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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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

Topics in Elementary Geometry

O. Bottema

Springer | 2008 | 142 páginas | PDF| 1,2 MB

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This small book has for a long time been a unique place to find classical results from geometry, such as Pythagoras' theorem, the nine-point circle, Morley's triangle, Poncelet's polygons, and many other subjects. In addition, this book contains recent, geometric theorems which have been obtained in this classical field over the past years. There are 27 independent chapters on a wide range of topics in elementary plane Euclidean geometry, at a level just beyond what is usually taught in a good high school or college geometry course. The selection of topics is intelligent, varied, and stimulating. In a small space the author provides many thought-provoking ideas. This book will fit in well with the increasing interest for geometry in research and education. This book was originally published in Dutch, and this will be the first English translation.

3-D Geometric Origami: Modular Polyhedra

Rona Gurkewitz, Bennett Arnstein

Dover Publications | 1996 | 80 pages | PDF | 5,7 Mb

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Innovative, stimulating and challenging book combines the art of paperfolding with making polyhedra-based models. Projects range from the relatively simple cube and tetrahedron to such mind-boggling fabrications as the double pentagonal pyramid and the truncated hexadecahedron. Instructions and diagrams included.

Key to Algebra

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Decimais

Key to Decimals: Decimal Concepts
Book 1 (Key to Decimals)
Steven Rasmussen, Spreck Rosekraus,
Key Curriculum Press | 1985 | PDF | 7 MB | 45 páginas

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Key to Decimals: Adding, Subtracting, Multiplying
Book 2 (Key to Decimals)

Key Curriculum Press | 1985 | PDF | 5,1 MB | 48 páginas
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Key to Decimals: Dividing
Book 3 (Key to Decimals)
Steven Rasmussen, Spreck Rosekraus
Key Curriculum Press | 1985 | PDF | 5 MB | 47 páginas

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Key to Decimals: Answers and Notes
Steven Rasmussen, Spreck Rosekraus
Key Curriculum Press | 1993 | PDF | 11,4 MB | 48 páginas

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Statistics in Action, Understanding a World of Data

Ann E. Watkins; Richard L. Scheaffer e George W. Cobb

Key Curriculum Press | 2008 - 2ª edição | 894 páginas | pdf | 28 MB

Ano de escolaridade: 11.º ano

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Contents
A Note to Students from the Authors ix
Statistical Reasoning: Investigating a
Claim of Discrimination 2
1.1 Discrimination in the Workplace: Data Exploration 4
1.2 Discrimination in the Workplace: Inference 11
Chapter Summary 20
Exploring Distributions 26
2.1 Visualizing Distributions: Shape, Center, and Spread 28
2.2 Graphical Displays of Distributions 42
2.3 Measures of Center and Spread 56
2.4 Working with Summary Statistics 74
2.5 The Normal Distribution 83
Chapter Summary 95
Relationships Between Two Quantitative Variables 104
3.1 Scatterplots 106
3.2 Getting a Line on the Pattern 116
3.3 Correlation: The Strength of a Linear Trend 140
3.4 Diagnostics: Looking for Features That the Summaries Miss 162
3.5 Shape-Changing Transformations 179
Chapter Summary 203
Sample Surveys and Experiments 216
4.1 Why Take Samples, and How Not To 219
4.2 Random Sampling: Playing It Safe by Taking Chances 231
4.3 Experiments and Inference About Cause 243
4.4 Designing Experiments to Reduce Variability 262
Chapter Summary 278
Probability Models 286
5.1 Constructing Models of Random Behavior 288
5.2 Using Simulation to Estimate Probabilities 301
5.3 The Addition Rule and Disjoint Events 315
5.4 Conditional Probability 325
5.5 Independent Events 339
Chapter Summary 349
Probability Distributions 356
6.1 Random Variables and Expected Value 358
6.2 The Binomial Distribution 382
6.3 The Geometric Distribution 393
Chapter Summary 402
Sampling Distributions 408
7.1 Generating Sampling Distributions 410
7.2 Sampling Distribution of the Sample Mean 426
7.3 Sampling Distribution of the Sample Proportion 446
Chapter Summary 458
Inference for Proportions 466
8.1 Estimating a Proportion with Confi dence 468
8.2 Testing a Proportion 490
8.3 A Confi dence Interval for the Diff erence of Two Proportions 518
8.4 A Signifi cance Test for the Diff erence of Two Proportions 526
8.5 Inference for Experiments 539
Chapter Summary 554
Inference for Means 560
9.1 A Confi dence Interval for a Mean 562
9.2 A Signifi cance Test for a Mean 580
9.3 When Things Aren’t Normal 602
9.4 Inference for the Diff erence Between Two Means 616
9.5 Paired Comparisons 640
Chapter Summary 663
Chi-Square Tests 672
10.1 Testing a Probability Model: The Chi-Square Goodness-of-Fit Test 674
10.2 The Chi-Square Test of Homogeneity 692
10.3 The Chi-Square Test of Independence 711
Chapter Summary 728
Inference for Regression 736
11.1 Variation in the Slope from Sample to Sample 739
11.2 Making Inferences About Slopes 755
11.3 Transforming for a Better Fit 771
Chapter Summary 790
Statistics in Action: Case Studies 798
12.1 Mum’s the Word! 800
12.2 Keeping Tabs on Americans 803
12.3 Baseball: Does Money Buy Success? 810
12.4 Martin v. Westvaco Revisited: Testing for Discrimination
Against Employees 817
Statistical Tables 824
Table A: Standard Normal Probabilities 824
Table B: t-Distribution Critical Values 826

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Discovering Algebra - An Investigative Approach

Jerald Murdock, Ellen Kamischke, e Eric Kamischke

Key Curriculum Press | 2007 - 2ª edição | 721 páginas | pdf | 21 MB

Anos de escolaridade: 8.º a 10.º ano

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Discovering Algebra will help you reach more of your students with meaningful activities that help them connect abstract mathematical concepts to concrete experiences.
The Discovering Algebra approach improves learning in many ways:

Investigations at the beginning of each lesson help you give all your students—regardless of their mathematical backgrounds—a shared experience from which to base their learning.
You will be able to teach an algebra course that is both rigorous and accessible to your students because the investigations give meaning to mathematics that all students, regardless of their skill level, can understand.
The investigations will often prompt more advanced students to dig deeper, giving you a natural way to extend the lesson and connect algebra to other topics.
Investigations, visual representations, and opportunities for discussion enable you to integrate multiple teaching modes into your classroom so that visual, auditory, and kinesthetic learners all benefit.
These investigations will also provide you with another tool to use when reviewing and building upon concepts in class. Many teachers tell us that their students find it easier to remember previously taught mathematical concepts and skills when reminded of the classroom activity that helped them learn the concept.