The Math Mojo Chronicles » math wars

More about Constructivism

Brian — Thu, 21 May 2009 19:37:53 +0000

Ah, math ed. I hate it. Yes, I hate it. It has become a corporate tug-of-war for the hearts and minds of petty pedagogues, and your kids are in the crossfire.

Should it be Math-U-See? TERC, Singapore, Saxon, or one of the other over-marketed mind-usurpers?

I like math. I love math. I hate to see it co-opted by these impostors. OK, some are worse than the others. Before you say, “Hey, but Math Mojo is also trying to sell me something…” let me tell you now – you are correct.

But I’m not trying too hard, and I don’t want you to buy in to my “brand.” There is no “Math Mojo” math. Math Mojo is my own silly wording for the way I like to think about how I deal with math. It has helped me go from someone who was mathophobic to someone who really loves the heart of math and the art of math. I don’t propose that I know anything better than anyone else – I just happen to have some Ideas that seem to prove useful to some people.

I would NEVER propose that it be used as a “curriculum” for anyone. To me, “curriculum” means, “this is what I think is important for you to know, and you better damned well know it because we will test you on it.” At least that’s what it means in schools. Schools – the same places that define “scholarship” as “money for football players.” I fart in curriculum’s general direction.

Something I can tell you is that my judgement should never be considered final for anyone but me (and even I don’t do that), and that no one else’s judgement should be, either.

But there are degrees. And someone recently wrote me to tell me about some posts he had written which address some of the issues with different curricula currently being hawked to your schools.

It needs to be stated right now that the posts I am linking to here do not entirely express my opinions. I just feel that they make a lot of important points. I am offering links to them here simply for your consideration. If you need to debate them, please take them up with the author, not me.

I will say that I generally don’t find any value in “traditionalist” or “constructivist” arguments. I feel that either extreme is a sham, and the math wars behind them are about as useful as debating how many angels can dance on the head of a pin. I tried to engage in it at one time, but the mind-numbing natterings of the different sides are ….zzzzzzzzz… pardon me, where was I?

The following links actually argue against constructivism, but in a very, ahem, “constructive” way. I don’t find them fodder for the war, just well-reasoned essays, although they don’t entirely express my views. And that probably speaks for them

My views? Well ….zzzzz.

So hear are some links from Barry Garelick:

http://www.thirdeducationgroup.org/Review/Essays/v5n2.htm

http://ednews.org/articles/one-step-ahead-of-the-train-wreck.html

U.S. Math Education is “Broken and Must Be Fixed” (?)

Brian — Thu, 04 Sep 2008 17:11:35 +0000

I read this in a recent blog post from The Economistblog.com:

Final Report

“International and domestic comparisons show that American students have not been succeeding in the mathematical part of their education at anything like a level expected of an international leader. Particularly disturbing is the consistency of findings that American students achieve in mathematics at a mediocre level by comparison to peers worldwide.”

As always, there’s something to this story, but it’s deeper than a short blog post can explore adequately. You just have to be mildly conscious to notice that American schools are generally doing a pathetic job of math education. But it’s not that easy to assess “blame,” or “what needs to be done.” There’s no simple answer to such a complex problem.

That it’s “broken” seems clear. But what is “it?” Each state, district, and even type of school is different. One thing that is clear is that creating simplistic “standards” (which are supposed to cover all federally funded schools) is just jaw-flapping by people who understand neither education, math, nor children.

Change for change’s sake is a silly impostor of a real cause. But there must be change for progress’s sake. So a consideration might be, “What kind of change, for whom, when, and how can we implement it – instead of just demanding it?”

I hope we don’t become even more of a nation of people who demand simplistic answers to complex questions. We demonize pretty bad math programs (yes, there are plenty, and I think the article is basically right to call “Everyday Math” one of them) but that doesn’t mean they have no good elements, or that we have to return to “tradition.”

That’s like saying, “We were the greatest car manufacturers when we had to hand-crank them to start them. If we want to be the greatest again, we need to put hand cranks back on cars.”

Although the premise has something to it, and I can certainly empathize with the commentary in the article which asks, “Can we get rid of “Everyday Math” now and go back to the old math?” – I also recognize that is probably not a useful solution.

The world changes. There are much better ways to teach nowadays than one way or the other, and it’s time we start working harder at using them, rather than insisting that there is “one best way,” that would work “if we would just do so-and-so.”

A first step might be to look at what works in each system (I imagine there are even parts of “Everyday Math” that don’t suck) and find out why, when, and for whom they work. Then put that in each teacher’s “toolbox” and go and find some more.

And then, for godssakes, let the teachers teach! Keep the textbook lobbyists and the politicians where they belong (in jail?), and away from young minds.

Another thing we might keep in mind is that the people who work on “Advisory Panels” tend to come from the industry they are advising (naturally). This sometimes leads to very myopic visions of what is wrong as “what is to be done.”

Everything with a grain of salt. No?

Hotcha!

Brian (a.k.a. Professor Homunculus )

“Math Wars”

Brian — Mon, 28 Jul 2008 01:39:34 +0000

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 )