Qualitative versus quantitative thinking: are we teaching the
right thing?
Eric Mazur
Gordon McKay
professor of Applied Physics and Professor of Physics
Harvard
University
For the past
eight years I have been teaching an introductory physics course for engineering
and science concentrators at Harvard University. Teaching this class, which
does not include any physics majors, is a challenging experience because the
students take this course as a concentration requirement, not because of a
genuine interest in physics. At the same time it can be a very rewarding
experience when, at the end of the semester, students show much more
appreciation for the subject matter.
I used to
teach a fairly traditional course in an equally “traditional lecture” type of
presentation, enlivened by classroom demonstrations. I was generally satisfied
with my teaching during these years --- my students did well on what I
considered pretty difficult problems and the feedback I received from them was
positive.
About a year
ago, however, I came across a series of articles by David Hestenes of Arizona
State University[1], which
completely and permanently changed my views on teaching. In these articles
Hestenes shows that students enter their first physics course possessing strong
beliefs and intuitions about common physical phenomena. These notions are
derived from personal experiences, and colour students' interpretations of
material presented in the introductory course. Instruction does very little to
change these ‘commonsense' beliefs.
For example,
after a couple of months of physics instruction, all students will be able to
recite Newton's third law --- `action is reaction' --- and most of them can
apply this law in problems. But a little probing beneath the surface quickly
shows that the students lack any fundamental understanding of this law.
Hestenes provides many examples in which the students are asked to compare the
forces of different objects on one another.
When asked, for instance, to compare the forces in a collision between a
heavy truck and a light car, a large fraction of the class firmly believes the
heavy truck exerts a larger force on the light car than vice versa. My first
reaction wass `Not my students...'! I was intrigued, however, and to test my
own students' conceptual understanding, I developed a computer program based on
the tests developed by Hestenes.
The first
warning came when I gave the test to my class and a student asked `Professor
Mazur, how should I answer these questions? According what you taught us, or by
the way I think about these things?' While baffled, I did not get the message
quite yet. The results of the test, however, where undeniably eye-opening: the
students fared hardly better on the Hestenes test than on their midterm
examination on rotational dynamics. Yet, I think the Hestenes test is simple
--- yes, probably too simple to be considered seriously for a test by many of
my colleagues --- while the material covered by the examination (rotational
dynamics, moments of inertia) was, in my opinion, of far greater difficulty.
I spent
many, many hours discussing the results of this test with my students
one-on-one. The old feeling of satisfaction turned more and more into a feeling
of sadness and frustration. How could these undoubtedly bright students,
capable of solving complicated problems, fail on these ostensibly `simple'
questions?
On the
following examinations I paired `simple,' qualitative questions with more
`difficult,' quantitative problems on the same physical concept. Much to my
surprise some 40% of the students did better on the quantitative problems than
on the conceptual ones. Slowly the underlying problem revealed itself: many
students concentrate on learning `recipes', or `problem solving strategies' as
they are called in textbooks, without bothering to be attentive to the
underlying concepts. Many pieces of
the puzzle
suddenly fell into place. The continuing requests by students to do more and
more problems and less and less lecturing --- doesn't the traditional lecture
overemphasize problemsolving over conceptual understanding? The unexplained
blunders I
had seen from apparently `bright' students --- problemsolving strategies work
on some, but surely not all problems. Students' frustration[2]
with physics --- how boring must physics be when it is reduced to a set of
mechanical recipes without any apparent logic. And yes, Newton's third law is
second nature to me --- it's obviously right, but how do I convince my
students? Certainly not by just reciting the law and then blindly using it in
problems...
Just a year
ago, I was entirely oblivious to this problem. I now wonder how I could be
fooled into thinking I did a credible job teaching introductory. While several
leading physicists have written on this problem[3],
I believe most instructors are still unaware of it. A first step in remedying
this situation is to expose the problem in one's own class. The key, I believe,
is to ask simple questions that focus on single concepts. The result is
guaranteed to be an eye-opener even for seasoned teachers.
This paper
was published in Optics and Photonics News, 3 (1992) 38, and is made
available as an electronic reprint with the permission of OSA. One print
or electronic copy may be made for personal use only. Systematic or
multiple reproduction, distribution to multiple locations via electronic or
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purposes, or modification of the content of the paper are prohibited.
Copyright OSA (http://www.osa.org/pubs/osajournals.org)
[1] Ibrahim Abou Halloun and David Hestenes, Am. J. Phys, 53, 1043 (1985); ibid. 53, 1056 (1985); ibid. 55, 455 (1987); Hestenes, David, Am. J. Phys, 55, 440 (1987)
[2] Sheila Tobias, They're Not Dumb, They're Different, Research Corporation: Tuscon, AZ (1990)
[3] See
for example: Arnold Arons, A Guide to Introductory Physics Teaching,
John Wiley & Sons: New York, NY (1990); Richard P. Feynman, The Feynman
Lectures, Vol. 1, (Addison Wesley, New York, N.Y., 1989) p. 11; Ken
Wilson, Phys. Today 44:9 (1991) p. 7173.