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Teaching Secondary Mathematics

Douglas K. Brumbaugh and David Rock
Lawrence Erlbaum Associates, Publishers
Publication Date: 
Number of Pages: 
[Reviewed by
Sharon Schaffer Vestal
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This book is divided into three parts: General Fundamentals, Mathematics Education Fundamentals, and Content and Strategies. The first part discusses general advice for teaching mathematics, such as lesson plans, NCTM standards, curriculum, planning, and advice on how to motivate students and help them read and write mathematics. The second portion of the book includes chapters on technology, problem solving, discovery, and proof. The last part focuses on content taught in a high school mathematics classroom by including chapters on general mathematics, algebra I, geometry, advanced algebra and trigonometry, pre-calculus, calculus, and probability and statistics.

The authors use a conversational writing style that makes the book very easy to read. There are several exercises throughout each chapter. At the end of each chapter, there is a section called “sticky questions,” which ask your opinion or what you would do in a specific situation. In the chapter on technology, for example, one of the questions is “When should a calculator be permitted as a tool in the mathematics curriculum?” (p. 167) Some of the “sticky questions” are mathematical; for example in the discovery chapter, one of the questions is “Two hundred logs are stacked. There are 20 logs on the bottom row, 19 on top of those, and so forth. How many rows are there? How many logs are in the top row? Devise a plan for explaining this solution to students.” (p. 225).

This section is followed by one called “problem solving challenges,” which includes interesting mathematics problems and solutions to the problems; and then there is a section called “learning activity,” which are activities that can be used in the classroom. This book could be used as a textbook for a secondary methods course and would also make a good reference book for mathematics education majors and classroom teachers.

The more I read the book, the more I liked it. It discusses topics such as discipline, equity, technology, and curriculum in a very straightforward and useful manner — most secondary books will include these topics but this book does a better job of giving examples and advice. One of the things that I liked most about this book is that it includes a lot of mathematics — great problems, exercises, and activities. It also emphasizes why secondary mathematics teachers need to study advanced mathematics so that they have a better grasp of the concepts and then can explain it better to students. The next time a mathematics education major asks why he/she needs to take abstract algebra, you can tell them to read this book!

Sharon Schaffer Vestal is an Assistant Professor of Mathematics at South Dakota State University in Brookings, SD. In her (lack of) free time, she enjoys spending time with her family.

 Preface. Part I: General Fundamentals. Introduction. Learning Theory, Curriculum, and Assessment. Planning. Skills in Teaching Mathematics. Part II: Mathematics Education Fundamentals. Technology. Problem Solving. Discovery. Proof. Part III: Content and Strategies. General Mathematics. Algebra I. Geometry. Advanced Algebra and Trigonometry. Pre-Calculus. Calculus. Probability and Statistics.