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Elementary School Mathematics for Parents and Teachers, Volume 2

Raz Kupferman
World Scientific
Publication Date: 
Number of Pages: 
[Reviewed by
Mark Bollman
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In my review of Volume 1 of this set, I stated that

The exposition is exceptionally clear, and keeps its audience in mind: in the end, this is “a book for adults on mathematics for children”.

“Adults” here includes parents as well as teachers; in the author’s words, “Every parent is automatically an educator!” There is considerable merit in including parents in the elementary mathematics conversation; it is a pleasure to see books like Kupferman’s that explain elementary math to adults. If our students, in their future role as teachers, can enlist parents as allies, everyone will benefit. These books are one good way to begin addressing that challenge.

Volume 1 covered elementary arithmetic and geometry as they appear in the K–2 curriculum. Volume 2 picks up where Volume 1 left off, taking the reader through mathematics typically encountered in grades 3–6: whole number arithmetic and fractions. A proposed third volume will cover topics typically falling under the “prealgebra” heading.

The second volume successfully continues the fine work in Volume 1, even picking up the story from where the first left off by starting at Chapter 19. There’s a lot to be said to adults about the topics included here, and a standard elementary school textbook isn’t designed to address that audience at their level.

On a personal level, I am pleased to see an elementary mathematics book whose section on divisibility tests discusses tests for divisibility by 7. This is missing from most textbooks at this level because it’s considerably more complicated than the other tests, yet I always add it into my classes because someone is bound to ask. Once you’ve done divisibility tests for all other single-digit integers (plus 11 and 12), the absence of a test for 7 seems like something’s been deliberately omitted — or worse, doesn’t exist. My students may never need to teach about that test in their classrooms, but if a bright fourth-grader ever asks about divisibility by 7, they’ll have an answer. If they read this book, they’ll have two answers.

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.

  • Multiplication of Multi-Digit Numbers
  • Division of Multi-Digit Numbers
  • The Order of Operations
  • Division with a Remainder
  • Prime and Composite Numbers
  • Common Multiples and Common Divisors
  • Divisibility Rules
  • Sequences
  • Fractions
  • Quotients of Natural Numbers
  • Fraction Comparison
  • Fraction Addition and Subtraction
  • Fraction Multiplication
  • Fraction Division