Ender comments on Truly Part Of You - Less Wrong
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There were actually a few times (in my elementary school education) when I didn't understand why certain techniques that the teacher taught were supposed to be helpful (for reasons which I only recently figured out). The problem of subtracting 8 from 35 would be simplified as such;
35 - 8 = 20 + (15 - 8)
I never quite got why this made the problem "easier" to solve, until, looking back recently, I realized that I was supposed to have MEMORIZED "15 - 8 = 7!"
At the time, I simplified it to this, instead. 35 - 8 = 30 + (5 - 8) = 20 + 10 + (-3) = 27, or, after some improvement, 35 - 8 = 30 - (8 - 5) = 30 - 3 = 20 + 10 - 3 = 27.
Evidently, I was happier using negative numbers than I was memorizing the part of the subtraction table where I need to subtract one digit numbers from two digit numbers.
I hated memorization.