WitCH 10: Malfunction

It’s a long, long time since we’ve had a WitCH. They have been not-so-slowly accumulating, however. And now, since we’re temporarily free of the Evil Mathologer, it is the WitCHing hour.

Due mostly to the hard work of Damo, all of the outstanding WitCHes have been resolved, with the exception of WitCH 8. That one will take time: it’s a jungle of half-maths. Our new WitCHes are not so tricky, although there is perhaps more to be said than indicated at first glance.

The first of our new batch of WitCHes is from the VCE 2018 Specialist Exam 1:

The Examiners’ Report gives the answer as \int_0^{\frac34}\left(2-t^2\right)dt. The Report also indicates that the average score on this question was 1.3/5, with 98% of students scoring 3 or lower, and over a third of students scoring 0.

Happy WitCHing.

I Know I Am, But What Are You?

A while ago we had cause to meet with a school principal. The principal happened to have a PhD in mathematics education, and it was on that basis that they began the conversation: “As a fellow mathematician …”. It will come as no great surprise that our association with the principal ended soon after.

The principal was doubly wrong: no, of course they are not remotely a mathematician; but, neither are we. Once upon a time, yes, but not now. We are no longer seriously engaged in mathematical research, in trying to discover the facts and the nature of mathematical truth.

But, to the principal and the principle. Of course it doesn’t matter whatsoever if a principal is not a mathematician. What matters a great deal, however, is if a principal falsely imagines that they are. If a school principal does not understand what it means to be a mathematician then they cannot possibly understand what a mathematician might offer to their school, or to education in general.

Such a lack of understanding, an ignorance of what it means to think deeply about mathematics, is now endemic in Australian mathematics education. The consequence is that mathematicians are treated asĀ inferior teachers and education academics, merely as weirdos with relevant training a proper subset of that of the education pros. The consequence is that clear and informed and deep mathematical thought is marginalised to the point of non-existence. The consequence is a pointless mathematics curriculum taught using painfully bad textbooks by poorly trained teachers and administered by organisations with no respect for or understanding of the nature of mathematical thought.

Mathematicians can be arrogant and annoying, and wrong. But mathematics education without the deep and continued involvement of good and serious mathematicians is pure insanity.