Difference Between the Phrases

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Last weekend, I reread the first section in Knowing and Teaching Elementary Mathematics and had a moment where my heart swooned yet again for mathematics:

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“For Tr Bernadette, the problem 64-46 was not, as suggested in the borrowing explanation, two separate processes of 4-6 and then 60-40. Rather, it was an entire process of ‘taking away a number in the forties from a number in the sixties.’ Moreover, Tr Bernadette thought that it was not that ‘you can’t subtract a bigger number from a smaller number,’ rather, that the second graders ‘are not able to do that.’ Finally, the solution was that ‘we go to *the other part of the number*’ (italics added), and ‘pull it over to our side to help.’ The difference between the phrases ‘other numbers’ and ‘the other part of the numbers’ is subtle, but the mathematical meanings conveyed are significantly different.”

~ Knowing and Teaching Elementary Mathematics, Piping Ma, pg 4

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