Proofs in abstract algebra, for example, require the ability to quickly and correctly manipulate symbols on paper (using already discovered rules/lemmas/theorems).
The repetitive practice is in this manipulation of symbols. It takes a long time and deliberative practice to learn this skill. You just practice by doing symbol repetition in different contexts, instead of doing the same thing over and over again like multiplication tables, because your symbol manipulation abilities have to be general [1].
If you try to teach, you will quickly discover that there is a wide difference in this ability for math majors by their final years. And the students who have poor symbol manipulation abilities inevitably struggle at the higher level concept application, because they keep making mistakes in the symbol manipulations and having to redo it.
[1] Contrast the training of 100m sprinters (multiplication table), who only run 100m on a fixed track that they will eventually race on, and the training of cross country runners (symbol manipulation), who practice on a variety of routes, because their races are on different routes.
The repetitive practice is in this manipulation of symbols. It takes a long time and deliberative practice to learn this skill. You just practice by doing symbol repetition in different contexts, instead of doing the same thing over and over again like multiplication tables, because your symbol manipulation abilities have to be general [1].
If you try to teach, you will quickly discover that there is a wide difference in this ability for math majors by their final years. And the students who have poor symbol manipulation abilities inevitably struggle at the higher level concept application, because they keep making mistakes in the symbol manipulations and having to redo it.
[1] Contrast the training of 100m sprinters (multiplication table), who only run 100m on a fixed track that they will eventually race on, and the training of cross country runners (symbol manipulation), who practice on a variety of routes, because their races are on different routes.