ChemProf's comment about teachers bullying socially awkward children made me think of a recent post on the Math Investigations (TERC) website in which a teacher points out that a certain type of student is languishing under Reform Math, and, while pointing this out, uses an all-too-familiar negative caricature:

There is another population that I think we are in danger of leaving behind, a population that used to do well in school mathematics: tidy math fans.

What is tidy math? Worksheets containing orderly rows of computation problems, all essentially the same problem, but with different numbers. Textbooks or teachers that cleanly demonstrate a method step by step and then ask students to do thirty problems using that same method. These are examples of tidy math.

Who are tidy math fans? Students who are neat and well-organized. Students who may not be too creative, but who pay attention and follow directions well. Students who are satisfied with knowing how and who are not bothered by not knowing why. Students who grow up, meet math teachers like myself at parties, and say "Oh, I've always liked math. I love how there's always one right answer to a problem." These are tidy math fans.

Neat, organized, not-too-creative directions-followers who don't ask why and want everything cut and dried. Yes, we all know who we're talking about here. Not people we'd want to be friends with, of course, but (as per Equity) we shouldn't totally abandon them either.

Our teacher continues:

Our teacher goes on to express concern about the mixed blessings that Investigations has brought (which apparently include making math more enjoyable to most students--a constituency of students whom I have yet to meet):

Tidy math fans do well in what we now call "traditional" math programs. But as some schools adopt new programs like Investigations, some of these students face a sudden drop in status, from one of the best math students in the class to an average, sometimes struggling student. Their self-esteem about their math ability plummets. It's no wonder that some of their parents (who themselves grew up with tidy math) put up a fuss about the new program and teaching style that is causing their children's loss of confidence.I can't help detecting just a whiff of schadenfreude here. After all, what's more satisfying than bringing down the type who would have out-shined you back when you were a student?

The rules for success and the very definition of what it means to do math have changed on them. Math is much harder now.

You might argue that this change is for the students' good. What tidy math fans were successful at before really wasn't mathematics anyway, and we do all students a favor by showing them what doing mathematics is really about. "Doing math has to do with thinking and reasoning about problems or situations that call for applying mathematical ideas and skills . . . Skills should be learned in the context of problems and situations and should not exist isolated from the problems and situations that give them their purpose." (Burns, p. 69.)The mathematicians I know consider Traditional Math far more mathematical than Reform Math, but why ask them? After all, they are all tidy math fans. Surely math educator and children's book author Marilyn Burns has a much better handle on what mathematics is really about.

In Beyond Arithmetic, Investigations authors advocate that students work on nonroutine mathematical problems. "With nonroutine problems, students should expect "messiness." There may be different paths to a solution, and there may be several different good solutions to a problem . . . Doing mathematics often means rough drafts, tentativeness, challenge, and hard work." (Mokros et al., p. 53.)And surely math education specialist Jan Mokros is a much better source on what doing mathematics involves than tidy, correct-answer-obsessed mathematicians are.

Our teacher goes on to express concern about the mixed blessings that Investigations has brought (which apparently include making math more enjoyable to most students--a constituency of students whom I have yet to meet):

Most students LOVE Investigations, messiness and all. I am excited about the many students who are turned on by Investigations, students who used to think math is boring. I'm thrilled to hear the stories of students who would rather continue with math time than go to recess. But I am also troubled by the few students who liked math better the old way.I have a few suggestions, but I'm afraid they may be a bit too tidy for the Powers that Be.

We need to recognize how hard the adaptation to "messy math" is for a few children. To achieve our vision of equity, we must support these children too, but how?

## 5 comments:

Whenever I hear discussion of "non-routine" problems and so on from advocates of curricula such as TERC, I wonder how the students being talked about would do with a page of word problems from Singapore math at the appropriate grade level. Could they do them? What problems can they do?

By the way, the teacher is correct about arithmetic not being "real math", in a way. But the better way to say that is that in k-3 or k-6 or somewhere in there you are not teaching mathematics but arithmetic; arithmetic is some subset of mathematics. You start there and move out.

...arithmetic is some subset of mathematics. You start there and move out.Very true. Furthermore, it's ridiculous to think that one can just jump in and "do 'real' math" without laying the foundation of arithmetic. Just another example of so-called educators expecting kids to run before they've learned to walk.

I stumbled across this great blog when looking to see if the math book publishers and school administrators can predict who will have trouble with their reform math programs. My 3rd grade Asperger kid is struggling mightily with a new one, enVisionMATH by Pearson (Scott Foresman-Addison Wesley)which has not been discussed much. Its only been out for 2 years and is number one selling in the country. Your quotes confirm that educators know some kids will have problems, and more troubling some do not care that they are causing problems. I suspect those with reading issues also drown. And the school has no idea how to teach it except to sit next to him and coach him thru each step of the inhumane, multi-step word problems. Since the state test scores "went up" last year, the school doesn't care if some kids drown, spending hours of frustration on HW and still failing new math.

I am excited about the many students who are turned on by Investigations, students who used to think math is boring. I'm thrilled to hear the stories of students who would rather continue with math time than go to recess. But I am also troubled by the few students who liked math better the old way.How many students have experience in the "old way" and the "messy way?" At the same age, of course, as we change as we mature. I think this is a purple cow, or red herring, the apocryphal student whose love of math is saved by progressive instruction.

I have a suggestion to support the "tidy math students." Offer two curricula, messy math and tidy math. Parents can select either one. After all, if the argument is that tidy math doesn't work for a certain section of the population, then it follows that messy math won't work for the rest of the population.

Allow the parents who work in quantitative professions to choose the math programs which, in their judgement, best prepare their children for quantitative professions. Don't refuse to allow lawyers' children access to the tidy math curriculum, but don't force tidy children to work with a messy math curriculum.

I'm not super math-y myself, but I have a math-y husband and a math-y father. As I understand it, real math people love "elegant solutions" which is another way to say "tidy math". I expect brute force "messy" solutions might be more popular in applied fields, but in pure math, "tidy" rules.

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