Some people have proposed that what drives the Reform Math movement is a desire to lower the achievement gap. I agree-up to a point. The gap has become a national obsession. Hopeful gap-narrowers are everywhere. The better intentioned of them honestly believe that the collaborative, student-centered, drill-and-algorithm-eschewing, symbol-de-emphasizing, "no one right answer" approach to math resonates with those who (supposedly for cultural, gender-based, and/or "learning style" reasons) have languished under "traditional math." These people mean well, but are ignorant of what peer-reviewed cognitive science research has revealed about what students need to master mathematics.
Then there are those with a more cynical attitude towards the gap: narrow it mainly by lowering the top. Dumb everything down, water it down further with excess verbiage and non-mathemnatical material, and only give full credit to students who write out verbal explanations. That way, students who once would have excelled will become bored and disengaged, and those whose math abilities far exceed their verbal and penmanship skills will get bogged down in the non-mathematical stuff.
For some, hostility to traditional math and to those who most excelled in it may be personal. Perhaps they themselves did not excel and have long felt stupid about that and harbored grudges against those who did. To them, Reform math provides validation, vindication, and, possibly, a perverse form of revenge.
But would-be gap closing isn't the only agenda behind Reform Math. Big swathes of the general populace buy into the idea that traditional math is boring and baffling and that classroom math needs to keep up with modern times. Then there are three specific groups whose interest in Reform Math is professional: those in the education business, those in the educational publishing business, and those in the math business.
Within the former group, we have the true believers: those who truly believe, whether from idiosyncratic prejudice or from brainwashing by ed schools, that Reform Math teaches deeper understanding and better prepares students for living in the 21st century.
Within the second group we have the stakeholders of textbook and software companies, as well as those in the professional development business. They benefit financially from the constant "reforming" of K12 math. The more you reform things away from what's curently traditional, the more easily you can convince schools to keep buying new material and paying for new training sessions.
Within the third group we have the mathematicians (or those who claim to be). Many of them have no sympathy for the drills of traditional math, which have little to do with what they like about math--and with their work as professional mathematicians. Perhaps, as young math whizzes, they didn't depend on such drills as much as ordinary humans do. It may never occur to them that most human beings can't simply play around with numbers and be ready for BC Calculus by 12th grade.
Others do concede that ordinary people are different, but go too far in separating the ordinary from the elected few. They think that the solution is to teach math to most kids entirely through concrete examples and real-life application--forget proofs and symbolic reasoning.
Finally, many college math professors hear Reform Math's buzz words--"higher-level thinking," "conceptual understanding"--and assume these will ameliorate, rather than exacerbate, the growing deficiencies they see in their undergraduate students, many of whom can't seem either to understand conceptually or do math except at a mindless, recipe-following level. When the more concerned of these math professors venture into workshops led by "math education experts," they assume that these experts mean the same they do by "deep, conceptual understanding." They take what they hear about Reform Math vs. traditional math on faith, and it doesn't occur to most of them (unless they have kids in school) that the so-called experts--many of whom seem like smart, well-intentioned people--may not be trustworthy. And that they themselves need to take a close look at the new curricula and at what sorts of problems are assigned at which grade levels.
One mathematician friend of mine who attended one of these "math education expert"-led workshops a few years ago was initially taken in by some of what he heard from the apparently smart, well-intentioned presenter. Below is the accompanying handout, with his notes at the top of the first page [click to enlarge]:
All this looks so much more conceptual than a mindless execution of the standard algorithms, doesn't it? But what this handout doesn't show is (1) the grade level of the student in question, and (2) all that the curriculum leaves out in the name of conceptual understanding and explaining one's answers in words, numbers, or pictures.
It was only after I showed my professor friend page by page, problem set by problem set, grade level by grade level, the actual curriculum that this workshop presenter was peddling that he completely changed his mind.
I've said it before and I'll say it again: no one--whether they are an "math education expert" or a math curriculum developer or a math professor or simply someone who believes in "21st century skills"--can claim to support Reform Math until they look closely at the curriculum and then agree to have their children get their entire K12 math education from it. No "but my child is different," and no Kumon or after-school Singapore Math or extra-curricular test prep allowed!