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

by Ron Aharoni

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 "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.

Genres: Mathematics, Education, Teaching, School

203 pages, Perfect Paperback

First published March 31, 2007

About the author

Ron Aharoni (Hebrew: רון אהרוני‎ ) is an Israeli mathematician, working in finite and infinite combinatorics. Aharoni is a professor at the Technion – Israel Institute of Technology, where he received his Ph.D. in mathematics in 1979. With Nash-Williams and Shelah he generalized the marriage theorem by obtaining the right transfinite conditions for infinite bipartite graphs. He subsequently proved the appropriate versions of the König theorem and the Menger theorem for infinite graphs (the latter with Eli Berger).


Aharoni is the author of several nonspecialist books; the most successful is Arithmetic for Parents, a book helping parents and elementary school teachers in teaching basic mathematics. He also wrote a book on the connections between Mathematics, poetry and beauty and a recent one on philosophy (The Cat That is not There, both in Hebrew). His last to date book is "Man detaches meaning", on a mechanism common to jokes and poetry.

Reviews

[Lindsay · Rating 5 out of 5]

I found this book surprisingly fascinating. It helped me to see the beauty of math in a new light. A great review of elementary math in preparation for homeschooling my kids, and I learned so many reasons behind concepts and fun tips that I never knew before. Great reference for the bookshelf!

[Anna Mussmann · Rating 4 out of 5]

Written by an Israeli mathematician who went into elementary schools and became (re)awakened to the often-misunderstood or overlooked beauty of simple mathematics, this volume is designed to teach parents about how early studies in math should be approached.

I am not a math person. Not at all. I actually *enjoyed* doing math in school--neat rows of numbers gave me a sense of satisfaction--but I had no interest in understanding it. It was all, "tell me what to do, and I'll do it through brute memorization--no confusing explanations for me!" My brain still processes numbers and math slowly.

Thus, I appreciated the first half of this book. The author looks at the burgeoning mathematical understanding of the first and second graders he taught. I wish I'd read this before teaching third grade math! I will need to read it again as I begin working with my own (quite mathematically-inclined) son. I am currently reading another book that discusses the way in which Chinese schools teach math, which added an extra angle of interest to Mr. Aharoni's arguments and his description of Israeli classrooms.

The second half of the book, a collection of explanations on specific mathematical issues, was less relevant to my current life. I may refer back when my kiddo is ready to learn about those operations.

[Leah Douglas · Rating 5 out of 5]

Short, easy, incredibly helpful. For instance, there are two kinds of subtraction problems. 3 balloons, 2 pop, now there’s 1 balloon. In this kind of subtraction, some go away. But there’s also another kind: 11 children in a class, 5 are girls, so how many are boys? None went away. This seems insignificant to an adult, but to a child who is very visual and literal, this distinction is actually very important. This book is full of stuff like this.

[Jlnpeacock Peacock · Rating 5 out of 5]

This is book introduces the subject of arithmetic and how it should be taught in such a delightful manner that I thought I would began again my mathematical education. As I read I began to see the real beauty of numbers and the sheer pleasure one can obtain in the understanding of the principles. Every parent should read this.

[Courtney White · Rating 5 out of 5]

Written by a professional mathematician who wound up teaching elementary mathematics. This is a simplified overview of all the arithmetic needed for 1st-6th grade. Great for a homeschool parent who wants to scrap the years long curriculum. I love the philosophy given to each stage of learning and the explanation of the education "math wars." Chapters are short and each section explains how he taught the lessons in a classroom setting. I wouldn't use this as a stand alone math philosophy for elementary education because it doesn't cover anything beyond arithmetic. I'll be pulling this off the shelf for the next 5 years as my kids grow.

[Damen Chan · Rating 3 out of 5]

我的數學成績相當不錯。但「教數學」與自己做數，肯定是兩回事。每次去教女兒做數學功課，都給我老鼠拉龜的感覺：加減乘除四則運算簡單明瞭，一下子就懂了，為什麼總是不明白？

現實是我沒有耐心。有道「害羞的學不好，沒耐性的教不好」。四則運算雖則簡單，卻是千年來多位智者不斷添磚加瓦的累積所成。要讓小朋友學懂數學，就像前人一樣要一步步來，就是最簡單的概念也值得再三解釋：小朋友若能了解計算的原則，基礎穩健的話，自然能進入數學的殿堂，享受解題之後的滿足感。

本書的作者是數學家，為什麼去教加減乘除？原因就是熱心數學敎育。比起一般的大學生，小朋友的反應直接而激烈，他完全感受到課堂能否達到教學目標，給他額外的教學滿足感。

本書就是他寫給教師和家長們的教學建議。書中介紹了四則運算、分數、小數、百分比等等幾乎所有小學的數學課題，在計算方面幾近是進行刨丁解牛式的解釋，在我看來自然只有不耐，但作為教師的參考書，應該提供了不少有用的建議。

本書對我有沒有用？算了吧，我可不是當教師的料啦。

好書。三星。

[Holly Hendricks · Rating 5 out of 5]

I loved this book! It was very easy to read, and the author communicates well the beauty and depth of elementary mathematics. I have taught math for years, and I learned insights into certain operations that I'd never learned before. This is a very practical, systematic approach to teaching not only the procedures but the deep meaning of each concept. Every math teacher should read it!

[Emily · Rating 4 out of 5]

This book was a harder read than I was expecting ("for Parents" doesn't mean it's written at a wholly popular level), but it was a good review for me and I appreciated the author's insights into teaching elementary math.

[Pedro Miguel · Rating 5 out of 5]

Do melhor que pode haver...fantastico .

[Misszchow · Rating 4 out of 5]

一本和自己想法接近的參考書。
怎樣把數學當成故事說出來，由實變虛的數學領域。

怎樣把你認為的理所當然的事一般化用未知數冠名。讓單純的人走進一個新秩序。

[Benjamin · Rating 4 out of 5]

This is a good book, I suppose, but it is unlikely to have a big impact on me. There are some worthwhile pedagogical insights in it, but they are fewer than I expected, and they are scattered through many subsections, which are often less than a page in length.

The math in the book boils down to the many implications of the distributive law and the wonderful utility of the decimal system. This is certainly worth explicitly appreciation, but does not, on its own, justify an entire book. I, at least, picked it for tips on communicating arithmetic.

The insight I found most striking was that there is a large conceptual leap for a child to abstract the following two different kinds of problems to the unified technique of subtraction. The first is where some number of objects are removed (you have four apples and eat three; how many are left) and the second is where there is some subset of a collection is enumerated (you have four apples and three are green; how many are red).

Another point I appreciated was Aharoni's explicit exhortation to simultaneously teach abstract arithmetic and applications. He doesn't reject the value of abstraction, but he does deny it's utility as a pedagogical shortcut. Or, more precisely, he sees abstraction as the prize at the end of varied repetition of many problems that solidly establish the given topic.

Finally, there was one section that probably had a lesson for my own mathematical development, as opposed to how to communicate things I already understand. Titled "Memorize or Calculate Anew?" he argues that there are some things so basic that they need to be memorized, not for their own sake, but because rederiving them from scratch each time will impede the pursuit of more complicated concepts. (He also rejects the idea that one will passively remember the results of the derivations without explicit memorization.) He likens it to refusing to learn the native language of the country you live in because you can muddle through with a translation dictionary.

my favorite quote: "If a question is hard, it usually means that some previous stage is missing."

[Heidi · Rating 4 out of 5]

Well, I did not finish this before having to take it back to the library, but my husband (the one who will be teaching the kids their maths) did. He liked it. We will be getting a copy of our own to have as a reference; the back half has a lot of practical advice for teaching math effectively.

[Jean-Marie · Rating 4 out of 5]

This is an excellent resource for parents of elementary age children.