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7/9/2013
10:55 AM
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You already own better algebra-teaching software than any educational software developer is making.

I found in teaching elementary algebra to disadvantaged adult learners that the progression from table to graph and then to formula/function/equation might have been the most powerful tool for "selling" algebra I ever encountered. Anyone can see intuitively that for many problems, if you just make a table big enough, trying out all the possible values will lead to a solution. From there, it's a short step to, but what if there are millions of values? Then they're ready to graph it and the answers are right there at the intersections. From there it's just the step to, but what if you need an answer more exact than the line you can draw, or more dimensions than two? Well, by then, they're used to the idea of formula/function/equation as description, and if a point satisfies more than one description, it's a solution. And they've crossed over to doing algebra.

The spreadsheet provides a natural bridge from arithmetic procedure to formula/function. At first, students will just input numbers, as if the spreadsheet were a calculator. Then they see that if they input variables, they don't have to type nearly so much, and then that this means having not just this answer this time, but all the answers to all problems of this type, all the time.

It's a wide and easy-to-cross bridge from the specific to the general, and from procedure to concept.

One of the big changes in mathematics in the last 30 years has been the idea of experimental math, i.e., of exploring how numbers work by setting up numerical processes and looking at the results; it's at the heart of chaos research, for example. Just as the computer has become the equivalent of the telescope or microscope for mathematicians, Excel can be used as an amateur "scope" for exploring numbers, in a way very much analogous to the way countless students have gotten a handle on science by finding a planet in the sky or exploring the ecology of pond water. Among other things, I've used Excel to teach how every fraction is a division, and division is equivalent to multiplying by the inverse. It could easily be used for many other projects beginning even from a very early age in arithmetic.

Spreadsheet algebra is such an effective and intuitive idea that it has been re-invented several times in the last 20 years, and some Googling around will turn up immense amounts about it. (Caution: "spreadsheet algebra" is also a term used in advanced mathematics research for a kind of non-linear matrix algebra, so your Googling may very well turn up an article or two that's a bit beyond you. Don't worry, just keep looking!)

Although there still needs to be a human being there to guide the student in exploring and using the spreadsheet, as a teaching device for actual algebra (as opposed to a drilling device for standardized tests) the spreadsheet still beats out thousands of purpose-designed products.

Doesn't that suggest something to you, educational software people?

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7/9/2013 | 6:57:07 PM
I suspect some parents think using Excel is cheating. Thanks for showing how this tool can be used productively as part of the learning process.

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