Textbook

Crossing the River with Dogs: Problem Solving for College Students, 2nd Edition

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Crossing the River with Dogs: Problem Solving for College Students, 2^nd edition promotes the philosophy that students learn best by working in groups and the skills required for real workplace problem solving are those skills of collaboration. The text aims to improve students’ writing, oral communication, and collaboration skills while teaching mathematical problem-solving strategies. 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, quantitative reasoning, liberal arts mathematics, mathematics for elementary teachers, or developmental mathematics course.

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Table of Contents

Preface Vii

Instructor Resources X

Acknowledgments Xi

Introduction 1

1 Draw A Diagram 11

2 Make A Systematic List 29

3 Eliminate Possibilities 49

4 Use Matrix Logic 75

5 Look For A Pattern 117

6 Guess And Check 147

7 Identify Subproblems 177

8 Analyze The Units 201

9 Solve An Easier Related Problem 237

10 Create A Physical Representation 269

11 Work Backwards 299

12 Draw Venn Diagrams 325

13 Convert To Algebra 355

14 Evaluate Finite Differences 385

15 Organize Information In More Ways 419

16 Change Focus In More Ways 449

17 Visualize Spatial Relationships 477

Appendix 507

Unit Analysis

Adding, Subtracting, Multiplying, And Dividing Fractions

Area And Volume Formulas

Properties Of Triangles

Properties Of Numbers

Glossary 000

Bibliography 000

Index Of Problem Titles 000

General Index 000

Photo Credits 000

Answers To More Practice Problems 000

New To This Edition

New, more challenging problem sets to allow instructors greater flexibility in choosing which problems to assign students for particular topics.
Problem sets and exposition in Chapter 4 Use Matrix Logic, Chapter 8 Analyze the Units, Chapter 12 Draw Venn Diagrams have been revised to make the material more clear, readable, and concise.
More illustrative examples have been added to better explain to students how to use particular problem-solving strategies.
An improved text design and layout boldly calls out section heads and explanations in order to make the text more readable and student-friendly.

Hallmark Features

Examples are solved as dialogues between fictitious students so students can see common errors and learn to avoid pitfalls.
Each chapter includes relevant examples of the strategy presented.
Chapters conclude with problem sets made up of three levels: A (routine), B (lengthy), and Classic Problems whose level can be determined by instructors.
Over a dozen distinct problem-solving strategies are developed in depth, including classic strategies as well as more contemporary strategies.
Icons appear to indicate examples, important information, and difficult material.