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Topic: Software
Replies: 0

 Paul Velleman Posts: 1,607 Registered: 12/6/04
Software
Posted: Apr 9, 1996 11:55 PM

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 well-prepared and less motivated than a typical AP class.
I also develop Data Desk, which is one of the approved packages for
AP-stats, and am working on a multimedia-based presentation of the
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
(y-y)/(x-x) 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 non-normal 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 AP-stats. 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.