 
Crossing the River with Dogs: Problem Solving for College Students
June 2008, ©2004
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Crossing the River with Dogs: Problem Solving for College Students has been adapted from the popular high school text to provide an accessible and coherent college-level course in mathematical problem solving for adults. Focusing entirely on problem solving and using issues relevant to college students for examples, the authors continue their approach of explaining classic as well as non-traditional strategies through dialogs among fictitious students. This text is appropriate for a problem solving, liberal arts mathematics, mathematics for elementary teachers, or developmental mathematics course.
Table of Contents
PREFACE vii
INSTRUCTOR RESOURCES x
ACKNOWLEDGMENTS xi
INTRODUCTION 1
1 DRAW A DIAGRAM 9
2 MAKE A SYSTEMATIC LIST 25
3 ELIMINATE POSSIBILITIES 43
4 USE MATRIX LOGIC 67
5 LOOK FOR A PATTERN 107
6 GUESS AND CHECK 135
7 IDENTIFY SUBPROBLEMS 163
8 ANALYZE THE UNITS 185
9 SOLVE AN EASIER RELATED PROBLEM 219
10 CREATE A PHYSICAL REPRESENTATION 249
11 WORK BACKWARDS 277
12 DRAW VENN DIAGRAMS 301
13 CONVERT TO ALGEBRA 327
14 EVALUATE FINITE DIFFERENCES 353
15 ORGANIZE INFORMATION IN MORE WAYS 385
16 CHANGE FOCUS IN MORE WAYS 411
17 VISUALIZE SPATIAL RELATIONSHIPS 435
APPENDIX 463
Unit Analysis
Adding, Subtracting, Multiplying, and Dividing Fractions
Area and Volume Formulas
Properties of Triangles
Properties of Numbers
GLOSSARY 471
BIBLIOGRAPHY 477
INDEX OF PROBLEM TITLES 479
GENERAL INDEX 483
PHOTO CREDITS 490
INSTRUCTOR RESOURCES x
ACKNOWLEDGMENTS xi
INTRODUCTION 1
1 DRAW A DIAGRAM 9
2 MAKE A SYSTEMATIC LIST 25
3 ELIMINATE POSSIBILITIES 43
4 USE MATRIX LOGIC 67
5 LOOK FOR A PATTERN 107
6 GUESS AND CHECK 135
7 IDENTIFY SUBPROBLEMS 163
8 ANALYZE THE UNITS 185
9 SOLVE AN EASIER RELATED PROBLEM 219
10 CREATE A PHYSICAL REPRESENTATION 249
11 WORK BACKWARDS 277
12 DRAW VENN DIAGRAMS 301
13 CONVERT TO ALGEBRA 327
14 EVALUATE FINITE DIFFERENCES 353
15 ORGANIZE INFORMATION IN MORE WAYS 385
16 CHANGE FOCUS IN MORE WAYS 411
17 VISUALIZE SPATIAL RELATIONSHIPS 435
APPENDIX 463
Unit Analysis
Adding, Subtracting, Multiplying, and Dividing Fractions
Area and Volume Formulas
Properties of Triangles
Properties of Numbers
GLOSSARY 471
BIBLIOGRAPHY 477
INDEX OF PROBLEM TITLES 479
GENERAL INDEX 483
PHOTO CREDITS 490
Hallmark Features
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Examples are solved as dialogues between fictitious students so students can see common errors and learn to avoid pitfalls
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Each chapter includes relevant examples of the strategy presented
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Chapters conclude with problem sets made up of three levels: A (routine), B (lengthy), and Classic Problems whose level can be determined by instructors
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Over a dozen distinct problem-solving strategies are developed in depth, including classic strategies as well as more contemporary strategies
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Icons appear to indicate examples, important information, and difficult material
Available Versions
Crossing the River with Dogs: Problem Solving for College Students
ISBN 978-0-470-41224-4
June 2008, ©2004
Paperback, 504 pages
Crossing the River with Dogs: Problem Solving for College Students
ISBN 978-0-470-46389-5
November 2008, ©2009
E-Book: Wiley Desktop Edition
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