Why You Need to Develop Automaticity in Procedures Even If You Only Care About Proofs/Derivations

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The proof of the law of cosines is a great example illustrating why it’s so important to develop automaticity in procedures even if you’re most interested in learning the proofs/derivations.

If you’re automatic on trig ratios and algebraic manipulations like expanding a binomial, then you can easily follow this derivation of the law of cosines.

“So you just drop an altitude, pythag the right triangle, sub some trig for the legs, expand & collect the algebra, and out pops the law of cosines? Wow, that actually makes perfect sense. Now that I see it I can’t unsee it.”

But if you don’t have automaticity on all those underlying procedures, you’ll struggle to follow it at all, and you’ll come away thinking that you need genius-level insight to wrap your head around it.

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