In order for children to learn to solve problems in a variety of ways, teachers require problem solving experiences and need resources for many types of problems. Problem Solving Strategies: Crossing the River with Dogs and Other Mathematical Adventures by Ted Herr and Ken Johnson (1994, from Key Curriculum Press) serves as both a resource for problem solving in math courses for prospective teachers and as a problem solving resource once these preservice teachers move into their own classrooms. Communication in mathematics, along with problem solving, is featured in the book.
The authors suggest that the book serve as a basis for a high school course. However, many students preparing for teaching careers have done very little problem solving. Thus, the material and written presentation is appropriate in a college math for teachers course. Herr and Johnson's book has several strengths: the number of examples written with full analysis, the emphasis on variations in approaching any problem, vignettes of classroom work, student explanations, and discussion of problems from several students' viewpoints. Accordingly, the problem solving work emphasizes student talk as well as altemative thinking for problems.
Many techniques are covered in the book. Strategies include the common ones used in preparing preservice teachers, such as drawing diagrams, creating systematic lists, finding pattems, working backwards, guessing with check, and using algebra. Herr and Johnson demonstrate these approaches in detail and provide several opportunities for guided practice. Furthermore, other strategiesincluding elimination, matrix logic, unit analysis, and finite differences are presented with the same thorough discussion. The last three chapters discuss methods of organizing information and nonroutine problems. The problems are interesting, but not always seen as applicable to the real world.
Problem Solving Strategies: Crossing the River with Dogs and Other Mathematical Adventures is an excellent resource for us as math educators and for our students who are striving to become elementary and middle school teachers.
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