voluminous nonsense

I had a good time Monday and Tuesday of this week teaching a section of the TCD MSc in Immunology.  There were so many students on the MSc, and the material was so new to them that I asked if the management would rise to a Teaching Fellow to help field the questions in the practical sessions.  I wouldn't have asked if I didn't have an Effective in mind: a young graduate of The Institute who did a stonking good final year research project with me and is now building that into a MSc by research in the Comparative Immunlogy group in Trinity. That turned out to be a good idea: by having to explain things, Ilaina the TF got to understand them better herself and also learned a lot of stuff that hadn't been necessary to pick up yet in her nascent post-graduate career. Meanwhile, back at the day job . . .

At The Institute, I teach a weird and wonderful set of subjects, few of which are what I was trained to do.  That's what makes the job so interesting although it was a teeny bit stressful when I started work three years ago: being 2 weeks or even 2 days ahead of the students in mastering the syllabus. I've had two sections of 1st Year QM remedial maths quantitative methods this term and the end of last week was time for their Xmas Exams. I do have standards, but I also want to get them over the line. Many of them have ingrained Math Anxiety and have probably had crap teachers who are at the edge of the competence (a bit like me teaching Environmental Chemistry). Nevertheless they want to do science and I don't want to hold them back with stuff that may well become easier when they use it for things that matter: their own experiments for example. I've long been a fan of Edward MacNeil's Mathsemantics, which book hinges on the observation that even quite handy number-wonks go all to pieces when the problem is embedded in a sentence and/or you have to define your units and/or you have to have an order-of-magnitude clue about what the answer should be.

In a metric world, one of the weirder units of measurement is a bale of 4-inch solids, which consists of 44 (?!) concrete blocks 100mm x 215mm x 450mm.  Why 44?  It's not because the molecular weight of carbon-dioxide is 44? And to point out that I get 44 flapjacks out of a swissroll tin is to suggest that these popular cookies are like door-stops. No, the answer is apparently that, because the density of concrete is about 2.35g/cu.cm, then 44 blocks weighs about 1 metric ton: it's convenient for loading trucks.

So I thought, I'd pop a question in tne QM exam, for the boys, like:
Q. What is the volume of 44 (100mm x 215mm x 450mm) concrete blocks in scientific notation and SI units [cu.m]? A. 0.426 cu.m. or 4.26 X 10^-1
Only one student got it right, having converted it, correctly, to 0.1m x 0.215m x 0.45m x 44.  Another was wrong wrong-almost-right at 4.257 X 10¹. The majority of the students plonked for 4.257 * 10⁸. On the assumption that mm are essentially the same as m.  A minority view had 4.257 * 10⁵ as the answer; under the mistaken impression that if
1mm is the 1/1000th part of 1m so
1cu.m is 1000x the size of 1cu.mm; when in reality it is 1000 x 1000 x 1000 times bigger.

Whatever about the maths, the thing that distresses me is that 425,000,000 cu.m. is about the volume of the entire domestic housing stock of the Republic of Ireland ! How could you write that down as an answer for the volume of half-a-hundred blocks; which wouldn't even make a garden shed large enough to shelter a lawn-mower.  What to do? Throw the kids out of the classroom!  Stop them doing pages of Victorian sum-copy exercises and make them measure timber and mix concrete and order up enough plywood to make a play-house in the garden. They'll soon get the measurements right if the first version of their play-house hasn't sufficient plywood for the roof. You can't invite your dolls to tea if the sandwiches get all wet from the rain.