In partial response to a recent note from Walter Felscher, which characterized *new math* in the words QUOTE: I well remember the years between 1970 and 1974 when "NewMath" was propagated for elementary schools, meaning the use of set-notation and the emphasis of cardinal over ordinal aspects. END QUOTE
There is no doubt that what Professor Felscher describes DID in fact exist - - but it was only one version of the *new mathematics*. In fact, it was one of the silliest, and perhaps the one LEAST related to the work of Jean Piaget. Piaget studied carefully how children actually think about various mathematical concepts. The *set theory* version of elementary school math had no regard whatsoever for how children actually build their ideas, but considered only how some logicians might reconstruct these ideas for far more sophisticated purposes unrelated to the thinking of children.
There were many other versions of the *new math*, many of which were NOT disasters, but yielded excellent results.