Recall First, Reason Second

To build automaticity: instead of deriving/reasoning a result before applying it, force yourself to first recall the result from memory, and then justify the it afterwards. Recall first, reason second.

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If you want to build automaticity, then you need to practice automatic recall.

That sounds obvious, but a common mistake even among serious learners is “I’ll derive/reason the results from scratch to create a cheat sheet, and then refer to the cheat sheet during practice problems that involve applying those results.”

It’s good to practice deriving/reasoning results from scratch when doing so is within grasp of your skill level and you haven’t done so in a while. However, that DOES NOT COUNT as automatic recall practice on the result itself.

It’s just like how recalculating your times tables on a reference sheet that you constantly refer to will prevent you from developing automaticity with multiplication.

So here’s what I recommend to do: instead of deriving/reasoning a result before applying it, apply it first and then derive/reason it after. Force yourself to recall the result from memory, and then justify the result afterwards.

By the way, this applies broadly, not just in math.

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