Beyond constructivism : models and modeling perspectives on mathematics problem solving, learning, and teaching

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:

http://tcct.soe.purdue.edu/booksULandULjournals/modelsULandUL 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.

Richard Lesh and Helen M. DoerrRichard Lesh and Kathleen Cramer and Helen M. Doerr and Thomas Post and Judith S. ZawojewskiRichard Lehrer and Leona SchaubleRichard Lesh and Guadalupe CarmonaPaul E. Kehle and Frank K. Lester, Jr.Helen M. Doerr and Richard LeshRoberta Y. Schorr and Richard LeshKaren Koellner Clark and Richard LeshKay McClainMartin van Reeuwijk and Monica WijersRichard Lesh and Judith S. Zawojewski and Guadalupe CarmonaWilliam Oakes and Anthony G. Rud, Jr.Geza KardosCharalambos D. Aliprantis and Guadalupe CarmonaTristan Johnson and Richard LeshMelissa J. DarkLyn English and Richard LeshJudith S. Zawojewski and Richard LeshJudith S. Zawojewski and Richard Lesh and Lyn EnglishGuershon Harel and Richard LeshRichard Lesh and Frank K. Lester, Jr. and Margret HjalmarsonJames A. Middleton and Richard Lesh and Michelle HegerSusan J. LamonKathleen CramerMarilyn Carlson and Sean Larsen and Richard LeshBeba Shternberg and Michal YerushalmyFrank K. Lester, Jr. and Paul E. KehleRichard Lesh and Helen M. Doerr

Preface	p. ix
Part I Introduction to a Models and Modeling Perspective
1 Foundations of a Models and Modeling Perspective on Mathematics Teaching, Learning, and Problem Solving	p. 3
2 Model Development Sequences	p. 35
3 Origins and Evolution of Model-Based Reasoning in Mathematics and Science	p. 59
4 Piagetian Conceptual Systems and Models for Mathematizing Everyday Experiences	p. 71
5 A Semiotic Look at Modeling Behavior	p. 97
Part II A Models and Modeling Perspective on Teacher Development
6 A Modeling Perspective on Teacher Development	p. 125
7 A Modeling Approach for Providing Teacher Development	p. 141
8 A Modeling Approach to Describe Teacher Knowledge	p. 159
9 Task-Analysis Cycles as Tools for Supporting Students' Mathematical Development	p. 175
10 Explanations Why? The Role of Explanations in Answers to (Assessment) Problems	p. 191
Part III 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?	p. 205
12 The EPICS Model in Engineering Education: Perspectives on Problem-Solving Abilities Needed for Success Beyond Schools	p. 223
13 The Case for Cases	p. 241
14 Introduction to an Economic Problem: A Models and Modeling Perspective	p. 255
15 A Models and Modeling Perspective on Technology-Based Representational Media	p. 265
16 A Models and Modeling Perspective on Skills for the High Performance Workplace	p. 279
Part IV Models and Modeling in Problem Solving and Learning
17 Ends-in-View Problems	p. 297
18 A Models and Modeling Perspective on Problem Solving	p. 317
19 A Models and Modeling Perspective on the Role of Small Group Learning Activities	p. 337
20 Local Conceptual Development of Proof Schemes in a Cooperative Learning Setting	p. 359
21 A Models and Modeling Perspective on Metacognitive Functioning in Everyday Situations Where Problem Solvers Develop Mathematical Constructs	p. 383
22 Interest, Identity, and Social Functioning: Central Features of Modeling Activity	p. 405
Part V Models and Modeling Before and After Middle School
23 Beyond Constructivism: An Improved Fitness Metaphor for the Acquisition of Mathematical Knowledge	p. 435
24 Using a Translation Model for Curriculum Development and Classroom Instruction	p. 449
25 Integrating a Models and Modeling Perspective With Existing Research and Practice	p. 465
26 Models of Functions and Models of Situations: On the Design of Modeling-Based Learning Environments	p. 479
Part VI Next Steps
27 From Problem Solving to Modeling: The Evolution of Thinking About Research on Complex Mathematical Activity	p. 501
28 In What Ways Does a Models and Modeling Perspective Move Beyond Constructivism?	p. 519
References	p. 557
Author Index	p. 583
Subject Index	p. 589

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