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Re: position vs displacement



John Clement wrote:

Also make no mistake about this. 30% of the general population is concrete
operational and only 30% is formal operational. You are getting students
below the formal operationl level coming into colleges and universities,
especially considering that only 20% of HS graduates are at the formal
operational level. (in Great Britain, I do not have stats for the US).
Position relativity can be a big issue. It is not just for elementary ed.

John M. Clement
Houston, TX


According to my recollection, this matter was discussed or referred to
in connection with the Workshop on Physics and the Development of
Reasoning led by Robert Karplus that I attended in 1976. I recall that
Arnold Arons had commented on it in journal articles. A web search led
to a letter to the AJP editor by Arnold B. Arons and Robert Karplus,
"Implications of Accumulating Data on Levels of Intellectual
Development,"
<http://physics.unl.edu/~rpeg/perc98/PERCpdfs/c_Appendices/appCAronsAndKarplus.PDF>.
Among the references listed in this letter is McKinnon, J. W. & Renner,
J.W. (1971), "Are colleges concerned with intellectual development?"
American Journal of Physics, 39, 1047, the title of which I found on a
UNL ADAPT web page by Robert Fuller, who was one of the leaders at the
Workshop in 1976 <http://physics.unl.edu/~rpeg/ADAPT.html>. I couldn't
find the McKinnon and Renner paper online, but another paper at
<http://www.eiu.edu/~scienced/5660/gotta/G-3-R-1b.html> by Constance
Kamee cites this paper, stating that McKinnon and Renner "found only 25%
of them [college freshmen] were capable of solid logical thinking at the
formal level." This is the result that I remember. I think it was
obtained in the US. Kamee also states that Schwebel found a figure of
20%, but it does not specify the population tested (at least in the part
of her article quoted.) I don't know Schwebel's location.

Hugh Logan
Flagler Beach, FL
[Still looking out for hurricane Frances and hoping to get this off
before the power goes out.]




John Clement wrote:



Pedagogical remark: The idea of relativity of position is obvious
to us. It's not a big surprise or a burden on students, but it
needs to be discussed explicitly. It gets short shrift in a lot
of texts.




Actually relativity in position is often a big surprise to students, and
when discussed explicitly they often will still not understand it. This


is


true especially of students with thinking skills below the formal
operational level. It requires a lot more than mere talking at them


about


it.




Many years ago, I saw a newspaper article that stated that elementary
school children were being taught
relativity. I think they were referring to Robert Karplus's SCIS program
for elementary science, which was based on Piaget's cognitive theory and
learning cycles. The relativity was most likely relativity of
position. I recall that SCIS utilized a polar coordinate frame to be
made on a plywood platform. It might have disappointed parents expecting
their children to be budding Einsteins, but it might have helped
students with thinking skills below the formal operational level that
John refers to.

Hugh Logan