It is natural for children to love mathematics, but they need teachers who love it, and they need what the mathematicians have: a world of puzzles and questions. Teaching math only from a text is like teaching history only from a scrambled list of dates.

Here are some people who have loved and do love math and some of the thoughts they considered.

Right Start Math is not a book; it's a beautifully designed program for all grades. Joan Cotter has degrees in engineering and math and is an AMI certified Montessori teacher. With all these qualifications, she has composed a math curriculum that incorporates Montessori's love for the child with a genuine mathematical intuition: this is how mathematicians think.

It has the best thought-out set of manipulatives and games I have ever seen. The games are not merely practice of concepts, which would be very good in itself, but they actually teach concepts. That is, they don't just reward the learning of concepts by letting you win if you did your homework; they actually engage you in the mastery of numbers, tables, etc, and this, not merely as rote, but as pattern and number. Everyone I know who is using this program loves it and this includes a good friend with six children under 12 years. The program is somewhat teacher intensive, for ten or fifteen minutes a day, but the children are happy.

This book is based on Glenn Doman's work, but it is perhaps easier on a mother who can't keep all those cards in order. Even if you don't do everything Dr. Doman says to do, you can give your children a good start in the concept of number.

After working with brain damaged children and developing materials that allowed them to excel, Glenn Doman eventually came to work with their siblings who used the same materials to achieve unimaginable things, and with joy. This is his book about that experience, updated now by his daughter.

If you would like to meet the St. Francis (poverello) of math, Paul Erdös is your man. He was massively famous and competent, he never made money at it; when he won prizes, he turned around and gave the funds to the nearest poor struggling mathematician he met. His story is here lovingly told by a fellow mathematician.

This wonderful Greek mathematician will help you see math a new way. This is not about basic presentations in math; it's about puzzles and curiosities — what mathematicians really think about.

A quick search under the phrase "patterns in nature" turn up all kinds of interesting-looking books. This one updates the original by Peter S. Stevens. (See below.)

Basically, there are eight or so patterns in nature. Understanding the mathematics behind each one helps you understand why they turn up where they do, and how their combinations in different size ranges gives such an endless supply of amazing things to see.

Though the book is very challenging to understand in its entirety, it is quite accessible as a discussion of the patterns to be found. If you can’t follow the equations, you can still see the pattern and remember how they appear in your world. Patterns have an orderly source.

At some point, a science or a math course should offer a reflection on the patterns generated by bubbles and their packing rules, waves and their interference rules, the Fibonacci series and the spirals it generates, and the branching rules that govern the growth of plants and also of rivers. These are the fundamental patterns of the universe. They turn up everywhere in nature, and* Ball particularly makes the point that in the rush to embrace Darwinism, the fact that biological entities must obey the laws of physics* is often ignored. Very important!

Theodore Andrea Cook

You know, if a math book has Hokusai's famous Great Wave on the cover, something exciting must be inside. Math is about pattern as well as number, and a mathematician author covers both.

In 1974, Peter Stevens wrote this wonderful text that is out of print. And how could it stay in print, being only black and white, while his followers have the advantage of color. But the original still has its own glories, particularly some things about architecture.

Ball’s work (above) is partly based on the earlier work of D’Arcy Thompson, called *On Growth and Form*, which is a little easier to read and much cheaper, being out of copyright, but also less colorful and engaging.

Still, this older book and the one by Peter Stevens offer a swath of unexpected information about patterns, including an amazing discussion of certain architectural wonders based on shell spirals.