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I'm coaching my son through high school math. One of the things I'm trying to impress upon him is focusing on understanding _why_ these formulas work rather than just memorizing the formulas themselves - if you understand why they work, you can always re-derive them if you need to, and you may forget the details of what they do, but you'll never forget the details of why they work once you understand them.



The best strategy for this in my opinion is to always ask “what’s the picture” (as in visualization)? I can’t remember the mechanical rules for say Newton’s method, but I have the picture of what Newton’s method does in my head. From that, I can quickly work out the algorithm.




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