(From the comments to The Birds, the Bees and Constructivist Math.)
... for me the key issue is not whether a math program promotes the retention of mathematical facts or concepts, but rather whether or not it stimulates or enables further learning. I think constructivist math programs, by continually frustrating kids, and by denying them basic competence, make it difficult for students to know whether or not they like math or have any real interest in it.
... there are some constructivists who believe that the end—as well as the beginning—of math instruction must always be real world applications. I disagree with this, since to me math is a language, and any pleasure I once derived from it came from this aspect of it.
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