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

Article

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.

Keywords

Didactic transposition History of science Optics Pre-service elementary teachers Scheme-facet structure 

Supplementary material

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References

  1. Aikenhead, G. S. (2007). Humanistic perspectives in the science curricula. In S. K. Abell & N. G. Lederman (Eds.), Handbook of research in science education (pp. 881–910). New York, NY: Routledge.Google Scholar
  2. Alexander, P. A., Schallert, D. L. & Hare, V. C. (1991). Coming to terms: how researchers in learning and literacy talk about knowledge. Review of Educational Research, 61(3), 315–343. doi:10.3102/00346543061003315.CrossRefGoogle Scholar
  3. Allchin, D. (2013). Teaching the nature of science: Perspectives & resources. Saint Paul, MN: SHiPS Education Press.Google Scholar
  4. Alonso, M. & Finn, E. J. (1992). Physics. Harlow, England: Addison-Wesley.Google Scholar
  5. Anderson, R. D. (2002). Reforming science teaching: what research says about inquiry. Journal of Science Teacher Education, 13(1), 1–12. doi:10.1023/A:1015171124982.CrossRefGoogle Scholar
  6. Andersson, B. & Bach, F. (2005). On designing and evaluating teaching sequences taking geometrical optics as an example. Science Education, 89(2), 196–218. doi:10.1002/sce.20044.CrossRefGoogle Scholar
  7. Andreou, C. & Raftopoulos, A. (2010). Lessons from the history of the concept of the ray for teaching geometrical optics. Science & Education, 20(10), 1007–1037. doi:10.1007/s11191-010-9302-7.CrossRefGoogle Scholar
  8. Born, M. & Wolf, E. (1980). Principles of optics (6th ed.). Oxford, England: Pergamon Press.Google Scholar
  9. Bruner, M. (1960). The process of education. New York, NY: Vintage.Google Scholar
  10. Carey, S. (2009). The origin of concepts. New York, NY: Oxford University Press.Google Scholar
  11. Chen-Morris, R. D. (2001). Optics, imagination, and the construction of scientific observation in Kepler’s new science. The Monist, 84(4), 453–486.CrossRefGoogle Scholar
  12. Chen-Morris, R. (2013). “The Quality of Nothing:” Shakespearean mirrors and Kepler’s visual economy of science. In O. Gal & R. Chen-Morris (Eds.), Science in the age of Baroque (pp. 99–118). Dordrecht, The Netherlands: Springer Netherlands. doi:10.1007/978-94-007-4807-1.
  13. Chevallard, Y. (2007). Readjusting didactics to a changing epistemology. European Educational Research Journal, 6(2), 131–137. doi:10.2304/eerj.2007.6.2.131.CrossRefGoogle Scholar
  14. Chevallard, Y. & Joshua, M.-A. (1991). La transposition Didactique: Du Savoir Savant au Savoir Enseigné [The didactic transposition: From Knowledge to Knowledge Taught Savant]. Grenoble, France: La Pensée Souvage.Google Scholar
  15. Chi, M. T. H. (2008). Three types of conceptual change: Belief revision, mental model transformation, and categorical shift. In S. Vosniadou (Ed.), Handbook of research on conceptual change (pp. 61–82). Hillsdale, MI: Erlbaum.Google Scholar
  16. Coelho, R. L. (2007). The law of inertia: how understanding its history can improve physics teaching. Science & Education, 16(1), 955–974.CrossRefGoogle Scholar
  17. Coelho, R. L. (2012). Conceptual problems in the foundations of mechanics. Science & Education, 21(1), 1337–1356. doi:10.1007/s11191-010-9336-x.CrossRefGoogle Scholar
  18. Colin, P., Chauvet, F. & Viennot, L. (2002). Reading images in optics: students’ difficulties and teachers’ views. International Journal of Science Education, 24(3), 313–332. doi:10.1080/09500690110078923.CrossRefGoogle Scholar
  19. Creswell, J. W. & Clark, V. L. P. (2011). Designing and conducting mixed methods research (2nd ed.). Thousand Oakes, CA: Sage.Google Scholar
  20. Darrigol, O. (2012). A history of optics from Greek antiquity to the nineteenth century. New York, NY: Oxford University Press.Google Scholar
  21. DiSessa, A. & Sherin, B. (1998). What changes in conceptual change ? International Journal of Science Education, 20(10), 1155–1191.CrossRefGoogle Scholar
  22. Duit, R., Treagust, D. & Widodo, A. (2008). Teaching science for conceptual change: Theory and practice. In S. Vosniadou (Ed.), International handbook of research on conceptual change (pp. 629–646). New York, NY: Routledge.Google Scholar
  23. Duit, R., Gropengießer, H., Kattmann, K., Komorek, M. & Parchmann, I. (2012). The model of educational reconstruction—A framework for improving teaching and learning science. In D. Jorde & J. Dillon (Eds.), Science education research and practice in Europe: Retrospective and prospective (pp. 13–38). Rotterdam, The Netherlands: Sense.Google Scholar
  24. Dupré, S. (2007). Playing with images in a Dark Room Kepler’s Ludi inside the Camera Obscura. In W. Lefèvre (Ed.), Inside the Camera Obscura—Optics and art under the spell of the projected image (pp. 59–74). Berlin, Germany: Max Planck Institute for the History of Science. Retrieved from www.mpiwg-berlin.mpg.de/Preprints/P333.PDF.
  25. Faria, C., Chagas, I., Machado, A. & Sousa, J. (2012). A science teacher education course in a science centre: a successful strategy to empower teachers to master museum resources exploration. Electronic Journal of Science Education, 16(2), 1–13.Google Scholar
  26. Feigenberg, J., Lavrik, L. V. & Shunyakov, V. (2002). Space scale: models in the history of science and students mental models. Science & Education, 11(4), 377–392. doi:10.1023/A:1016050526156.CrossRefGoogle Scholar
  27. Fetherstonhaugh, A., Happs, J. & Treagust, D. (1987). Student misconceptions about light: a comparative study of prevalent views found in Western Australia, France New Zealand, Sweden and the United States. Research in Science Education, 17(1), 157–164. doi:10.1007/BF02357183.CrossRefGoogle Scholar
  28. Galili, I. & Hazan, A. (2000a). Learners’ knowledge in optics: interpretation, structure and analysis. International Journal of Science Education, 22(2), 57–88. doi:10.1080/095006900290000.CrossRefGoogle Scholar
  29. Galili, I. & Hazan, A. (2000b). The influence of an historically oriented course on students’ content knowledge in optics evaluated by means of facets-schemes analysis. American Journal of Physics, 68(S3), 3–15. doi:10.1119/1.19518.CrossRefGoogle Scholar
  30. Garrison, J. W. & Bentley, M. L. (1990). Science education, conceptual change and breaking with everyday experience. Studies in Philosophy and Education, 10(1), 19–35.CrossRefGoogle Scholar
  31. Goldberg, F., Bendall, S. & Galili, I. (1991). Lens, pinholes, screens, and the eye. The Physics Teacher, 9, 221–224.CrossRefGoogle Scholar
  32. Harrison, A., Grayson, D. & Treagust, D. F. (1999). Investigating a grade 11 student’s evolving conceptions of heat and temperature. Journal of Research in Science Teaching, 36, 55–87.CrossRefGoogle Scholar
  33. Hecht, E. (1987). Óptica [Optics]. Lisboa, Portugal: Fundação Caloust Goulbenkian.Google Scholar
  34. Heywood, D. S. (2005). Primary trainee teachers’ learning and teaching about light: some pedagogic implications for initial teacher training. International Journal of Science Education, 27(12), 1447–1475. doi:10.1080/09500690500153741.CrossRefGoogle Scholar
  35. Höttecke, D. & Silva, C. C. (2011). Why implementing history and philosophy in school science education is a challenge: an analysis of obstacles. Science & Education, 20(3–4), 293–316. doi:10.1007/s11191-010-9285-4.CrossRefGoogle Scholar
  36. Höttecke, D., Henke, A. & Riess, F. (2012). Implementing history and philosophy in science teaching: strategies, methods, results and experiences from the European HIPST project. Science & Education, 21(9), 1233–1261. doi:10.1007/s11191-010-9330-3.CrossRefGoogle Scholar
  37. Jong, T. D. & Ferguson-Hessler, M. (1996). Types and qualities of knowledge. Educational Psychologist, 31(2), 105–113. doi:10.1207/s15326985ep3102_2.CrossRefGoogle Scholar
  38. Keil, F. C. & Newman, G. E. (2008). Two tales of conceptual change: What changes and what remains the same. In S. Vosniadou (Ed.), Handbook of research on conceptual change (pp. 83–801). New York, NY: Routledge.Google Scholar
  39. Lakatos, I. (1970). History of science and its rational reconstructions. In Proceedings of the Biennial Meeting of the Philosophy of Science Association (Vol. 1970, pp. 91–136). Chicago, IL: University of Chicago Press.Google Scholar
  40. Leach, J. & Scott, P. (2002). Designing and evaluating science teaching sequences: an approach drawing upon the concept of learning demand and a social constructivist perspective on learning. Studies in Science Education, 38(1), 115–142. doi:10.1080/03057260208560189.CrossRefGoogle Scholar
  41. Lijnse, P. L. (1995). “Developmental research” as a way to an empirically based “didactical structure” of science. Science Education, 79(2), 189–199. doi:10.1002/sce.3730790205.CrossRefGoogle Scholar
  42. Lijnse, P. L. (2000). Didactics of science: The forgotten dimension in science education research? In R. Millar, J. Leach & J. Osborne (Eds.), Improving science education: The contribution of research (pp. 308–326). Philadelphia, PA: Open University Press.Google Scholar
  43. Lijnse, P. L. (2004). Didactical structures as an outcome of research on teaching–learning sequences? International Journal of Science Education, 26(5), 537–554. doi:10.1080/09500690310001614753.CrossRefGoogle Scholar
  44. Lindberg, D. (1976). Theories of vision from al-Kindi to Kepler. London, England: The University of Chicago Press.Google Scholar
  45. Matthews, M. R. (1989). History, philosophy, and science teaching: a brief review. Synthese, 80(1), 1–7. doi:10.1007/BF00869945.CrossRefGoogle Scholar
  46. Matthews, M. R. (1994). Science teaching: The role of history and philosophy of science. New York, NY: Routledge.Google Scholar
  47. Méheut, M. & Psillos, D. (2004). Teaching–learning sequences: aims and tools for science education research. International Journal of Science Education, 26(5), 515–535. doi:10.1080/09500690310001614762.CrossRefGoogle Scholar
  48. Mihas, P. & Andreadis, P. (2005). A historical approach to the teaching of the linear propagation of light, shadows and pinhole cameras. Science & Education, 14(7–8), 675–697. doi:10.1007/s11191-005-1793-2.CrossRefGoogle Scholar
  49. Minstrell, J. (2001). The role of the teacher in making sense of classroom experiences and effecting better learning. In Carver, S. M., & Klahr, D. (eds.), Cognition and instruction: Twenty-five years of progress (pp. 121–149). Mahwah, NJ: Laurence Erlbaum Associates.Google Scholar
  50. Nersessian, N. J. (1989). Conceptual change in science and in science education. Synthese, 80, 163–183.CrossRefGoogle Scholar
  51. Pfundt, H. & Duit, R. (1994). Bibliography: Students’ alternative frameworks and science education (4th ed.). Kiel, Germany: Institut fur die Padagogik de Naturwissenschaften.Google Scholar
  52. Posner, G., Strike, K., Hewson, P. W. & Gertzog, W. A. (1982). Accommodation of a scientific conception: toward a theory of conceptual change. Science Education, 66(2), 211–227.CrossRefGoogle Scholar
  53. Psillos, D. (2004). An epistemological analysis of the evolution of didactical activities in teaching–learning sequences: the case of fluids. International Journal of Science Education, 26(5), 555–578. doi:10.1080/09500690310001614744.CrossRefGoogle Scholar
  54. Raftopoulos, A., Kalyfommatou, N. & Constantinou, C. P. (2005). The properties and the nature of light: the study of Newton’s work and the teaching of optics. Science & Education, 14(7–8), 649–673. doi:10.1007/s11191-004-5609-6.CrossRefGoogle Scholar
  55. Resnick, R., Walker, J. & Halliday, D. (2007). Fundamentals of physics (8th ed.). Wiley.Google Scholar
  56. Ronchi, V. (1970). The nature of light: A historical survey. London, England: Heinemenn.Google Scholar
  57. Rusanen, A. M. & Pöyhönen, S. (2012). Concepts in change. Science & Education, 22(6), 1389–1403. doi:10.1007/s11191-012-9489-x.CrossRefGoogle Scholar
  58. Schoenfeld, A. H. (2012). Problematizing the didactic triangle. ZDM Mathematics Education, 44(5), 587–599. doi:10.1007/s11858-012-0395-0.CrossRefGoogle Scholar
  59. Scott, P., Asoko, H. & Leach, J. (2007). Student conceptions and conceptual learning in science. In S. K. Abell & N. Lederman (Eds.), Handbook of research on science education (pp. 31–56). New York, NY: Routledge.Google Scholar
  60. Sequeira, M. & Leite, L. (1991). Alternative conceptions and history of science in physics teacher education. Science Education, 75(1), 45–56. doi:10.1002/sce.3730750105.CrossRefGoogle Scholar
  61. Shapiro, A. E. (2008). Images: real and virtual, projected and perceived, from Kepler to Dechales. Early Science and Medicine, 13(3), 270–312. doi:10.1163/157338208X285044.CrossRefGoogle Scholar
  62. Straker, S. (1981). Kepler, Tycho, and the “Optical Part of Astronomy”: the genesis of Kepler’s theory of pinhole images. Archive for History of Exact Sciences, 24(4), 267–293.CrossRefGoogle Scholar
  63. Tiberghien, A., Psillos, D. & Koumaras, P. (1995). Physics instruction from epistemological and didactical bases. Instructional Science, 22(1), 423–444.CrossRefGoogle Scholar
  64. Viennot, L. (2003). Teaching physics. Dordrecht, The Netherlands: Kluwer Academic Publishers.Google Scholar
  65. Viennot, L. & Kaminski, W. (2006). Can we evaluate the impact of a critical detail? The role of a type of diagram in understanding optical imaging. International Journal of Science Education, 28(15), 1867–1885. doi:10.1080/09500690600620979.CrossRefGoogle Scholar
  66. Viennot, L., Chauvet, F., Colin, P. & Rebmann, G. (2005). Designing strategies and tools for teacher training: the role of critical details, examples in optics. Science Education, 89(1), 13–27. doi:10.1002/sce.20040.CrossRefGoogle Scholar
  67. Vosniadou, S. (2002). On the nature of naive physics. In M. Limón & L. Mason (Eds.), Reconsidering conceptual change. Issues in theory and practice (pp. 61–76). Amsterdam, The Netherlands: Kluwer Academic Publishers.Google Scholar

Copyright information

© Ministry of Science and Technology, Taiwan 2015

Authors and Affiliations

  • Paulo Maurício
    • 1
  • Bianor Valente
    • 1
  • Isabel Chagas
    • 2
  1. 1.Escola Superior de Educação de LisboaInstituto Politécnico de LisboaLisbonPortugal
  2. 2.Instituto de EducaçãoUIDEF - Unidade de Investigação e Desenvolvimento em Educação e FormaçãoLisbonPortugal

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