Get the latest tech news

A balanced review of Math Academy

And some thoughts on motivation and structure, for autodidacts

Meanwhile, the two people from our cohort who did become professional mathematicians were entirely different: they didn’t drill at all, but instead interrogated gaps in their understanding, found novel ways to develop their intuition, and overall focused on subtle conceptual aspects of a topic that could never conceivably be formulated as exam questions. I’d never considered this approach until I read David M. Bressoud’s fantastic book Calculus Reordered, which argues among other things that the conceptual basis of integration—as accumulation of thin slices—is a more intuitive starting point than tangents to a curve or rates of change. Talk to high school math teachers, and you’ll see that it’s also problematic to start with integration: problems can quickly grow too challenging algebraically, deviation from the standard sequence can leave you without much external support, and students can lose motivation when the applications move beyond areas and volumes.

Get the Android app