At 10:58 AM 4/20/01 -0500, jim clark wrote:
> What does a t-distribution mean to a student who does not
>know what a binomial distribution is and how to calculate the
>probabilities, and who does not know what a normal distribution
>is and how to obtain the probabilities?
good question but, NONE of us have an answer to this ... i know of NO data
that exists about going through various different "routes" and then
assessing one's understanding at the end
no one has evidence who has commented today about this ... nor yesterday
about this ... nor any member of this list
to say that we know that IF we want students to learn about and understand
something about t and its applications ... one must:
1. do binomial first ...
2. then do normal
3. then do t
is mere speculation
without some kind of an experiment where we try various combinations and
orderings ... and see what happens to student's understandings, we know not
of what we assert (including me)
off the top of my head, i would say that one could learn alot about a t
distribution studying it ... are you suggesting that one could not learn
about calculating probabilities within a t distribution without having
worked and learned about calculating probabilities in a normal distribution?
as far as i know, the way students learn about calculating probabilities is
NOT by any integrative process ... rather, they are shown a nice drawing of
the normal curve, with lines up at -3 to +3 ... with values like .02, .14,
.34 ... etc. within certain whole number boundaries under the curve, and
then are shown tables on how to find areas (ps) for various kinds of
problems (areas between points, below points, above points)
if there is something real high level and particularly intuitive about
this, let me know. you make it sound like there is some magical "learning"
here ... some INductive principle being established ... and, i don't see it
i don't see one whit of difference between this and ... showing some t
distributions, giving them a table about areas under these, and having them
find areas below points, above points, and between points ...
now, going from binomial to the normal is a bit different ... going from a
highly gappy binomial distribution to a smooth one ...
but i contend that one does NOT need to have experience in finding
probabilities WITH the normal to fully understand what probability
statements mean using the various t distributions ...
if someone wants to do binomial ... THEN move to normal ... THEN move to t
because they like that sequence ... fine. but, please don't say that one
MUST follow that sequence inorder to know something about either a normal
and/or a t
again, all of these pedagogic assertions are ONLY that ... assertions ...
but, with no evidence behind them
unless one can cite a study or two on the matter?
> In fact, what does the
>whole idea of a distribution in general and sampling distribution
>in particular mean for students when the basics are omitted? It
>is far more important to give solid foundations in the
>entry-level course than to "make room" for more sophisticated
>tests that students will only vaguely understand.
>
>Best wishes
>Jim
>
>============================================================================
>James M. Clark (204) 786-9757
>Department of Psychology (204) 774-4134 Fax
>University of Winnipeg 4L05D
>Winnipeg, Manitoba R3B 2E9 [EMAIL PROTECTED]
>CANADA http://www.uwinnipeg.ca/~clark
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>
>
>
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==============================================================
dennis roberts, penn state university
educational psychology, 8148632401
http://roberts.ed.psu.edu/users/droberts/drober~1.htm
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