Happy Catholic recommends The Uncommon Reader, by Alan Bennett. On the basis of the quote she took from the book, I bought it for my kindle while I was typing that reference. It is now ready for reading!
One of my purposes in writing this book is to give readers who haven’t had the opportunity to see and enjoy real mathematics the chance to appreciate the mathematical way of thinking. I want to reveal not only some of the fascinating discoveries, but, more important, the reasoning behind them…The thinking in each chapter uses at most only elementary arithmetic, and sometimes not even that. Thus all readers will have the chance to participate in a mathematical experience….