Advertisement

Analysing the Competency of Mathematical Modelling in Physics

  • Edward F. RedishEmail author
Conference paper
Part of the Springer Proceedings in Physics book series (SPPHY, volume 190)

Abstract

A primary goal of physics is to create mathematical models that allow both predictions and explanations of physical phenomena. We weave maths extensively into our physics instruction beginning in high school, and the level and complexity of the maths we draw on grows as our students progress through a physics curriculum. Despite much research on the learning of both physics and math, the problem of how to successfully teach most of our students to use maths in physics effectively remains unsolved. A fundamental issue is that in physics, we don’t just use maths, we think about the physical world with it. As a result, we make meaning with mathematical symbology in a different way than mathematicians do. In this talk we analyse how developing the competency of mathematical modelling is more than just “learning to do math” but requires learning to blend physical meaning into mathematical representations and use that physical meaning in solving problems. Examples are drawn from across the curriculum.

Keywords

Physics Class Test Charge Physical Intuition Math Class Biology Student 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgments

The author gratefully acknowledges conversations and collaborations with the members of the NEXUS/Physics team and the University of Maryland’s Physics Education Research Group. This material is based upon work supported by the Howard Hughes Medical Institute and the US National Science Foundation under Awards No. DUE-12-39999 and DUE-15-04366. Any opinions, findings, and conclusions or recommendations expressed in this publication are those of the author and do not necessarily reflect the views of the National Science Foundation.

References

  1. AAMC/HHMI. (2009). Scientific Foundations for Future Physicians: Report of the AAMC-HHMI Committee.Google Scholar
  2. AAAS. (2011). Vision and change in undergraduate biology education: A call to action. AAAS Press.Google Scholar
  3. Baddeley, A. (1998). Human Memory: Theory and practice (revised Ed.). Allyn & Bacon. ISBN: 978-0205123124Google Scholar
  4. Bing, T. J., & Redish, E. F. (2009). Analysing problem solving using math in physics: Epistemological framing via warrants. Physical Review Special Topics-Physics Education Research, 5(2), 020108. doi: 10.1103/PhysRevSTPER.5.020108 ADSCrossRefGoogle Scholar
  5. Bing, T. J., & Redish, E. F. (2012). Epistemic complexity and the journeyman-expert transition. Physical Review Special Topics-Physics Education Research, 8, 010105. doi: 10.1103/PhysRevSTPER.8.010105
  6. Bridgman, P. W. (1922). Dimensional analysis. Yale University Press, p. 2. ISBN: 978-1451002621Google Scholar
  7. diSessa, A. A. (1993). Toward an Epistemology of Physics. Cognition and Instruction, 10, 105–225. http://jstor.org.proxy-um.researchport.umd.edu/stable/3233725 CrossRefGoogle Scholar
  8. Dreyfus, B., Geller, B. D., Gouvea, J., Sawtelle, V., Turpen, C., & Redish, E. F. (2014). Chemical energy in an introductory physics course for the life sciences. American Journal of Physics, 82, 403–411. doi: 10.1119/1.4870391.ADSCrossRefGoogle Scholar
  9. Elby, A., & Hammer, D. (2001). On the substance of a sophisticated epistemology. Science Education, 85(5), 554–567. doi: 10.1002/sce.1023 ADSCrossRefGoogle Scholar
  10. EUR-LEX. (2006). Recommendation 2006/962/EC of the European Parliament and of the Council of 18 December 2006 on key competences for lifelong learning [Official Journal L 394 of 30.12.2006]. http://eur-lex.europa.eu/legal-content/EN/TXT/?uri=URISERV%3Ac11090
  11. Evans, V. & Green, M. (2006). Cognitive linguistics: An introduction. Lawrence Erlbaum. ISBN: 0-8058-6014-2Google Scholar
  12. Fauconnier, G., & Turner, M. (2003). The way we think: Conceptual blending and the mind’s hidden complexities. Basic Books. ISBN: 9780465087860Google Scholar
  13. Geller, B., Dreyfus, B., Gouvea, J., Sawtelle, V., Turpen, C., & Redish, E. F. (2014). Entropy and spontaneity in an introductory physics course for life science students. American Journal of Physics, 82, 394–402. doi: 10.1119/1.4870389.ADSCrossRefGoogle Scholar
  14. Griffiths, D. J. (1999) Introduction to electrodynamics (3rd Ed.). Prentice Hall. ISBN: 013805326X.Google Scholar
  15. Gupta, A., & Elby, A. (2011). Beyond epistemological deficits: Dynamic explanations of engineering students’ difficulties with mathematical sense making. International Journal of Science Education, 33(18), 2463–2488. doi: 10.1080/09500693.2010.551551.ADSCrossRefGoogle Scholar
  16. Hammer, D. (2000). Student resources for learning introductory physics. American Journal of Physics, 68, S52–S59. doi: 10.1119/1.19520 ADSCrossRefGoogle Scholar
  17. Hammer, D., & Elby, A. (2003). Tapping epistemological resources for learning physics. J. Learning Sci., 12, 53–90. http://jstor.org.proxy-um.researchport.umd.edu/stable/1466634 CrossRefGoogle Scholar
  18. Hammer, D., Elby, A., Scherr, R. E., & Redish, E. F. (2005). Resources, framing, and transfer. In J. Mestre (Ed.), Transfer of learning: Research and perspectives (p. 1593111649). Information Age Publishing. ISBN: 978-1593111649Google Scholar
  19. Lakoff, G., & Johnson. M. (1980/2003). Metaphors we live by. University of ChicagoPress. ISBN: 780226468013.Google Scholar
  20. Langacker, R. W. (1987). Foundations of cognitive grammar, Vol 1: Theoretical perspectives. Stanford University Press. ISBN: 9780804738514Google Scholar
  21. Moore, K., Gianini, J., & Losert, W. (2014). Toward better physics labs for future biologists. American Journal of Physics, 82, 387–393. doi: 10.1119/1.4870388.ADSCrossRefGoogle Scholar
  22. National Research Council. (2003). Bio 2010: Transforming undergraduate education for future research biologists. National Academy Press. ISBN: 978-0-309-08535-9Google Scholar
  23. Redish, E. F. (2005). Problem solving and the use of math in physics courses, in Proceedings of the Conference, World View on Physics Education in 2005: Focusing on Change, Delhi. 21–26 Aug 2005. arXiv:physics/0608268 [physics.ed-ph].
  24. Redish, E. F. (2014). Oersted lecture: How should we think about how our students think? American Journal of Physics, 82, 537–551. doi: 10.1119/1.4874260.ADSCrossRefGoogle Scholar
  25. Redish, E F., & Cooke, T. (2013). Learning each other’s ropes: Negotiating interdisciplinary authenticity, Cell Biology Education - Life Science Education, 12, 175–186. doi: 10.1187/cbe.12-09-0147
  26. Redish, E. F., & Kuo, E. (2015). Language of physics, language of math. Science and Education, 25(5–6), 561–590. doi: 10.1007/s11191-015-9749-7.ADSCrossRefGoogle Scholar
  27. Redish, E. F., Bauer, C., Carleton, K. L., Cooke, T. J., Cooper, M., & Crouch, C. H., et al. (2014). NEXUS/Physics: An interdisciplinary repurposing of physics for biologists. American Journal of Physics, 82(5), 368–377. doi:  10.1119/1.4870386 ADSCrossRefGoogle Scholar
  28. Sherin, B. (2001). How students understand physics equations. Cognition and Instruction, 19, 479–541.http://jstor.org.proxy-um.researchport.umd.edu/stable/3233857 CrossRefGoogle Scholar
  29. Tannen, D. (1994). Framing in discourse. D. Tannen Oxford University Press, 14–56. ISBN: 978-0195079968Google Scholar
  30. Toulmin, S. (1958). The uses of argument. Cambridge University Press. ISBN: 0521092302Google Scholar
  31. Watkins, J., Coffey, J. E., Redish, E. F., & Cooke T. J. (2012). Disciplinary authenticity: Enriching the reforms of introductory physics courses for life-science students. Physical Review Special Topics-Physics Education Research, 8, 010112. 17 p. doi: 10.1103/PhysRevSTPER.8.010112

Copyright information

© Springer International Publishing Switzerland 2017

Authors and Affiliations

  1. 1.Department of PhysicsUniversity of MarylandCollege ParkUSA

Personalised recommendations