Deliberate Practice: The Most Effective Form of Active Learning
justinmath.com
justinmath.com
Deliberate practice requires repeatedly practicing skills that are beyond one’s repertoire. However, this tends to be more effortful and less enjoyable, which can mislead non-experts to practice within their level of comfort.”
This seems to be one of the key factors. But how do we apply deliberate practice to mathematics? Unless we are planning to enter math competitions, speed doesn’t seem to be relevant to make mathematical discoveries.
You don't have to be blazing fast but you do need to have sufficiently tight feedback loops so that you can get through a high volume of action-feedback-adjustment cycles. It's the compounding of a massive number of those cycles that produces a massive gain in performance.
Also, in order to make mathematical discoveries -- or more generally, in order to grapple with advanced content at all -- you need to develop a level of automaticity on your foundational skills.
This makes sense. So in this regard there is an analogy with sports where you need to perform foundational skills without thinking.