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Teaching School Mathematics: Algebra

Hung-Hsi Wu
American Mathematical Society
Publication Date: 
Number of Pages: 
[Reviewed by
Mark Bollman
, on

Joint review of

If you’re not familiar with the important work that Professor Wu has done in elementary mathematics education in the past decade or so, this quote from the preface to Teaching School Mathematics: Pre-Algebra might be a bit jarring:

These two volumes are designed not to show you how mathematics is really just common sense and lots of fun, but to help you teach the mathematics of middle school in a way that meets the minimal standards of human communication.

With that sentence, the tone is set: there is a serious dimension to these books that is often not present in standard “mathematics for teachers” textbooks. This is a challenge faced by some of us who teach these classes: are we doing “serious” mathematics? This series doesn’t bother with the typical chapters on problem solving and elementary set theory that are very much the norm in books for this course, but strikes a blow for serious work by diving right into fractions.

“Serious work” is repeatedly contrasted here with TSM, or “textbook school mathematics”, which is cited as a source of mathematical errors and a barrier to maintaining mathematical integrity in the K–8 curriculum. As an example, TSM’s treatment of the laws of exponents is cited in the Algebra volume as possibly the best example of how traditional practices interfere with five fundamental principles of mathematics:

  1. Precise definitions are essential.
  2. Every statement must be supported by reasoning.
  3. Mathematical statements are precise.
  4. Mathematics is coherent.
  5. Mathematics is purposeful.

While no working mathematician would be likely to argue with these ideas, to see them at the forefront of a textbook at this level is at once refreshing in its forthrightness and striking in its novelty. We need books for future teachers that take this approach to our subject.

In my 15 or so years teaching Mathematics for Elementary Teachers, I have repeatedly tried to sell it to students by asserting that there’s a lot of depth behind what looks to the casual observer as fairly simple mathematics. That doesn’t always work — my college requires minimal mathematics from all of its students, not just prospective teachers, which diminishes the receptiveness of the target audience — but it doesn’t mean that I’ll stop trying. This pair of books has great potential to assist all of us who struggle in that quest. It may be quite a while before my students are ready to learn directly from these books, but I’m finding elements of Wu’s arguments that make their way into my classroom right now.


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Mark Bollman ( is professor of mathematics and chair of the department of mathematics and computer science 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.

See the table of contents in the publisher's webpage.