Abstract
A characterization of the modelling process in science is proposed for science education, based on Mario Bunge’s ideas about the construction of models in science. Galileo’s Dialogues are analysed as a potentially fruitful starting point to implement strategies aimed at modelling in the classroom in the light of that proposal. It is argued that a modelling process for science education can be conceived as the evolution from phenomenological approaches towards more representational ones, emphasizing the role of abstraction and idealization in model construction. The shift of reference of theories—from sensible objects to conceptual objects—and the black-box models construction process, which are both explicitly presented features in Galileo’s Dialogues, are indicated as highly relevant aspects for modelling in science education.
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Notes
McMullin did not claim that Galileo invented all of them; instead, he tried to emphasize that all of them played a significant role in the development of the new science advocated by Galileo (McMullin 1985).
This line of reasoning, based on representing physical variables using geometrical objects, can be found in Galileo since his earlier studies about pendulums, as in the work On Motion (1590) and the letters he exchanged with his patron Guidobaldo del Monte (1545–1607).
"Suspend three balls of lead, or other heavy material, by means of different lengths such that while the longest makes two vibrations the shortest will make four and the medium three; this will take place when the longest string measures 16, either in hand breadths or in any other unit, the medium 9 and the shortest 4, all measured in the same unit. Now pull all these pendulums aside from the perpendicular and release them at the same instant; you will see a curious interplay of the threads passing each other in various manners but such that at the completion of every fourth vibration of the longest pendulum, all three will arrive simultaneously at the same terminus, whence they start over again to repeat the same cycle". (Crew and de Salvio 1914, p. 107).
"Accordingly I took two balls, one of lead and one of cork, the former more than a hundred times heavier than the latter, and suspended them by means of two equal fine threads […] the heavy body maintains so nearly the period of the light body that neither in a hundred swings nor even a thousand will the former anticipate the latter by as much as a single moment, so perfectly do they keep step". (Crew and de Salvio 1914, p. 84).
"Attach two threads of equal lenght—say 4 or 5 yards—two equal leaden balls and suspend them from the ceiling; now pull them aside from the perpendicular, the ont through 80 or more degrees, the other not more than four or five degrees […] if two persons start to count the vibrations, one the large, the other the small, they will discover that after counting tens and even hundreds they will not differ by a single vibration, not even by a fraction of one". (Crew and de Salvio 1914, pp. 254–255). It should be noted that, in the situation described here, it would be easy to verify that the two pendula would desynchronize very rapidly, since the pendulum period increases with amplitude. Only for small amplitudes the period is independent of the initial angular displacement: it is an approximation. As he refers to 80 degrees or more, Galileo most likely never did this experiment, even though he presents it as an experimental result. This indicates that even to develop black-box models, which are considered the more superficial and closer related to experimental evidence, the epistemic subjects' theoretical commitments still play a very significant role. By the same token, in actual modelling practices, including educational ones, what subjects consider to be observational facts tend to be influenced by their own expectations and conceptions.
"Theorem II, Proposition II: The spaces described by a body falling from rest with a uniformly accelerated motion are to each other as the squares of the time-intervals employed in traversing these distances" (Crew and de Salvio 1914, p.174).
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Machado, J., Braga, M.A.B. Can the History of Science Contribute to Modelling in Physics Teaching?. Sci & Educ 25, 823–836 (2016). https://doi.org/10.1007/s11191-016-9844-4
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DOI: https://doi.org/10.1007/s11191-016-9844-4