Greetings from Dar es Salaam, writing this from my balcony with a pleasant breeze coming from the Indian Ocean. Adapting back to life here, so driving once again, an automatic not a manual, indicators on the right of the steering wheel not the left, and able to make a small amount of use of the horn to mean, "I'm coming past and I don't know whether you've seen me, so here's a warning" which is in accordance with the UK highway code and actually very sensible. I incline to the view that the horn in the UK is now used too infrequently and almost exclusively to tell other drivers off, thereby denying ourselves quite a useful safety tool.
But what's on my mind is an incident last week whilst still in the UK. I had agreed to bring back with me 10 copies each of 'Carols for Choirs' books 1 and 2 for the cathedral for the Christmas carol services. So, ordered them when I arrived and went to pick them up last week. All fine except for one thing, when the moment came to pay I was asked for UKP37.
UKP37? Really? You are going to let me leave the shop with 20 volumes costing well over UKP10 each at a price valuing them each at less than UKP2? I pointed this out straight away, being the honest (smug?) citizen that I am. Part of me now regrets not telling them until I was just about to walk out, would they have realised at some later stage that they were out by a factor of about 10?
I have previously mentioned in this blog post the little war I wage from time to time against low numeracy standards in shops, normally when the assistant reaches for a calculator to do a sum which can easily be done in less time than it takes to find the calculator, let alone work out what buttons need to be pressed. But this is slightly different, I don't have a massive problem with the use of the calculator in the first instance, the problem here is failing to recognise that the answer being given is obviously wrong - because, I suspect, only one volume for each of the books I was buying was included without a discount for bulk purchase. But in an era when calculator tools of various types are everywhere around us, it is surely an assessment as to whether the answer being given is reasonable which is useful, rather than being able to do the exact calculation ourselves at a much lower speed than a calculating device?
Roin Riall and Professor David Burghes, a well known figure in UK mathematics education circles, wrote a paper in 2000 in which they examined the matehmatical entry requirements for jobs like warehouse officer and shop assistant on the one hand, and the mathematical demands of the jobs once people were actually doing them. Perhaps not surprisingly they found a big mismatch between the two, with long multiplications being required without a calculator when, actually in the work place reality, any such calculation would never be done by hand. So, one might consider that in assessing people's preparedness to do such jobs, rather than ask them to calculate 3.91 x 4.12, better to ask:
3.91 x 4.12 is equal to:
If one has a basic understanding of times tables, powers of ten and approximations, this question is very straightforward. But it would, presumably, have given the shop assistants selling me 'Carols for Choirs' pause for thought.
In the course for primary teachers I run on mathematics, mostly recently in Uganda described in this blog post,I look at long multiplication and, start with the traditional algorithm, the end result looking something like this:
Now, being able to do this is jolly useful if one has a job which requires doing a constant stream of such multiplications through the working day - but who does nowadays? Alternatively, being able to do calculations in this way is no problem if one understands exactly what is going on and why.
Two other methods I show end up looking like this:
Particularly this last method, called 'Gelosia', has proved very popular in the classes I've done, with units, tens, hundreds etc. automatically lined up ready for adding. The teachers I've like it are, however, concerned that their pupils will be marked down because they're not using the approved method, although people I know from examination boards say that this is not a problem - although, if this is true, it's not clear to me why teachers think that it is.
So, what am I trying to suggest here? I like the idea that we can, if necessary, do long multiplications. But there is no need to teach time efficient methods given that we are going to do them very infrequently, much better to use methods which make it clear what is going on. And let's use the time released to ensure that our basic arithmetic, timestables and understanding of powers of ten are good enough that we can identify when calculations are very obviously wrong.
More generally, I find the question, "What's important?" fascinating, I have plans to write a book under this title once I'm retired, meanwhile, I have a couple more blog posts to come under this heading, one on church music. Meanwhile, I've already mentioned that the General Election is due on October 25th, it is noticeable having been away for 3 weeks that there are appreciably more posters around the place. I hope and pray for a peaceful time as ideas are debated but meanwhile, have approximately 120 litres of drinking water in the flat and have started to fill my freezer with portions from casseroles. I'll keep you informed.