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Despite claiming you don't understand the gain, you just said it: students gain a more complete understanding of how multiplication and subtraction are related
by ronaldx 13y ago
Despite claiming you don't understand the gain, you just said it: students gain a more complete understanding of how multiplication and subtraction are related to division, which is the primary goal of this stage of math education.
- wolfgke 13y agoIf this is your goal you better teach the student about how to define addition and multiplication using the the formalization from the Peano axioms, i. e. +(0, y) = y for all y in N +(S(x), y) = S(+(x, y)) for all x, y in N *(0, y) = 0 for all y in N *(S(x), y) = +(y, *(x, y)) for all x, y in N I know no way that states more clearly how addition and multiplication are related. Division is than simply stated as: for given a, b in N find x such that *(b, x) = a. This states clearly how multiplication (obvious) and addition (by definition of multiplication) is related to division.
- gnoway 13y agoThe only difference between this method and 'traditional' long division is the use of a fixed product of the divisor with each iteration instead of trying to find the largest possible number to subtract. If anything, this just shifts the emphasis away from multiplication to subtraction, which I think is strange. That said, I don't have a big problem with this as a method for learning division. I think my reaction is related more to the memory of 'show your work!' and the thought that this would mean more work to show.