Gary Stager posed about Constance Kamii yesterday in Facebook and Sylvia Martinez pointed to this helpful overview. "By telling a child how to solve problems and memorize facts, we are trying to shortcut a developmental process that just can't be shortcut – and in the end, will actually delay progress and make it less likely that they will develop the deeper understanding they will need for lifelong mathematical ability." I think that pointing to mathematical rules and algorithms as 'shortcuts', and the weakness if this approach becomes more apparent of time in what philosophers and cognitive scientists call a 'combinatorial explosion' - literally, the tadk of memorizing ruled becomes greatet than the tadk of creating and internal model or rrpresentation of the domain.
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