Starting with Physics: A Problem-Solving Activity for High-School Students Connecting Physics and Mathematics

  • E. BagnoEmail author
  • H. Berger
  • E. Magen
  • C. Polingher
  • Y. Lehavi
  • B. Eylon


Problem-solving plays a central role among the various manifestations of the interrelations between physics and mathematics in the high-school physics classroom.

Research on the problem-solving habits of physics high-school students shows that they often start and end solving problems by looking for seemingly relevant formulas, thus decrementing the development of their physics understanding. From another perspective, teachers were found to employ in their teaching different phys-math patterns which share in common one aspect: they all begin from physics (qualitatively) before moving on to mathematics.

Here we describe a study on the use of a classroom activity (“Starting with Physics”) that attempts to motivate students to employ, when solving problems, physics concepts and principles before using formulas and other mathematical manipulations technically. Students receive only the first part of a problem consisting of a textual description of a phenomenon and the relevant mathematical information, without any subsequent questions. They are asked to describe and explain the phenomenon by using physics concepts and principles without using equations.

A study was carried out in physics high-school classes that used this activity. The findings indicate that most of the students managed to adequately describe the events using appropriate physics concepts and principles and that the mathematics that they utilized helped them promote their physics understanding. The students were cognizant of the rationale of the activity’s design and its important contribution to their learning. This activity is highly appreciated by physics teachers. They claim that it emphasizes the common underlying physical principles of apparently different problems and supports problem-solving in physics. However, it is necessary to carry it out with the same students several times in order to bring about its habitual use.


Physics-mathematics interrelations Physics concepts and principles Qualitative explanations Reflection and metacognition Qualitative problem-solving 


  1. Bagno, E., Berger, H., & Eylon, B. S. (2008). Meeting the challenge of students’ understanding of formulae in high-school physics: A learning tool. Physics Education, 43(1), 75–82.CrossRefGoogle Scholar
  2. Berger, H., Eylon, B., & Bagno, E. (2008). Professional development of physics teachers in an evidence-based blended learning program. Journal of Science Education and Technology, 17(4), 399–409.CrossRefGoogle Scholar
  3. Bing, T. J., & Redish, E. F. (2009). Analyzing problem solving using math in physics: Epistemological framing via warrants. Physical Review Special Topics – Physics Education Research, 5, 020108.CrossRefGoogle Scholar
  4. Byun, T., & Lee, G. (2014). Why students still can’t solve physics problems after solving over 2000 problems. American Journal of Physics, 82, 906.CrossRefGoogle Scholar
  5. Chi, M. T. H., Feltovich, P. J., & Glaser, R. (1981). Categorization and representation of physics problems by experts and novices. Cognitive Science, 5(2), 121–152.CrossRefGoogle Scholar
  6. Eylon, B., Berger, H., & Bagno, E. (2008). An evidence-based continuous professional development program on knowledge integration in physics: A study of teachers’ collective discourse. International Journal of Science Education, 30, 619–641.CrossRefGoogle Scholar
  7. Harrison, C., Hofstein, A., Eylon, B., & Simon, S. (2008). Evidence-based professional development of teachers in two countries. International Journal of Research in Science Education, 30, 577–591.Google Scholar
  8. Heller, K., & Heller, P. (2010). Cooperative problem solving in physics – A User’s manual: Why? What? How? Alexandria: The National Science Foundation.Google Scholar
  9. 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.CrossRefGoogle Scholar
  10. Kim, E., & Pak, S.-J. (2002). Students do not overcome conceptual difficulties after solving 1000 traditional problems. American Journal of Physics, 70, 759.CrossRefGoogle Scholar
  11. Lehavi, Y., Bagno, E., Eylon, B. S., Mualem, R., Pospiech, G., & Böhm, U. (2015). Towards a PCK of physics and mathematics interplay. In The GIREP MPTL 2014 Conference Proceedings.Google Scholar
  12. Lehavi, Y., Bagno, E., Eylon, B. S., Mualem, R., Pospiech, G., Böhm, U., Krey, O., & Karam, R. (2017). Classroom evidence of teachers’ PCK of the interplay of physics and mathematics. In T. Greczyło & E. Dębowska (Eds.), Key competences in physics teaching and learning (Springer proceedings in physics) (Vol. 190, pp. 95–104). Cham: Springer.CrossRefGoogle Scholar
  13. Linn, M. C., & Eylon, B. S. (2006). Science education: Integrating views of learning and instruction. In P. A. Alexander & P. H. Winne (Eds.), Handbook of Educational Psychology (2nd ed., pp. 511–544). Mahwah: Lawrence Erlbaum Associates.Google Scholar
  14. Linn, M. C., & Eylon, B. S. (2011). Science learning and instruction: Taking advantage of technology to promote knowledge integration. New York: Routledge.CrossRefGoogle Scholar
  15. Mason, A., & Singh, C. (2010). Helping students learn effective problem solving strategies by reflecting with peers. American Journal of Physics, 78, 748.CrossRefGoogle Scholar
  16. Pospiech, G., & Geyer, M.-A. (2016). Physical – Mathematical modelling in physics teaching. In Electronic proceedings – Key competences in physics teaching and learning (pp. 38–44). Wroclaw: Institute of Experimental Physics, University of Wrocław. Abgerufen von. Scholar
  17. Pospiech, G., & Oese, E. (2014). Use of mathematical elements in physics – Grade 8. In Active learning – In a changing world of new technologies (pp. S. 199–S. 206). Prag: Charles University in Prague, MATFYZPRESS Publisher.Google Scholar
  18. Redish, E. F., & Kuo, E. (2015). Language of physics, language of math: Disciplinary culture and dynamic epistemology. Science & Education, 24, 561. Scholar
  19. Reiser, B. J. (2004). Scaffolding complex learning: The mechanisms of structuring and problematizing student work. Journal of the Learning Science, 13, 273–304. Scholar
  20. Sherin, B. (2001). How students understand physics equations. Cognition & Instruction, 19, 479.CrossRefGoogle Scholar
  21. Uhden, O., Karam, R., Pospiech, G., & Pietrocola, M. (2012). Modelling mathematical reasoning in physics education. Science & Education, 20(4), 485. Scholar
  22. Van Heuvelen, A. (1991). Learning to think like a physicist: A review of research-based instructional strategies. American Journal of Physics, 59(10), 891–897.CrossRefGoogle Scholar
  23. Yerushalmi, E., & Eylon, B. (2016). Problem solving in science learning. In R. Gunstone (Ed.), Encyclopedia of science education. Heidelberg: Springer.Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • E. Bagno
    • 1
    Email author
  • H. Berger
    • 1
  • E. Magen
    • 1
    • 2
  • C. Polingher
    • 1
    • 3
  • Y. Lehavi
    • 1
    • 4
  • B. Eylon
    • 1
  1. 1.The Weizmann Institute of ScienceRehovotIsrael
  2. 2.Ostrovsky High SchoolRaananaIsrael
  3. 3.Hemda Schwartz-Reisman Science Education CenterTel AvivIsrael
  4. 4.The David Yellin Academic College of EducationJerusalemIsrael

Personalised recommendations