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.








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. 

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