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a slightly different thread




At the risk of starting another plethora of comments: (actually in the hope
thereof), let pose the following question or thought.

Much of the difference in viewpoints seems to come down to the following
(and I realize that there is more than this to the difference, but this
point is the one I'd like to read your opinions on):

Breadth Vs. Depth.

The highly interactive approaches seem to favor the depth approach. We
cover fewer topics at greater depth (student understanding) by
"non-traditional" means that intrinsically are slower, hence coverage must
be less

Pehaps, the "traditional" methods might be simplified as saying, we cover
more breadth and get more coverage, by perhaps more efficient means; but at
the sacrifice of deep conceptual understanding.

I believe both opinions have merit and the answers as to which is better,
breadth or depth depends on what you view as the role of the introductory
course. And one's opinion may be different depending on the audience.
Should the introductory course be the place where deep understanding takes
place or should it be the place where a wide variety of ideas and topics are
introduced brought to the aquaintance of the students. Personally I can
answer this both ways for both types of audiences (those for whom this is
the terminal course and those that go on in engineering and the sciences).

My opinions are tempered by the fact that I know it took me years to achieve
whatever depth of knowledge I have and almost strikes me as ludicrous that
much depth can be achieved in one year to beginning students. Also, when I
teach advanced courses, I think I prefer my students to have a small amount
of familiarity with a lot of different ideas; the advanced course is where I
try to develope the depth. On the other hand, I'm not immune to the results
I see on tests regarding how good of a conceptual understanding students
have from the introductory course (and incidently I think that a problem
solving test can reveal a lot about conceptual understanding that many
students have).

I could go on, but I won't; I would like to thank everybody on all sides of
these issues who have given their thoughts and opinions. These discussions
have given me pause and fodder for thought. And I believe they are all
given in the hearfelt belief of trying to do whats best for our students and
thereby for society at large; and are given by people who care. THANKS

Joel