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



It strikes me that it does not really matter how someone _presents_ ideas,
regardless of who they are, Newton or Galileo, etc., if we are interested
in understanding how (and helping) students come to understand the ideas.
What matters much more is how someone came to construct ideas we find
significant, because that is how someone else (some or many of our
students, maybe?) might do so also. It is well documented that the path
taken to arrive at ideas is often not the path laid out in explanation of
the ideas. This is the case in the history of science and with modern
textbooks.

Now this does not mean that the path laid out in explanation is to be
discounted, but it remains to be examined and tested to see the extent to
which it might actually be productively followed by actual students. We
have ample evidence in the case of modern textbooks that explanations can
and usually do fail rather miserably for a majority of the students. On
the other hand, the way people actually came to such ideas (historically)
has already 'passed the test' of "Could someone come to construct such
ideas this way?" Not that this is necessarily how _everyone else_ should
do it, but it has passed the test of 'could someone do it this way?' I'm
_not_ saying that an historical pathway is the _only_ one that can be
employed by or seen in student conceptual development.

The point here is not whether some line of reasoning makes sense to us.
Instead, the point is whether it is a path that makes sense to the
students, people who have not already constructed these understandings;
that they might actually 'follow.'

As an example of the discrepancy between what is written as an explanation
and the path taken to the ideas, I would point out that Newton was familiar
with what is now sometimes called a Newtonian pendulum, specifically the
multiple pendulum with the spheres hanging so that they are in contact with
each other. Newton refers to it as evidence in the scholium supporting N3.
I believe that he had considered this (as evidenced from his notebooks)
even while he was 'home from the plague.' Hence, one might conclude that
this is where Newton got his understanding and inspiration for N3. But...
Cohen in about April of 1981 published an article in Scientific American in
which he illustrates through letters and tracts Newton produced just a year
or so before the publication of the Principia that Newton was still working
out the significance of N3 in explaining planetary orbits at that time,
years after he was 'home from the plague.' Yet, I believe that you will
not find that Newton points to this particular significance of N3 when he
is justifying it in that scholium, early in the Principia. Hence, I would
maintain that he did not, in his own explanation, illustrate the path by
which he 'arrived at' his understanding of N3.

Dewey

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Dewey I. Dykstra, Jr. Phone: (208)385-3105
Professor of Physics Dept: (208)385-3775
Department of Physics/SN318 Fax: (208)385-4330
Boise State University dykstrad@varney.idbsu.edu
1910 University Drive Boise Highlanders
Boise, ID 83725-1570 novice piper
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