A Book for Grownups about Children's Mathematics,

by Ron Aharoni,

Translation from Hebrew

ISBN 978-0-9779852-5-8 vii+196 pp., 5.5 in x 8.5 in, softcover

Front cover.

Front matter: i-vii ,

Sample pages: 6-8 , 32 , 52-53 , 141-143 , 196

Back cover

It is a guide for parents who wish to be involved in the mathematics studies of their children. The principles of first to sixth grade arithmetic, and methods of their teaching, are described in a clear and simple way. This is also a book of second chance for those who wish to revisit their childhood mathematics from a new, mature perspective. It is also a must read for elementary school teachers, as well as for their college instructors.

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 to really understand the subject and its structure.

By Alexander Bogomolny, at his award-winning math web resource
Cut The Knot:

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 learnt 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. He has harsh words for a textbook where all examples of "real world" fractions referred to pieces of pizza. Students taught from that textbook had difficulty dividing a square into equal parts. Further on, he emphasizes the role of the teacher as a mediator and importance of naming math objects: operations and their parts (e.g., a *quotient*). He also argues against using calculators in elementary grades.

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

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.

By Linda Seebach, from her ''Opinion'' column in
Rocky Mountain News:

A couple of years ago I wrote a column about Israeli mathematician Ron Aharoni, and what he learned about math when he taught it to elementary schoolchildren. He expanded his ideas into a book, Arithmetic for Parents, and because he'd seen the column, the publisher of a new English translation sent me an e-mail asking if I would like to see a review copy. (...); The subtitle is A Book for Grownups About Children's Mathematics, and it's aimed at parents who want to help their children with math, or for that matter at any adult who'd like to revisit the mathematics of their childhood in the hope that it would be less traumatic on the second go-round. It's excellent, and I would expect that many math teachers would benefit from reading it.(...)

By Megan R. Bovill, in Mathematical Association of America, online book review column "Read This!"

(...) Arithmetic for Parents is a very enjoyable read: quick, easy, light, digestible. (...); Aharoni illuminates the inner workings of arithmetical algorithms, making the logic clearer even to someone who is well practiced in math. He offers a glimpse into the minds of children, explaining how to break down arithmetic into bite-size pieces appropriate for students who need or want to see the exact process in order to make sense of it. (...) All in all, I am very glad that I read the book and feel that I benefited from what it had to offer. (...) Ultimately, Aharoni does a fabulous job of breaking down algorithms and explaining thoroughly why each step is occurring and how to make sense of it. His ability to understand and address young children s difficulties in mathematics is impeccable.

By Maria Miller,
at Homeschool Math Blog:

I want to tell you a little bit about this book, because I think it is exceptionally good, and a very worthwhile book to read if you're a teacher OR a parent. Ron Aharoni (...) was in for a big surprise when he entered the fourth, fifth, and first grade classes in a backward town in northern Israel, in 2000. (...) During his teaching career in the elementary school he actually learned a LOT of mathematics ... not new facts, but subtleties: how that concepts we adults think are easy, are actually built upon other simpler concepts and notions, and how children need to be explained ALL those little steps. (...)