Vision in Elementary Mathematics

by W.W. Sawyer

Here is a presentation of elementary mathematics that anyone can appreciate, especially those with imagination. As the title suggests, the author's technique relies on visual elements, and his approach employs the most graphic and least "forbidding" aspects of mathematics. Most people, he observes, possess a direct vision that permits them to "see" only the smaller numbers; with the larger numbers, however, vision fails and mental chaos ensues.
Sawyer addresses this difficulty, speaking both for those who like recreational mathematics and for those who teach, suggesting a variety of methods used by many effective teachers — techniques of visualizing, dramatizing, and analyzing numbers that attract and retain the attention and understanding of students. His topics, ranging from basic multiplication and division to algebra, encompass word problems, graphs, negative numbers, fractions, and many other practical applications of elementary mathematics.
A valuable resource for parents and teachers, this book will captivate any reader seeking an improved understanding of mathematics.

Genres: Mathematics

368 pages, Paperback

First published January 27, 2003

About the author

Walter Warwick Sawyer (or W.W. Sawyer) was a mathematician, mathematics educator and author, who taught on several continents.
https://en.wikipedia.org/wiki/Walter_...

Reviews

[Kyle · Rating 5 out of 5]

I read Sawyer's A First Look at Numerical Functional Analysis, and quite enjoyed it as an introduction to the topic. This book is all about how to teach elementary mathematical skills in algebra to kids. It covers the topic from a variety of angles and with lots of figures and explanatory notes. I think he makes some great points about teaching mathematics and makes it clear that these are suggestions on how to teach, not a prescription. It gave me a couple of new ways of explaining math concepts to others, and why certain conventions are followed. It also stresses that when teaching children don't get too rule-oriented or too philosophical. The material does not seem dated (although English units and English money do appear), and could easily be used today in teaching (and probably is).

He also has a good sense of humor. For example, "The multiplication symbol was invented by some man, and presumably that man had the right to say what it meant. The philosophers stress that we may define a symbol in any way we like. So, if we liked, we could define 1/2*1/2 as 'a blood orange'. But philosophers tend to lose sight of the fact that nobody chooses to do so. The nature of the universe steers our thinking in a very definite direction."