Math from Three to Seven. Zvonkin worked with his young kids and some of their friends, and documents his successes and failures with them. He had lots of great ideas for getting very young children to think about deep math. When I read it last year, I had access to an online copy. I have just now ordered a real book, so I can turn down my favorite pages and find them again quickly.
The people at the Math Circle Library have been working with the folks at AMS to change the pricing structure for the math circle books. The prices of seven of the twelve books in the Math Circle Library series have been reduced to $18.75*. I ordered Math from Three to Seven, Math Circle Diaries (aimed at grades 5 to 7), and Invitation to a Mathematical Festival.
More about the book... Paul Zeitz, who edited the English translation of this book (originally published in Russian), said in his introduction:
As anyone who has taught or raised young children knows, mathematical education for little kids is a real mystery. What are they capable of? What should they learn ﬁrst? How hard should they work? Should they even “work” at all? Should we push them, or just let them be?If you buy it, let me know what you think.
There are no correct answers to these questions, and Zvonkin deals with them in classic math-circle style: He doesn’t ask and then answer a question, but shows us a problem — be it mathematical or pedagogical — and describes to us what happened. His book is a narrative about what he did, what he tried, what worked, what failed, but most important, what the kids experienced.
This book is not a guidebook. It does not purport to show you how to create precocious high achievers. It is just one person’s story about things he tried with a half-dozen young children. On the other hand, if you are interested in running a math circle, or homeschooling children, you will ﬁnd this book to be an invaluable, inspiring resource. It’s not a “how to” manual as much as a “this happened” journal. ... Just about every page contains a really clever teaching idea, a cool math problem, and an inspiring and funny story.
*The pricing on the AMS site may be a bit confusing. They show a list price and a lower price for "all individuals". If you haven't set up an account, the price will initially show up as the $25 list price. Once I logged in, it changed to $18.75.