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Diversifying Mathematics Teaching:Advanced Educational Content and Methods for Prospective Elementary Teachers

Sergei Abramovich
World Scientific
Publication Date: 
Number of Pages: 
[Reviewed by
Mark Bollman
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One thing that occasionally frustrates me about teaching the “Mathematics for Elementary Teachers” course is the notion that there’s more to the math that my students will eventually teach and that they’re not likely to get there in only one course, which is all my college offers. I try to get past the simple math covered in a standard textbook where I can, but local circumstances make that challenging.

Enter Sergei Abramovich and this book, whose subtitle, Advanced Educational Content and Methods for Prospective Elementary Teachers, suggests that a different way is possible, even desirable. Like me, Abramovich faces a curriculum where he only has one mathematics content course to work with teachers; this book is written from the perspective of what could be done with more time.

It turns out that there’s a lot. The exact topics include enumerative combinatorics, partitioning of integers, informal geometry, and the interplay between theoretical and experimental probability — but they could have been almost anything. What one takes away from this book is the notion that there’s a lot of potential to do more with these students, and the book stands as a resource for anyone who shares that opinion.

Of late, I’ve been telling my future elementary teachers that when it comes to math and science, they should take two-thirds of their cue from courtrooms: they should tell the truth and nothing but the truth, but perhaps not the whole truth, as they should know their material to a level beyond the textbooks they’re using. I use this phrasing in an effort to explain why it’s important to learn more than just what they’ll be called on to teach. When a parent at a conference asks “You know, I’ve always wondered, why do we ‘invert and multiply’ when dividing fractions?”, they should have an answer ready. It’s the best response I’ve found yet for the question “Why do I have to learn about algebra if I want to teach kindergarten?”, or any of several variations on that theme. Books like Abramovich’s are a welcome addition to our options as we try to do our best by these students, and by extension, their future students.

Mark Bollman ( is Professor of Mathematics at Albion College in Michigan. His mathematical interests include number theory, probability, and geometry. Mark’s claim to be the only Project NExT fellow (Forest dot, 2002) who has taught both English composition and organic chemistry to college students has not, to his knowledge, been successfully contradicted. If it ever is, he is sure that his experience teaching introductory geology will break the deadlock.

  • Preface
  • Teaching Elementary Mathematics: Standards, Recommendations and Teacher Candidates' Perspectives
  • Counting Techniques
  • Counting and Reasoning with Manipulative Materials
  • We Write What We See (W4S) Principle
  • Partitioning Integers into Like Summands
  • Hidden Curriculum of Mathematics Teacher Education
  • Informal Geometry
  • Probability as a Blend of Theory and Experiment
  • Using Counter-Examples in the Teaching of Elementary Mathematics
  • Bibliography
  • Index