Tuesday, February 24, 2009

our maths decline

A disturbing set of numbers

Nalini Joshi, President of the Australian Mathematics Society:
The international table of mathematics skills, the four-yearly Trends in International Mathematics and Science Study, shows that our achievement scores in Year 8 mathematics have steadily declined since 1995. In the latest results in 2007, Britain and even the US, countries we used to beat, significantly outperformed Australian Year 8 students in mathematics. Unless we can stop the decline of well-trained mathematics teachers in our schools, this will continue.

The deepening tragedy of our education system is that this vicious cycle propagates itself. For years the numbers taking advanced or intermediate courses in Year 12 mathematics in Australian schools have steadily dwindled, and the students completing a major in mathematics at university has declined. As a proportion of total graduates, our universities now produce fewer than half as many graduates with qualifications in mathematics or statistics as other developed nations. The result is a decline in qualified maths teachers...

Students also face rising inequity in the current system. There are almost certainly differences in the public and private education systems. There has been a dramatic expansion in private mathematics coaching in Australia in recent years. Businesses offering tutoring or software for school students have proliferated across shopping centres over the past decade as parents have moved to supplement school education increasingly with private tuition in mathematics. The looming economic downturn means that a much smaller proportion of families will be able to afford this.

As a mathematician and a parent, I do not understand why Australians must tolerate an education system that is inferior to that in America or Britain. Nor do I understand why we should accept a growing disparity in access to mathematics education across our school system. All Australian children deserve qualified mathematics teachers. Yet in Australia, policy-makers have either ignored the problems or taken only fragmented steps and half-measures to address them.

Read the whole article for some half hearted measures that have been taken to improve maths education a little, eg. halving of HECS fees for University students enrolled in science and mathematics courses

Some thoughts:
At the beginning the author says:
Yet Australian school children are coming out of schools not knowing that doing a calculation with pencil and paper is the way to learn mathematics. While the federal Government is ploughing money into infrastructure, we are staring at the vista of shiny new classrooms and rows of laptops with no mathematics teachers.
I agree that maths education is declining in Australia to an alarming and depressing extent but don't agree that there is only one way to fix it. The Australian will always advocate for a back to basics or traditional "pencil and paper" approach. Maths education could also be improved with innovative and creative approaches using laptops. However, improvement in either way does require teachers who understand maths and we are failing many students in that regard.

I am also wondering if it suits our ruling class to keep most of the population both mathematical ignorant and mathophobic. We currently seem to have a swathe of policies to do with economics and the environment that if exposed to a mathematically literate population would possibly be the subject of mass derision.
"He who refuses to do arithmetic is doomed to talk nonsense"
- John McCarthy: Progress and its Sustainability

1 comment:

Mark Miller said...

Yet Australian school children are coming out of schools not knowing that doing a calculation with pencil and paper is the way to learn mathematics.

This statement is just wrong, but it reflects a common notion of mathematics. I was discussing this with Alan Kay a few months ago. If I had read this 4 months ago I would've largely agreed with it (except to say that calculators and/or computers could supplement for paper, as you said). Kay told me that for decades there's been confusion in our educational system about the terms "mathematics" and "arithmetic". Arithmetic is the process by which we calculate with integers or real numbers, whether with paper, a calculator, an abacus, etc. Kay told me that mathematics ("real mathematics" as he termed it) is, to quote Bertrand Russell, "p implies q". It has some relationship to arithmetic, but it is much, much more than that.

I was never explicitly told this distinction when I went through school. I could tell there was a difference, for example, between calculating 9 X 5 and finding x for x + 5 = 7, though there was still arithmetic involved in finding x. The first time I saw something different was going on was in geometry, where we did no arithmetic at all, just proofs.

When I was in primary school we used the terms "arithmetic" and "math" interchangeably. More often than not we used the term "math" for arithmetic, even though "arithmetic" would sometimes be on our textbook covers. In terms of discussing what we were doing we hardly ever used the word "arithmetic", usually "math". I think it's useful to make a distinction with these terms because it implies that there's something else out there to learn, and for many people there is, if they're interested in it. I only recently discovered this.

I asked Kay if he had any books to recommend for learning "real mathematics", and he suggested "the Jerry King book". I did a look-up for King and found only one book that's been out for a while called "The Art of Mathematics". I've been reading that and I like it so far. King has a new book that just came out called "Mathematics in 10 Lessons: The Grand Tour".

Another book I found and I like (so far) is "Mathematics: A Cultural Approach", by Morris Kline. I perused it, and it looks like Kline goes through history and shows how mathematical ideas developed. As an exercise he shows the reader the mathematics that was discovered at the time. I think he did this in hopes that readers would gain a sense of discovery about mathematics, similar to the way in which the original discoverers did. He used a line I loved: "The logic of discovery is much more interesting than the logic of the discovered."

With regard to Joshi's fear that Australia may lose the discipline of mathematics due to computers and apathy, I've seen a trend towards that here. Students have calculators now that can solve Calculus problems on their own. I began to think a couple years ago about how mathematics has value even if one never uses the particular mathematics they learned. It helps develop faculties for logical thinking, simplification, and elegance, for example. Unfortunately, as you've pointed out earlier, a lot of people don't understand this. They think in disgust "I was taught this and i never used it again," and think of the whole exercise as pointless. Maybe they were taught by incompetents.

Mathematics is still taught as part of standard curricula in this country, but there seem to have been moves made to banish it in certain districts. A woman by the name of M. J. McDermott made a video about this a few years ago. I wrote about her presentation at http://tekkie.wordpress.com/2007/02/11/got-math/

McDermott also appeared to advocate for a "back to basics" approach. Unfortunate, but better than the alternative, which appears to want to advocate only teaching arithmetic on calculators, since that's "practical".