Skip to main content
SpringerLink
Log in

What part of the concept of acceleration is difficult to understand: the mathematics, the physics, or both?

  • Original Article
  • Published:
ZDM Aims and scope Submit manuscript

Abstract

In this paper, details of student difficulties in understanding the concept of acceleration and the mathematical and physical/intuitive sources of these are delineated by utilizing the teaching experiment methodology. As a result of the study, two anchoring analogies are proposed that can be used as a diagnostic tool for students’ alternative conceptions. These can be used in teaching to highlight the peculiarity of acceleration concept. This study portrays how seeing acceleration as ‘rate of change’ of a quantity (velocity) and recognizing the consequences of such a definition are hindered in certain ways which in turn negatively affect learning the concept of force. This is also an example that illustrates that a rather “simple” mathematical concept (i.e., rate of change) for the expert can become a complex phenomenon when embedded in a physical concept (i.e., acceleration) which is consistently found to be as a misconception among learners at various levels that is widely occurring and very resistant to change.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

References

  • Arons, A. B. (1997). Teaching introductory physics. New York, NY: Wiley.

    Google Scholar 

  • Basson, I. (2002). Physics and mathematics as interrelated fields of thought development using acceleration as an example. International Journal of Mathematical Education in Science and Technology, 33(5), 679–690.

    Article  Google Scholar 

  • Bayraktar, S. (2009). Misconceptions of Turkish pre-service teachers about force and motion. International Journal of Science and Mathematics Education, 7(2), 273–291.

    Article  Google Scholar 

  • Bezuidenhout, J. (1998). First-year university students’ understanding of rate of change. International Journal of Mathematical Education in Science and Technology, 29(3), 389–399.

    Article  Google Scholar 

  • Bowers, J., & Doerr, H. M. (2001). An analysis of prospective teachers’ dual roles in understanding the mathematics of change: Eliciting growth with technology. Journal of Mathematics Teacher Education, 4(2), 115–137.

    Article  Google Scholar 

  • Camp, C. W., & Clement, J. J. (1994). Preconceptions in mechanics. Lessons dealing with students’ conceptual difficulties. Dubuque, IA: Kendall/Hunt Publishing Company.

    Google Scholar 

  • Carrejo, D. J., & Marshall, J. (2007). What is mathematical modelling? Exploring prospective teachers’ use of experiments to connect mathematics to the study of motion. Mathematics Education Research Journal, 19(1), 45–76.

    Google Scholar 

  • Castells, M., Enciso, J., Cerveró, J. M., López, P., & Cabellos, M. (2007). What can we learn from a study of argumentation in the students answers and group discussion to open physics problems? In R. Pintó & D. Couso (Eds.), Contributions from science education research (pp. 417–431). Dordrecht, The Netherlands: Springer.

    Chapter  Google Scholar 

  • Champagne, A. B., & Klopfer, L. E. (1982). A causal model of students’ achievement in a college physics course. Journal of Research in Science Teaching, 19(4), 299–309.

    Article  Google Scholar 

  • Champagne, A. B., Klopfer, L. E., & Anderson, J. H. (1980). Factors influencing the learning of classical mechanics. American Journal of Physics, 48(12), 1074–1079.

    Article  Google Scholar 

  • Cobb, P., & Steffe, L. P. (1983). The constructivist researcher as teacher and model builder. Journal for Research in Mathematics Education, 14(2), 83–94.

    Article  Google Scholar 

  • Confrey, J., & Smith, E. (1994). Exponential functions, rates of change, and the multiplicative unit. Educational Studies in Mathematics, 26(2–3), 134–164.

    Google Scholar 

  • diSessa, A. A. (1982). Unlearning Aristotelian physics: A study of knowledge based learning. Cognitive Science, 6(1), 37–75.

    Article  Google Scholar 

  • Driver, R., Squires, A., Rushworth, P., & Wood-Robinson, V. (1994). Making sense of secondary science: Research into children’s ideas. New York, NY: Routledge.

    Google Scholar 

  • Ebison, M. G. (1993). Newtonian in mind but Aristotelian at heart. Science & Education, 2(4), 345–362.

    Article  Google Scholar 

  • Griffith, W. T. (1985). Factors affecting performance in introductory physics courses. American Journal of Physics, 53(9), 839–842.

    Article  Google Scholar 

  • Hackworth, J. (1994). Calculus students’ understanding of rate. Unpublished Master’s thesis, Department of Mathematical Sciences, San Diego State University. http://pat-thompson.net/PDFversions/Theses/1994Hackworth.pdf. Accessed 28 July 2009.

  • Halloun, I. A., & Hestenes, D. (1985). Common sense concepts about motion. American Journal of Physics, 53(11), 1056–1065.

    Article  Google Scholar 

  • Herbert, S., & Pierce, R. (2008). An ‘emergent model’ for rate of change. International Journal of Computers for Mathematical Learning, 13(3), 231–249.

    Article  Google Scholar 

  • Hestenes, D. (2009). Modeling science education. In A. Bilsel & M. U. Garip (Eds.), Proceedings of the frontiers in science education research conference (pp. 3–14). Famagusta, North Cyprus: Eastern Mediterranean University Press.

    Google Scholar 

  • Hestenes, D., & Wells, M. (1992). A Mechanics baseline test. The Physics Teacher, 30(3), 159–166.

    Article  Google Scholar 

  • Hestenes, D., Wells, M., & Swackhamer, G. (1992). Force concept inventory. The Physics Teacher, 30(3), 141–158.

    Article  Google Scholar 

  • Hewitt, P. G. (2006). Conceptual physics (10th ed.). San Francisco, CA: Pearson–Addison-Wesley.

    Google Scholar 

  • Hubber, P., Tytler, R., & Haslam, F. (2010). Teaching and learning about force with a representational focus: Pedagogy and teacher change. Research in Science Education, 40(1), 5–28.

    Article  Google Scholar 

  • Jagger, J. M. (1987). Students’ understanding of acceleration. Mathematics in School, 16(4), 24–25.

    Google Scholar 

  • Jones, A. T. (1983). Investigation of students’ understanding of speed, velocity and acceleration. Research in Science Education, 13(1), 95–104.

    Article  Google Scholar 

  • Lamon, S. J. (2008). Teaching fractions and ratios for understanding: Essential content knowledge and instructional strategies for teachers (2nd ed.). www.eBookstore.tandf.co.uk: Taylor and Francis e-Library.

  • Onslow, B. (1988). Terminology: Its effect on children’s understanding of the rate concept. Focus on Learning Problems in Mathematics, 10(4), 19–30.

    Google Scholar 

  • Orton, A. (1984). Understanding rate of change. Mathematics in School, 13(5), 23–26.

    Google Scholar 

  • Ravi, R. (2007). The definition of reaction rate: A closure. Chemical Engineering Communications, 194(3), 345–352.

    Article  Google Scholar 

  • Safi, F. (2009). Exploring the understanding of whole number concepts and operations: A case study analysis of prospective elementary school teachers. Unpublished doctoral dissertation, University of Central Florida.

  • Steffe, L. P., & D’Ambrosio, B. S. (1996). In D. F. Treagust, R. Duit, & B. J. Fraser (Eds.), Improving teaching and learning in science and mathematics (pp. 65–76). New York, NY: Teachers College Press.

  • Steffe, L. P., & Thompson, P. W. (2000). Teaching experiment methodology: Underlying principles and essential elements. In A. E. Kelly & R. A. Lesh (Eds.), Handbook of research design in mathematics and science education. Mahwah, NJ: Lawrence Erlbaum.

    Google Scholar 

  • Steiner, C. J. (2009). A study of pre-service elementary teachers’ conceptual understanding of integers. Unpublished doctoral dissertation, Kent State University, Kent.

  • Thompson, P. W. (1994a). The development of the concept of speed and its relationship to concepts of rate. In G. Harel & J. Confrey (Eds.), The development of multiplicative reasoning in the learning of mathematics (pp. 179–234). Albany, NY: SUNY Press.

    Google Scholar 

  • Thompson, P. W. (1994b). Images of rate and operational understanding of the fundamental theorem of calculus. Educational Studies in Mathematics, 26(2–3), 229–274.

    Article  Google Scholar 

  • Thompson, P. W., & Thompson, A. G. (1994). Talking about rates conceptually. Part I. A teacher’s struggle. Journal for Research in Mathematics Education, 25(3), 279–303.

    Article  Google Scholar 

  • Thornton, R. K., & Sokoloff, D. R. (1998). Assessing student learning of Newton’s laws: The force and motion conceptual evaluation and the evaluation of active learning laboratory and lecture curricula. American Journal of Physics, 66(4), 338–352.

    Article  Google Scholar 

  • Tobias, J. M. (2009). Preservice elementary teachers’ development of rational number understanding through the social perspective and the relationship among social and individual environments. Unpublished doctoral dissertation, University of Central Florida, Orlando.

  • Trowbridge, D., & McDermott, L. C. (1980). Investigation of student understanding of the concept of acceleration in one dimension. American Journal of Physics, 49(3), 242–253.

    Article  Google Scholar 

  • Tzur, R. (1995). Interaction and children’s fraction learning. Unpublished doctoral dissertation, University of Georgia, Athens.

  • Wilhelm, J. A., & Confrey, J. (2003). Projecting rate of change in the context of motion onto the context of money. International Journal of Mathematical Education in Science and Technology, 34(6), 887–904.

    Article  Google Scholar 

  • Woods, R., & Thorley, R. (1993). Understanding conceptual change teaching through case studies of students’ learning. In The proceedings of the third international seminar on misconceptions and educational strategies in science and mathematics. Ithaca, NY: Misconceptions Trust.

Download references

Author information

Authors and Affiliations

  1. Gazi Üniversitesi, Ankara, Turkey

    Mehmet Fatih Taşar

Authors
  1. Mehmet Fatih Taşar
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mehmet Fatih Taşar.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Taşar, M.F. What part of the concept of acceleration is difficult to understand: the mathematics, the physics, or both?. ZDM Mathematics Education 42, 469–482 (2010). https://doi.org/10.1007/s11858-010-0262-9

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11858-010-0262-9

Keywords

Search

Navigation