A three-for-one today! Here are three books I wanted to mention to you, dear reader, for one reason or another.

A Wealth of Numbers
Benjamin Wardhaugh

Princeton Press kindly sent me a review copy of this book. As an anthology of popular mathematics writing from the 1500’s to the present, it’s not the sort of book I usually review here—but it’s nonetheless fascinating. The featured excerpts are, by turns gripping, dull, lucid, incomprehensible, hilarious, irrelevant, and fun. I didn’t learn a whole lot of new mathematics by reading this anthology, but it gave me some eye-opening perspective on how people have thought and written about mathematics over the last 500 years.

Dead Reckoning: Calculating Without Instruments
Ronald W. Doerfler

There’s a lot of controversy over the use of calculators and computers in math classrooms. Should they be welcomed as labor-saving devices that allow students to explore mathematics in new ways, or eschewed as crutches that turn students into button-pushing automata with no real understanding? It’s an important debate, but it seems to me that those who argue against calculators sometimes have a nonetheless impoverished view of the alternative: just the ability to do the standard Western algorithms for the four basic arithmetic operations, and understand why the algorithms work.

This book (which I received as a gift about six months ago) isn’t intended to enter that debate directly—but it is a far-ranging survey of methods for pencil-and-paper (or mental) calculation. There are general algorithms, of course, (and not just for arithmetic, but for square roots, logarithms, trig functions…) but there are also all sorts of tricks and special cases which arise from, and engender, intimate familiarity with numbers. Is it "practical"? Well, not really. But that’s certainly not the point. I had so much fun reading through this book and trying out all the different algorithms: multiplying in my head, computing square roots to many decimal places using just a single sheet of paper… Honestly I don’t remember any of the actual algorithms anymore, but I came away with better number sense—and I may just pull it out and try some of the algorithms again. Eventually some of them are bound to stick!

Mathematical Literacy in the Middle and High School Grades
Faith Wallace and Mary Anna Evans

I mention this book particularly because it contains (in a box on page 67) an essay by yours truly! I wrote something about the experience of writing this blog and inspiring readers with mathematical beauty.

I no longer teach middle or high-school students, but the idea of using literacy to inspire interest in math makes a lot of sense to me (and of course, it’s perfectly applicable at the college level as well). There are all sorts of interesting ideas in here—some of which I will never use (discussing statistics and voting via American Idol) but others of which I’d love to try someday (using biography or fiction to inspire mathematical interest).