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Topic: Ignorance and Innocence in the Teaching of Mathe­mat­ics

How if the understanding of mathe­ma­tics on the part of the judge of the educator is simply wrong? 

So wrong that what he is trying to put across in his "methods of teaching" textbook, or mea­suring in his resear­ches on how children learn, sim­ply cannot be understood because it is at bottom senseless?

That examples of this phenomenon were as much the rule as the exception in the period 1940-1950 will give some insight into the causes of the "The New Math" phenomenon that fol­lowed.  In evaluating the way mathematics was being taught in the schools on the eve of The New Math, it will be worth while not only to examine what textbooks were saying, or school examina­tions examining, but also to see what future teachers were being taught by their own professors in the colleges.

http://www.math.rochester.edu/people/fa … /igno.html