First, a little background. I strongly encouraged my students to get a graphing calculator for Algebra, but it is not a requirement. Just over half of them have one right now. The math department has a partial set of graphing calculators that I can check out if they're not being used, and they also have a set of 15 laptops running Windows XP.
I'm beginning to plan the lessons where we'll start looking more closely at linear relationships, including tables of values and graphing (in addition to equations). One of the things I hope to do is intro it to them as a recursive routine and hopefully help them see the connection between the rule, the table of values, the graph, and ultimately the slope of the line. The activity I'm planning right now has them use a graphing calculator and a recursive routine to help them generate points, then they graph those points by hand and we look at the relationship between the problem, the points, and the graph.
I could definitely do this with graphing calculators. Since the students are working in groups, the students have enough graphing calculators that every group could have one, and the math department has some that I can bring in to supplement in case any group doesn't happen to have one that day. But as I was planning on what I was going to show them on the projector/Smart Board, I found myself creating it in Geogebra (which is just a fantastic program, even though I don't know it very well yet).
I find it easier to use Geogebra than the TI Smartview that emulates the calculator on the screen, and I certainly like the clarity of the graphics much better.In Geogebra, I use the spreadsheet function to create the equivalent of lists and/or recursive routines on the graphing calculator, then use that to plot the points on the graph. I can then add colors to the graph, easily change my scales and views on the axes, and just manipulate the heck out of it.
I think initially the push toward graphing calculators was because they were relatively inexpensive (compared to computers) and portable, and therefore it was more realistic to expect students to purchase them, or for math departments to get class sets of them. Therefore I was assuming I was going to choose graphing calculators over computers for activities such as this. But now as the cost of devices has come down, and as more and more students have close-to-full-time access to some kind of computing device, I wonder if it might make sense to transition back to using computers for something like this. Aren't we now at the point where we can assume that students will most likely (at least as they get older) have access to computing devices more often then they will graphing calculators?
Certainly the idea of a recursive routine works just as well on Geogebra/a spreadsheet as it does on a graphing calculator, and perhaps better as they have to think more about the process. (On the graphing calculator we would probably use the ANS key to generate that recursive routine, which might obscure what was going on. On Geogebra, we would write the spreadsheet formula, which is more . . .ahem . . .transparent.) Geogebra is more flexible than the graphing calculator in many respects, although certainly the graphing calculator does things Geogebra does not. So I wonder if it makes more sense to try to get the laptops and have them use those one per group for activities such as this. (Also keep in mind that Geogebra is free for Mac OS X, Windows and Linux, so no cost to schools or to students if they want to install at home. It runs fine on our netbooks running Linux.)
So, this is a long-winded wind up to the point of this - what do you think? Does it make more sense to use graphing calculators, or transition to using computing devices for math learning/instruction/exploration? I'd love to hear your perspective, whether it's as a math teacher, an ed tech-type person, or some other interested reader.