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Software
Posted:
Apr 9, 1996 11:55 PM


I have read the various comments on teaching with software. Let me add my 2 cents. Background: I have taught statistics for 20 years and was an early advocate of using computers for teaching. I teach at Cornell  which is not as different from teaching AP students as you might think; if anything my students are less wellprepared and less motivated than a typical AP class. I also develop Data Desk, which is one of the approved packages for APstats, and am working on a multimediabased presentation of the introductory statistics materials to be published by AddisonWesley Interactive (which I'll talk about at AERA later this week).
Comment: Computers, properly used, can indeed improve students' understanding of statistics concepts. Contrary to what has been suggested by some, students do not generally learn concepts by following algorithms or programming; the algorithms in statistics are often unintuitive and confusing. (For example, the formula for a Least Squares regression slope doesn't look much like the (yy)/(xx) formula for slope that students know from algebra.) But computer software can offer multiple displays of data and the ability to relate them to each other and to the original data with such actions as brushing (moving the mouse over the points to hilight them on one plot  and see them instantly hilight on all other displays and in the data table). A good statistics package should emphasize graphics, let students identify individual points easily (e.g. with a mouse click), and show the consequences of changing or deleting values (e.g. by updating plots and calculations in place.) These and similar behaviors let students see beyond the calculations and think about what the data are trying to tell us. And, of course, computers can do simulations. The only way I know to get across the idea that each sample is different and is different from the population, and yet each sample resembles the population in essential ways  the heart of the idea that randomness is not haphazard  is to have students make histograms of several samples from a known population. Each is different, yet each resembles the parent population just as each child in a family is different but resembles the parents. Once you do it, you have a sense of how it works. Just seeing one example on paper doesn't have the same impact.
At a higher level, we can't prove the Central Limit Theorem for this class  and even if we could, the proof is not convincing (even to statisticans). The result is, frankly, magical. (Pascal saw it as proof of the existence of God  but then he saw many things as proof of God.) But each student can draw many samples from a nonnormal population, average them, and watch as the histogram of the means approaches a Normal shape. It still may not convince, but it does help to explain what the CLT says.
I do concur that a calculator such as the TI83 is a great tool for students in APstats. But, I don't think that it can do what a good computer package, properly used by the teacher, can do.
 Paul Velleman
Claimer: In case you missed it above, I develop Data Desk, so I am not unbiased about either the use of computers in teaching or which package you should use. However, I do write from 20 years of practical experience.



