Varying the problem helps, as does varying your approach to the problem. Studying math generally involves many years of working progressively complex problems. But this is different from a “kata”, which is a set of moves rigorously repeated in a specific order and invariant manner*.
Psychologically speaking, a kata functions to take a set of moves that the student consciously understands and build muscle memories that can execute the moves effectively at the sub-second timescale of a fight. Reasoning uses different cognitive systems, although once a behavior is consciously understood it is often useful to practice until mental subroutines are developed that enable quick, unreflective execution of the behavior.
*There will be some variation as the student goes from not being good at the kata to being very good at the kata, but that variation is unwanted. The better you are at the kata the less variation there is.
Varying the problem helps, as does varying your approach to the problem. Studying math generally involves many years of working progressively complex problems. But this is different from a “kata”, which is a set of moves rigorously repeated in a specific order and invariant manner*.
Psychologically speaking, a kata functions to take a set of moves that the student consciously understands and build muscle memories that can execute the moves effectively at the sub-second timescale of a fight. Reasoning uses different cognitive systems, although once a behavior is consciously understood it is often useful to practice until mental subroutines are developed that enable quick, unreflective execution of the behavior.
*There will be some variation as the student goes from not being good at the kata to being very good at the kata, but that variation is unwanted. The better you are at the kata the less variation there is.