I have been reading a lot of books about deliberate practise recently like Angela Duckworth's "Grit", "Talent is Overrated" - Colvin and "Peak" - Ericsson and Pool. I want to apply these principles.
Can you suggest some concrete steps to implement the principles deliberate practise in my mathematical studies ?
As far as I understand, deliberate practise has two main principles :
It is focussed - For example, if you're a tennis player, it isn't just to play the most games or to hit the most number of balls as fast as you can. Rather, it would be to specifically practise the motion of the forehand and focus on the wrists, elbows and shoulder to ensure that the form is as correct as it can be. If you're a cricketer, it isn't to just hit the most number of balls, but to ensure that the bat lift is straight, the weight transfer is right, head is steady and that the elbows, wrists and feet move as accurately as possible for the best possible shot. It is to put deliberate focus into those things and correct the form, rather than just focus on hitting the ball the most number of times. While doing mathematics, what can I choose as specific goals to improve ? In sports, it's easy to choose a small part of the form to improve. But, it's not so obvious what this goal should be in Mathematics.
It has constant feedback - If you're a tennis player, you become conscious of which part of your swing is wrong exactly and decide if the ball doesn't have too much top spin. Having gotten that feedback, you specifically start tailoring that part of your swing consciously to increase the amount of top spin. If you're a writer, you don't just write more. You analyse your writing, and realise that your character psychology is fine but your description of events and settings isn't. So, you find some writings where those parts are excellent and specifically focus on improving that aspect of your writing. How do I analyze what mathematics I'm doing as good or bad ?
I want a set of concrete steps I can follow to improve my mathematical skills. I should note, that by mathematical skill, I mean ability to solve problems (Like the Olympiad type, which will later help me in research). I'm not asking for advice to increase my grade or marks. I'm interested in improving my mathematical ability.