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 (.785D^{3}
instead of .52D^{3}). 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.