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Methods of Comparison
Posted:
Oct 27, 1995 2:00 PM


Concerning the comparison of learning experiences using graphing calculators. I'm sure many different forms of well designed controlled experiments can and have been conducted. Be careful with the appeal to argument by analogy with that of FDA's rules for approving a "newly invented alternate" to aspirin. The rules (procedure) are complex and involve clinical trials. These trials are designed so that significant differences (if they exist) can be measured with credible statistical power. Even if a manufacturer want's to introduce a different colored aspirin (let alone a new formulation or variation of), some form of well designed trial is necessary.
Does it all matter ? People in the industry tell me that not all aspirins are the same. While they may all deliver the same therapeutic value for a given set of conditions, the quality of what happens outside these bounds vary drastically.
From my own limited experience with graphing calculators, I know that there are great differnces from model to model. Not all use the same programming logic (e.g. reverse Polish logic). Maybe some are more pedagogically sound than others? Think of all the programming languages available for use. As technology moves on, less mental labor will be needed to generate highly informative graphics. Maybe some will soon deliver in colors.
We need to start teaching about the concepts underlying the calculations. What is a function ? What do the graphs of this or that class of functions look like under these or those conditions... Is there always an asymptote ? etc.. These kind of questions are not answerable by the same forms of logic necessary to bang out an answer on the calculator. I'm appealing to the geometric aspect of math matics of course. We need to develop our geometric intuition more. This is occuring more among researchers as they learn to exploit the power of the computer. Not suprisingly, geometry has never been a "big" thing in school. We have algebra I, algebra II, advanced algebra, algebra and trig, and so on. Have often do you see a geometry I, II, etc ? Geometry seems to have been on the decline since the 1920s; maybe earlier. I don't know why. My guess is that our technology moved in a direction which required the logic underlying algebraic manipulation. I don't really know. There are many forms of geometries. With these graphing calculators we have the opportunity of opening our student's minds to them.
Al Barron barron@prius.jnj.com



