Re: Formal explanations vs. pathways of understanding (was: momentum before force

[palmer@sfu.ca (Leigh Palmer)]

> To suggest that we lead students up all the blind alleys is not what I was
> advocating.  It is possible to discern the _issues_ in which the scientists
> in history were engaged and to find ways of getting students engaged in
> similar ones.  Having the students retrace or for us to recount the history
> without engaging students in the issues is a waste of time and no more
> productive than what we are doing on the average today.  If the _students_
> are not engaging and comparing _their_ ideas with the phenomena then little
> change in _their_ ideas should be expected, but isn't that change in
> _their_ ideas the point?  (If not, then maybe physics education is _not_
> for the purpose of helping students develop their understanding of the
> world of physical phenomena, but for some other purpose instead.)

I'm sorry, I did misunderstand your intent. I agree that there is merit
in engaging the student in the pursuit of truths. In Kepler's case the
situation was that his problem was to interpret a large body of data he
had managed to wrest away from Tycho's sons. He got Mars, and those were
the best data for his purposes. The data were taken by a man who had an
axe to grind: he had his own model of the universe. Kepler was hired to
interpret the data in that way even though Kepler himself was inclined
toward a different model. When Tycho unexpectedly died, Kepler's income
and those constraints ended simultaneously. He made off with his treasure
(I don't remember how he fed himself) and then spent a very long time
pondering the observations.

I doubt that today's students could be engaged in this particular case by
reams of numbers, but if perhaps the numbers could be provided in a data
base and manipulated using, say, a spreadsheet, perhaps the students just
might rise to the challenge. I'm pessimistic. I don't think I would have
been able to do it. Many of my students are brighter than I am (you don't
seem to like me suggesting they are less able than Newton) but I doubt
that many would be up to the task, even simplified. The story above,
however, amplified with details, can be a great motivator.

I guess I have no objection to your suggestion, Dewey, but I would like
another example. Presenting the counting balls (as I call them) to a
class of prepared students will produce few Eurekas. Guessing that the
collisions must be treated individually is difficult. Again, I don't
think I would have got it had I not been shown.

All this smacks of a fad of a decade or more ago, the discovery approach.
I don't see this being used much any more. As with many such methods, it
works well for an enthusiastic, dedicated group but it becomes less
effective when passed on to less committed folk. The initial proponents
eventually lose interest and the idea dies, only to be rediscovered by a
later generation. Perhaps it is the enthusiastic teacher, and not her
particular methodology, which produces results.

Leigh