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The point is that they forbid the children that can subtract from learning algebra

I suspect if you told these 8 graders who “can’t subtract” you were going to give them $100 and ask them for $110 back you’d find they understand both subtraction and negative numbers.

It's different when it's written down as a math expression or word problem. 100-110 becomes 110-100. 17-9 becomes a finger counting exercise. Small errors get propagated in ways that make a distracting mess to sort out. None of this is conducive to learning algebra.

> It's different when it's written down as a math expression or word problem

Isn't this the actual core of the problem then? If a kid can do $100-$100 but can't do 20-8, the problem is he doesn't understand how to map the things in real life he knows, to the symbols you're showing him.

If only there were some way of doing math where different symbols were substituted such that people could recognize patterns that they had difficulty understanding with the original symbols.

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