Schoenfeld Mathematical Problem Solving

1. Auflage 2014
ISBN: 978-1-4832-9548-0
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 409 Seiten, Web PDF

This book is addressed to people with research interests in the nature of mathematical thinking at any level, topeople with an interest in 'higher-order thinking skills' in any domain, and to all mathematics teachers. The focal point of the book is a framework for the analysis of complex problem-solving behavior. That framework is presented in Part One, which consists of Chapters 1 through 5. It describes four qualitatively different aspects of complex intellectual activity: cognitive resources, the body of facts and procedures at one's disposal; heuristics, 'rules of thumb' for making progress in difficult situations; control, having to do with the efficiency with which individuals utilize the knowledge at their disposal; and belief systems, one's perspectives regarding the nature of a discipline and how one goes about working in it. Part Two of the book, consisting of Chapters 6 through 10, presents a series of empirical studies that flesh out the analytical framework. These studies document the ways that competent problem solvers make the most of the knowledge at their disposal. They include observations of students, indicating some typical roadblocks to success. Data taken from students before and after a series of intensive problem-solving courses document the kinds of learning that can result from carefully designed instruction. Finally, observations made in typical high school classrooms serve to indicate some of the sources of students' (often counterproductive) mathematical behavior.

Alan Schoenfeld is the Elizabeth and Edward Conner Professor of Education and Affiliated Professor of Mathematics at the University of California at Berkeley. He is a Fellow of the American Association for the Advancement of Science and of the American Educational Research Association (AERA), and a Laureate of the education honor society Kappa Delta Pi; he has served as President of AERA and vice President of the National Academy of Education. He holds the International Commission on Mathematics Instruction's Klein Medal, AERA's Distinguished Contributions to Research in Education award, and the Mathematical Association of America's Mary P. Dolciani award. Mathematical Problem Solving is laid the foundations for the field's work on mathematical thinking and problem solving. The ideas in the book have been referred to as the 'industry standard for research on mathematical problem solving."

Autoren/Hrsg.

Schoenfeld, Alan H.

Inhaltsverzeichnis

1;Front Cover;1
2;Mathematical Problem Solving;4
3;Copyright Page;5
4;Table of Contents;8
5;Dedication;6
6;Preface;12
7;Acknowledgments;16
8;Introduction and Overview;18
9;Part One: Aspects of Mathematical Thinking: A Theoretical Overview;26
9.1;Chapter 1. A Framework for the Analysis of Mathematical Behavior;28
9.1.1;Overview;28
9.1.2;Typical Problems, Typical Behavior:The Four Categories Illustrated;31
9.1.3;Resources;34
9.1.4;Heuristics;39
9.1.5;Control;44
9.1.6;Belief Systems;51
9.1.7;Summary;61
9.2;Chapter 2. Resources;63
9.2.1;Routine Access to Relevant Knowledge;63
9.2.2;The Broad Spectrum of Resources;71
9.2.3;Flawed Resources and Consistent Error Patterns;78
9.2.4;Summary;84
9.3;Chapter 3. Heuristics;86
9.3.1;Introduction and Overview;86
9.3.2;What a Problem Is and Who the Students Are;91
9.3.3;Toward More Precise and Usable Descriptionsof Heuristic Strategies;93
9.3.4;The Complexity of Implementing a "Straightforward" Heuristic Solution;101
9.3.5;Heuristics and Resources Deeply Intertwined;108
9.3.6;Summary;112
9.4;Chapter 4. Control;114
9.4.1;Introduction and Overview;114
9.4.2;On the Importance of Control: A Look at a Microcosm;117
9.4.3;Modeling a Control Strategy for Heuristic Problem Solving;123
9.4.4;Toward a Broader View of Control;131
9.4.5;Literature Related to Control;144
9.4.6;Summary;160
9.5;Chapter 5. Belief Systems;162
9.5.1;Selections from the Relevant Literature;163
9.5.2;A Mathematician Works a Construction Problem;174
9.5.3;The Student as Pure Empiricist: A Model of Empirical Behavior;177
9.5.4;How the Model Corresponds to Performance;181
9.5.5;A Deeper Look at Empiricism: CS and AM Work Problem 1.1;182
9.5.6;Further Evidence Regarding Naive Empiricism: DW and SP Work Four Related Problems;191
9.5.7;Summary;201
10;Part Two: Experimental and Observational Studies, Issues of Methodology, and Questions of Where We Go Next;204
10.1;Overview;204
10.2;Chapter 6. Explicit Heuristic Training as a Variable in Problem-Solving
Performance;206
10.2.1;A Brief Discussion of Relevant Literature;207
10.2.2;Experimental Design;210
10.2.3;Results;220
10.2.4;Two Methodological Questions;225
10.2.5;Discussion;226
10.2.6;Implications and Directions for Extension;229
10.2.7;Summary;231
10.3;Chapter 7. Measures of Problem-Solving Performance and Problem-Solving Instruction;233
10.3.1;A Brief Discussion of Relevant Work;234
10.3.2;The Experimental and Control Treatments;236
10.3.3;Measure 1 : A Plausible-Approach Analysis of Fully Solved Questions;240
10.3.4;Discussion of Testing Results;247
10.3.5;Measure 2: Students' Qualitative Assessments of Their Problem Solving;248
10.3.6;Measure 3: Heuristic Fluency and Transfer;250
10.3.7;A Brief Discussion of Control Issues;255
10.3.8;Summary;256
10.4;Chapter 8. Problem Perception, Knowledge Structure, and Problem-Solving Performance;259
10.4.1;Background;260
10.4.2;Method;264
10.4.3;Results of the Sortings;269
10.4.4;Discussion;276
10.4.5;Summary;280
10.4.6;Appendix: Problems Used in the Card Sort;282
10.5;Chapter 9. Verbal Data, Protocol Analysis,and the Issue of Control;287
10.5.1;Overview;287
10.5.2;Background, Part 1 : Verbal Methods;289
10.5.3;Through a Glass Darkly: A Close Look at Verbal Data;292
10.5.4;Background, Part 2: Other Protocol Coding Schemesand Issues of Control;300
10.5.5;The Major Issues for Analysis:A Brief Discussion of Two Protocols;305
10.5.6;A Framework for the Macroscopic Analysis ofProblem-Solving Protocols;309
10.5.7;Episodes and the Associated Questions;314
10.5.8;The Full Analysis of a Protocol;318
10.5.9;A Further Discussion of Control: More Data from Students, and the Analysis of an Expert Problem Solver's Protocol;323
10.5.10;Brief Discussion: Limitations and Needed Work;331
10.5.11;Summary;333
10.5.12;Appendix 9.1: A Single-Person Protocol of the Cells Problem;334
10.5.13;Appendix 9.2: Protocol 9.2;336
10.5.14;Appendix 9.3: Protocol 9.3;341
10.5.15;Appendix 9.4: Protocol 9.4;348
10.5.16;Appendix 9.5: Protocol 9.5;357
10.6;Chapter 10. The Roots of Belief;362
10.6.1;A Discussion of Two Geometry Protocols;363
10.6.2;A Brief Analysis of Protocol 10.1;364
10.6.3;A Brief Analysis of Protocol 10.2;366
10.6.4;A Brief Discussion;371
10.6.5;The Strength of Empiricism: More Data;372
10.6.6;The Origins of Empiricism;374
10.6.7;Summary;390
10.6.8;Postscript;392
10.6.9;Appendix 10.1: Protocol 10.1;392
10.6.10;Appendix 10.2: Protocol 10.2;399
11;References;405
12;Author Index;416
13;Subject Index;420