Like most first-year teachers, I couldn’t believe some of the gaps in my kids’ knowledge. My geometry students scowled at word problems, mangled the distributive property, and handled fractions with the same fondness you’d show a steaming diaper. Privately, I grumbled. Why didn’t their old teachers cover this stuff properly? Why is it my job to pick up the pieces?
Two years later, I got the chance to teach the same kids trigonometry. I still couldn’t believe some of the holes in their background. What’s their problem with special right triangles? Where’s their intuition about proof? Why didn’t they learn this stuff? As soon as I found myself blaming the last guy, I realized.
The last guy was me.