Skip to main content
SpringerLink
Log in

Mathematical Representations in Physics Lessons

  • Chapter
  • First Online:
Mathematics in Physics Education

Abstract

Physics is characterized by the use of specific types of representations. These representations play an important role in the teaching and learning of physics. This chapter/article starts with a general description of representations from a cognitive sciences' and semiotics' view and presents the state of theory about representations in physics education with focus on mathematical ones. Based on this, an adapted classification of representations in physics lessons is presented. This is followed by theoretical considerations and empirical findings about the relevance of (different) representations for learning and understanding physics and students' difficulties in this context. Furthermore, two models are introduced that are part of current research and offer an approach to analyse different changes of representations in physics classes. Ultimately, several implications for teaching will be derived.

The authors contributed equally to this work.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 139.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 179.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    Airey and Linder (2009) use the term semiotic resources and distinguish between tools, activities, and representations. In our argumentation this distinction is not important; tools and activities can be seen predominantly as handling with objective representations.

  2. 2.

    Fredlund et al. (2012) use the terminology of semiotic resources as well; therefore they call it the disciplinary affordance of a semiotic resource.

References

  • Adu-Gyamfi, K., Stiff, L. V., & Bossé, M. J. (2012). Lost in translation: Examining translation errors associated with mathematical representations. School Science and Mathematics, 112(3), 159–170.

    Article  Google Scholar 

  • Ainsworth, S. (2006). DeFT: A conceptual framework for considering learning with multiple representations. Learning and Instruction, 16, 183–198.

    Article  Google Scholar 

  • Ainsworth, S. (2008). The educational value of multiple-representations when learning complex scientific concepts. In J. K. Gilbert et al. (Eds.), Visualization: theory and practice in science education (pp. 191–208). Dordrecht: Springer.

    Chapter  Google Scholar 

  • Ainsworth, S., Bibby, P. A., & Wood, D. J. (1998). Analysing the costs and benefits of multi-representational learning environments. In M. Someren (Ed.), Learning with multiple representations (pp. 120–134). Pergamon, as cited in Bauer (2015).

    Google Scholar 

  • Airey, J. (2009). Science, language and literacy. Case studies of learning in Swedish University physics. Uppsala: Uppsala University.

    Google Scholar 

  • Airey, J., & Linder, C. (2009). A Disciplinary Discourse Perspective on University Science Learning: Achieving Fluency in a Critical Constellation of Modes. Journal of Research in Science Teaching, 46(1), 27–49.

    Article  Google Scholar 

  • Bagno, E., Eylon, B.-S. & Berger, H. (2011). How to promote the learning of physics from formulae? In: GIREP-EPEC & PHEC 2009 International Conference (=Physics Community and Cooperation Vol. 2), pp. 77–83.

    Google Scholar 

  • Bauer, A. (2015). Argumentieren mit multiplen und dynamischen Repräsentationen. Würzburg: Würzburg University Press.

    Google Scholar 

  • Bruner, J. S. (1974). Entwurf einer Unterrichtstheorie. Berlin: Berlin Verlag.

    Google Scholar 

  • Bossé, M. J., Adu-Gyamfi, K., & Cheetham, M. R. (2011). Assessing the difficulty of mathematical translations: Synthesizing the literature and novel findings. International Electronic Journal of Mathematics Education, 6(3), 113–133.

    Google Scholar 

  • Chandler, P. & Sweller, J. (1991). Cognitive load theory and the format of instruction. Cognition and Instruction, 8(4), 293–332, as cited in Bauer (2015).

    Google Scholar 

  • diSessa, A. A. (2004). Metarepresentation: Native competence and targets for instruction. Cognition and Instruction, 22(3), 293–331.

    Article  Google Scholar 

  • Dolin, J. (2016). Representations in science. In R. Gunstone (Ed.), Encyclopedia of science education (pp. 836–838). Springer Science+Business Media Dordrecht 2015, Corrected Printing 2016.

    Chapter  Google Scholar 

  • Duval, R. (2006). A cognitive analysis of problems of comprehension in a learning of mathematics. Educational Studies in Mathematics, 61(1). Springer, 103–131.

    Google Scholar 

  • Eriksson, U., Linder, C., Airey, J., & Redfors, A. (2014). Introducing the anatomy of disciplinary discernment: an example from astronomy. European Journal of Science and Mathematics Education, 2(3), 167–182.

    Google Scholar 

  • Fredlund, T., Airey, J., & Linder, C. (2012). Exploring the role of physics representations: An illustrative example from students sharing knowledge about refraction. European Journal of Physics, 33, 657–666.

    Article  Google Scholar 

  • Geyer, M. –A., & Pospiech, G. (2015). Darstellungen funktionaler Zusammenhänge im Physikunterricht. Darstellungswechsel in der Sekundarstufe 1. In PhyDidB –Didaktik der Physik –Beiträge zur DPG-Frühjahrstagung Wuppertal 2015.

    Google Scholar 

  • Gilbert, J. K. (2016). Chapter 7. The contribution of visualisation to modelling-based teaching. In J. K. Gilbert & R. Justi (Eds.), Modelling-based teaching in science education (Models and modeling in science education) (Vol. 9, pp. 121–148). Cham: Springer.

    Google Scholar 

  • Hattikudur, S., Prather, R. W., Asquith, P., Alibali, M. W., Knuth, E. J., & Nathan, M. (2012). Constructing graphical representations: Middle schoolers’ intuitions and developing knowledge about slope and Y-intercept. School Science and Mathematics, 112(4), 230–240.

    Article  Google Scholar 

  • Hoffmann, L. (1987). Kommunikationsmittel Fachsprache. Eine Einführung. 3., durchgesehene Auflage. Berlin: Akademie-Verlag (=Sammlung Akademie-Verlag Bd.44. Sprache).

    Google Scholar 

  • Janßen, W., & Pospiech, G. (2015). Versprachlichung von Formeln und physikalisches Formelverständnis. In S. Bernholt (Hrsg.), Heterogenität und Diversität – Vielfalt der Voraussetzungen im naturwissenschaftlichen Unterricht. Gesellschaft für Didaktik der Chemie und Physik, Jahrestagung in Bremen 2014 (S. 636–638). Kiel: IPN.

    Google Scholar 

  • Janvier, C. (1987). Translation process in mathematics education. In Problems of representation in the teaching and learning of mathematics (pp. 27–32). Hillsdale: Lawrence Erlbaum.

    Google Scholar 

  • Karam, R., & Pietrocola, M. (2010). Recognizing the structural role of mathematics in physical thought. In M. F. Tasar & G. Çakmakci (Eds.), Contemporary science education research: International perspectives (pp. 65–76). Ankara: Pegem Akademi.

    Google Scholar 

  • Kim, E., & Pak, S.-J. (2002). Students do not overcome conceptual difficulties after solving 1000 traditional problems. American Journal of Physics, 70(7), 759–765.

    Article  Google Scholar 

  • Kozma, R. (2003). The material features of multiple representations and their cognitive and social affordances for science understanding. Learning and Instruction, 13, 205–226.

    Article  Google Scholar 

  • Kozma, R. B., Russell, J., Jones, T., Marx, N., & Davis, J. (1996). The use of multiple, linked representations to facilitate science understanding. In S. Vosniadou (Ed.),. (Hrsg.) International perspectives on the design of technology-supported learning environments (pp. 41–60). Mahwah: L. Erlbaum Associates, as cited in Bauer (2015).

    Google Scholar 

  • Leinhardt, G., Zaslavsky, O., & Stein, M. K. (1990). Functions, graphs, and graphing: Tasks, learning, and teaching. Review of Educational Research, 60(1), 1–64.

    Article  Google Scholar 

  • Leisen, J. (2004). Der Wechsel der Darstellungsformen als wichtige Strategie beim Lehren und Lernen im DFU. Fremdsprache Deutsch, 30, 15–21.

    Google Scholar 

  • Leisen, J. (2005). Wechsel der Darstellungsformen. Ein Unterrichtsprinzip für alle Fächer. Der Fremdsprachliche Unterricht Englisch, 78, 9–11.

    Google Scholar 

  • Lemke, J. L. (1998). Multiplying meaning: Visual and verbal semiotics in scientific text. In J. R. Martin & R. Veel (Eds.), Reading science: Critical and functional perspectives on discourse of science (pp. 87–113). London: Routledge.

    Google Scholar 

  • Lemke, J. L. (2002). Mathematics in the middle: Measure, picture, gesture, sign, and word. In M. Anderson, A. Saenz-Ludlow, S. Zellweger, & V. Cifarelli (Eds.), Educational perspectives on mathematics as semiosis: From thinking to interpreting to knowing (pp. 215–234). Ottawa: Legas Publishing.

    Google Scholar 

  • Lemke, J. L. (2004). The literacies of science. In E. Wendy Saul (Ed.), Crossing borders in literacy and science instruction (pp. 33–47). Newark, DE/Arlington, VA: International Reading Association/NSTA Press.

    Google Scholar 

  • Linder, C. (2013). Disciplinary discourse, representation, and appresentation in the teaching and learning of science. European Journal of Science and Mathematics Education, 1(2), 43–49.

    Google Scholar 

  • Malle, G., Wittmann, E. C., & Bürger, H. (1993). Didaktische Probleme der elementaren Algebra. Wiesbaden: Springer.

    Book  Google Scholar 

  • Mayer, R. E. & Sims, V. (1994). For whom is a picture worth 1000 words - Extensions of a dual-coding theory of multimedia learning. Journal of Educational Psychology, 86(3), 389–401, as cited in Bauer (2015 ).

    Google Scholar 

  • McDermott, L. C., Rosenquist, M. L., & van Zee, E. H. (1987). Student difficulties in connecting graphs and physics: Examples from kinematics. American Journal of Physics, 55(6), 503–513.

    Article  Google Scholar 

  • Nitsch, R. (2015). Diagnose von Lernschwierigkeiten im Bereich funktionaler Zusammenhänge. Eine Studie zu typischen Fehlermustern bei Darstellungswechseln. Wiesbaden: Springer Spektrum.

    Book  Google Scholar 

  • Peirce, C. S. (1960). Collected papers of Charles Sanders Peirce (2. Aufl.). Cambridge, MA: Belknap Press of Harvard University Press.

    Google Scholar 

  • Pietrocola, M. (2008). Mathematics as structural language of physical thought. In M. Vicentini & E. Sassi (Eds.), Connecting research in physics education with teacher edu-cation, Bd. 2. ICPE.

    Google Scholar 

  • Planinic, M., Ivanjek, L., Susac, A., & Milin-Sipus, Z. (2013). Comparison of university students’ understanding of graphs in different contexts. Physical Review Special Topics – Physics Education Research, 9(2), 020103, 1–9.

    Google Scholar 

  • Pospiech, G., & Oese, E. (2014). The use of mathematical elements in physics – View of grade 8 pupils. In L. Dvořák & V. Koudelková (Eds.), ICPE-EPEC 2013 Conference Proceedings. Active learning – In a changing world of new technologies (pp. 199–205). Charles University in Prague, MATFYZPRESS publisher.

    Google Scholar 

  • Prediger, S. (2013). Darstellungen, Register und mentale Konstruktion von Bedeutungen und Beziehungen – mathematikspezifische sprachliche Herausforderungen identifizieren und bearbeiten. In M. Becker-Mrotzek, K. Schramm, E. Thürmann, & H. Vollmer (Eds.), Sprache im Fach – Sprachlichkeit und fachliches Lernen (pp. 167–183). Waxmann, Münster u.a.

    Google Scholar 

  • Prediger, S., & Wessel, L. (2011). Darstellen – Deuten – Darstellungen vernetzen. Ein fach- und sprachintegrierter Förderansatz für mehrsprachige Lernende im Mathematikunterricht. In S. Prediger & E. Özdil (Eds.), Mathematiklernen unter Bedingungen der Mehrsprachigkeit – Stand und Perspektiven der Forschung und Entwicklung in Deutschland (pp. 163–184). Waxmann, Münster u. a.

    Google Scholar 

  • Prediger, S., & Wessel, L. (2012). Darstellungen vernetzen. Ansatz zur integrierten Entwicklung von Konzepten und Sprachmitteln. Praxis der Mathematik in der Schule. Sekundarstufen I und II, 45(Jg. 54), 28–33.

    Google Scholar 

  • Rebello, S., & Cui, L. (2008). Retention and transfer of learning from mathematics to physics to engineering. American Society for Engineering Education.

    Google Scholar 

  • Redish, E. F. (2016). Analysing the competency of mathematical modelling in physics. In G. Tomasz & E. Dbowska (Eds.), Key competences in physics teaching and learning (pp. 25–40). Cham: Springer International Publishing.

    Google Scholar 

  • Redish, E. F., & Kuo, E. (2015). Language of physics, language of math: Disciplinary culture and dynamic epistemology. Science & Education, 24(5–6), 561–590.

    Article  Google Scholar 

  • Schnotz, W., & Bannert, M. (2003). Construction and interference in learning from multiple representation. Learning and Instruction, 13, 141–156.

    Article  Google Scholar 

  • Schulz von Thun, F. (n.y.). Das Kommunikationsquadrat. https://www.schulz-von-thun.de/die-modelle/das-kommunikationsquadrat (downloaded on 2018-06-11).

  • van Someren, M. (Hrsg.). (1998). Learning with multiple representations. Pergamon, as cited in Bauer (2015).

    Google Scholar 

  • Strahl, A., Schleusner, U., Mohr, M., & Müller, R. (2010). Wie Schüler Formeln gliedern – eine explorative Studie. PhyDid, 1(9), 18–24.

    Google Scholar 

  • 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(2), 020101.

    Article  Google Scholar 

  • Uhden, O. (2015). Verständnisprobleme von Schülerinnen und Schülern beim Verbinden von Physik und Mathematik. Zeitschrift für Didaktik der Naturwissenschaften, 22, 1–12.

    Google Scholar 

  • van der Meij, J., & Jong, T. d. (2006). Supporting students’ learning with multiple representations in a dynamic simulation-based learning environment. Learning and Instruction, 16(3), 199–212. https://doi.org/10.1016/j.learninstruc.2006.03.007, as cited in Bauer (2015).

    Article  Google Scholar 

  • Waldrip, B., Prain, V., & Carolan, J. (2010). Using multi-modal representations to improve learning in junior secondary science. Research in Science Education, 40, 65–80.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of Physics, TU Dresden, Dresden, Germany

    Marie-Annette Geyer & Wiebke Kuske-Janßen

Authors
  1. Marie-Annette Geyer
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Wiebke Kuske-Janßen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Marie-Annette Geyer .

Editor information

Editors and Affiliations

  1. Technische Universität Dresden, Dresden, Germany

    Gesche Pospiech

  2. DCFA - Section of Mathematics and Physics, University of Udine, Udine, Italy

    Marisa Michelini

  3. The Weizmann Institute of Science Rehovot, Israel

    Bat-Sheva Eylon

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Geyer, MA., Kuske-Janßen, W. (2019). Mathematical Representations in Physics Lessons. In: Pospiech, G., Michelini, M., Eylon, BS. (eds) Mathematics in Physics Education. Springer, Cham. https://doi.org/10.1007/978-3-030-04627-9_4

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-04627-9_4

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-04626-2

  • Online ISBN: 978-3-030-04627-9

  • eBook Packages: EducationEducation (R0)

Publish with us

Policies and ethics

Search

Navigation