About fifteen, perhaps twenty years ago I was talking to a good friend who is an academic in maths education. He was saying that Casio was interested in getting input into the educational potential of their graphical calculators.
I thought there was a real opportunity here. One could build the case for much more graphical teaching of mathematics using the analogy of the power of the graphical user interface. One could rework substantial parts of the curriculum and it would help sell graphical calculators. Probably wouldnt make anyone but the calculator suppliers rich if it made them rich but in the world where academics worry where their next research grant is coming from it seemed like it might be the thing. A slick and technology savvy way to dress up some research into maths education which might get one money from both education departments and corporates with hardware and software to sell. And pioneer something both inevitable and worthwhile at the same time.
My friend wasnt really interested in that kind of research and I didnt think much more about it. But I did think by the time my kids were at school that the time for this kind of research would already be well behind us that the whole of maths education, and education more generally, would have been transformed.
It took only five odd years from the time they became small, cheap and plentiful for calculators to be seen as legitimate aids in maths. It took perhaps another five years for them to have pretty much relegated slide rules and log tables to the dustbin (though not obviously the teaching of the mathematics of logs).
So by the time I took my kids to school I figured that there must have been a quiet revolution in which spreadsheets must have invaded what? a third, two thirds of the maths curriculum. Data bases might have invaded some of it too.
So I waited expectantly as the kids were kitted out with laptops and Microsoft Office (apparently OpenOffice wouldnt be good enough for these treasures!)
I figured that spreadsheets might be brought in when tables were taught. Dont know when that is maybe year 3 or 4. From then on as one taught different operations on numbers one could spend some time showing how a bit of playing with Excel – pulling down a row of numbers generated by a formula here, creating a chart there could help kids get the hang of what these functions were doing.
There would of course be areas where a spreadsheet wasnt much use. But having said that I cant off hand think of any. It is certainly true that Excel would be more powerful in some areas than others. But then having said that Im not sure I can think of areas where spreadsheets wouldnt be pretty useful. I was going to say that teaching the basic functions Excel would be useful tabulating the effects of and comparing different functions. I was then going to say that maybe spreadsheets wouldnt be much good for algebra but of course theyd be great. Spreadsheets are algebraic in inspiration let x be an empty cell. Hello?
Anyway, my daughter is now in year eight. And she does know about spreadsheets. I think shes been taught their basic use. But almost no use is made of them in maths otherwise. My son in year four does maths extension and I keep coming up with great projects for him to do in Excel. I suggested that he use the randomize function (Id program it for him) to work out the odds of different dice throws in monopoly statistically and compare it to the mathematics of probability. We did this and he could see the law of large numbers demonstrate itself before his eyes.
I suggested he run tipping comps with Excel, and for instance experiment with different ways of calculating odds. Tipping comps generally give you one point for getting the winner of some sporting game correct. But that encourages conservatism and herd behaviour. What you need is a system that gives you a bigger reward for tipping an outsider.
So I proposed a formula to my son and he proposed this at school. I said Id put up a prize for the winner in this comp (which would not disrupt the existing comp which is already running). But my son was told it would be too complicated and would confuse the other kids. The maths teachers dont seem particularly keen on Excel or particularly good at it either. Anyway, spreadsheets are such awesome tools, such an incredibly simple and versatile way to show the power of the quite simple mathematics they are learning that I remain amazed indeed amazedly amazed that so little use is made of it.
Now I can anticipate one objection that allowing the use of Excel would provide them with a shortcut and that good teaching should be teaching them how mathematics works not giving them shortcuts where, for instance they can solve elaborate problems without really knowing the maths behind it.
Im afraid I dont think this objection stands up. Its of course true that we want kids to understand most of the maths they use. (Though the existing teaching of maths doesnt come up that well against this criterion. One can often skip those early lessons teaching the logic of a particular technique and it doesnt slow you down in the tests which almost invariably test the techniques. In any event, one tends to come to a good understanding of theory not at the beginning of being taught something, but as one works with it in a practical way.) In any event the same point can be made of calculators or any other tool logarithms, slide rules, etc.
Generally the practice and the theory should be reinforcing each other. And not only do spreadsheets provide very quick ways for kids to get the hang of a whole bunch of mathematical techniques they can drag a column down and watch how a function changes with different inputs and graph it, and compare it to other columns. Spreadsheets are just incredibly useful. A bit of facility with spreadsheets can enable people with quite modest mathematical or perhaps I should say arithmetic technique to be pretty useful. And of course thats one of the things that turns kids onto their subjects. Not only is it useful, but it also leverages the skills they have (to use an ugly word). They learn some idea or technique and then they can work with it in powerful, visual ways, combine it with others, see how it works in different circumstances use trial and error to check out its workings almost instantly.
Likewise the use of databases should be taught say from year 5 or 6 on. The whole idea behind databases of arrays of data that can be manipulated and interrogated in any imaginable way – is incredibly powerful. Its also pretty simple, and should surely be part a relatively early part – of a decent mathematical, scientific or logical education.
Oh Troppodillians, what sayest thou?