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.

Yea verily

Oh Troppodillians, what sayest thou?

Funny you should mention this, Nick. At school I use spreadsheets all the time to demonstrate maths at work. All it needs is for me to write a problem on the board, then plug in my laptop to the data projector, fire up Excel, and demonstrate to the students the numbers being crunched.

By the way, it all started with power transmission line models (here’s a line, here are the parameters, what are the currents, voltages, power factors, etc through the system?), but we soon realised Excel could be used for pretty much any calculation demonstration.

You mean you actually want kids to be able to analyse and solve problems with maths Nicholas? Streuth, wouldn’t that cut into their ‘making the community more aware’ time?

If automated tools generate sets of numbers from which students can discover patterns, then that is a good thing. It’s just another form of play, which is an excellent learning method.

As for teaching logs, I think the slide rules demonstrate the principle best. When I was tutoring after slide rules disappeared, I’d get kids to make their own slide rules (by using two normal rulers with the “log” marks scrawled on after looking them up with a calculator). All of a sudden, kids could physically relate why logs are added together to do multiplication.

The problem with these automated tools is when they are used as a crutch, and there is no checking of the figures. This is a problem not with kids, but with managers who look at the bottom line of a spreadsheet or the graph and (in cargo cult mode) accept the result uncritically.

Personally, if tutoring today, I’d use spreadsheets to generate data, put in errors, and ask kids to search for the screwups. The same thing applies to datasets with relational databases.

Yes, I agree David.

Actually I think it does. When learning multiplication etc in the early years of school we were not allowed to use calculators. I am not sure if that is still the case, but it worked for me.

On the general point I think that everything you say applies almost as strongly to any subject that deals with numbers. Science, Commerce, Economics etc. It’s probably a little more important in maths, but not much. I got the impression from your post that you believe that spreadsheets and even databases should be taught as part of the Maths curriculum. If so I think I have to disagree with you. I am all for teaching these things as early as possible, and for them to use spreadsheets as an integral part of their maths but they really are different skills. I would hate for my kids to finish school believing that Maths is just computational number crunching without every really gaining an appreciation for the power of maths to acheive elegant powerful solutions in of itself.

Why are they not used? I think the reason is pretty simple. Unless you know how to use them, teaching them is near impossible. We regularly get new accountants turning up who do not know how to drag down a column of figures, much less do the sort of Monte-carlo analysis you were describing on the law of large numbers above. What chance a trainee maths teacher knows how to do this?

What Andrew said.

I’ll also add that if you start teaching Kids any particular spreadsheet (whatever brand), you’ll inevitably distract their attention from the core stuff (like what pi is, and why it’s important) with instruction in a lot of skills that are package dependent.

Similarly with databases – teach kids relational databases? Oh heck, it’s not similar at all – first up, relational database theory (which is the genuinely mathematical end of the business) is already pretty heavy going and second there’s the small matter of – ahem – coding when you’re building and using a database. More distractions, and more confusion.

I have never taught kids. But lately I have taght MBA’s…..The linking in Excel is especially useful for sensitivity analysis. And generating random datasets and plots and allowing the students to see the results change before their eyes with each simulation is the best way I know to convey the concept that all data analyses have statsitical error. I have posted about Excel at http://blogs.mbs.edu/fishing-in-the-bay/?p=96#more-96.

I’m really taken aback by the conservatism of the nay-sayers on this thread. Of course one doesn’t teach the spreadsheet as the quick way to the answer – it’s just a tool. As I said, like a calculator, a slide rule, log tables, trig tables. But a vastly more powerful one.

Swio,

I think you’re right. I got the impression as I posted the post that I was linking the teaching of spreadsheets too closely to maths. I didn’t redraft it, but I don’t really want to link it to maths, though maths would be a perfectly good place to teach it – as would science or even some social studies kind of unit. It’s not very important. As you say it’s got braoder application than just maths – cdn’t agree more.

Andrew,

Funny thing is I had a conversation at dinner with my kids about the ‘Monte Carlo’ simulation as you call it. They remembered the exercise and what it conveyed – both would have been under ten when we did the exercise. They’re not geniuses.

Gummo,

Can you tell me in what sense you regard pi as an important mathematical concept? What would distinguish an important mathematical concept from an unimportant one? Why do you think that imparting a working knowledge of spreadsheets as a tool would be in conflict with teaching an understanding of pi? I’ve not met that many school students with a very deep knowledge of pi. How would they get that knowledge and mightn’t spreadsheets be used to help them grasp certain aspects of pi’s importance?

As for package dependent skills. I wonder if any of my skills in excel are package dependent. I seem to be able to use them in other spreadsheets.

[…] we barely use the obvious tools that are successors to the slide-rule and the calculator, namely the spreadsheet in maths education. How we don’t teach our kids computer skills and on and on. I impressed upon Peter the […]

[…] we barely use the obvious tools that are successors to the slide-rule and the calculator, namely the spreadsheet in maths education. How we don’t teach our kids computer skills and on and on. I impressed upon Peter the […]