Most of us can learn to play chess in 10 hours. Few can become grandmasters. Most Hacker News readers have gotten through calculus. Few have gotten through the

Most of us can learn to play chess in 10 hours. Few can become grandmasters. Most Hacker News readers have gotten through calculus. Few have gotten through the mathemamatics needed to study elementary particle physics, let alone abstract mathematics. Raising the ceiling in yourself or your students is far more important than the time it takes. By the way, speed of learning is very important in not becoming discouraged and in motivation so it strongly correlates to ceiling. I taught my wife fractions in her late 40’s. My Mom taught it to me much faster when I was 8. My wife, a ballerina and professional dancer, tried to teach me to dance. Not only was I abysmally slow at uptake, but my ceiling was very low.