Proving the Obviously Untrue

Entries from Saturday, March 24. 2007

"Anyone can teach maths" Sat, Mar 24. 2007

How many times I have heard this quote. I beg to differ. I was on my way home from work yesterday, listening to BBC radio 2. A woman was on making a music request.

The presenter (Stuart Maconie) asked her what she did for a living.

Woman: "I'm a teacher"
SM: "What do you teach?"
Woman: "Maths"
SM: "What were you teaching today?"
Woman: "Maths" (Duh)
SM: "No, I mean, was it quadratic equations or something?"
Woman: "Yes, actually..."

More chatter...

SM: "What's the volume of a cone?"
Woman: $\frac{1}{3} \pi r^2$

More chatter...

SM: "What's the volume of a sphere?"
Woman: $\frac{1}{3} \pi r^2$
SM: "They can't both be that"

Yes, that's right, they can't both be that. That would be because both answers are totally wrong. Not only are they wrong, they are not even dimensionally correct. In other words, any formula that represents a volume has to essentially be a distance times a distance times a distance. Count them, three distances multiplied together. This idiot gave the formula for an area; so it's not just the incorrect formulae that bothered me, or the fact that this was a maths teacher, but the fact that the formulae couldn't possibly be correct. Anyone with some insight into mathematics would know that. I would have known better when I was 18. Now there are some excellent maths school teachers, doing the job for the love of it, because it's certainly not for the pay, but there are some awful ones too, I know because:

I had one of them;
my daily job largely consists of undoing the damage they have wreaked on my students.

Of course, she was probably caught off guard, as if that's an excuse for not knowing these formulae if you're a professional mathematician, but in that case the correct answer was "I don't remember". Argh! Ok, I feel a bit better now. Oh, the correct formulae are of course $\frac{1}{3} \pi r^2 h$ for a cone (note, $r \times r \times h$ , three distances) and $\frac{4}{3} \pi r^3$ (note, $r \times r \times r$ , three distances).