Responding to some positive remarks about progressive mathematics education, Wayne Bishop (seen above), a founding member of the anti-progressive reform group Mathematically Correct wrote:

Such speculation sounds beautiful, of course, but I have yet to meet

any mathematician who was taught in a full-blown "discovery"

environment.

This prompted me to write the following open letter:

Dear Wayne and Posse:

Reading your comment about what sort of mathematicians you've never met, I must point out that I've yet to meet one who was taught in a post-racial American classroom, either. That's because neither environment exists, or perhaps like post-racial American classrooms, a fully-realized (is it just a coincidence that you used 'full-blown,' a term I only hear used in connection with cases of AIDS?) K-12 discovery environment exists in some tiny little isolated pockets of the country, so tiny and so few that it's merely a drop in the ocean of indifferent, mostly traditional teaching, materials, and curriculum. Of course, there are districts that use some progressive reform curricula in K-5 or K-8, a very few who use them in K-12. But then, books aren't "discovery learning" or student-centered teaching. They're books. Last I checked, teachers and pedagogy are a major component of what goes on in mathematics classrooms. Classroom culture. School culture. Loads of other factors. Which textbook was purchased may not even reflect which resources are used. I've been in many classrooms where teachers have two or more sets of books and pull from all of them, none of them, or some other variant. At any rate, finding those discovery classrooms that might or might not produce mathematicians, doctors, lawyers, or members of Mathematically Correct is a challenge. Finding ones that fit MY view of high-quality, inquiry-based, student-centered discovery learning with good mathematical content and good problem tasks is not a trivial matter.

This is especially so if we're discussing, ahem, full-blown discovery from K to 12 and then through college and graduate school. And mathematicians would necessarily have to have completed graduate school, right? So you're complaining about not meeting someone who under current conditions cannot likely exist. Let's not miss the fact that the curricula and methods you decry weren't even in the wind for the most part until the early to mid 1990s. Doing the math. . . gee, whiz: it would be pretty surprising to find a professional mathematician who was in a discovery learning oriented mathematics classroom from K - 20 (Kindergarten through Ph.D) Because the environment required doesn't exist in all likelihood and certainly not in one district in enough classrooms to cover K-12 over the requisite years, let alone a university where one would find it from freshman year through the end of doctoral classes.

So you've given us a tautology. No doubt you've not found a lot of dead people who are alive, either. Great job, Brownie!

Then again, have you met many mathematicians at all lately, Wayne? Particularly recently-minted ones? I didn't think so.

You went on:

Many of us correctly believe that we should have been

taught more, and more quickly, but the idea of not learning as much

as possible (ostensibly, from knowledgeable teachers and/or

well-written mathematics books) before embarking on discovering new

and exciting mathematics is purely the stuff of ed school insight,

You made that up. Where is it written in "ed school insight" that we should not want students to learn as much as possible, and from excellent teachers, texts (and other sources you seem to always forget about).

But then we have your usual intentional distortion of what "discovery" entails.

Let's keep this simple for the slower readers in the audience: when is 15 - 9 = ? a problem, and when is it an exercise?

Not to keep you in suspense, it's a problem when you haven't been explicitly shown how to do it or make sense of it. It's an exercise when it's something you already know and are asked to merely repeat what you know to demonstrate that you know it.

If I give that question to the vast majority of first grade students, for them it's a problem. If I give it to the vast majority of high school students, it's MOSTLY an exercise, though for some it's STILL a problem, sad to say. Left to figure out what this could mean, students will figure out one or more ways to have it make sense to them. Given the chance to share ideas under the guidance of a wise and knowledgeable teacher, they will decide what makes mathematical sense and choose the method(s) that work well for them. And given the chance to think, they'll likely keep right on thinking. For 13 years of K-12 and well beyond that. Of course, your own genius children and yourself aside, you don't trust most kids. You really think most kids need Saxon Math or something equally dull. And that most teachers (whom you trust even less than you do children) can't possibly learn to do anything better for their students than take them through a million years of a billion exercises culled from the teacher-proof materials of the late Saint Saxon of the Increments. So utterly pessimistic. So utterly mind-killing. But I suspect that for the majority of kids, that's just what you would love to see.

What IS discovery learning? Is it requiring that students "re-invent" all of the K-12 mathematics curriculum as they go? Of course not. No one has ever suggested anything of the kind except for you and your buddies when you try to scare the pants of the ignorant and gullible. And you do SUCH a good job of it. Kind of like the mathematics educational equivalent of WMD and yellow-cake uranium from Niger, etc. Tell your ugly Big Lies often enough, of course, and no one who didn't already know what you're up to might have a hard time distinguishing reality from your fantasy spook stories.

Is discovery learning creating "new and original" mathematics in K-12? Yes and no. It's new and original to each student as she constructs her own understanding of mathematical ideas. (And once in a great while, K-12 kids actually DO come up with something original. But that's not really the point and you know that fact fully well (or at least that we over here in the real world know it), despite your willingness to feign otherwise). But kids are generally not going to go to many places that they haven't been put in a position to go. If the questions asked and the manner in which they are asked and the classroom and school cultures in which they are asked are suitable, the sky may well be the limit as to what is possible or even likely that kids will do in mathematics or any subject. And when the opposite is the case, then kids will almost never go anywhere worthwhile or meaningful when it comes to thinking about mathematics as much more than a set of rules, facts, and procedures to be memorized at least long enough to pass today's test.

It's interesting that someone as utterly lacking in intellectual joy or curiosity as you managed to become a professional mathematician, though not a particularly prolific one from what I can gather of your output. Seems like you settled into a very mundane position at a less-than-demanding school and decided that to puff up your own importance you'd declare yourself an expert on K-12 mathematics education. And you did a nice job of blustering your way into some level of national prominence (or notoriety, depending upon one's perspective). And so you got to show up at some school board meetings and some state or local hearings, maybe a national one here and there, and declare that the sky is falling because people want to provide kids with a richer, more exciting environment in which to learn mathematics than you ever had. You must be VERY proud of yourself, indeed. Seriously.

But boy, does that progressive education stuff threaten and disturb your little world. And so you latched onto the post-Reagan rhetorical ploy of how to undermine progressive thinking and work: preemptive strikes! It's brilliant. If you're politically, socially, personally, educationally,or philosophically regressive, accuse the other guys of being what you clearly are before they get a chance to point out the obvious about you.

MC, HOLD and similar groups are just a small part of the national manifestation of this sort of tactic. You get to call black people, native Americans, and anyone else you choose "racists" if they advocate an approach to math education that goes against your grain. What could be sweeter? You get to call yourself a reformer, when your idea of reform is "Back to the one-room Iowa school house of my youth" or just back to SOMETHING, even a something that for the vast majority of us never existed and never will. Or back to Saxon Math. Gevalt, it's enough to evoke tears from a gargoyle.

It's hard not to laugh when you cite the seminal group who created Mathematically Correct. Even though you managed to attract a couple of self-proclaimed "socialists," to the last member MC comprises people with conservative souls when it comes to education. You tried to pass yourself off for years on the math-teach list-serve as a "life-long liberal Democrat." That may be the single most absurd and transparent lie ever told.

While no one would suggest that a few of the MC/HOLD cabal are highly-regarded mathematicians, you don't quite get to declare yourself (or David Klein or Jerry Rosen) to be in the elite just by rubbing elbows or what-have-you with Jim Milgram. And having Jim Milgram in your fold doesn't make any of the rest of you (or him, for that matter) knowledgeable about ANYTHING that goes into effective K-12 mathematics TEACHING (I have to suspend my disbelief about college and graduate school teaching).

This really does come back to Lou Talman's recent question to Robert Hansen about how arrogant Lou would be were he to declare himself an expert in engineering because he's a knowledgeable professional mathematician. Robert didn't get it, or played at not getting it, but no one else can miss the point. It's arrogant to step way outside one's area of expertise (alleged or real) and then bash the knowledge and professionalism of the actual experts in that field, merely because there is some area of overlap (yes, the word 'mathematics' does overlap). But knowing math well and teaching math well or understanding what it takes to do so are not the same thing. The second two clearly require the first but don't necessarily follow from having it. And that's where you and your MC/HOLD buddies just go utterly off the rails and never come close to jumping back on again in the two decades or so that you've been trying to call yourselves everything you're not.

Deborah Ball and Magdalene Lampert, to name two non-mathematicians you no doubt would deride (behind their backs if not to their faces, or at least I recommend you not try the latter tack) as 'educationists' whose schools should be blown up (you're lucky: they work at the same one here in Ann Arbor), know more in their little fingers about teaching K-12 mathematics than you'll ever know if you live to be 1,000 years old. You are simply not ever going to figure out the things they figured out without all your advanced knowledge of abstract algebra (even when you try to pull the wool over the eyes of some readers here by throwing out a bunch of jargon to hide the fact that multiplication isn't repeated addition and never is going to be repeated addition. If it were, you'd long ago have addressed my inquiry about why those real mathematicians amongst whom you fancy yourself to belong all seem to think we need two fundamental operations for rings and fields and all the structures in between. You know it's not because they think that the latter is just some version of the former. But you can't bring yourself to say it because you'd be agreeing that there's something wrong about the traditional American curriculum. Horrors!!!)

Were you lucky enough to see Ball or Lampert teach kids, I think your head would explode. Well, not really, because your ability to shut out what you don't want to see, to come up with a thousand reasons why what you see can't be what's really going on is truly remarkable. It no doubt keeps you sane in the face of tons of facts that would produce an overload of cognitive dissonance in most people.

And if all else fails, you'll bring up test scores. Or religion. Or one of your dozens of other dishonest ploys.

I wonder if it ever occurred to you that we can tell more about what goes on in a classroom by actually observing what goes on in a classroom than by all the multiple guess tests in the universe?

Probably not.

But please, Wayne: no more red herrings and lies about what discovery learning is or why YOU'VE never met a mathematician who was trained in such an educational environment in K-12. Instead, talk about the millions who never had a chance in hell of becoming mathematically educated even minimally because they were never shown actual mathematics or any way to think mathematically. And hang your head in shame for continuing to try to prevent that from happening merely because it threatens you in a host of ways.

Well, not to be unfair, let me give you most of the last words:

not professional mathematicians let alone (and statistically

speaking, more important) those who need a strong mathematics

background to pursue their areas of interest. For example, none of

the seminal group who created Mathematically Correct word is

mathematics per se (although some of us became involved very early).

Two were PhD's from Stanford, one of statistics and another in

genetics (later recruited as full professor with tenure to Brown),

another was a PhD in geophysics from USC, another was an independent

contractor electrical engineer, etc., united serendipitously one

evening with a single common thread; all were teaching their children

(and sometimes small groups of their children's friends as well)

mathematics to compensate for their school's use of one of the better

of the math reform curricula, CPM under the misnomer College

Preparatory Mathematics about which I have had some experience:

http://mathematicallycorrect.com/cpmwb.htm

Groovy. Just remember:

**your**Ph.D wasn't from Stanford or anywhere close to it in quality. Nor do you teach at Brown, USC or anywhere near that caliber of institution. You don't get credit because some people who do happen to agree with you to sit in the same room sometimes and share your narrow and elitist views. But if you bet me one Jim Milgram, I'll see you with a Hyman Bass, and raise you a Deborah Ball and a Magdalene Lampert. You've got nothing on your side to match the likes of them, or the many outstanding K-12 mathematics teachers who get what all this is really about. You know: kids learning and doing mathematics and thinking mathematically. Not being little Saxon robots. Or robots of any kind.Independent, democratic, student-generated thinkers and inquirers: they're not just in English class any more.

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