



Arithmetic for Parents by Ron Aharoni
A Book for Grownups about Children's Mathematics
Translation from Hebrew by Danna Reisner
Many people would like to help their children with their arithmetic studies, but are too afraid to return to a subject that was so painful for them as children. However, they forget that they have acquired many new tools since their school days. The adult has more forbearance, abstraction skills, the capability to deal with complex sentences, and the patience to wait until the whole picture emerges. All these skills can be used to deal more easily and quickly with the principles of elementary school mathematics.
The purpose of this book is to provide the guidance required to do so. It offers assistance to the parent who wishes to be an active participant in his or her child's arithmetic studies. As a matter of fact, that is how the book was born. The parents at my son's school asked for written instructions, so that they could help their children with mathematics. What began as modest notes, slowly evolved and eventually reached the proportions of a book.
Yet books, like ideas, have a life of their own. Sometimes they lead their writer no less than he leads them. And thus it happened that the book gradually took on a different form. One of the insights I came by while teaching in elementary school is that elementary mathematics isn't simple at all. It has depth and beauty. This message slowly found its way into the book and gave it an additional direction: a description of the beauty of elementary mathematics and, consequently, mathematics in general. Thus my original target audience expanded to include the reader who wishes to return to his childhood mathematics, from a different angle. For this group of readers the book provides a second chance. Those who have learned how to multiply fractions or how to perform long division, but never understood why it was done exactly so, are invited to take a look from a new, mature perspective.
The book is also aimed at a third audience, no less important for me: teachers and educators. To them the book sends a clear message: Proper teaching of mathematics depends more on an understanding of the mathematical principles than on educational tricks. It requires familiarity with the way the fine mathematical layers lie one upon the other. Furthermore, it is best done by direct, concrete experience with the concepts, and no intermediaries.
Partial extraction from the foreword of Arithmetic for Parents.
Arithmetic for Parents
Contents
Foreword
Introduction
Part One: Elements
What is Mathematics?
The Three Mathematical Ways of Economy
The Secret of Mathematical Beauty
Layer upon Layer
Whole Numbers
Meaning and Calculations
The Decimal System
What is Learned?
Part Two: Principles of Teaching
Conveying Abstractions
Diversity and Fixation
Why Teaching is Difficult
Mediation
Magic Words
The Calculator and Other Aids
The Courage for Simplicity
Part Three: Arithmetic from First to Sixth Grades
A. Meaning
The Meaning of Addition
The Meaning of Subtraction
The Essence of Multiplication
The Two Meanings of Division
Meaning and Word Problems
B. Calculation
The Calculation of Addition
Subtraction: Loan or Reorganize?
The Calculation of Multiplication
Memorize or Calculate Anew?
Calculation of Division Begins on the Left
C. Fractions
Divisions and Fractions
Multiplying and Dividing Fractions
A Conversation on Division by Fractions
Solved Exercises on Fractions
The Common Denominator
The Least Common Denominator
Mixed Numbers
D. Decimals
Decimal Fractions
Calculation in Decimal Fractions
Percentages  a Universal Language for Fractions
E. Ratios
Proportionality
More Ratio Problems
Afterword
Appendix: Turning Points in the History of Modern Mathematics Education
Samples and more information













Our recommendation:
This book is recommended as 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.








