest, Identity, and Social Functioning: Central Features of Modeling Activity

James A. Middleton, Richard Lesh, and Michelle Heger

PART V: MODELS AND MODELING BEFORE AND AFTER MIDDLE SCHOOL

23 Beyond Constructivism: An Improved Fitness Metaphor for the Acquisition of Mathematical Knowledge

Susan J. Lamon

24 Using a Translation Model for Curriculum Development and Classroom Instruction

Kathleen Cramer

25 Integrating a Models and Modeling Perspective With Existing Research and Practice

Marilyn Carlson, Sean Larsen, and Richard Lesh

26 Models of Functions and Models of Situations: On the Design of Modeling-Based Learning Environments

Beba Shternberg and Michal Yerushalmy

27 From Problem Solving to Modeling: The Evolution of Thinking About Research on Complex Mathematical Activity

Frank K. Lester, Jr., and Paul E. Kehle

28 In What Ways Does a Models and Modeling Perspective Move Beyond Constructivism?

Richard Lesh and Helen M. Doerr

References

Author Index

Subject Index