Why Johnny Doesn't Get It

Beginning of article

My wife and I home school our 15-year-old son, William. Each night after work, I take my "Dad" hat off and put on my "math teacher" hat.

When I first began teaching William algebra, I used traditional textbooks and the traditional flash-card approach to instruction. After extensive explanation, repetitive problem-solving, and occasional frustration, he was largely able to master the straightforward equations and formulas that he had been drilled on.

At a certain point in the learning process, I presented William with a series of problems that could be solved easily through the formulas he had learned, but that also required an understanding of how to apply the …