Although education technology is a growth industry, according to John Barnes of Information Week, it is sadly lacking in comprehensive arithmetic teaching solutions. A quarter century ago, RAND looked at the options available to aid students master basic mathematical concepts and found them severely lacking. Today, the situation is not much different.
There are plenty of programs that will guide students through rote memorization of things like the quadratic formula or the steps of long division. But few will go into details about how such formulas are derived to give students a deeper understanding of math fundamentals.
According to Barnes, parents who wish to give their kids a leg up can wait around until a good targeted solution is finally developed and marketed, or they can take tips from expert teachers like Tom Button and Teresa Rojano to adopt a simple spreadsheet program for just such a purpose.
Consider, to begin with, that variables and parameters in spreadsheets are very similar to what they are in ordinary algebra. For that matter, Microsoft Excel notation (and most of the Open Office software notation) is either algebra notation outright, or so close that only simple explanations need to be given (“in algebra the multiplication asterisk is understood, in Excel you have to put it in,” “what we call a function in algebra is what a formula is in Excel,” etc.).
A basic insight of algebra is that a function can be thought of as a rule OR a table OR a graph. (I’m capitalizing because it’s the Boolean logical OR rather than ordinary English “or.”) In fact, they are three different ways of looking at the same thing. Similarly, a spreadsheet formula can be used to generate a table of data, and the spreadsheet’s graphing features can be used to turn it into a graph.
Burton has already tested this approach on adults who were trying to renew their own math knowledge. A spreadsheet can serve as a crutch to help students make that leap from the specific to the general – “from procedure to the concept. “
Using spreadsheets goes along with a teaching approach made popular over the past 30 years called experimental math. Give students an opportunity to play with a larger and larger set of numbers and then ask them to hazard guesses about what happens when the set of numbers is infinitely large. A spreadsheet allows them to extensively test their guesses, refine them and finally to understand the underlying concepts in a way that endless drilling will not.
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.