Purposeful Ramblings Through My Mind

The question always comes up in debates about teaching mathematics: how come the Japanese do so well at math, when they stress rote memorization, if memorization is the wrong way to go about teaching math? (It's usually said in a tone of smug satisfaction, as though there's no possible comeback other than to admit that a constructivist approach to mathematics must clearly be wrong because the Japanese aren't doing it.)

The answer: a little from column A, and a little from column B.

The Japanese do indeed expect kids to memorize a lot of facts, but that doesn't mean they teach by modeling procedures and then assigning students practice questions to follow those procedures. No, they present a problem which the students do not yet have the skills to solve, then the kids work in small groups to figure out the problem. At the end of the lesson, the teacher summarizes what was learned, and students are assigned a small number of questions to practise on at home.

In other words, they use EXACTLY the method we're being told to use - with the exception that they do not allow calculator use.

The single biggest difference between North America and Japan is the number of school days - Japanese students have far more. The next biggest difference is in average expectations. When American moms are asked what mark is acceptable in math, they generally say a B or a C. Japanese moms expect an A.

So - high expectations, a constructivist and problem-solving approach to mathematics, high support in the form of parental help and extra tutoring - that's nine-tenths of the items we're expected to include in our mathematics programs.

Oh, and I should point out that the rumours about this kind of math instruction ignoring basic computation skills are false. We do drill math facts; we just make sure to drill them AFTER students have achieved comprehension, rather than before or instead of.

For future reference: http://www.gphillymath.org/ExempPaper/TeacherPresent/Mastrull/SMastrull.pdf

This is from Piet's journal, still screened over there because he's getting a better night's sleep than I am, on the education thread from a few days ago. I don't think professormass will mind me reposting his comment, and I'm pretty sure oakthorne won't mind being referenced in it, either. I'm leaving it unlocked because those gentlemen aren't on my friends list and have a right to see this. And I'm posting it here because, until Piet unscreens the comment, I can't answer it over there. :)

First, professormass's comment:

Something occurs to me (and I apologize for butting into the conversation -- as you know, velvetpage, I'm keenly interested in education):

The sweeping generalizations and the arguments against making those generalizations are missing a key point — the education system must address generalization, because it's trying to work for the mythical "average student," casting a net that catches as many kids as it reasonably can. The exceptions will always and must always be the issue. No bureaucratic system can account for the wide variety of learning styles present in the complexity of human nature.

People oakthorne and myself are exceptions. So, yes, much of pyat and velvetpage's arguments hold water, with the percentage of the population who aren't exceptions.

I think that the biggest point of difference I'd have with them is what percentage of the population represents exceptions to things like "
A middle-class person who doesn't get that education might be able to keep their middle-class status with a job that doesn't require it", where "requiring it" is a highly subjective thing, in most cases. My field, for example, routinely requires anywhere for 6-12 years of degrees, diplomas and certifications; I have none, and still operate at an executive level.

A friend of mine, a schoolteacher, told me that he thought the percentage of exception was something like 1%. I think it's more like 25%.

Modern school systems have almost always served the needs of the majority. When pyat says "it's getting better," I read, "it's serving a broader swath of the majority."

There will always be exceptions to the rule. After having done much research, I'd tend to say that public education has succeeded in catching a slightly broader swath than when I was trapped in the system. I don't think it will ever catch all the exceptions.

So, really, the question is: what to do with the exceptions? What safety net can be cast for people like oakthorne and myself? Can one be cast?

Now my reply:

Arguably, Piet and I are exceptions, too. As I believe Piet stated somewhere else, he was identified “gifted” but nearly flunked out several times, getting by with barely-passing grades. I was at the opposite end – I excelled with so little effort that I spent much of my class time in elementary schools with a novel open under my desk, because I was bored silly. And yet we managed to make system work for us, in our own ways.

That said, you’re right – the education system works best for the people who test out as average and slightly above-average in intelligence. It generally works all right for those slightly below-average, because they’re able to access extra help that is sent their way, and it often works just fine for those at the top of the intelligence scale because they learn to play the system. But for all the special placements, resource help, gifted classes, and what have you, that the school boards put in place to cast that wider net, there will always be those who don’t quite fit it. Most of those will benefit by taking everything they can out of the education system and then going their own way. But the fact that it doesn’t work for them doesn’t diminish the value of education overall; it only speaks to the need to address individual needs as broadly as possible, or as you say, to cast a broader net.

In terms of the number of kids with a diagnosed exceptionality (at the top or bottom – this number includes gifted) you and your friend are both wrong: it’s between ten and fifteen percent, statistically. But the school board makes concerted attempts to catch most of those within their net.

I believe my school, and for that matter a fairly large chunk of the schools in Ontario (not all, yet, but we’re moving that way) are doing a better job of this than ever before. I now routinely teach to four or five different levels in my classroom at a time. I have smart kids who are feeling challenged and rewarded, and I have low-average and below-average kids who are learning as fast as their brains will let them, and the kids in the middle aren’t being forgotten, either. I have a learning-disabled gifted kid (neither of those are official diagnoses, the first because his parents don’t want him labeled and the second because the LD got in the way of the intelligence testing when we did it) who is enjoying school for the first time in his life. I’m teaching him to game the system – how to get what he needs from it as he goes on to grade six, what it’s important to do, what can be ignored – because there’s no reason this kid can’t succeed at the highest levels and get the kind of career you only get through education. (He wants to be a lawyer.)

Part of the reason he’s going to make it is that nobody’s telling him that school isn’t important, or that many people can succeed without it, or that the system is out for its own benefit. Those things are true some of the time, but they’re not helpful overall. They’re excuses for people who did not succeed within the education system. Some of the time, those who didn’t succeed within the system manage to succeed outside of it, as you and oakthorne have done. More often, that is not the case.

And here we get to the crux of the matter. I’m quite willing to admit that school doesn’t work for everyone, and that some people succeed just fine without it. What I’m NOT willing to admit, and indeed will argue against with all the force at my command:

1) that this is the rule for most, even for most of those we would classify as exceptions;
2) that the existence of holes in the net in any way diminishes the value of the educational system;
3) that teaching the conclusion we’ve been arguing against (that advancing your education through traditional channels is a worthless endeavour) is going to help the people who take the lesson to heart;
4) that in fact, people who hear that lesson and learn it well stand an equal chance of succeeding at their various endeavours in life, as measured by the level of control they have or can access over their own workplace and community, as those who remain within the educational system.

Please note that I think it’s possible to enter the education system at differing points and still succeed within it. A child who is homeschooled until high school often ends up doing better when they finally do access formal education, in large part (I believe) because their parents took a very active interest in their education and made sure that they understood the value of an education – traditional or otherwise. But sooner or later, most people who succeed at the highest level they’re capable of, do it by making use of some facet of the education system.

So, to answer your question: I think the net that is catching more and more kids still has something of value to offer to the exceptions, especially the exceptions at the top of the spectrum. The clearest evidence of this is the fact that three exceptions have now come forward in this journal or another, to argue their case. They've done it with varying degrees of rhetoric, but they've all done it with a good grasp of written English. Put simply, they're attacking the educational system with tools that they accessed through an educational system. It didn't fail them as far as they say it did. (Yes, I include you, professormass, in that assessment.) The higher up one goes in education, the smaller the net the system is attempting to cast, for exactly the reasons you've stated - not everyone needs it. For an adult, the choice to work within the system or circumvent it (or simply ignore its impact) is a choice. There should be (and are) mechanisms in place to help those who wish to access that system but are having difficulty doing so. But the onus is on the student to take what they need from the system - not on the system to offer whatever the student needs. The focus shifts further and further away from the responsibility of the system and more and more towards the responsibility of the student. The student who either fails at that responsibility, or decides not to take it on, needs to take a hard look at where the problem was. Many of them cut their own hole in the net.