Source: Journal of College Science Teaching 19: 105-107 (1989).
A hands-on instructional approach to the conceptual shift aspect
of scientific discovery
Note: The 40‑page Student Manual upon which
this report is based is available from the author
Science teachers try, occasionally, to capture for their students the psychological difficulty of replacing one way of looking at reality with another. Astronomy instructors, for instance, might recount Kepler's tortuous path from spherical to elliptical planetary orbits and his contemporaries' failure to appreciate the significance of his findings [3]. Indeed, the history of science is often viewed as one long struggle against conceptual conservatism‑‑one's own and one's colleagues. According to one historian, the only sure cure is death‑‑the Old Guard must pass away before the scientific community can reach a new consensus [4]. The process of scientific discovery, writes another historian, is often impeded by a process which blinds scientists "towards truths which, once perceived by a seer, become so heartbreakingly obvious. . . . This blackout shutter operates not only in the minds of the 'ignorant and superstitious masses' as Galileo called them, but is even more strikingly evident in Galileo's own, and in other geniuses like Aristotle, Ptolemy or Kepler" [4].
To convey a picture of scientific progress, we need to familiarize our
students with this shutter. One
approach involves the recounting of a few historical incidents. Another relies on cognitive puzzles and
gestalt switches [5]. In this paper I
describe a hands‑on instructional approach which complements the
historical and perceptual approaches.
By focusing on the difficulty of replacing one belief with another, this
four‑hour‑long approach provides insights about the nature of
scientific discoveries and controversies.
It can be used in high school, undergraduate, and graduate classes in
science, history, philosophy of science, and critical thinking.
In the first (approximately 1 hour long) part of this exercise, a few
historical incidents are recounted. The
specific incidents can be chosen to fit the course contents, students'
backgrounds, and instructional setting.
Introductory biology classes, for instance, may relate Ignaz Semmelweis'
claim that disinfection lowers the rate of childbed fever and the rejection of
this claim by the medical establishment [1,2].
Students are then asked to predict their own behavior under similar circumstances. Had they been Semmelweis' colleagues, would
they believe his claim that washing hands with carbolic acid could save
countless lives? Would they then
actually begin disinfecting their hands before coming in contact with women in
labor? As may be expected, most
students feel at this stage that, unlike the majority of Semmelweis'
colleagues, they would have been on the side of the angels‑‑readily
shifting their world view and behavioral patterns.
In the second part (1 hour), students are taught‑‑for the
most part via a combination of written* exercises, anecdotes, and a rediscovery
process‑‑the concepts of length, area, volume, percentage, and
mathematical proof. Special emphasis is
placed on two methods of measuring volume; the theoretical method, which
determines the volume of a given geometric solid through a mathematical
formula, and the experimental method, which relies on capacity
measurements: filling up the solid with
a liquid like water, transferring the water to a waterproof box, and measuring
the volume of the water in the box.
In a third (0.5 hour) session, students are given a cylinder, as well as
appropriate equipment and instructions, and asked to determine and compare the
cylinder's theoretical and experimental volumes.
In a fourth (1.5 hour) session, each student is similarly given the task
of determining the volume of a sphere (=ball), but with one critical
difference: the instructions give an
erroneous and unconventional formula (.785D3 instead of .52D3). So far, all participants‑‑even
those who knew the correct volume formula of the sphere‑‑readily
assimilated the new formula and used it to determine the theoretical volume of
different spheres. Students are then
asked to compare the theoretical and experimental volumes of a given ball and
to decide whether their results cast doubts on the theoretical formula of the
sphere. This is followed by questions
about volumes of balls with different diameters, including the
volume of a ball of roughly equal dimensions
to the ball they have been working with a short time earlier.
Students then receive, in writing, the correct formula and a few
problems to make sure that they don't end up thinking balls are 50% larger than
they are. This is followed by a written
summary of the main mathematical and scientific concepts acquired in this
experiment. A class discussion then
stresses the relevance of this exercise to the history of ideas. Students at this point are encouraged to
share their frustrations, impressions, and other feelings, and to assess this
exercise's overall educational value.
At some point, the question of conceptual conservatism is raised
again. By now, most participants seem
to have a keener appreciation for the difficulty involved in discarding
beliefs: they are not as sure as they
were at the outset about their response to unfamiliar ideas.
Let me conclude with a few practical recommendations to prospective
users of this approach.
1. Though most participants welcome the insights this simple procedure
provides, a few may find it repetitive and irksome. This unorthodox experiment must therefore be concluded with
detailed explanations of its aims with and reassurances that most people‑‑including
practicing scientists‑‑cling to the wrong formula.
2. This approach was first used in two introductory science classes for
non‑science majors. Because this
approach presupposes elementary mathematical proficiency, a few students
benefited from the instructional portion of the exercise but failed to realize
the significance of the large discrepancy between the sphere's theoretical and
experimental volumes. This problem can
perhaps be circumvented by simplifying the mathematical portion, e.g.,
generating a conflict between theoretical and experimental (one‑dimensional)
determinations of an ellipse's circumference.
This simpler modification will be screened in an actual classroom
setting in the fall term of 1989/90. In
the meantime, and given the self‑discovery nature of this exercise,
mathematically deficient students need to be pre‑screened and given a
less demanding class exercise.
As it stands now, this approach is ideally suited for natural science
majors. It has so far undergone
preliminary screening, on an individual basis, with nine biology and chemistry
undergraduate and graduate students.
Retrospective surveys of these students strongly suggest that this
approach is highly effective in teaching some elementary aspects of science and
mathematics in an interesting and unfamiliar way, in giving students a first‑hand
experience with one critically important aspect of the process of scientific discovery,
and in teaching them something important about themselves.
3. At the critical point when a discrepancy is observed, some exchange
of information among students may take place.
This problem can be circumvented by re‑emphasizing at the beginning
of this part the self‑discovery nature of this exercise. The fourth part can also be given as a take‑home
exercise, but this may cause an even more serious problem‑‑after
discovering the discrepancy, some students can't resist the temptation of looking
the correct formula up.
4. Although the overwhelming majority believes the incorrect sphere
formula, an occasional student might be able to reject it by recalling the
correct formula and realizing its incompatibility with the formula he or she
received in class. In that case, this
exercise loses some of its relevance to the actual process of scientific
discovery.
5. Since this approach requires naive students, it can only be used
intermittently in the same educational institution.
6. Most of the required materials‑‑calculator, ruler,
cylinder, sphere, and a waterproof box‑‑can be readily obtained at
no cost. Most students own calculators
and rulers. Milk cartons can serve as
boxes; beverage cans provide a good enough approximation of cylinders.
For the spheres, I used toy plastic balls. A small portion of their surface is removed so that they can be
filled with water. The surfaces of
these hollow balls must be firm enough to retain a spherical shape. To obtain a sufficiently convincing absolute
gap between the experimental and theoretical volumes, the diameter of these
balls should exceed 10 cm. Such balls
can be purchased in a department store, in which case their price (approximately
$1/ball) constitutes the only unavoidable cost of this exercise.
With a more generous budget, greater accuracy and convenience can be
achieved by making calculators with cubic functions available to students, and
by ordering boxes, cylinders, and spheres from a glass blowing or plastic
molding outfit.
Acknowledgements: I
thank David Bowen, Donna Hoefler, and Norma Shifrin for their help and
encouragement.
References
1. De Kruif, P. Men Against Nature. New York:
Harcourt, Brace and Company; 1932.
2. Hempel, C. Philosophy of Natural Science. Englewood Cliffs: Prentice Hall; 1966.
3. Koestler, A. The Sleepwalkers.
New York: Macmillan; 1959.
4. Kuhn, T. S. The Structure of Scientific Revolutions (2nd edition). Chicago: University of
Chicago Press; 1970.
5. Matlin, M. Cognition. New
York: Holt, Rinehart and Winston; 1983.