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Integers, Fractions and Arithmetic: A Guide for Teachers

Judith D. Sally and Paul J. Sally, Jr.
Publisher: 
Mathematical Sciences Research Institute/American Mathematical Society
Publication Date: 
2012
Number of Pages: 
208
Format: 
Paperback
Series: 
MSRI Mathematical Circles Library
Price: 
39.00
ISBN: 
9780821887981
Category: 
Textbook
[Reviewed by
Charles Ashbacher
, on
03/30/2013
]

While there is some debate around the edges concerning what K-8 teachers of mathematics need to know, there is little questioning of what they need to know very well. This book is based on a series of twelve interactive seminars that cover what K-8 teachers need to know very well. The seminar titles are:

Number systems
Divisibility and order in the integers
GCD’s [sic] and the division algorithm
Prime numbers and factorization into primes
Applications of prime power factorization
Modular arithmetic and divisibility tests
More modular arithmetic
The arithmetic of fractions
Properties of the multiplication of fractions
Addition of fractions
The decimal expansion of a fraction
Order and the number line

Each of the seminars begins with a short statement of the subject matter followed by a series of seminar exercises where each is followed by explanations of how to solve it and what the exercise demonstrates. Having taught a theory course for students studying to be K–8 teachers, I can attest to the value of these seminar exercises. While some of them were similar to the examples I developed in class, I found myself mentally deconstructing the exercises and thinking through how I would have used them in my class.

It is clear while you are reading this book that the seminars are effective in teaching the teachers what they need to know to effectively present K–8 math. School district administrators will find a great deal of material that can be used to create continuing education classes for their staff to both refresh and improve their mathematical ability.


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.

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