Mathematical Problem Solving

Cover......Page __sk_0000.djvu
Copyright......Page __sk_0002.djvu
Contents......Page __sk_0005.djvu
Preface......Page __sk_0009.djvu
Acknowledgments......Page __sk_0013.djvu
Introduction and Overview......Page __sk_0015.djvu
Part 1. Aspects of Mathematical Thinking: A Theoretical Overview......Page __sk_0023.djvu
Overview......Page __sk_0025.djvu
Typical Problems, Typical Behavior: The Four Categories Illustrated......Page __sk_0028.djvu
Resources......Page __sk_0031.djvu
Heuristics......Page __sk_0036.djvu
Control......Page __sk_0041.djvu
Belief Systems......Page __sk_0048.djvu
Summary......Page __sk_0058.djvu
Routine Access to Relevant Knowledge......Page __sk_0060.djvu
The Broad Spectrum of Resources......Page __sk_0068.djvu
Flawed Resources and Consistent Error Patterns......Page __sk_0075.djvu
Summary......Page __sk_0081.djvu
Introduction and Oerview......Page __sk_0083.djvu
What a Problem Is and Who the Students Are......Page __sk_0088.djvu
Toward More Precise and Usable Descriptions of Heuristic Strategies......Page __sk_0090.djvu
The Complexity of Implementing a \"Straightforward\" Heuristic Solution......Page __sk_0098.djvu
Heuristics and Resources Deeply Intertwined......Page __sk_0105.djvu
Summary......Page __sk_0109.djvu
Introduction and Overview......Page __sk_0111.djvu
On the Importance of Control: A Look at a Microcosm......Page __sk_0114.djvu
Modeling a Control Strategy for Heuristic Problem Solving......Page __sk_0120.djvu
Toward a Broader View of Control......Page __sk_0128.djvu
Literature Related to Control......Page __sk_0141.djvu
Summary......Page __sk_0157.djvu
5. Belief Systems......Page __sk_0159.djvu
Selections from the Relevant Literature......Page __sk_0160.djvu
A Mathematician Works a Construction Problem......Page __sk_0171.djvu
The Student as Pure Empiricist: A Model of Empirical Behavior......Page __sk_0174.djvu
How the Model Corresponds to Performance......Page __sk_0178.djvu
A Deeper Look at Empiricism: CS and AM Work Problem 1.1......Page __sk_0179.djvu
Further Evidence Regarding Naive Empiricism: DW and SP Work Four Related Problems......Page __sk_0188.djvu
Summary......Page __sk_0198.djvu
Overview......Page __sk_0201.djvu
6. Explicit Heuristic Training as a Variable in Problem-Solving Performance......Page __sk_0203.djvu
A Brief Discussion of Relevant Literature......Page __sk_0204.djvu
Experimental Design......Page __sk_0207.djvu
Results......Page __sk_0217.djvu
Two Methodological Questions......Page __sk_0222.djvu
Discussion......Page __sk_0223.djvu
Implications and Directions for Extension......Page __sk_0226.djvu
Summary......Page __sk_0228.djvu
7. Measures of Problem-Solving Performance and Problem-Solving Instruction......Page __sk_0230.djvu
A Brief Discussion of Relevant Work......Page __sk_0231.djvu
The Experimental and Control Treatments......Page __sk_0233.djvu
Measure 1: A Plausible-Approach Analysis of Fully Solved Questions......Page __sk_0237.djvu
Discussion of Testing Results......Page __sk_0244.djvu
Measure 2: Students\' Qualitative Assessments of Their Problem Solving......Page __sk_0245.djvu
Measure 3: Heuristic Fluency and Transfer......Page __sk_0247.djvu
A Brief Discussion of Control Issues......Page __sk_0252.djvu
Summary......Page __sk_0253.djvu
8. Problem Perception, Knowledge Structure, and Problem-Solving Performance......Page __sk_0256.djvu
Background......Page __sk_0257.djvu
Method......Page __sk_0261.djvu
Results of the Sortings......Page __sk_0266.djvu
Discussion......Page __sk_0273.djvu
Summary......Page __sk_0277.djvu
Appendix: Problems Used in the Card Sort......Page __sk_0279.djvu
Overview......Page __sk_0284.djvu
Background, Part 1 : Verbal Methods......Page __sk_0286.djvu
Through a Glass Darkly: A Close Look at Verbal Data......Page __sk_0289.djvu
Background, Part 2: Other Protocol Coding Schemes and Issues of Control......Page __sk_0297.djvu
The Major Issues for Analysis: A Brief Discussion of Two Protocols......Page __sk_0302.djvu
A Framework for the Macroscopic Analysis of Problem-Solving Protocols......Page __sk_0306.djvu
Episodes and the Associated Questions......Page __sk_0311.djvu
A Full Analysis of a Protocol......Page __sk_0315.djvu
A Further Discussion of Control: More Data from Students, and the Analysis of an Expert Problem Solver\'s Protocol......Page __sk_0320.djvu
Brief Discussion: Limitations and Needed Work......Page __sk_0328.djvu
Summary......Page __sk_0330.djvu
Appendix 9.1: A Single-Person Protocol of the Cells Problem......Page __sk_0331.djvu
Appendix 9.2: Protocol 9.2......Page __sk_0333.djvu
Appendix 9.3: Protocol 9.3......Page __sk_0338.djvu
Appendix 9.4: Protocol 9.4......Page __sk_0345.djvu
Appendix 9.5: Protocol 9.5......Page __sk_0354.djvu
1O. The Roots of Belief......Page __sk_0359.djvu
A Discussion of Two Geometry Protocols......Page __sk_0360.djvu
A Brief Analysis of Protocol 10.1......Page __sk_0361.djvu
A Brief Analysis of Protocol 10.2......Page __sk_0363.djvu
A Brief Discussion......Page __sk_0368.djvu
The Strength of Empiricism: More Data......Page __sk_0369.djvu
The Origins of Empiricism......Page __sk_0371.djvu
Summary......Page __sk_0387.djvu
Appendix 10.1: Protocol 10.1......Page __sk_0389.djvu
Appendix 10.2: Protocol 10.2......Page __sk_0396.djvu
References......Page __sk_0402.djvu
Author Index......Page __sk_0413.djvu
Subject Index......Page __sk_0417.djvu