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!

## 5 comments:

As Robert Craigen, math professor at U. of Manitoba, has posted elsewhere, those who claim to support reform math talk a good game about "understanding" but they have little clue as to what a mathematician means by "understanding". In particular, the ability to articulate reasons -- that is, to prove things, is central. They think that saying "I used such-and-such strategy" is "articulating a reason" but it does not actually demonstrate understanding. Even the so-called "personal strategies" that students supposedly invent are rarely generated by them. A simple proof of this is that they are already sketched out to be evaluated, in the curriculum frameworks. If a truly original approach was used by a student most fuzzies would have no idea how to evaluate it to determine whether or not it is valid. And when it comes to the great theorems of elementary arithmetic, such as why ratios of integers always correspond to repeating decimals, they draw a blank -- generally these are reduced to inductive "explorations"; the deductive element is completely lost. So apparently, they have no clue.

It's also a response to a straw-man argument. They wrongly think they know what traditional ed looked like: sage on the stage, drill and kill; and race in the opposite direction to escape the burning straw-man they created.

I think it's true that traditional math is boring and baffling for great swathes of the population - like the clerk who was amazed at my mystical prowess in adding $5.50 to $1.75

in my head!!Just imagine what it's like for her to get a mortgage.The problem with Reform Math is it throws the baby out with the bathwater: if math is boring and baffling, let's nobody learn math. Instead, let's all write little essays about number playtime.

The result, of course, is not that nobody is bored and baffled - plenty of kids are bored and baffled by Reform Math - but that the boredom and bafflement are more evenly distributed (at the expense of evenly distributed innumeracy). Rich and poor, smart and dumb alike are bored and baffled by TERC Investigations. Bye-bye Achievement Gap!

I think that one of the items you left out of your inventory of motivations behind Reform Math is subjectivity in assessment. In traditional math, there is a right answer, and it's easily seen who has arrived at it. This leads to quick perception of an achievement gap.

In Reform Math, adequate progress is nicely amenable to pencil-whipping, as the teacher gets to judge how much credit to extend for the explanation of how a wrong answer was reached. It could be an easy matter to make the achievement gap disappear in a third grade Reform Math classroom, as the matter under judgment becomes not accurate arithmetic but prowess at bullshitting the teacher. There's many a young fellow out there who can't add double digit numbers but is a whiz at making up stories.

Yeah, they're doing such a great job at solving "real-world problems" that four HS grads were incapable of calculating sales tax with the aid of a calculator and had so little number sense as to be unaware that an answer of $16 for a $10 purchase, with 6% sales tax, had to be wrong. When I, a customer, walked them through the background (6% means six cents on each dollar) and the method, their awed reaction was, "Wow, you must be a math teacher!" No, I simply learned 6th-grade arithmetic.

While it is true that "mathematics" is beyond many people, basic arithmetic, fractions, decimals and percentages are not. In the days before calculators and cash registers that do all the calculations, ordinary people did these things by hand - and most were HS grads or less. It does, however, require effort and most people need explicit instruction and dedicated practice.

The whole spiral math disaster made more sense when I read that such curricula were specifically designed for the full-inclusion, heterogeneous classroom (not sure if it's true but it makes sense); because nothing has to be mastered, the pretense that all are learning is enabled. The fact that they are not learning won't become obvious until years later, when they are shut out of the math track that includes HS calculus, struggle with HS algebra and need college remediation; they can't learn those things without having mastered the fundamentals of arithmetic. There's no foundation under the math house and it will sink into the sand.

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