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This is how I was taught algebraic multiplication (using little plastic xs and ys and 1s instead of lines on paper) and I found it extremely helpful and it's still more or less how I visualize multiplication, dimensional analysis, etc in my head. I can see it making basic arithmetic easier to learn as well.

I was virtually immune to rote practice of intellectual tasks as a kid and mostly still am. I don't think I'm the only one, witness the near universal inability of US adults to perform long division, despite it being drilled into every schoolchild for hours on end.

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