“Math Wars”
If you’re new here, you may want to subscribe to my RSS feed. Thanks for visiting!
Photo credits: two unknown and one from monkeymucker
Edited by Brian
I recently read a post at:
dolcevitaacademy, which talked a bit about something that is close to my heart, which is: should you focus on teaching concrete skills first, or rather on concepts? (I’ve blogged about that on the post about Math Skills v. Math Concepts.)
This seems to be about what the “math wars” are about.
If you don’t know what the math wars are, here’s the quick and dirty on them:
At some point, around the early sixties, American educators decided that what we needed to improve our math education was a new way to teach math. This was probably due to our getting our butts kicked by the Soviets in the Space Race for awhile in the late fifties.
Some genius came up with “The New Math,” which was basically a somewhat new way to teach math; it had nothing to do with any kind of actually new math . I mean, two plus two still equalled four.
Since then, “traditionalist” and “constructivists” have been sniping at each other about “which way is the best way.” (I like to snipe at both.)
Sheesh!
For people who are supposed to be “educated,” why don’t they realize that there really never is one best way for most things (especially something as subjective as teaching and learning)? Chasing after the “One Best Way” is a Snark Hunt, that leads you to nothing but frustration.
“The One Best Way” is just a term that people who are struggling to enforce their way on others use, instead of being honest and saying “MY WAY,” (as in, “You’ll do it MY WAY or or the highway.” That is not about what’s best for the students, no matter how much the pedagogue says it is. It’s about the pedagogue’s insecurity.
Insecurity, of course, is what the Space Race was all about, and what economies are usually about. And schools are set up for nothing if not to make little consumers and worker-bees for whatever economy the society chooses.
I submit that if you want obedient shoppers and salespeople, sure, go ahead, stick with the traditional methods.
And if you want airy-fairy children, who feel good about their level of accomplishment, despite that fact that most of them don’t know a multiple from a factor, then by all means, try any fad that comes down the pike.
On the other hand, if you want your children to appreciate the wonder of understanding, the joy of abstract thinking, along with mastery of skills that will help them accomplish tasks and solve problems, then it’s time to jettison the false dichotomy of “traditionalist” or “constructivist” philosophies.
Admittedly, there are uses for skills-based courses, like “Consumer Math,” as well as philosophically based courses, like, “Number Theory.” But for a solid grounding in basic math, people need to appreciate elements of both, in order to develop a more mature awareness of the power and beauty of mathematics and the worlds it describes and explores.
To Each his/her own (Imagine that!)
Another point that you seldom see addressed, is that each student already comes to each math class with his/her own experiences and learning strategies and preferences, although they are generally not aware of it.
A teacher of any value should have the acuity to sense some of the ways the student can be approached, and teach to that style; at least until the student and teacher have some rapport. Once the student is “on the path” to learning, the teacher can then assess the gaps in the student’s learning style, and begin leading the student to new strategies.
I feel that the US is on an absolutely miserable path with the creepily misnamed, “No Child Left Behind” act. It is the perfect storm of bad teaching style, bludgeoning “standardized tests,” hypocritical talk of “accountablility,” (let’s see some administrators and policy-makers, not to mention semi-retarded politicians held to account for their blunders, first, OK?) and cruel unfunded mandates.
One Idea to change this might be to actually trust the people we train and pay to teach to do just that. Teachers are so handcuffed by stupid school policies and over-active “hover-parents,” that they have to be lawyers, nurses, social workers, etc. before they ever get to teach.
A way to trust these teachers might be to actually be one. I don’t mean school-teachers, I mean home-teachers. Since teachers, no matter how good, are not allowed to teach to their abilities, it’s the duty of every parent to become a bigger part of their child’s education.
That’s why home-schoolers, after-schoolers and un-schoolers get my greatest appreciation. Parents know their kids best, and regardless of the parent’s expertise in any field, they can always learn the material to teach, and no school-policy weenies can mess them up. That’s why they blow the public schools away, even on the tests that public schools make up for themselves.
So if you’re not a homeschooler (not everyone can be, for a variety of reasons), you can at least look into the afterschooling movement. They are dedicated parents who supplement their children’s public-school education with large doses of love and attention.
The best teachers are the ones who leave the dogma in the “dogma-house” and teach with an open mind, and a clear eye for how the student is doing, and the ability to be flexible in their response, without having to clobber that kid with tests and grades.
’nuff said.
Hotcha!
Brian (a.k.a. Professor Homunculus )
Tags: , ,
If you liked this article, please add it on Digg, del.icio.us, or StumbleUpon. It will help Math Mojo help others.
Print This Post
Comment by Michael Paul Goldenberg
I think you need to read a little more history of US mathematics education. Your account of the New Math, which has little or nothing to do with the current wave of reform initiatives and programs, and is only obliquely relevant to the current Math Wars, simply fails to capture what that earlier movement was about, what happened, what went wrong, what could easily have gone right instead, the subsequent French attempt by the Bourbaki group of professional mathematicians to do something similar there, etc.
One comment on the current war: it is NOT like you suggest. You don’t have people on the reform end looking for any holy grail of math teaching. Instead, reformers are looking to learn more about what is more and what is less effective and trying to craft methods, tools, and materials that increase the likelihood that kids will learn mathematics and want to learn it.
On the other side, you have those who appear to believe that there is nothing new under the sun that’s good and nothing good under the sun that’s new. While some of these folks may be politically liberal, or at least of a certain stripe of left wing politics, most are conservatives and reactionaries, in spirit and in politics, who decry new materials, new educational technologies, and especially any sort of student-centered pedagogy. They worship stark and disorganized drill-oriented materials like Saxon Math, which promises to take teachers out the equation by providing a “teacher-proof” set of lessons and problems that, if followed EXACTLY as written, will bring all kids to the mathematical promised land. Or they look towards Singapore as providing the perfect solution to American students’ needs. These folks DO seem to believe there’s one best way to teach (mathematics and everything else), and it just happens to be the stuff they like. I don’t know any serious-minded mathematics teacher, researcher, or teacher educator who buys into such foolishness. Nor do I know any who think the current crop of reform approaches are “best,” or that the goal is to find a single “best.”
You do your readers a disservice to reduce the Math Wars to a battle between hands-on and abstract, and to one between two different rigid approaches. While I would have to agree that the anti-reformers do believe in a single best way, direct instruction, which they think is time-tested (it is, of course, but it has failed millions of students), I know my colleagues on the progressive education side of the war aren’t naive enough to think one size of instruction will ever serve all.
Professor Homunculus sez:
Mr. Goldenberg’s opinions and knowledge of math education in the U.S. are much more informed than mine. For those of you who have not been to his blog, you should go there and bookmark it soon. It is http://rationalmathed.blogspot.com. I read it regularly. It’s a great read, and a valuable resource.
I think maybe I have may not have expressed myself as I wanted to, because from this comment it seems like I must have implied that I am somehow against reform. I will go back and re-assess what I’ve put down, and try to express myself a little better in the future.
There are several points which I’d like to dispute in Mr. Goldenberg’s argument, but his facts are probably unimpeachable, and his opinions are to be respected.
I’m also sorry that it seems I am reducing the Math Wars to anything at all. I was just giving the “quick and dirty” as I see it. Of course it is not meant to be the all-encompassing story, and of course I should have dutifully mentioned that there is much more to be said about it, much of which you can read on Mr. Goldenberg’s much more complete blog.
I am not convinced that Mr. Goldenberg’s description of the situation of the Math Wars is quite accurate, either, and there are points for lively debate. Michael, at the risk of fawning, I must say that I am flattered that someone I read with so much admiration has even stopped by my blog.
Thanks for your comment. I hope you don’t mind that I disagree with you on some serious points you’ve made, and I hope to address them soon.
Comment by Michael Paul Goldenberg
Happy to have intelligent debate on these and related issues. It’s hard to get that in some quarters, where things are reduced to a lot of name calling (not that I mind), but mostly a lot of “pseudo-facts” and scare tactics.
One thing that frustrates me a great deal in all this: I’ve actually gotten the chance to see brilliant teaching done by non-traditionalists (who may not be cut from the cloth of so-called reform math, either). I have in mind in particular Deborah Ball and Magdalene Lampert’s work in 3rd and 5th grade classrooms, respectively, c. 1990, and a “lesson” Robert Kaplan of The Math Circle group in Cambridge, MA did at the mathematics club at Northwestern University c. 2003. I seriously doubt that most of those who froth at the mouth over the “horrors” of reform have ever seen or experienced this sort of teaching. Sadly, I fear that for some, even if they did see any of it, they’d be blind to what was going on and makes me call this brilliant teaching. One thing about Kaplan’s work: it’s certainly not done with trivial mathematics, but it embodies many of the same principles I see informing Ball’s and Lampert’s practices with younger students (and I hear Bob can do a heck of a job with kids, too).
Naturally, I don’t expect anyone to take my version of the Math Wars at face value. I ALWAYS suggest that if you want to see what the Math Wars are like, go to the web sites of the fiercest anti-reform “math warriors”: http://mathematicallycorrect.com - browse around at random, read the rhetoric, connect to some of their links, feel the hate. If you can, try analyzing the rhetoric and ask yourself if it’s plausible that so many very bright people and dedicated educators would be promulgating something that looks much like the travesties the Mathematically Correct, NYC-HOLD, and other anti-reform hate groups describe. Hyman Bass, a world class algebraist, has worked for about a decade now with Deborah Ball. Does anyone serious suggest he would do this if he didn’t take her and her work deeply seriously? Well, judge for yourself. By their works (and words) shall ye know them, and in the case of Mathematically Correct & Company, their choice of words is telling, to say the least.
Professor Homunculus sez:
Michael,
Thanks for the update. I have been agonizing over a reply, because first of all, most of my original complaints were to be made about the traditionalist, who I find the most entrenched. It appears that you, and maybe others, interpreted my main beef with reform, which isn’t the case.
Another reason for my hesitation to reply, is that a great part of my argument would be that I found what I think is a pretty bad hole in your argument, but I don’t want to disagree with much of your position (because I truly don’t).
That (possible) hole is this:
You seemed to take issue with my mis-characterizing (is that a word?) of the sides in the math war, then you basically go on to say the real story is “reformists good - traditionalists bad.” I don’t find that quite the case.
We may be mischaracterizing what the other person is trying to say, or we may be expressing our thoughts less than perfectly. That is why I don’t want to go back and forth and address points the other person isn’t making, you know? So I’ll be careful to to attribute some of the points that I’m going to try to make as a rebuttal of your points.
As far as brilliant teaching by non-traditionalists, of course there is some of that. In fact, it is exactly what I am shooting for. I am a non-traditionalist, and my target is nothing less than brilliance (which I have no hope of attaining, but it’s fun to try!)
On the other hand, I have seen some real retards grasp at non-traditional methods and muck up as bad as the psycho-nazi math teachers from hell I had in school mucked up the “traditional” way. It’s the entire false dichotomy of traditional/non-traditional that gets me.
Just because tradition doesn’t work in all situations doesn’t mean reform does. Naturally, I know you know that, but sometimes the argument suggests that lots of people don’t.
May I point out that it doesn’t help to say that if you want to see what the math wars are about, to go to the hate-filled sites of some seriously twisted educators, like some of the ones you mention?
That’s like saying, “If you want to see what Muslims are like, go to some whacky jihadist sites and just see what they are saying.” Of course I am not accusing you of saying that, but I think you can see how the case loses credibility if we use an argument that isn’t quite fair.
I can’t stand those authoritarian, pig-headed, ignorant (”If it was good enough for my pappy, and it was good enough for me, it’ll be good enough for you, by God!”) sites like the ones you mentioned, either. But there is another side to the Math Wars. It takes two sides to make a war, and just because one is probably worse (much worse) than the other, doesn’t mean the the opposition is blameless.
And that is where my argument begins. I have seen some really naïve, counterproductive “reforms.” That doesn’t for a second mean that I think all reform is bad. I’m the guy who wrote the piece about rote memorization being a disease, after all. I don’t think anyone who reads this blog would call me a traditionalist.
A lot of progress has been made by non-traditional forces in the recent past. Even many of the methods of antiquity are better than the drill-and-kill that the traditionalist “No Child Left Unscrewed” act endorses. (There may not be one best method to teach, but that miserable creation of twisted, authoritarian minds mandates what just might be the one worst method.)
The fact that there are some good reform methods does not ensure that many teachers can actually teach them, though. Unfortunately, although I’ve even seen some good points about TERC (which, to be frank, I generally detest), I have never seen a program that can change bad teachers to good ones. So often I seen teachers who haven’t a clue spouting something that they learned from some shiny new reform method and mangling it so badly, that it almost makes me pine for my 10th grade algebra teacher, Frau Bluecher.
It seems that although there are some very gifted educators who use very effective methods, those gifts don’t translate well.
It’s also not going out on a limb to say that some of the programs that the traditionalist are against really are pretty much junk. No side is in any issue is totally devoid of garbage.
If I may give an an example (anecdotal, I know, and by no means convincing; but it may illustrate why there is reason enough to suspect that reform per se is not a magic bullet):
I present a very non-traditional math program for schools in my state (NY). Time after time some well-meaning but hopelessly ineffective teacher tries to convince me that s/he “also teaches that.” Generally that teacher has seen some shallow instruction on a technique or two that I use, and has done the typical “show-and-tell” presentation of it to his/her students. That, I suppose, has something to do with teaching, in their minds.
A lot of what passes for reform is this kind of “half-inch deep” new-age pap. Certainly I understand that this is not what you and the dedicated reformers are suggesting, but, in fact, this is what it too often amounts to.
To be sure, part of it can be blamed on the lack of time and preparation that teachers get under the current NCLB situation. Just as big part of it may be due to the fact that there is so much unfiltered disinformation about what works or not in the reform movement.
I’m aware that you have no gripe with the “lattice method” of multiplication, for example. There might be cases where the lattice method is not bad, but I can’t really imagine that there is any case at all where there wouldn’t be about a thousand methods that are better. Over and over I experience teachers who don’t understand a thing about multiplication touting the lattice method as some new “magic” method. One of the most popular math videos on YouTube makes it seem like that method is some sort of “wonder method.”
At best it is a silly little diversion that might make a kid scratch his head. Maybe if it was used to explain how the algorithm worked, perhaps in an algebra class, it might be interesting. But as a method to actually multiply, or learn multiplication it’s a joke. It’s a minor puzzle, and teachers use it simply to “make math fun” in that pandering, “don’t-worry, you-don’t-have-to-actually-learn-anything-see-it’s-just-a-game” way. Kind of like “Learn Math with Barney” simplistic pap. This is my main beef with the way reforms are actually used. It’s not the innovators I have a beef with, it’s the people who use the innovations to avoid confronting the actual task of teaching that I find so ineffective.
There is also the uncomfortable point that, for some children, in some situations, the traditionalist method sometimes is the best, as much as I hate to admit it.
To sum up my point, I still think all sides should be considered, and the decision should be made by having deepest possible knowledge of the most tools, and the acuity to tell which one each individual student and situation warrants. Neither side seems to have a grip on this.
As far as the closed-minded goofballs with chalk-dust for blood at some at the more reactionary traditionalist sites, I couldn’t agree with you more. I think a lot of them should be court-ordered to stay away from young people and schools until they get some serious help. We must keep in mind that not all traditionalists are of their ilk, though.
To get the taste of that whole side of the equation out of my mouth, I can’t wait to google Deborah Ball, Magdalena Lampert et.al. to find some new inspiration. Thanks for the heads-up on their work.
I’ll continue to visit and recommend your great blog at http://rationalmathed.blogspot.com.
All the best,
Your friend in rationality (well, I try),
Brian
Comment by sally
Brian, I appreciate your points re: the difference between a curriculum being superior in theory (or better, as tested) vs. in practice by the average teacher. Even if there were a single BEST WAY to teach (which it is reasonable to view skeptically), is it scalable? Will teachers be willing and able to understand it and teach it effectively? Not to knock teachers, but resistance is only to be expected, and the efficacy of the technique is going to vary a lot from teacher to teacher.