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Reconceptualizing Mathematics Part 1, 2, and 3

Judith Sowder, Larry Sowder, and Susan Nickerson
W. H. Freeman
Publication Date: 
Number of Pages: 
[Reviewed by
Charles Ashbacher
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Great breadth of coverage is generally an excellent strategy, until you are forced to make decisions regarding what is to be left out. This set of two books covering the fundamental mathematics for elementary school teachers contains all of the topics that one would need to know to handle the entire elementary school curriculum.

The first volume contains the following material:

  • Part 1: Reasoning about numbers and quantities
  • Part 2: Reasoning about algebra and change
  • Part 3: Reasoning about shapes and measurement

The second volume has only part 4: Reasoning about chance and data.

Specific content of the first volume is: number systems, operations on whole numbers, estimation and mental computation, working with fractions, ratios and proportions, simple number theory, graphing and rates of change, polyhedra, symmetry, transformation geometry, area, surface area, volume and measurements. The specific content of the second volume is: uncertainty, the basic rules of probability, sampling and statistics, representing and describing data with one variable, correlation, confidence intervals and expected value.

I have taught a course called “Fundamentals of Arithmetic and Logic” that is designed for elementary education majors. All of the content of that course is a subset of the material in this book. The explanations are clear, so my students would have had no trouble in following the reasoning. My difficulty would have been in deciding what material to cut, as strong arguments can be made for including every section. If you can easily make such decisions, then this is a book that you should consider for your course in mathematics for elementary education majors. If you are one of those fortunate to have two such courses, then there will be no difficulty.

Charles Ashbacher splits his time between consulting with industry in projects involving math and computers, teaching college classes and co-editing The Journal of Recreational Mathematics. In his spare time, he reads about these things and helps his daughter in her lawn care business.

The table of contents is not available.