Sometimes I fantasize about writing the best math book ever written: I would pick my favorite topics that always seem to go missing from the standard curriculum and seamlessly use them to motivate mastery of math skills, but also as a launching point for an exploration of the most beautiful, mind-blowing topics in math. I’d use tessellations of planes and spheres to explore fractions and angles, and by seeing which angles add up to 1, actually generate new tilings; I’d use the profoundly simple results of modular arithmetic to explore divisibility, primes, and algebra; I’d talk about lasers bouncing off mirrors and billiard balls bouncing around tables, and connect it to the astounding focal properties of conic sections. If I had time, I might even throw in some topology and graph theory–real 20th century mathematics in a math course! The book would be well written and engaging, with a real author behind it, not a committee.
And then I realize that the book has already been written.
The title is Mathematics, A Human Endeavor, by Harold Jacobs. If you’re involved in mathematics even remotely, and especially if you work at the middle school or high school level, or with gifted younger kids, or have any stake in math or math education whatsoever, get your hands on this book.
Now here’s a mystery: the book was apparently widely used for some time in the 70s and after. Why didn’t its use persist?
If you’re looking for some other thoughts on the book, here are the reviews on amazon, nearly all gushingly positive.