Mark Twain : “It’s easier to fool people than to convince them that they have been fooled.”
Looking at the history of the National Council of Teachers of Mathematics (NCTM) activity in pedagogies pushed, textbooks recommended, sorta-standards designed, points of emphasis made, switches of horses in midstream, and results, I say:
“It’s easier to fool the NCTM than to convince them that they have been fooled.”
While these days few persons argue with the push to increase student proficiency in the following:
#1 Procedural Fluency,
#2 Problem Solving, and
#3 Conceptual Understanding,
it remains to be seen if the NCTM can figure out the best ways to do that or even a pretty good way to increase proficiency. Given NCTM history, it is Buyer Beware with current NCTM advice.
In the late 1950s and 60s the push was “New Math,” which emphasized “Conceptual Understanding” and had little practice with few examples. [[death to “example-based instruction” could have been the sub-title]] … and it did not work.
The 1970s were a time of recognition of and attempted recovery from “New Math” damage.