The design of the new math was the fault of mathematicians. I taught my older daughter to read by a combination of look-say and phonics. It went very well. At the end of second grade, she was reading at 7th grade level, and that was a year after I stopped teaching her. However, I also tried to teach her math via the "new math" workbooks. Whether it was Russell's influence or Bourbaki's it based numbers on sets and we had {picture of teddy bear, toy truck, elephant} as examples, i.e. with the curly brackets. The problem with new math is that it is not interesting. It wouldn't be bad if the curly bracket examples lasted only one day, but it had to be dragged out because of the grade level. Even addition and multiplication tables are more interesting than the intersection and union of explicitly given sets. My opinion is that what generates interest in mathematics is geometry in the style of Euclid with theorems whose truth is not obvious and whose proofs are challenging. New math was a disaster with my daughter, because it is boring.