588 pages | Grade 9–College
by Ted Herr and Ken Johnson

Problem Solving Strategies: Crossing the River with Dogs and Other Mathematical Adventures teaches mathematical reasoning by emphasizing that any problem can be solved in many ways. Students learn 22 problem-solving techniques, and many come to see themselves as mathematically powerful. Each chapter covers a single strategy. Students are given time to practice and then choose a strategy or combination of strategies from among those previously learned, challenging them to find the best solution.

Sample Problem

Five family members and their five dogs (each family member owned one of the dogs) were hiking when they encountered a river to cross. They rented a boat that could hold three living things: people or dogs. Unfortunately, the dogs were temperamental. Each was comfortable only with its owner and could not be near another person, not even momentarily, unless its owner was present. Dogs could be with other dogs, however. The crossing would have been impossible except that Lisa's dog had attended a first-rate obedience school and knew how to operate the boat. No other dogs were that well educated. How was the crossing arranged, and how many trips did it take?

From Chapter 11 of Problem Solving Strategies

Comprehensive and Easy to Use

• Problem Solving Strategies is a comprehensive source of information about problem-solving strategies and techniques, designed to be especially easy for students to work through. 
• Solutions are designed to be particularly easy to follow, with steps in solution figures highlighted. 
• Most chapters include a write-your-own feature, giving students the opportunity to write problems that can be solved by using the strategy studied in that chapter. Students solve their own problems themselves and then give them to other students to solve.
• The structure of the book, tips on assessment, and ideas for class management are the outcome of extensive classroom testing by the authors and other teachers. As a result, Problem Solving Strategies is a realistic course that is easily implemented.

Strengthens Mathematical Communication

• Problem Solving Strategies employs cooperative learning techniques and encourages students to work together. Anxiety decreases as students discuss and share their ideas. 
• Students give oral presentations, honing their communication skills and learning to present logically developed solutions—skills that will help them succeed in school and the workplace. 
• Students build portfolios, which form the basis for their assessment. 
• Students' problem sets are graded on a five-step system that includes trying the problem, understanding the problem, choosing and implementing a solution strategy, getting the answer, and explaining the solution. You'll find yourself evaluating how your students think from a comprehensive perspective.

An Exciting Option for Any Curriculum

• Use it as a post-algebra text for students who might not otherwise take an advanced mathematics course or who want to learn skills they can apply to other classes and disciplines. 
• Use it for community college students who want a relevant beginning to their continued study of mathematics. 

This curriculum will empower all your students, developing creative-thinking skills that will last a lifetime. As the course progresses, you'll see a dramatic change in students' attitudes. They'll start to enjoy the challenge of the class, and many will come to see themselves as mathematically enabled. In future courses, those students will be the first to volunteer ideas—not because they know all the answers, but because they know how to tackle the problem!