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The comment on Peano's pedagogical failure is an interesting one. I am not sure the link to oral tradition is the right one, though. Some how this should connect with "didactic transformation" or "didactic transposition". Tkuvho (talk) 05:39, 25 November 2010 (UTC)[reply]
But Peano also used to give oral classroom presentations. The question is not whether or not to teach orally, but how to teach orally. It seems to me that Peano thought that the foundations of mathematics are also the foundations of a young person's learning. The same thinking was at the bottom of the new math. The pedagogical failure of both shows the two foundations are not the same. Didactic transformation is the recognition that mathematics as seen by researchers needs to be transformed before it can be taught effectively in such a way as to relate to the students' intuition and background. Tkuvho (talk) 03:17, 26 November 2010 (UTC)[reply]