Gifted Issues Discussion homepage Forums General Discussion Thurston on maths education

I was just reminded of this paper which I think I read long ago but which I don't remember being mentioned here. Recommended.
http://arxiv.org/abs/math/0503081

For those who don't know, William Thurston is a famous mathematician and a Fields Medalist.
http://en.wikipedia.org/wiki/William_P._Thurston

Interesting. Thanks for the link.

Was, I'm afraid; he died last summer.

I would say that this is also true for entry into programs like SET at Johns Hopkins.

ColinsMum, I've been thinking a lot about your criticisms of the SAT and am now completely in agreement with you about it not being a good test for gauging math talent. While it's true that a few of the math questions on the SAT can be described as "tough" there really are only a few on each test (they're usually the last question or two in a given section). And even so, just as the Thurston noted, the test is assessing a very narrow range of ideas and applications.

The SAT continues the trend of modern mathematics education as a whole (in the US anyway). The US math education system is organized around problems that can be solved quickly using standard algorithms. There is very little in the way of assignments that require what Thurston called reaching into yourself for ideas. IMO, this problem affects science education as well (and maybe other areas). As we push for more participation and increase the stakes, we end up teaching the students less about how to dig deep inside and end up with superficialities.

I've also been thinking about how this approach affects our national research enterprise (and is affected by it). As anyone in academia knows, US academic researchers today are assessed on the number of papers they publish and the amount of grant money they obtain. The latter depends on the former and as competition increases, projects assessed as "best" are really "projects most likely get the anticipated results" and therefore are overwhelmingly incremental in nature. So, do it fast and get it published is an extension of what postdocs and new faculty members have been taught all their lives in many ways.

And there is no room for slow, risky, but potentially groundbreaking work in this model.

Yes, it seems to be more-more-more-faster-more-faster-faster.


There's no time to teach set theory or deductive reasoning and construction of proofs. Nope. We're too busy teaching even secondary students with food and manipulatives to "enliven" the curriculum (hey, maybe the problem isn't that the kids need to be entertained so much as that you need to actually TEACH THEM SOMETHING REAL), and throwing practice tests at kids. They won't see any proofs on standardized tests... so why teach it...

(Maddening.)


The problem with even those handful of challenging problems is that if you're not speedy Gonzales with a calculator, you seldom have ENOUGH time to really dig into them there at the end of the section. DD had that problem with the geometry problems-- she was spending time ENJOYING them.

So *that's* the real source of the obeisity epidemic-- an enriched appetite for math. The kids are having their pi and eating it too, and it isn't imaginary. (Cue the groans.)

The internet is better.

This and the linked article by Thurston was the reminder I needed to reign myself in a little bit. I forget that DD isn't even three yet and she doesn't need to be doing school math even if she wants to. We should be focusing on nurturing her creativity, imagination, intuitive understanding of numbers, and problem-solving skills.


I think it's fair enough to point out that some precocious students do just fine once they reach adulthood and are no longer a "child prodigy" but I can also see the challenge of having to live up to that identify and overcoming/transforming it.

Interesting article from 1990. Some school districts must have listened to him or others with the same criticisms. What has truly amazed me with our school district's math curriculum over the last dozen years (only time period I have actual first-hand knowledge) is the breadth of the curriculum. The tree is certainly far less spindly than when I went to school in the 1970's and 1980's. For example, there is kiddie algebra and graphs from second grade, probabilities/statistics and solids geometry from third grade as well as an emphasis on constructed responses/mini-proofs once the students can write well in second grade. That emphasis has also translated to state tests and county tests also requiring constructed responses in math and lots of essay writing in reading.