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A Didactic Sequence of Elementary Geometric Optics Informed by History and Philosophy of Science

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Abstract

The concepts and instruments required for the teaching and learning of geometric optics are introduced in the didactic process without a proper didactic transposition. This claim is secured by the ample evidence of both wide- and deep-rooted alternative concepts on the topic. Didactic transposition is a theory that comes from a reflection on the teaching and learning process in mathematics but has been used in other disciplinary fields. It will be used in this work in order to clear up the main obstacles in the teaching-learning process of geometric optics. We proceed to argue that since Newton’s approach to optics, in his Book I of Opticks, is independent of the corpuscular or undulatory nature of light, it is the most suitable for a constructivist learning environment. However, Newton’s theory must be subject to a proper didactic transposition to help overcome the referred alternative concepts. Then is described our didactic transposition in order to create knowledge to be taught using a dialogical process between students’ previous knowledge, history of optics and the desired outcomes on geometrical optics in an elementary pre-service teacher training course. Finally, we use the scheme-facet structure of knowledge both to analyse and discuss our results as well as to illuminate shortcomings that must be addressed in our next stage of the inquiry.

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Notes

  1. According to Duit et al. (2012), the major ideas of the Model of Educational Reconstruction are included in the didactic transposition.

  2. We use history of science (HC) and not philosophy of science (PS) as our main guide in constructing our DT. However, much of our study of the HC was oriented by the PS. As Lakatos (1970) said (citing Kant), “Philosophy of science without history of science is empty; history of science without philosophy of science is blind.” Moreover, the acronym HPS is well rooted in the literature even when only HC is used.

  3. The terms transmissive and decontextualized refer to a teaching-learning that “transmits content that is socially sterile, impersonal, frustrating, intellectually boring, and/or dismissive of students’ life-worlds” (Aikenhead, 2007, p. 886) and is not inquiry based (Anderson, 2002).

  4. In Alexander et al. (1991), framework is clear in the load of non-cognitive elements embedded in prior knowledge. Garrison & Bentley (1990) drawing on Posner et al. (1982) theory of conceptual change criticize its purely cognitive approach, for “What make science so difficult for so many is that often students must learn new canons of rationality” (p.24). Moreover “there are other cognitive, or precognitive, yet not necessarily conceptual” considerations ignored in Posner et al. and similar approaches to conceptual change, such as “interest, (selective) attention, systematic doubt and the process of abstraction, to name a few” (Idem). Rusanen & Pöyhönen (2012) reinforce this approach when stating that “when conceptual change occurs (…) [students] conceptions of phenomena in a certain domain undergo a restructuring process that affects ontological commitments, inferential relations, and standards of explanations.” (p. 1390)

  5. Vosniadou (2002) shows that prior knowledge or misconceptions are “complex knowledge system that consists of a network of beliefs or presuppositions.”(p. 65) This agrees in many features both with Chi’s (2008) connection between a concept and an ontological belief and DiSessa & Sherin’s (1998) descriptions of concepts as a cluster of phenomenological primitives. Keil & Newman (2008) explicitly assume that “concepts are, to some degree, parts of theory-like structures (…)” (p. 84) and Carey (2009) the thesis of two types of concepts: the one embedded in systems of core cognition or embedded in intuitive theories. In all these research, concepts are seen as complex structures.

  6. We had study a total of 25 empirical studies in optical previous conceptions. To an overall view of preconception literature until 1994, see Pfundt & Duit (1994).

  7. The pinhole camera presented Kepler with a challenge that he was able to solve (Straker, 1981) and at the same time provided some insights concerning the function of the eye (Dupré, 2007; Shapiro, 2008). Moreover, the pinhole camera was an instrument with a paramount importance in Astronomy before Galileo’s telescope (Lindberg, 1976; Straker, 1981) and since it casts an inverted image as the system cornea plus crystalline does in the retina—although of a different nature (Goldberg, Bendall & Galili, et al., 1991)—we considered it useful as one of the first approach in the teaching-learning of image formation in the retina.

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Authors and Affiliations

  1. Escola Superior de Educação de Lisboa, Instituto Politécnico de Lisboa, Campus de Benfica do IPL, 1549-003, Lisbon, Portugal

    Paulo Maurício & Bianor Valente

  2. Instituto de Educação, UIDEF - Unidade de Investigação e Desenvolvimento em Educação e Formação, Lisbon, Portugal

    Isabel Chagas

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  1. Paulo Maurício
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  2. Bianor Valente
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Correspondence to Paulo Maurício.

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Maurício, P., Valente, B. & Chagas, I. A Didactic Sequence of Elementary Geometric Optics Informed by History and Philosophy of Science. Int J of Sci and Math Educ 15, 527–543 (2017). https://doi.org/10.1007/s10763-015-9662-1

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