Arithmetic for Parents: A Book for Grownups about Children's Mathematics - Softcover

Ron Aharoni

Softcover

ISBN 10: 0977985253 ISBN 13: 9780977985258

Publisher: Sumizdat, 2007

Synopsis

The book is an English translation from Hebrew of a very popular in Israel guide for parents eager to help their kids to understand math. It reflects the author's unique experience as both a research mathematician and elementary school teacher.

Part 1 discusses the nature of mathematics, its power, its beauty, and the source of the difficulties in studying it. Part 2 introduces the reader into principles of good teaching. Part 3 is an easy going, informal guide, filled with personal stories, historical anecdotes and teaching suggestions, addressing all twists and turns of basic arithmetic taught in grades 1 through 6.

To a mathematics educator, the book sends two important messages. One is that basic mathematics, although unsophisticated, is rather deep, consisting of many neatly aligned layers, none of which can be skipped without the danger of causing "math anxiety"; The other is that good pedagogy depends not so much on various tricks and cognitive theories, but on thorough understanding of basic mathematics and its neatly layered structure. And the book teaches the reader -- a parent, or a teacher -- to really understand the subject and this structure.

By Alexander Givental, Prof. of Math., UC Berkeley and Sumizdat.

There is a Wikipedia article about the book.

Reviews of the book can be found in: "Opinion" column by Linda Seebach of "Rocky Mountain News" for March 24, 2007; Homeschool Math blog by Maria Miller; "Read This!" column of "Online Book Reviews" by The Mathematical Association of America; the award-winning math web resource "Cut The Knot" by Alexander Bogomolny.

About this title

About the Author

Ron Aharoni, a professor of mathematics at the Israel Institute of Technology, accepted his friend's invitation to teach mathematics in elementary school. Since then he has devoted much of his time to primary mathematics education. Aharoni played a major role in a successful fight against "fuzzy math"; in his country, and in the implementation of a competent, no-frills curriculum. In this book, he shares with the reader -- a parent , or a teacher -- the insights he gained concerning elementary mathematics and mathematical education. His next book is about Mathematics, Poetry, and Beauty.

Review

The book under review is an outcome of a rare experiment: an university math professor (a high caliber professor at that from one of the best universities in the world) who has responded to a challenge to teach in elementary school shares the acquired insights about teaching young children and their mathematics. The book is a very enjoyable read, the advice proffered is sound, the pedagogy is illustrated by numerous examples. I highly recommend the book to the grown ups concerned with young children education (...)

In the Introduction, the author outlines the sequence of events that led him to taking up teaching elementary grades in a small town on the Northern outskirts of Israel and describes the surprise experiences that came out of that experiment. The greatest surprise was in that the teaching of elementary grades provided him - a professional mathematician - an opportunity to learn mathematics: not any new facts of course but the subtleties inherent in the elementary mathematics. (As an aside, this part supplies a crashing argument in the hotly discussed topic as to whether or not elementary school teachers can be expected to possess math expertise.)

The first part is a collection of interrelated essays that discuss the fundamental role of abstraction in mathematics, the mathematical beauty, the peculiar economy of thought and expression that characterizes mathematics and the its hierarchical organization. There are also chapters on the whole numbers, the decimals and general thoughts of what might be expected to be learned in elementary school. Mathematical economy is beautifully classified as being achieved in three ways: Order (by looking for patterns), Generalization (by abstracting common features from different areas) and Concise Representation (the decimal system serving as an example.)

The second part is deftly subtitled The Road to Abstraction as conveying an abstraction is a fundamental need and principle of teaching mathematics. The author's methodology is to start with familiar and diversify the examples to help students grasp the abstraction as a common feature of several examples and prevent them from attaching unintended importance to auxiliary details (...)

The third part is the largest - it takes about two thirds of the book. The third part opens with a chapter on the meaning of arithmetic operations. For example, there is a real (for children) difference between questions such as:
There are five apples of which 2 have been eaten. How many apples have been left?
In a family of 5 siblings, 2 are boys. How many girls are in the family?
Joseph has 5 toys, Reena has 2. How many more toys does Joseph have?

All are naturally solved by subtraction 5 - 2 = 3. However, in the first, subtraction means a removal of two items. In the second, it means classification of objects into two types and counting each type separately. In the third, subtractions means comparison.

With the same attention to detail and profound insights, he then talks of the nature and rules of calculations, of fractions, decimals, and ratios. It is plain fascinating how much meaningful information is hidden behind simple arithmetic facts. There is so much that children may miss! There is so much to be learned in order to acquire a working grasp of the concepts of the elementary mathematics.

The book will be helpful to and enjoyed by teachers, parents who attend to their kids' study and, of course, the home schooling parents. It's a treasure trove of ideas usually missed out in textbooks and teacher manuals.

--From "Cut The Knot" website by Alexander Bogomolny

Edition details

• Publisher: Sumizdat
• Publication date: 2007
• ISBN 10: 0977985253
• ISBN 13: 9780977985258
• Binding: Perfect Paperback
• Language: English
• Number of pages: 203