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We often see students starting to practice only after they claim to understand a concept (or worse still not practising at all after claiming to understand a concept fully). I’m not sure if it’s because they think they have an eidetic memory like Mike Ross from Suits “And once I understand it. I never forget it.” but truth be told the two forces of understanding and practice do not move alternately, but rather, simultaneously. As an illustration, it’s more like a gear model:
General thinking:
What is more likely:
A few remarks off hand:
1) Practice helps to stress-test the level of your understanding in terms of depth and breadth;
2) Practice helps to train your speed and minimise odds of carelessness (read here https://www.aces-aspire.com/post/how-to-cure-carelessness-in-math);
3) Practice helps you to gain exposure on how questions can be worded (we do see students using excuses like “questions were funny” recently too)
So kids, don’t spend too much time trying to understand a concept fully (who is there to help judge the “fully” anyway?) before getting your hands dirty. Practice is an essential part of the process too, it doesn’t exist outside/after understanding. Practice helps you to understand how a concept functions, how a technique works and allows you to internalise the teachings properly.
I can watch Michael Jordan shoot free-throws 100 times, understand his pre-shoot ritual, angle of elbow etc but I can never be a good shooter until I practice, review my mistakes, check against his video and go back to practice again!
True competence can only be backed up by both understanding and practice!
Alvin