Skip to main content

Comparing Student Understanding of Graphs in Physics and Mathematics

  • Chapter
  • First Online:
Mathematics in Physics Education

Abstract

In this chapter we address the question of similarities and differences in students’ strategies and difficulties with graphs in the context of mathematics and physics and the question of possible transfer of knowledge between these domains. We divide mathematics into context-free mathematics and mathematics with context, but we limit contexts in this domain only to those which do not require special conceptual knowledge. The domain of physics is represented by kinematics, where graphs play an important role, but which also requires knowledge of basic kinematics concepts and relations. We review, compare, and synthesize the results from four of our studies which included high school and first-year university students from Croatia and Austria. We raise the question of how to promote transfer of knowledge between physics and mathematics and how to build stronger and more unified student knowledge of graphs. We also point to important student difficulties which may act as obstacles in that process.

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

Access this chapter

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

References

  • Araujo, I. S., Veit, E. A., & Moreira, M. A. (2008). Physics students’ performance using computational modeling activities to improve kinematics graphs interpretation. Computers in Education, 50, 1128.

    Article  Google Scholar 

  • Bassok, M., & Holyoak, K. J. (1989). Interdomain transfer between isomorphic topics in algebra and physics. Journal of Experimental Psychology: Learning, Memory, and Cognition, 15(1), 153.

    Google Scholar 

  • Beichner, R. J. (1994). Testing student interpretation of kinematics graphs. American Journal of Physics, 62, 750.

    Article  Google Scholar 

  • Bond, T. G., & Fox, C. M. (2001). Applying the Rasch model: Fundamental measurement in the human sciences. Mahwah: Lawrence Erlbaum.

    Book  Google Scholar 

  • Bransford, J. D., & Schwartz, D. L. (1999). Rethinking transfer: A simple proposal with multiple implications. Review of Research in Education, 24, 61–100.

    Google Scholar 

  • Bransford, J. D., Brown, A. L., & Cocking, R. R. (1999). How people learn: Brain, mind, experience, and school. Washington, DC: National Academy Press.

    Google Scholar 

  • Brasell, H. M., & Rowe, B. M. (1993). Graphing skills among high school physics students. School Science and Mathematics, 93, 63.

    Article  Google Scholar 

  • Christensen, W. M., & Thompson, J. R. (2012). Investigating graphical representations of slope and derivative without a physics context. Physical Review Physics Education Research, 8, 023101.

    Article  Google Scholar 

  • Cui, L. (2006). Assessing college students’ retention and transfer from calculus to physics (PhD Thesis). Kansas State University.

    Google Scholar 

  • Dreyfus, T., & Eisenberg, T. (1990). On difficulties with diagrams: Theoretical issues. In G. Booker, P. Cobb, & T. N. De Mendicuti (Eds.), Proceedings of the Fourteenth Annual Conference of the International Group for the Psychology of Mathematics Education (Vol. 1, pp. 27–36). Oaxtepex: PME.

    Google Scholar 

  • Forster, P. A. (2004). Graphing in physics: Processes and sources of error in tertiary entrance examinations in Western Australia. Research in Science Education, 34, 239.

    Article  Google Scholar 

  • Graham, T., & Sharp, J. (1999). An investigation into able students’ understanding of motion graphs. Teaching Mathematics and its Applications, 18, 128.

    Article  Google Scholar 

  • Habre, S., & Abboud, M. (2006). Students’ conceptual understanding of a function and its derivative in an experimental calculus course. Journal of Mathematical Behavior, 25, 57–72.

    Article  Google Scholar 

  • Hadjidemetriou, C., & Williams, J. S. (2002). Children’s’ graphical conceptions. Research in Mathematics Education, 4, 69.

    Article  Google Scholar 

  • Hammer, D., Elby, A., Scherr, R. E., & Redish, E. F. (2005). Resources, framing, and transfer. In J. Mestre (Ed.), Transfer of learning from a modern multidisciplinary perspective (pp. 89–120). Greenwich: Information Age Publishing.

    Google Scholar 

  • Ivanjek, L., Planinic, M., Hopf, M., & Susac, A. (2015). Student difficulties with graphs in different contexts. In K. Hahl, K. Juuti, J. Lampiselkä, A. Uitto, & J. Lavonen (Eds.), Cognitive and affective aspects in science education researchSelected papers from the ESERA 2015 conference (pp. 167–178). Cham: Springer International Publishing AG.

    Google Scholar 

  • Ivanjek, L., Susac, A., Planinic, M., Milin-Sipus, Z., & Andrasevic, A. (2016). Student reasoning about graphs in different contexts. Physical Review Physics Education Research, 12, 010106.

    Article  Google Scholar 

  • Kerslake, D. (1981). Graphs. In K. M. Hart (Ed.), Children’s understanding of mathematics: 11–16 (pp. 120–136). London: John Murray.

    Google Scholar 

  • Lave, J. (1988). Cognition in practice: Mind, mathematics and culture in everyday life. Cambridge: Cambridge University Press.

    Book  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 

  • Linacre, J. M. (2006). WINSTEPS Rasch measurement computer program. Chicago: Winsteps.com.

    Google Scholar 

  • Linacre, J. M. A user’s guide to WINSTEPS. www.winsteps.com

  • 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, 503.

    Article  Google Scholar 

  • Michelsen, C. (2005). Expanding the domain – Variables and functions in an interdisciplinary context between mathematics and physics. In A. Beckmann, C. Michelsen, & B. Sriraman (Eds.), Proceedings of the 1st International Symposium of Mathematics and its Connections to the Arts and Sciences. The University of Education, Schwäbisch Gmünd, Germany, pp. 201–214.

    Google Scholar 

  • Nguyen, D. H., & Rebello, N. S. (2011). Students’ understanding and application of the area under the curve concept in physics problems. Physical Review Physics Education Research, 7, 010112.

    Article  Google Scholar 

  • Planinic, M., Milin-Sipus, Z., Katic, H., Susac, A., & Ivanjek, L. (2012). Comparison of student understanding of line graph slope in physics and mathematics. The International Journal of Science and Mathematics Education, 10(6), 1393.

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Potgieter, M., Harding, A., & Engelbrecht, J. (2008). Transfer of algebraic and graphical thinking between mathematics and chemistry. Journal of Research in Science Teaching, 45(2), 197–218.

    Article  Google Scholar 

  • Swatton, P., & Taylor, R. M. (1994). Pupil performance in graphical tasks and its relationship to the ability to handle variables. British Educational Research Journal, 20, 227.

    Article  Google Scholar 

  • Tuminaro, J. (2004). A cognitive framework for analyzing and describing introductory students’ use and understanding of mathematics in physics. PhD thesis, University of Maryland, College Park.

    Google Scholar 

  • Tuminaro, J., & Redish, E. F. (2007). Elements of a cognitive model of physics problem solving: Epistemic games. Physical Review Physics Education Research, 3, 020101.

    Article  Google Scholar 

  • Wemyss, T., & van Kampen, P. (2013). Categorization of first-year university students’ interpretations of numerical linear distance-time graphs. Physical Review Physics Education Research, 9, 010107.

    Article  Google Scholar 

  • Woolnough, J. (2000). How do students learn to apply their mathematical knowledge to interpret graphs in physics? Research in Science Education, 30, 259.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Maja Planinic .

Editor information

Editors and Affiliations

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

Planinic, M., Susac, A., Ivanjek, L., Milin Šipuš, Ž. (2019). Comparing Student Understanding of Graphs in Physics and Mathematics. In: Pospiech, G., Michelini, M., Eylon, BS. (eds) Mathematics in Physics Education. Springer, Cham. https://doi.org/10.1007/978-3-030-04627-9_10

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-04627-9_10

  • 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