math education

[cellio]

Being of a certain age, I learned arithmetic the conventional way and neatly dodged New Math. I knew things had changed since then -- at least in the ability of high-school graduates to do arithmetic unassisted -- but I didn't realize just how strange things had gotten. amergina posted a link to this (longish) news story broadcast: math education: an inconvenient truth. Sigh.

To summarize, some (apparently-big-name) published curricula are now skipping conventional methods to teach new ways of doing arithmetic. Some are different ways of breaking down the problems; others are primarily notational differences. All of them seem, on average, slower and more error-prone.

Now granted, I sometimes do arithmetic by the "reason through it" process the reporter dislikes (what did they call that, clusters?), but it's kind of specialized. For example, a 15% tip reduces to a 10% tip and half again; that's fast and easy. If I'm multiplying by a number ending in 9 or 1, it's often easier to reduce to another problem and then deal with the leftovers. If I need the square root of 4862 (I just pulled that number out of thin air), I can't tell you exactly what it is but I know it's a bit less than 70. Sometimes I think in patterns like that. I think this is a fine thing to teach people after they have mastered conventional write-it-down-and-work-it-out methods. Not before, and certainly not instead of. (And I think it's better if you can give them an educational environment in which they figure out these "tricks" for themselves, like I did.)

I assume these new teaching methods (which include "use calculators") are largely responsible for many people being unable to get order of magnitude right. Those of the previous generation undoubtedly said that about the move away from slide-rules, but I never used a slide-rule (except as a novelty) and I can approximate... I once had a calculator-armed teenage clerk at a produce stand insist that my bag of vegetables came to over $200. Even if he had no instincts about what vegetables cost, he should have been able to tell that the price codes he'd read off the list didn't add up to that and maybe he'd mistyped something.

(When shopping I tend to keep rough a mental tally, so when I get to the check-out I know approximately what the total should be. I gather that this is unusual. It's just the way I learned to shop, probably from a time when you had to make sure you didn't exceed cash on hand. Now I use plastic for everything, but the habit remained.)

Well, I guess I can take comfort in one thing: if what they say about mental exercise is correct, I should be pretty close to immune to Alzheimer's. :-)

Comments

[benzado.livejournal.com]

Having spent a year studying Mathematics Education, this whole thing is depressing to me. What you basically have here are scientists who do good research and find a way to teach mathematics so that children will actually understand it. So they publish their research and somebody else attempts to put it in the schools. But then you have teachers that have been teaching for 30 years and don't care for new ideas or really poor training programs that don't help the teachers understand how to teach them.

Usually the program requires some fundamental changes (like, let's make sure the kids learn this smaller set of topics than crash through this huge set of topics) which are only half-heartedly supported by the school (the state's standardized tests demand you cover all of these things by January). So the program is kind of implemented half-assedly, and parents complain to the school board, which is made up of elected people with no educational training whatsoever, who deride these newfangled ideas as stupid hogwash and wind up vilified on TV like above, and then everybody says "let's go back to basics" and all the research that the scientists did that might one day lead the way to some gender equity in mathematics is thrown down the drain for another ten years.

educating parents

[(Anonymous)]

I think Benzado has hit the nail on the head: any curriculum has to have the parents behind it. Personally, I think that is one reason why the new curriculums work so hard to teach the parents about the curriculum. It's easier to defend what you know and the new curriculums are not what the parents know.

As to Monica's question about whether parents will wait the eight years or not, the answer depends on whatever is happening in your state's required annual testing. Since it can't ever be the kid's fault they aren't meeting the standards, there have to be other reasons why the kids are failing. The teacher unions pretty much make sure it can't be the teacher's fault. The administrations just push paper. Curriculum is the only possible reason the kids are failing. Just as with any other important issue, an educated electorate is the best case scenario. It's easy to read a simple article (or watch a video :-) )talking about how a curriculum scars children for life but it's much harder to do the work of actually learning about the curriculum and how it works.

Ultimately, I think our children get out of school what we parents put into it, but then again, I'm an over-involved parent.

Valorie

Re: educating parents

[benzado.livejournal.com]

If I may be more cynical, a curriculum doesn't have to have the parents behind it if the parents would kindly get out of the way. Most new curricula involve some component to inform parents because, if they don't, the parents will object that their children don't "appear" to be learning math.

Also, a child's home life is the strongest predictor of academic performance, and the one thing a parent has the least influence over.

Re: educating parents

[cellio]

If you can get the subset of parents who would actually take interest in their kids' schoolwork in the loop, it might help them help their kids instead of scratching their heads and saying "huh? math wasn't like that when I was a kid...".

Re: educating parents

[benzado.livejournal.com]

My point was that there is a subset of parents who "take interest" by second guessing the teacher and, if they don't understand the methods, fight the teacher. One of the reasons "new math" failed in the '60s was that the educators promoting the curriculum didn't take these parents into account.

Those parents aren't going away and I'm not necessarily saying they are a bad thing --- sometimes the teacher isn't very good --- but the point is that promoting changes in education requires a lot of P.R. and political work; you cannot unfortunately expect that new methods take hold based on their merit.

Re: educating parents

[benzado.livejournal.com]

Oops, I meant "a child's home life is the strongest predictor of academic performance, and the one thing a parent teacher has the least influence over."