The Liberal Arts Tradition by Jain and Clark
The first book on this list might not obviously be about teaching math, but in fact the authors teach advanced math at a small, private, Christian classical school in Florida. They have some of the best writing I’ve ever seen about the importance of mathematics in classical education.
Today the desire among math educators to cultivate “number sense” reflects this ancient desire to have deep reasoning in arithmetic.–Clark and Jain
Make It Stick by Peter C. Brown and Henry L. Roediger III
Another book that isn’t obviously about mathematics, yet contains wonderful information about to structure your child’s math education. Make It Stick is a fantastic book just to learn how to learn better, but the idea of interleaved and varied practice is especially foreign to most US math curricula.
In math education, massing is embedded in the textbook: each chapter is dedicated to a particular kind of problem, which you study in class and then practice by working, say, twenty examples for homework before you move on. … When you have learned under conditions of massed or blocked repetition, you have had no practice on that critical sorting process. … For our learning to have practical value, we must be adept at discerning “What kind of problem is this?” so we can select and apply an appropriate solution.
Several studies have demonstrated the improved powers of discrimination to be gained through interleaved and varied practice.pg 53; Brown, Roediger III, and McDaniel
The Math Gene by Keith Devlin
In the US, we tend to think that either children are “mathy” or they’re not, and there’s not really much to be done about it. We’re shameless about saying, “I’m not really good at math” in a way we would never say, “I’m not good at reading.” Devlin wrote an entire book to argue against the idea that some people are just intuitively mathy, and it’s a good book.
Whatever it is that causes the interest, it is that interest in mathematics that constitutes the main difference between those who can do mathematics and those who claim to find it impossible.–Devlin
A Mathematician’s Lament by Paul Lockhart
This is actually an extended essay, but it’s quite powerful. Lockhart argues that the joy of mathematics should be given to all.
The saddest part of all this “reform” are the attempts to “make math interesting” and “relevant to kids’ lives.” You don’t need to make math interesting–it’s already more interesting than we can handle! And the glory of it is its complete irrelevance to our lives. That’s why it’s so fun!pg. 8; Lockhart
The Number Sense by Stanislas Dehaene
Dehaene is a neuroscientist writing in his second language, and so this is a fairly dense piece of work, albeit written for the general public. However, if you can stick with it, he explains some of the most frustrating and key parts of teaching math. For example, his analogy for the times tables is amazing.
What would happen if you had to memorize an address book that looked like this:
Charlie David lives on George Avenue
Charlie George lives on Albert Zoe Avenue
George Ernie lives on Albert Bruno Avenue.
And a second one for professional addresses like this:
Charlie David works on Albert Bruno Avenue
Charlie George works on Bruno Albert Avenue
George Ernie works on Charlie Ernie Avenue
Learning these twisted lists would certainly be a nightmare. Yet they are nothing but addition and multiplication tables in disguise. … The six above addresses are thus equivalent to the additions 3 + 4 = 7, 3 + 7 = 10, and 7 + 5 = 12, and to the multiplications 3 x 4 = 12, 3 x 7 = 21, and 7 x 5 = 35.–Dehaene