I just saw Arthur Benjamin’s passionate lightning session on where Math education should be focused (hint: statistics). It reminded me of the aforelinked session from Sir Ken Robinson. It set a few thoughts in motion.
First, Arthur Benjamin is right. In full accordance with Ken Robinson’s theory — that most education is a prolonged form of university entrance, wherein the curriculum and culture favors you heavily to become a university professor — the geekier subject of calculus wins out. Don’t get me wrong; calculus is completely necessary for millions of people to do their job properly, and it is an important subject in many spaces. But statistics, probability and distribution is absolutely essential to understand the onslaught of data we face increasingly often.
When the Internet came into public consciousness around the early-to-mid 90’s, and increasingly since, early education teachers felt that it was important to train students in recognizing accurate and reputable sources of information. (This debate is still raging; pull up a seat to a mother tongue professor and mention Wikipedia and sourcing.) Maybe the concern was overblown, but the basic idea is rational: not everything is equally true, and being able to question information creates a healthy relationship to it.
Being able to understand statistics is another tack in the same plank, especially since people poised to mislead will be likely to abuse numbers and reports as well. What about the scenario where the information is unconvincing, but weak numbers appear to back the thesis up? Giving students half the solution is effectively like not giving them anything.
Understanding statistics is an important skill in ordinary living in the same way that being able to perform quick calculations is an important skill; just on slightly different planes. It’s not just that people will appreciate learning something if there’s a practical application, it’s that when there’s a practical application, you’re more likely to learn since it’s not just an abstract phenomenon that will drop out of your mind the minute the class is over.
In fact, let me make another case for remaking a curriculum.
- Throw out all the classes. Everything. Start with a blank slate.
- For 60 to 70% of the time, bring in classes in order of complexity, but only bring in classes with universal practical applicability. For the first few grades, this will be very close to what you have today, since more abstract thinking requires a foundation of practical thinking and maturity. Everyone needs to read, write, count, calculate and interact with the culture around them.
- For the remaining time, bring in two kinds of things. Bring in classes relating to art of various kinds and physical activity. Despite being a fun break “for some few”, the art classes also have practical applicability, although you wouldn’t know it from what’s available today. As Ken Robinson says, some people need to be immersed in their activity to concentrate and to produce, and for some of those people, that requires connecting with an art form.
Also bring in classes relating to exposure of new things, fields and professions. Everything in any class should be informative and non-boring, but this especially so.
It’s already too hard to grow up and being unsure what you want to be. Exploring different directions well before you have to make a choice grounds your thinking. There’s a risk, as with the situation in general, that some people will be overloaded with the choice. Trust me: We’re now no worse off than we already are. On the other hand, prejudice is lower in low ages and openness is higher; a bunch of kids are going to open their eyes to a line of professions or interests that they didn’t at all know they liked.
- Place all classes of specific practical applicability where they belong. Many people will never use calculus in a practical fashion, and they only spend so much time in school. Knowing more about it than is strictly necessary steals time away from subjects that could be more important to them individually. That might be English class, physical education, some other Math subject, or dancing. Who knows?
That won’t solve everything. But I’m pretty sure that it would bring some perspective to education again.
Good luck with statistics. The history of the Monty Hall problem suggests that even very basic statistical problems defy intuition very effectively. And there’s much more to it. Many people struggle to add fractions, I don’t see them being happy with abstract statistics. I also doubt that many people actually do need to perform statistics. What should be taught instead – and you mention that – is the ability to not pass out and believe everything somebody says just because it contains a number and you go OMG-MATHS-DIFFICULT!!1!
I also disagree with your focus on practical use. It is nice to have practical uses, but focusing on them can easily ruin the chance of learning and appreciating the greater concepts. Without understanding those it’ll be hard for students to develop independent thoughts of their own.
By ssp · 2009.07.05 20:36
All the more reason to prepare for that level of reasoning.
I don’t say everything has to be predicated on practical use, just that there’s a lot of room for optimization. Having kids succeed in more easily approachable (not dumbed down) classes will boost their confidence and make them more receptive to developing independent thought. With some luck, giving them access to lots of influences will also allow them to put the pieces together.
It’s a bit hard for some people who work in education to take this to heart, since the state of the art is abysmal in places right now, but we should not settle for less than everyone passing. People will rise to a challenge if you give them that trust, and kids especially start out believing they can do everything. Not everything is the fault of teachers, of course, but it’s through failure after failure in monotone, lifeless sessions, fueled by standardized testing and “teacher’s key”-level homework that they devolve into cynical, depressed creatures, robbed of their self-esteem, convinced that they aren’t smart enough, who can’t wait until the bell rights.
This situation is not set in stone. We can give every one of these students the tools they need to handle life. We just can’t do it while we maintain that at best, a set percentage will wallow in their own decrepitude in one subject or the other.
By Jesper · 2009.07.05 21:12
It’s astonishing how many of my friends spend 14 years in school without learning the most basic idea of how probability works (they think there’s some kind of supernatural connection between people because they thought of somebody and then got called by that person) or what exactly science actually is (they think it’s just another religion you have to “believe in”).
By LKM · 2009.07.05 21:17
But Stats is yuk (and arbitrary)… gimme some number theory anyday
By Nathan Edwards · 2009.07.05 21:20
Frankly, I’d be impressed by a maths curriculum which leaves the majority of pupils with an understanding of division and percentages. :-/
By Jens Ayton · 2009.07.06 01:05
Of course it’d be great to teach everybody conditional probabilities. But that stuff isn’t easy and you need a bunch of theoretical tools under your belt to handle it properly. Once you taught all that, most of the students will probably have stopped caring and don’t manage to connect the formulæ to real problems.
I keep thinking that many other ‘applied’ aspects of mathematics are similar in the sense that they are either applications made up by maths teachers which just fail to be real or relevant, that they are ‘business’ stuff which amounts to mere computational tedium and doesn’t help understanding or that they are so real that they require a rather deep understanding of the problem and the maths involved.
The latter problems should be great, but how many of them are there at a level accessible to pupils? (I mean you could create a great narrative from an iPod, say, and cover a wide range of pure and applied maths from functional analysis to signal processing to the effciency of FFT just by touching how music playback works. But each of those topics is quite elaborate and probably a bit too hard for school level teaching.)
To quite an extent I firmly believe that teachers are a problem as well. I had dozens of students who wanted to become maths teachers in my classes over the years. And (as usual) 90% of them left me the impression that the best they can do is struggle with their exams because they had the shit scared out of them at some stage and they gave up revising and thinking but just focus on passing. How can they possible become good teachers with so little confidence in the subject and their own skills?
Quite ironically, pupils (or their parents) are to blame as well. They expect the nausea inducing lessons because they cannot bring themselves to trust a teacher who does more sensible teaching which does not lend itself to formalised testing and out of the box support lessons right away. One of my maths teachers at school did a programme with us where things were taught differently (and in a very appealing way). It was cancelled by the school after a while because parents kept nagging them about the ’strange’ maths classes. A (smart) non-maths friend I got to know later had a teacher who used the same programme but went through with it. He said that, even though he never really liked maths, it was the only time he found the subject very appealing because it was about thinking and discussing rather than mind numbing number callisthenics.
By ssp · 2009.07.07 20:51
There are two kinds of good teachers.
Teachers who worked through their own “scared shitless” fear and learned about the art of teaching well within the confines of the system as it exists today. They are good at their subject, they are good at actual teaching, and they are good at “being a teacher”, by which I refer to all the connected meta-abilities required of a teacher besides teaching and subject knowledge.
Teachers who are there because they can talk, explain and interact engagingly. These people appear left and right in your life, but not in droves. You probably know about five or six of these, and one or two of them from school where they were actual teachers. This personality does not necessarily correlate at all with being a certified professional Teacher, but they do a better job than most of them. You can’t help but a) be interested and b) learn when you’re around these people.
I have a feeling that although the level of 1s could be raised through better teacher vetting, it’s also closer to saturation. We need both.
I had a religion teacher once.
He’d hand out his tests ahead of time; before we’d start a new religious subject or a new religion, we’d have it in our hands and it just wouldn’t help us at all. After that, he’d sit us down for two hours, with a ten minute break in the middle, and talk. Engagingly. At length and breadth.
He’d draw charts on the whiteboard, like a timeline explaining the breach between Sunnis and Shi’ites and about Abu Bakr. He’d write down names and years and tell us to write those down if we cared, but that nothing more high-res than century granularity would matter on the test.
You had to be present all the time to pass. I think you were allowed to entirely miss one question of six on every test. If you weren’t present, he’d ask you to make a copy of a friend’s notes. The questions all said to tell him about this or that, and left room for personal interpretation. I know that he used this concept from the very beginning of his 30 year teacher career, but it’s almost as if he had invented it to counter cheating.
Our class took this subject with two other classes. About half of their lineup was notorious for skipping. Almost everyone showed up, and some of the “worst” kids participated with interest. Everyone present passed.
We had almost no homework. Maybe one page of reading every fourth session.
I used to think that if everyone worked like this teacher did, you’d be exhausted; you couldn’t keep it up. I no longer think that. I think that because of the abysmal level of the other subjects, we were all having trouble keeping up despite the subject being engaging. If every subject was like this, you wouldn’t need to be in school for as long, because you’d actually learn quite a lot. Everyone happily rose to the challenge, even the grizzled students. What if they weren’t grizzled? What would they be capable of?
This is not a perfect model; it takes a really good teacher to execute and you’d have some trouble trying to apply it to a subject that primarily produces creative output, like shop or drawing. But it’s a perfectly legitimate technique that I’m privileged to have seen at work; I just wish it was more widespread, and that, like ssp says, those that dare to treat tradition as mutable guidance aren’t put on some prestige-based shortlist by school administrators wearing blinders.
By Jesper · 2009.07.07 21:54