Problem Solving Through Recreational Mathematics

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Problem Solving Through Recreational Mathematics is a textbook in mathematics on problem solving techniques and their application to problems in recreational mathematics, intended as a textbook for general education courses in mathematics for liberal arts education students. It was written by Bonnie Averbach and Orin Chein, published in 1980 by W. H. Freeman and Company, and reprinted in 2000 by Dover Publications.

Contents

Audience and reception

Problem Solving Through Recreational Mathematics is based on mathematics courses taught by the authors, who were both mathematics professors at Temple University. [1] [2] It follows a principle in mathematics education popularized by George Pólya, of focusing on techniques for mathematical problem solving, motivated by the idea that by doing mathematics rather than being told about its "history, culture, or applications", liberal arts education students (for whom this might be their only college-level mathematics course) can gain a better idea of the nature of mathematics. [1] [3] By concentrating on problems in recreational mathematics, Averbach and Chein hope to motivate students by the fun aspect of these problems. However, this approach may also lead the students to lose sight of the important applications of the mathematics they learn, [3] and contains little to no material on mathematical proof. [2] [4]

The book's exercises include some with detailed solutions, some with less-detailed answers, and some that provide only hints to the solution, providing flexibility to instructors in using this book as a textbook. [1] [5] Cartoons and other illustrations of the concepts help make the material more inviting to students. [1]

As well as for general education at the college level, this book could also be used to help prepare students going into mathematics education, [1] and for mathematics appreciation for secondary school students. It could also be used as a reference by secondary school mathematics teachers in providing additional examples for their students, [5] [6] or as personal reading for anyone teenaged or older who is interested in mathematics. [6] Alternatively, reviewer Murray Klamkin suggests using the books of Polyá for these purposes, but adding Problem Solving Through Recreational Mathematics as a supplement to these books. [3]

Topics

The book begins with an introductory chapter on problem-solving techniques in general, [4] including six problems to motivate these techniques. [1] The rest of the book is organized into eight thematic chapters, each of which can stand alone or be read in an arbitrary order. [3] [4] The topics of these chapters are:

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References

  1. 1 2 3 4 5 6 7 8 9 10 Dees, Roberta L. (November 1981), "Review of Problem Solving Through Recreational Mathematics", The Arithmetic Teacher, 29 (3): 54–55, JSTOR   41190004
  2. 1 2 Wolfe, Hugh C. (May 1981), "Review of Problem Solving Through Recreational Mathematics", Physics Today , 34 (5): 84–84, Bibcode:1981PhT....34e..84A, doi:10.1063/1.2914582
  3. 1 2 3 4 Klamkin, Murray S. (March 1983), "Review of Problem Solving Through Recreational Mathematics", The American Mathematical Monthly , 90 (3): 216–218, doi:10.2307/2975564, JSTOR   2975564
  4. 1 2 3 4 5 6 7 8 9 Mortimer, Mike (January 1982), "Review of Problem Solving Through Recreational Mathematics", Mathematics in School, 11 (1): 35, JSTOR   30213691
  5. 1 2 King, Richard H. (April 1981), "Review of Problem Solving Through Recreational Mathematics", The Mathematics Teacher , 74 (4): 301–302, JSTOR   27962454
  6. 1 2 3 4 5 6 7 8 Austin, Keith (March 1982), "Review of Problem Solving Through Recreational Mathematics", The Mathematical Gazette , 66 (435): 71–72, doi:10.2307/3617323, JSTOR   3617323
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