Thursday, February 10, 2011

Mathematics Education

The end of a very frustrating day in academia. It's mostly off-topic (not dealing directly with the storm to come), but shines some light on why it is coming at all.

Below is an edited version of an email which I sent to a colleague in our college of education.

I am also rather distressed by your comment:

"A PhD is a terminal degree which means we are capable of self-teaching material we are unfamiliar with".

I know a great deal of mathematics, computer science, statistics, engineering and physics. I would still have much trouble teaching something like Abstract Algebra, and I have had several courses in the subject. It's not all 'just math'.

The problem, which is very close to that of our meeting today, is that mathematics is one of the most tiered subjects there is. As one of my administrative superiors told me, many subjects have an 'Intro' course, after which one can take any number of courses. This just isn't true for our discipline, until about the senior level. That is why we take the issue of prerequisites and previous material so seriously.

It is also upsetting to experts in other fields (especially education) that success at one level of mathematics is no guarantee that one will ever succeed at higher levels. A previous administrative superior couldn't understand it at all, which is one of the reasons why he publically stated that learning algebra was unnecessary 'for anyone'.

In (not so) short, this is why I take the problem of training future mathematics and science teachers so seriously. With all too many school administrators having the idea (as another administrative superior told me) that 'anyone can teach math', no wonder that we have the problems that we do.

I have been party to many discussions on mathematics education on usenet and elsewhere. Every single time, my honorable opponent criticizes how the subject is taught. They then either offer no ideas at all, or ones which have already been shown to fail elsewhere.

Ponder this: Mathematics has been taught as a discipline in its own right for about 2,500 years. The subject itself lends itself to brutal editing and revision, so that only the most robust facts and proofs survive. Given those millions of man-years of developing and teaching the subject, isn't it reasonable to suppose that we are doing some of it correctly, or at least we might know better than outsiders?


Chrysalis said...

Hmm...forgive me if I skimmed and read you wrong, butI rather enjoy the different approaches to Math I had in college (university) - perhaps that's the value?

I understand we can diversify so much that it creates confusion rather than minimizing it.

However, one of the best minds of our time, Albert Einstein, had a rare ability to balance the finite with the abstract.

This balance is often the key to teaching any discipline, yes?

Salis Grano said...

Not quite sure what the motivating issue was, but yes, I entirely agree that mathematics is highly cumulative.

The subject is often about revisiting familiar specific material is a more abstract and generalised way.

If you haven't got a good understanding of, say, real analysis and set theory, you are unlikely to do well in general topology.

James Higham said...

Have to admit I haven't dwelt too much on Maths but I might now.

Paddington said...

@chrysalis - the issue was to have an engineering/education major walk into a classroom to teach proofs in discrete mathematics. The education prof to whom I was writing just thought that all of the math was apparently 'close enough'.

Anonymous said...

My standard comment about this is in the form of a paradox: it seems that people in general believe "mathematics" (by which they mean anything above elementary arithmetic) is impossibly difficult, and yet somehow hold simultaneously that it is easy to teach. Possibly it is because they have only met mathematical exercises of a kind that can be instantly marked with a tick or a cross; in other words, they judge the teaching of mathematics as a whole by those trivial parts of it they have themselves encountered.

Sackerson said...

I think your university college of ed colleague has proved that once you've learned to read and write, there is no need for high school or college. His/her next challenge is to look for a job, either in primary education or industry.

Paddington said...
This comment has been removed by the author.
Paddington said...

@anonymous - this actually goes along with a fascinating study in the US some years back, which showed that competence is inversely correlated with confidence. This explains many of our politicians, and is supported by direct studies comparing the US with South Korea. The latter students were much better, yet rated themselves as mediocre. The former seriously underperformed, yet rated themselves as superior.

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