Abstract
This article discusses the role of mathematics during physics lessons in upper-secondary school. Mathematics is an inherent part of theoretical models in physics and makes powerful predictions of natural phenomena possible. Ability to use both theoretical models and mathematics is central in physics. This paper takes as a starting point that the relations made during physics lessons between the three entities Reality, Theoretical models and Mathematics are of the outmost importance. A framework has been developed to sustain analyses of the communication during physics lessons. The study described in this article has explored the role of mathematics for physics teaching and learning in upper-secondary school during different kinds of physics lessons (lectures, problem solving and labwork). Observations are from three physics classes (in total 7 lessons) led by one teacher. The developed analytical framework is described together with results from the analysis of the 7 lessons. The results show that there are some relations made by students and teacher between theoretical models and reality, but the bulk of the discussion in the classroom is concerning the relation between theoretical models and mathematics. The results reported on here indicate that this also holds true for all the investigated organizational forms lectures, problem solving in groups and labwork.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Adúriz-Bravo, A. (2012). A ‘Semantic’ view of scientific models for science education. Science and Education, 22(7), 1593–1611.
Angell, C., Guttersrud, Ø., Henriksen, E. K., & Isnes, A. (2004). Physics: Frightful but fun pupils’ and teachers’ views of physics and physics teaching. Science Education, 88, 683–706.
Angell, C., Lie, S., & Rohatgi, A. (2011). TIMSS Advanced 2008: Fall i fysikk-kompetanse i Norge og Sverige. NorDiNa, 7(1), 17–31.
Develaki, M. (2007). The model-based view of scientific theories and the structuring of school science programmes. Science and Education, 16(7), 725–749.
Due, K. (2009). Fysik, lärande samtal och genus: en studie av gymnasieelevers gruppdiskussioner i fysik. Diss. Umeå : Umeå universitet, 2009. Umeå.
Duit, R., Niedderer, H., & Schecker, H. (2007). Teaching Physics. In Abell & Lederman (Eds.), Handbook of research on science education. London: Lawrence Erlbaum Associates.
Erduran, S., & Dagher, R. (2014). Reconceptualizing the nature of science for science education: Scientific knowledge, practices and other family categories. Contemporary Trends and Issues in Science Education (Vol. 43). Dordrecht: Springer.
Freudenthal, H. (1991). Revisiting mathematics education. China lectures. Dordrecht: Kluwer Academic Publishers.
Galili, I., & Hazan, A. (2000). Learners’ knowledge in optics: Interpretation, structure and analysis. International Journal of Science Education, 22, 57–88.
Giere, R. N. (1988). Explaining science: A cognitive approach. Minneapolis: University of Minnesota Press.
Giere, R. N. (1997). Understanding scientific reasoning (4th ed.). San Diego: Harcourt Brace College Publishers.
Hanson, N. R. (1958). Patterns of discovery. Cambridge: Cambridge University Press.
Hansson, L. (2014). Students’ views concerning worldview presuppositions underpinning science: Is the world really ordered, uniform, and comprehensible?”. Science Education, 98(5), 743–765.
Hobden, P. (1998). The role of routine problem tasks in science teaching. In B. J. Fraser & K. G. Tobin (Eds.), International handbook of science education (pp. 219–231). London: Kluwer Academic Publishers.
Kaiser, G., & Sriraman, B. (2006). A global survey of international perspectives on modelling in mathematics education. Zentralblatt für Didaktik der Mathematik, 38(3), 302–310.
Karam, R. (2014). Framing the structural role of mathematics in physics lectures: A case study on electromagnetism. Physical Review Special Topics-Physics Education Research, 10, 010119-1–010119-23.
Koponen, I. T. (2007). Models and modelling in physics education: A critical re-analysis of philosophical underpinnings and suggestions for revisions. Science and Education, 16(7–8), 751–773.
Krey, O. (2014). Learners’ beliefs and conceptions about the role of mathematics in physics. In C. P. Constantinou, N. Papadouris & A. Hadjigeorgiou (Eds.), E-Book Proceedings of the ESERA 2013 conference: Science education research for evidence-based teaching and coherence in learning. Part [2] (co-ed. J. Lavonen and A. Zeyer). Nicosia, Cyprus: European Science Education Research Association. ISBN: 978-9963-700-77-6.
Kuo, E., Hull, M. M., Gupta, A., & Elby, A. (2013). How students blend conceptual and formal mathematical reasoning in solving physics problems. Science Education, 97, 32–57.
Lederman, N. G. (2007). Nature of science: Past, present, and future. In S. K. Abell & N. G. Lederman (Eds.), Handbook of Research on Science Education (pp. 831-879).
Lesh, R., & Zawojewski, J. S. (2007). Problem solving and modeling. In F. Lester (Ed.), The second handbook of research on mathematics teaching and learning (pp. 763–804). Charlotte, NC: Information Age Publishing.
Michelsen, C. (2006). Functions: A modelling tool in mathematics and science. Zentralblatt für Didaktik der Mathematik, 38(3), 269–280.
Nilsen, T., Angell, C., & Grönmo, L. S. (2013). Mathematical competencies and the role of mathematics in physics education: A trend analysis of TIMSS Advanced 1995 and 2008. Acta Didactica Norge, 7(1), art6.
Pask, C. (2003). Mathematics and the science of analogies. American Journal of Physics, 71(6), 526–534.
Petri, J., & Niedderer, H. (1998). A learning pathway in high-school level quantum atomic physics. International Journal of Science Education, 20(9), 1075–1088.
Pietrocola, M. (2008). Mathematics as structural language of physical thought. In M. Vicentini & E. Sassi (Eds.) Connecting research in physics education with teacher education (Vol. 2). International Commission on Physics Education.
Redfors, A., & Ryder, J. (2001). University physics students’ use of models in explanations of phenomena involving interaction between metals and electromagnetic radiation. International Journal of Science Education, 23(12), 1283–1302.
Strömdahl, H. (2012). On Discerning critical elements, relationships and shifts in attaining scientific terms: The challenge of polysemy/homonymy and reference. Science & Education, 21, 55–85.
Suppe, F. (2000). Understanding scientific theories: An assessment of developments 1969–1998. Philosophy of Science, 67, S102–S115. (Proceedings).
Taber, K. S. (2000). Multiple frameworks? Evidence of manifold conceptions in individual cognitive structure. International Journal of Science Education, 22, 399–417.
Torigoe, E. T., & Gladding, G. E. (2011). Connecting symbolic difficulties with failure in physics. American Journal of Physics, 79(1), 133–140.
Tuminaro, J., & Redish, E. F. (2007). Elements of a cognitive model of physics problem solving: epistemic games. Physical Review Special Topics Physics Education Research, 3(02010), 1–22.
Uhden, O., Karam, R., Pietrocola, M., & Pospiech, G. (2012). Modelling mathematical reasoning in physics education. Science and Education, 21(4), 485–506.
van Fraassen, B. (1980). The scientific image. Oxford: Clarendon Press.
Yackel, E., & Cobb, P. (1996). Sociomathematical norms, argumentation and autonomy in mathematics. Journal for Research in Mathematics Education, 27(4), 458–477.
Acknowledgments
This project has been supported by the Swedish Research Council (721-2008-484).
Author information
Authors and Affiliations
Corresponding author
Appendix
Appendix
Rights and permissions
About this article
Cite this article
Hansson, L., Hansson, Ö., Juter, K. et al. Reality–Theoretical Models–Mathematics: A Ternary Perspective on Physics Lessons in Upper-Secondary School. Sci & Educ 24, 615–644 (2015). https://doi.org/10.1007/s11191-015-9750-1
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11191-015-9750-1