Ben always dreaded being asked for his “teaching philosophy,” he writes at Math with Bad Drawings. It seems to come out as: “We buzzword to buzzword, not for the buzzword, but for the buzzword.”
Now he’s got it in 11 words: Math is big ideas, approached from as many angles as possible.
For example, here’s a big idea:
He teaches from the historical, verbal and scientific angles. Then comes practice.
Math without any computational practice is a mushy math, a math with no spine. To understand what makes, say, linear equations tick, you’ve got to solve ‘em, graph ‘em, play with ‘em in a hundred different ways. You can’t grasp patterns until you’ve worked through examples. Without multiplication facts at your fingertips, you’re unlikely ever to apprehend deep truths about the distributive property. If you’ve never spent a day multiplying out products of the form (ax + b)(cx + d), then you’ll never internalize the methods for factoring quadratics.