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Global blind spot in understanding trigonometric derivatives: A multinational analysis

Yossi Ben-Zion1,*, Roni Segal1, Jianqiang Liu2, Chun-Ming Wang2, Atanu Rajak3, and Noah D. Finkelstein4

  • *Contact author: benzioy@biu.ac.il
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Phys. Rev. Phys. Educ. Res. 21, 020137 – Published 27 October, 2025

DOI: https://doi.org/10.1103/t2fv-2spd

Abstract

Trigonometric derivatives are fundamental in both mathematics and physics, yet their correct application, particularly the distinction between radians and degrees, remains a significant challenge for college students worldwide. This study identifies a widespread “blind spot” in understanding trigonometric derivatives and their implications for physical systems, highlighting a critical gap in physics education. A multinational survey of 769 college students, primarily undergraduate and graduate science, technology, engineering, and mathematics (majors, from Israel, the United States, China, and India assessed their ability to differentiate between radians and degrees in mathematical and physical contexts, focusing on harmonic motion. Results reveal that only 26.3% of students correctly identified that the well-known expressions for trigonometric derivatives hold exclusively in radians, while 70.7% incorrectly assumed that both radians and degrees are valid. Notably, students demonstrated improved recognition of radians in physical contexts (59% correct responses) compared to mathematical ones, suggesting that students rely on familiar physical equations as cognitive reference points when applying mathematical concepts. These misunderstandings appear globally, suggesting a universal challenge. The findings highlight the need for curriculum reforms to better connect mathematical formalism with physical application.

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References (41)

  1. R. Shankar, Fundamentals of Physics I: Mechanics, Relativity, and Thermodynamics (Yale University Press, New Haven, 2019).
  2. L. Bollen, P. van Kampen, C. Baily, and M. De Cock, Qualitative investigation into students’ use of divergence and curl in electromagnetism, Phys. Rev. Phys. Educ. Res. 12, 020134 (2016).
  3. F. R. Yeatts and J. R. Hundhausen, Calculus and physics: Challenges at the interface, Am. J. Phys. 60, 716 (1992).
  4. B. R. Wilcox and S. J. Pollock, Upper-division student difficulties with the Dirac delta function, Phys. Rev. ST Phys. Educ. Res. 11, 010108 (2015).
  5. L. Bollen, P. van Kampen, and M. De Cock, Students’ difficulties with vector calculus in electrodynamics, Phys. Rev. ST Phys. Educ. Res. 11, 020129 (2015).
  6. B. R. Wilcox and S. J. Pollock, Upper-division student difficulties with separation of variables, Phys. Rev. ST Phys. Educ. Res. 11, 020131 (2015).
  7. D.-H. Nguyen and N. S. Rebello, Students’ difficulties with integration in electricity, Phys. Rev. ST Phys. Educ. Res. 7, 010113 (2011).
  8. R. E. Pepper, S. V. Chasteen, S. J. Pollock, and K. K. Perkins, Observations on student difficulties with mathematics in upper-division electricity and magnetism, Phys. Rev. ST Phys. Educ. Res. 8, 010111 (2012).
  9. L. Cui, N. S. Rebello, and A. G. Bennett, College students’ transfer from calculus to physics, AIP Conf. Proc. 818, 37 (2006).
  10. M. Carli, S. Lippiello, O. Pantano, M. Perona, and G. Tormen, Testing students ability to use derivatives, integrals, and vectors in a purely mathematical context and in a physical context, Phys. Rev. Phys. Educ. Res. 16, 010111 (2020).
  11. E. F. Redish, Using math in physics: Overview, Phys. Teach. 59, 314 (2021).
  12. E. Breitenberger, The mathematical knowledge of physics graduates: Primary data and conclusions, Am. J. Phys. 60, 318 (1992).
  13. O. Uhden, R. Karam, M. Pietrocola, and G. Pospiech, Modelling mathematical reasoning in physics education, Sci. Educ. 21, 485 (2012).
  14. E. Palmgren and T. Rasa, Modelling roles of mathematics in physics, Sci. Educ. 33, 365 (2024).
  15. S. W. Brahmia and P. W. Thompson, Framing the fundamental theorem of calculus through physics-based quantities, arXiv:2501.04219.
  16. B. L. Sherin, How students understand physics equations, Cognit. Instr. 19, 479 (2001).
  17. G. Fauconnier and M. Turner, The Way We Think: Conceptual Blending and the Mind’s Hidden Complexities (Basic books, New York, 2008).
  18. F. Zhao and A. Schuchardt, Development of the Sci-math Sensemaking Framework: categorizing sensemaking of mathematical equations in science, Int. J. STEM Educ. 8, 10 (2021).
  19. B. P. Schermerhorn and J. R. Thompson, Making context explicit in equation construction and interpretation: Symbolic blending, Phys. Rev. Phys. Educ. Res. 19, 020149 (2023).
  20. J. A. Czocher, H. L. Hardison, and S. S. Kularajan, A bridging study analyzing mathematical model construction through a quantities-oriented lens, Educ. Stud. Math. 111, 299 (2022).
  21. S. Kapon and M. Schvartzer, Guided inquiry into a physics equation, Cognit. Instr. 42, 159 (2024).
  22. J. D. Gifford and N. D. Finkelstein, Categorical framework for mathematical sense making in physics, Phys. Rev. Phys. Educ. Res. 16, 020121 (2020).
  23. J. D. Gifford and N. D. Finkelstein, Applying a mathematical sense-making framework to student work and its potential for curriculum design, Phys. Rev. Phys. Educ. Res. 17, 010138 (2021).
  24. G. Galle and D. Meredith, The trouble with trig, Phys. Teach. 52, 112 (2014).
  25. K. Weber, Students’ understanding of trigonometric functions, Math. Educ. Res. J. 17, 91 (2005).
  26. S. Van den Eynde, J. Deprez, M. Goedhart, and M. De Cock, Undergraduate students’ difficulties with boundary conditions for the diffusion equation, Int. J. Math. Educ. Sci. Technol. 53, 2176 (2022).
  27. R. J. Beichner, Testing student interpretation of kinematics graphs, Am. J. Phys. 62, 750 (1994).
  28. W. M. Christensen and J. R. Thompson, Investigating graphical representations of slope and derivative without a physics context, Phys. Rev. ST Phys. Educ. Res. 8, 023101 (2012).
  29. D. Halliday, R. Resnick, and J. Walker, Fundamentals of Physics (John Wiley & Sons, New York, 2013).
  30. R. A. Serway, J. W. Jewett, and V. Peroomian, Physics for Scientists and Engineers (Saunders College Publishing, Philadelphia, PA, 2000), Vol. 2.
  31. P. A. Tipler and G. Mosca, Physics for Scientists and Engineers (Macmillan, London, 2007).
  32. E. F. Redish, Using Math in Physics: 3. Anchor equations, Phys. Teach. 59, 599 (2021).
  33. S. Hasan, D. Bagayoko, and E. L. Kelley, Misconceptions and the certainty of response index (CRI), Phys. Educ. 34, 294 (1999).
  34. M. Potgieter, E. Malatje, E. Gaigher, and E. Venter, Confidence versus Performance as an Indicator of the Presence of Alternative Conceptions and Inadequate Problem‐Solving Skills in Mechanics, Int. J. Sci. Educ. 32, 1407 (2010).
  35. D. B. Wright and S. M. Wolff, Justifying responses affects the relationship between confidence and accuracy, Exp. Psychol. 71, 144 (2024).
  36. M. Eric, Peer Instruction: A User’s Manual (Prentice Hall, Upper Saddle River, NJ 1997).
  37. E. F. Redish and J. R. Burciaga, Teaching Physics: With the Physics Suite (John Wiley & Sons, Hoboken, NJ, 2003), Vol. 1.
  38. P. B. Kohl, D. Rosengrant, and N. D. Finkelstein, Strongly and weakly directed approaches to teaching multiple representation use in physics, Phys. Rev. ST Phys. Educ. Res. 3, 010108 (2007).
  39. P. B. Kohl and N. D. Finkelstein, Student representational competence and self-assessment when solving physics problems, Phys. Rev. ST Phys. Educ. Res. 1, 010104 (2005).
  40. A. B. Arons, Teaching Introductory Physics (Wiley, New York, 1996).
  41. , “Data tables of Global Blind Spot in Understanding Trigonometric Derivatives: A Multinational Analysis,” Zenodo (2025), 10.5281/zenodo.17234682.

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Phys. Rev. Phys. Educ. Res. 21, 020137– Published 27 October, 2025
  • Received 4 March 2025
  • Accepted 16 September 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

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