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Calculating and Understanding: Formal Models and Causal Explanations in Science, Common Reasoning and Physics Teaching

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Abstract

This paper presents an analysis of the different types of reasoning and physical explanation used in science, common thought, and physics teaching. It then reflects on the learning difficulties connected with these various approaches, and suggests some possible didactic strategies. Although causal reasoning occurs very frequently in common thought and daily life, it has long been the subject of debate and criticism among philosophers and scientists. In this paper, I begin by providing a description of some general tendencies of common reasoning that have been identified by didactic research. Thereafter, I briefly discuss the role of causality in science, as well as some different types of explanation employed in the field of physics. I then present some results of a study examining the causal reasoning used by students in solid and fluid mechanics. The differences found between the types of reasoning typical of common thought and those usually proposed during instruction can create learning difficulties and impede student motivation. Many students do not seem satisfied by the mere application of formal laws and functional relations. Instead, they express the need for a causal explanation, a mechanism that allows them to understand how a state of affairs has come about. I discuss few didactic strategies aimed at overcoming these problems, and describe, in general terms, two examples of mechanics teaching sequences which were developed and tested in different contexts. The paper ends with a reflection on the possible role to be played in physics learning by intuitive and imaginative thought, and the use of simple explanatory models based on physical analogies and causal mechanisms.

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Notes

  1. A. Comte (1830) Cours de philosophie positive, Paris, Rouen Frères, Tome 2, 28e leçon, pp. 435–436 e 454. “Tous les bons esprits reconnaissent aujourd’hui que nos études réelles sont strictement circonscrites à l’analyse des phénomènes pour découvrir leurs lois effectives, c’est-à-dire leurs relations constantes de succession et de similitude, et ne peuvent nullement concerner leur nature intime, ni leur cause, ou première ou finale, ni leur mode essentiel de production. … Toute hypothèse scientifique, afin d’être réellement jugeable, doit exclusivement porter sur les lois des phénomènes, et jamais sur leurs modes de production.”

  2. However, in the same paper, Heisenberg uses expressions that clearly indicate a causal connection, even if in the presence of a certain indeterminacy of some dynamic quantities. Referring to the Compton or photoelectric effect, he writes: “When a light quantum that hits an electron is reflected or diffracted from it and then, again refracted through the microscope, it provokes the photoelectric effect"; and "Of such light a single quantum is enough to hurl the electron outside of its orbit”. It seems to me that some physicists tend to generalize in a hurried and exaggerated way. Starting with some results of quantum physics that are in contrast with some characteristics of causality for some situations, they arrive at general philosophical conclusions.

  3. “Realism is… A doctrine according to which being is independent of the knowledge that conscious subjects may have of it at a given time: esse is not equivalent to percepi. Idealists hold that the intellect knows only its own states: see the commentaries on contemporary physics, which deny the existence of any given external to our representations (to measurements made by observers). Realism and idealism are opposed term for term, each asserting what the other denies. The first posits that thought is inside the being; the second posits that the being is contained in thought” (Largeault J. “Réalisme”, Encyclopaedia Universalis 8, 2002).

  4. It is possible to compare these three types of physical explanation to three of the four kinds of causes indicated by Aristotle (350 B.C.). The efficient cause, "the causes whence the principle of change occurs, all that acts". The material and formal causes, “the causes out of which, of these some as substrate [material], others as concept [formal] e.g., "the letters of syllables, the material of man-made objects, fire and other elements of bodies, the parts of the whole, and the premises of the conclusion.” Aristotle speaks also about reciprocal causes, which act "as fatigue causes vigor and vigor, fatigue". In Physics, book II (B), 3.

  5. Here it seems me that the author commits a rather common error in the interpretation of the laws of co-existence (or formal laws). An equation of the type pV = nRT represents a relationship at a given time between the indicated quantities for an ideal gas in a state of equilibrium. However, the author thinks that the equation further asserts that if at a given time the pressure varies in a region of the gas, at the same time the temperature and/or density will vary so as to maintain the relationship continuously valid. To the contrary, this is not in fact the case. The law establishes a relationship between quantities for a state of equilibrium. If something changes in a part of the gas, the gas is no longer in equilibrium; therefore the equation is no longer applicable. It only says to us that if and when a state of equilibrium is re-established, the indicated quantities will assume the values necessary to satisfy the equation once again. The passage from the initial to the second equilibrium state happens in a finite time and as a result of local interaction processes in the situation of non-equilibrium. The same reasoning holds good for Coulomb’s theorem of electrostatics E = σ/ε, to which the author also makes reference.

  6. This fact is reflected by the various other names attached to this view, e.g. “semantic view” (in contrast to the linguistic-syntactic approach of the statement view), “non-statement view”, “model-theoretic view”, “structuralist” (see Develaki 2007; Grandy 2003).

  7. For example, a special issue of the journal Science & Education was recently devoted to this subject: Science & Education (2007), 16 (7–8): 647–881, Special issue: Models in Science and in Science Education.

  8. It could be objected that the question is a trap question, because of an abrupt change of explanatory level, passing from a macroscopic and phenomenological description to one microscopic which refers to fundamental theories. However, short talks, focusing on the contact interaction between water and ear, had been sufficient for the teachers who answered the question to understand their error. This confirms that it was a customary and automatic reasoning scheme and logical short circuit, therefore really representing a spontaneous tendency of thought.

  9. See for example the books Matthews (1994) and McComas (1998). The journal Science & Education published many articles on these themes, as an example a recent issue is dedicated to the teaching of "nature of science" (2008, Vol. 17, n. 2–3, Special Issue: Teaching and Assessing the Nature of Science). In USA, the National Science Education Standards (http://www.nap.edu/readingroom/books/nses/overview.html) and the Standard for Science Teachers Preparation (http://www.nsta.org/pdfs/NSTAstandards2003.pdf and http://www.msu.edu/~dugganha/NOS.htm), include a section dedicated to “Nature of Science”.

  10. This is not always what happens. For example Guilbert and Meloche (1993), hold that many teachers have what they term an “empiricist-realist” conception of science. This supposedly ingenuous, antiquated view involves, among other things, the myth of the progressive construction of knowledge, and the idea that science concerns the description of the world as it really is: "it seems, according to some students, that it is even possible to distinguish the true from the false". Against this conception, these authors counter that students should be led to a subtle, modern constructivist model, according to which theories are merely speculative constructions allowing a more systematic collection of observations, and reality does not exist independently of us. It is odd that precisely the authors who support instrumentalist and relativist conceptions, and who maintain that true or false, better or worse theories do not exist (each one with its own field of validity and effectiveness, depending on context and aims), at the same time introduce their own conception as the proper and correct epistemological model, and contrast it to others denigrated as ingenuous and antiquated. If no scientific theory is better than the others and there is no truth to discover, then to be consistent, epistemological theories as well would have to be considered all at the same level, with no one better than others.

  11. I. Newton, Philosophiae Naturalis Principia Mathematica, book I, section I, especially the final Scholium. The adjective "vanishing" and the verb “to vanish” (evanescens—evanescentes and evanescere, in Latin) are also attributed by Newton to parallelograms, angles, segments, arches, triangles (cf. Lemmas III, VI, VII, VIII, XI etc.).

  12. Anaxagoras, Greek philosopher (500–428 B.C.): “In his treatise On Nature, he explains the origin of bodies without positing elements like water, fire, etc., but by means of homeomeries (a term introduced by Aristotle): material particles that join together in order to form the bodies but which, in contrast to atoms, have the same qualities as the bodies that they constitute” (Durozoi G. & Roussel A. Dictionnaire de Philosophie, Paris, Nathan, 1997, pp. 19–20).

  13. Arons (1990, p. 64) thinks that “Students need explicit help and guidance in learning to visualize effects that elude direct sense perception. The deformation of apparently rigid objects in the context now under consideration is usually the first opportunity in a physics course, and its importance should not be underestimated. Later, such visualization is essential to understanding what happens…” in many physical situations.

  14. Duhem develops many examples to demonstrate that the first typology supposedly prevails among the French (and Germans), and the second among the English (apart from Napoleon, who is classified among the second category). In particular, he strongly criticises the exaggerated details of mechanical models elaborated in that period to explain electric phenomena: “the theory of electrostatics constitutes a set of abstract notions and general statements, expressed in the clear and precise language of geometry and algebra, connected by the rules of a strict logic … this set totally satisfies the thought of a French physicist… It is not the same for an Englishman; these abstract notions do not satisfy his need to imagine concrete, material, visible things… It is in order to satisfy this need that he creates a model… The use of similar models… is a constant in English physics; some make only a moderate use of these models, others appeal to them at each step. Here is a book that aims to expound modern theories of electricity; we find only ropes that move on pulleys… tubes that pump water… cog-wheels that mesh into one on another; we thought we were entering into the calm and ordered realm of the deductive reason, and we find ourselves in a workshop.” The book to which Duhem refers, published in French translation in 1891, was obviously of an Englishman, O. Lodge.

  15. The distinction must be considered more operational and didactic (intuitive?) than psychological and theoretical, because a rigorous distinction between intuitive and analytical knowledge presents many difficulties and “it is not even clear what we mean by intuitive knowledge” (Bruner 1963). In the same book, Bruner gives a short definition of intuition: 'the intellectual technique of arriving to plausible but tentative formulations without going through the analytical steps by which such formulations would be found to be valid or invalid conclusions'.

References

  • Aitken, F., & Tobazéor, R. (1998). Une histoire de pression: la compressibilité des liquides. Bulletin de la S.F.P., 114, 4–9.

    Google Scholar 

  • Andersson, B. (1986). The experiential Gestalt of causation: A common core to pupils’ preconceptions in science. European Journal of Science Education, 8(3), 155–171.

    Google Scholar 

  • Aristotle. (350 B.C). Physics. An English translation can be found in R.P. Hardie and R.K. Gaye, The Internet Classics Archive, http://classics.mit.edu//Aristotle/physics.html by D.C. Stevenson, Web Atomics, 1994–2000.

  • Arons, A. B. (1990). A guide to introductory physics teaching. New York, NY: Wiley.

    Google Scholar 

  • Bachelard, G. (1934). Le nouvel esprit scientifique. Paris: PUF.

    Google Scholar 

  • Bachelard, G. (1949). Le rationalisme appliqué. Paris: PUF.

    Google Scholar 

  • Benzi, M. (2003). Scoprire le cause. Milano: Franco Angeli.

    Google Scholar 

  • Besson, U. (2004a). Students' conceptions of fluids. International Journal of Science Education, 26(14), 1683–1714.

    Google Scholar 

  • Besson, U. (2004b). Some features of causal reasoning: Common sense and physics teaching. Research in Science & Technological Education, 22(1), 113–125.

    Google Scholar 

  • Besson, U., & Viennot, L. (2003). Pressure in fluids in the presence of gravity. In L. Viennot, Teaching physics (chap. 3). Dordrecht: Kluwer Academic Publishers.

  • Besson, U., & Viennot, L. (2004). Using models at the mesoscopic scale in teaching physics: Two experimental interventions in solid friction and fluid statics. International Journal of Science Education, 26(9), 1083–1110.

    Google Scholar 

  • Besson, U., Borghi, L., De Ambrosis, A., & Mascheretti, P. (2007). How to teach friction: Experiments and models. American Journal of Physics, 75(12), 1106–1113.

    Google Scholar 

  • Besson, U., Borghi, L., De Ambrosis, A., & Mascheretti, P. (2009). A three-dimensional approach and open source structure for the design and experimentation of teaching learning sequences: The case of friction. International Journal of Science Education (in press).

  • Bowden F. P., & Tabor, D. (1950–1964). Friction and lubrication of solids (Vols. 1–2). Oxford University Press.

  • Brecht, B. (1970). Ecrits sur la politique et la société. Paris: L’Arche.

  • Bridgman, P. W. (1958). The physics of high pressure. London: G. Bell and Sons, Ltd.

    Google Scholar 

  • Brown, D. E. (1992). Using examples and analogies to remediate misconceptions in physics: Factors influencing conceptual change. Journal of Research in Science Teaching, 29, 17–34.

    Article  Google Scholar 

  • Bruner, J. (1963). The process of education. Cambridge, MA: Harvard University Press.

    Google Scholar 

  • Bunge, M. (1959). Causality. The place of the casual principle in modern science. Cambridge, MA: Harvard University Press.

    Google Scholar 

  • Bunge, M. (2003). Twenty-five centuries of quantum physics: From Pythagoras to us, and from subjectivism to realism. Sci & Educ, 12, 445–466.

    Article  Google Scholar 

  • Caldas, H. (1999). Atrito. O que diz a Fisíca, o que os alunos pensam e o que os livros explicam. Vitória-ES, Brazil: Editora da Universidade Federal do Espírito Santo.

    Google Scholar 

  • Caldas, H., & Saltiel, E. (1995). Le frottement cinétique : analyse des raisonnements des étudiants. Didaskalia, 6, 55–71.

    Google Scholar 

  • Chabay, R. W., & Sherwood, B. A. (1999). Bringing atoms into first-year physics. American Journal of Physics, 67(12), 1045–1050.

    Article  Google Scholar 

  • Chevallard, Y. (1991). La transposition didactique. Grenoble, FR: La Pensée Sauvage.

    Google Scholar 

  • Clement, J., Brown, D., & Zietsman, A. (1989). Not all preconceptions are misconceptions: Finding “anchoring conceptions” for grounding instruction on students’ intuitions. International Journal of Science Education, 11(5), 554–565.

    Article  Google Scholar 

  • Develaki, M. (2007). The model-based view of scientific theories and the structuring of school science programmes. Sci & Educ, 16(7–8), 725–749.

    Article  Google Scholar 

  • DiSessa, A. A. (1983). Phenomenology and the evolution of intuition. In D. Gentner & A. L. Stevens (Eds.), Mental models. Hillsdale, New Jersey: Lawrence Erlbaum.

    Google Scholar 

  • Dorato, M. (2000). Il software dell’universo. Milano: Bruno Mondadori.

    Google Scholar 

  • Driver, R., Guesne, E., & Tiberghien, A. (Eds.). (1985). Children’s ideas in science. Philadelphia: Open University Press.

    Google Scholar 

  • Duhem, P. (1906–1914). La théorie physique, son objet, sa structure. Reprint: 1981, Vrin, Paris.

  • Duhem, P. (1908). Sozein ta phainomena. Essai sur la notion de théorie physique de Platon à Galilée, Hermann, Paris. Reprint: 1990, Vrin, Paris.

  • Duit, R. (1991). On the role of analogies and metaphors in learning science. Sci Educ, 75(6), 649–672.

    Article  Google Scholar 

  • Duit, R., & Glynn, S. (1996). Mental modelling. In G. Welford, J. Osborne, & P. Scott (Eds.), Research in science education in Europe, current issues and themes (pp. 166–176). London: The Falmer Press.

    Google Scholar 

  • Dumont, B. (1985). L’influence du langage et du contexte dans des épreuves de type “logique”, Thèse de doctorat, Université Paris VII.

  • Gadda, C. E. (1974). Meditazione milanese.. Torino: Einaudi.

  • Gilbert, J. K., & Boulter, C. (1998). Learning science through models and modelling. In B. J. Fraser & K. G. Tobin (Eds.), International handbook of science education (pp. 53–66). Dordrecht: Kluwer Academic Publisher.

    Google Scholar 

  • Giuliani, G. (1998). What physicists are talking about? Il Nuovo Cimento, 20D, 1183–1186.

  • Giuliani, G. (2007). On realism and quantum mechanics. Il Nuovo Cimento, 122B, 267–276.

    Google Scholar 

  • Grandy, R. E. (2003). What are models and why do we need them? Sci & Educ, 12, 773–777.

    Article  Google Scholar 

  • Grandy, R. E., & Dushl, R. A. (2007). Reconsidering the character and role of inquiry in school science: Analysis of a conference. Sci & Educ, 16(2), 141–166.

    Article  Google Scholar 

  • Guilbert, L., & Meloche, D. (1993). L’idée de science chez des enseignants en formation : un lien entre l’histoire des sciences et l’hétérogénéité des visions ? Didaskalia, 2, 7–30.

    Google Scholar 

  • Gutierrez, R., & Ogborn, J. (1992). A causal framework for analysing alternative conceptions. International Journal of Science Education, 14(2), 201–220.

    Article  Google Scholar 

  • Gutwill, J., Frederiksen, J., & Ranney, M. (1996). Seeking the casual connection in electricity: Shifting among mechanistic perspectives. International Journal of Science Education, 18(2), 143–162.

    Article  Google Scholar 

  • Halbwachs, F. (1971). Réflexions sur la causalité physique. Causalité linéaire et causalité circulaire en physique. In M. Bunge, et al. (Eds.), Les théories de la causalité. Paris: PUF.

    Google Scholar 

  • Halloun, I. A. (2007). Mediated modeling in science education. Sci & Educ, 16(7–8), 653–697.

    Article  Google Scholar 

  • Hammer, D. (2000). Student resources for learning introductory physics. American Journal of Physics, 68(7), S52–S59.

    Article  Google Scholar 

  • Harré, R. (1972). The philosophies of science. Oxford: Oxford University Press.

    Google Scholar 

  • Heisenberg, W. (1927). Über den anschaulichen Inhalt der quantentheoretischen Kinematik und Mechanik. Zeitschrift für Physik, 43(3–4), 172–198.

    Article  Google Scholar 

  • Hempel, C. (1965). Aspects of scientific explanation and other essays in the philosophy of science. New York: The Free Press.

    Google Scholar 

  • Hestenes, D. (1987). Toward a modeling theory of physics instruction. American Journal of Physics, 55(5), 440–454.

    Article  Google Scholar 

  • Hestenes, D. (1992). Modeling games in the newtonian world. American Journal of Physics, 60, 732–748.

    Article  Google Scholar 

  • Jefimenko, O. D. (2004). Presenting electromagnetic theory in accordance with the principle of causality. European Journal of Physics, 25, 287–296.

    Article  Google Scholar 

  • Koponen, I. T. (2007). Models and modelling in physics education: A critical re-analysis of philosophical underpinnings and suggestions for revisions. Sci & Educ, 16(7–8), 751–773.

    Article  Google Scholar 

  • Laudisa, F. (2005). La causalità in fisica. In V. Allori, M. Dorato, F. Laudisa, & N. Zanghì (Eds.), La Natura delle cose (pp. 395–428). Roma: Carocci.

    Google Scholar 

  • Mach, E. (1883). Die Mechanik in ihrer Entwickelung historisch-kritisch dargestellt. Leipzig: Brockhaus.

    Google Scholar 

  • Matthews, M. R. (1994). Science teaching. The role of history and philosophy of science. New York: Routledge.

  • Matthews, M. R. (2007). Models in science and in science education: An introduction. Sci & Educ, 16(7–8), 647–652.

    Article  Google Scholar 

  • Maxwell, J. C. (1856). On Faraday’s lines of force. In The scientific papers of James Clerk Maxwell (Vol. 1). Cambridge University Press, 1890.

  • McComas, W. F. (1998). The nature of science in science education: Rationales and strategies. Dordrecht: Kluwer Academic Publishers.

  • Menzies, P., & Price, H. (1993). Causation as a secondary quality. British Journal for the Philosophy of Science, 44, 187–203.

    Article  Google Scholar 

  • Norman, D. A. (1983). Some observations on mental models. In D. Gentner & A. L. Stevens (Eds.), Mental models (pp. 7–14). Lawrence Erlbaum, Hillsdale: NJ.

    Google Scholar 

  • Ogborn, J. (1993). Approche théorique et empirique de la causalité. Didaskalia, 1, 29–47.

    Google Scholar 

  • Persson, B. N. J. (1998). Sliding friction. Physical principles and applications. Berlin: Springer-Verlag.

    Google Scholar 

  • Piaget, J. (1965). Sagesse et illusion de la philosophie. Paris: PUF.

    Google Scholar 

  • Piaget, J. (1971). Causalité et opération. In J. Piaget & R. Garcia (Eds.), Les explications causales. Paris: PUF.

    Google Scholar 

  • Planck, M. (1949). Vorträge und Erinnerungen. Stuttgart: Hirzel. Italian translation: La conoscenza del mondo fisico, Bollati Boringhieri, Torino, 1993.

  • Popper, K. (1968). Three views concerning human knowledge. In Conjectures and refutations (chap. 3). New York: Harper & Row Publishers.

  • Portides, D. P. (2007). The relation between idealisation and approximation in scientific model construction. Sci & Educ, 16(7–8), 699–724.

    Article  Google Scholar 

  • Psillos, D. (1995) Adapting instruction to students’ reasoning. In D. Psillos (Ed.), European research in science education, Proceedings of the Second Ph.D. Summer School, Thessaloniki (pp. 57–71).

  • Psillos, D., & Koumaras, P. (1993). Multiple causal modelling of electrical circuits for enhancing knowledge intelligibility. In M. Caillot (Ed.) Learning electricity and electronics with advanced educational technology, NATO ASI series F, vol. 115, Springer-Verlag, Berlin, pp. 57–75.

  • Roux, P., & Seigne, J.-R. (2001). L’énergie en mécanique et en thermodynamique. Bulletin de l’Union des Physiciens, 95(832), 491–507.

    Google Scholar 

  • Rozier, S., & Viennot, L. (1991). Students’ reasoning in thermodynamics. International Journal of Science Education, 13(2), 159–170.

    Article  Google Scholar 

  • Russell, B. (1912). On the notion of cause. Proceedings of the Aristotelian Society, XIII, 1–26.

    Google Scholar 

  • Salmon, W. (1984). Scientific explanation and the causal structure of the world. New Jersey: Princeton University Press.

    Google Scholar 

  • Sherwood, B. A., & Chabay, R. W. (1993). Conceptual model for understanding the behaviour of electrical circuits. In M. Caillot (Ed.), Learning electricity and electronics with advanced educational technology, NATO ASI series F, Vol.115, Springer-Verlag, Berlin, pp. 23–35.

  • Sierpinska, A. (1985). Obstacles épistémologiques relatifs à la notion de limite. Recherches en Didactique des Mathématiques, 6(1), 5–67.

    Google Scholar 

  • Silva, C. C. (2007). The role of models and analogies in the electromagnetic theory: A critical case study. Sci & Educ, 16(7–8), 835–848.

    Article  Google Scholar 

  • Steinberg, M. S. (1983). Reinventing electricity. In H. Helms & J. Novak (Eds.), Proceeding of the international seminar on misconceptions in science and mathematics (pp. 406–419). Ithaca: Cornell University.

    Google Scholar 

  • Tiberghien, A. (1994). Modelling as a basis for analysing teaching-learning situations. Learning and Instruction, 4(1), 71–87.

    Article  Google Scholar 

  • Tiberghien, A. (1996). Construction of prototypical situations in teaching the concept of energy. In G. Welford, J. Osborne, & P. Scott (Eds.), Research in science education in Europe, current issues and themes (pp. 100–114). London: The Falmer Press.

    Google Scholar 

  • Viennot, L. (1996). Raisonner en Physique, la part du sens commun, Bruxelles: De Boeck. English Translation: Reasoning in Physics, the Part of Common Sense. Kluwer, Dordrecht, 2001.

  • Wittgenstein, L. (1921) Tractatus logico-philosophicus, English translation by C.K. Ogden, 1922, Kegan and Co., London.

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    Ugo Besson

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Besson, U. Calculating and Understanding: Formal Models and Causal Explanations in Science, Common Reasoning and Physics Teaching. Sci & Educ 19, 225–257 (2010). https://doi.org/10.1007/s11191-009-9203-9

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