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more about decimals
Posted:
Nov 27, 2002 8:29 PM


Nancy and Martha gave me some things to think about and expand on; mainly, the idea of number sense.
I don't teach algorithms either but rather I do try to get students engaged in thinking about the relationships that underpin algorithms. For example, I have them play with powers of ten in the place value system, moving left or right in the system as they multiply or divide by powers of ten. It's a playful thing and gets them thinking about certain relationships. They seem to love the idea that any number to the zero power is 1. I don't drill on it but I do then extend the ideas that evolve from multiply fractions to the base10 to see what happens to, as they say, "the number of zeroes down there." This leads readily to the algorithm of moving the decimal point around when multiplying. One class insisted that there should be a comparable algorithm for division and we generated it but decided that it's too cumbersome  as one student said "too many moving parts." They seem to thrive on parsimony, particularly if they've been involved in the generation of it.
thanks for the replies. Oh, about the "erroneous" multiplication of decimals system that a student evolved ... I asked the student if I could talk about it in class and he approved. I then discussed what I saw and indicated that it was erroneous. I then asked if anyone would like to play with it to come and show us how and why it's erroneous, or, would they simply like me to show them. There are about 4 "teams" of students working on it and will come back with their insights next week ... talk to me later ... mark
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