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Case study examining graduate student sensemaking using the epistemic game framework for Laplace’s equation in upper-level electrostatics

Jaya Shivangani Kashyap and Chandralekha Singh

  • Department of Physics and Astronomy, University of Pittsburgh, 3941 O’Hara Street, Pittsburgh, Pennsylvania 15260, USA

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Phys. Rev. Phys. Educ. Res. 21, 020125 – Published 10 September, 2025

DOI: https://doi.org/10.1103/4b9y-j71m

Abstract

This case study used individual interviews to investigate graduate students’ sensemaking in upper-level electrostatics in the context of problems that can be efficiently solved for the electric potential using Laplace’s equation. Although there are many technical mathematical issues involved in solving Laplace’s equation, the focus of this research is not on those issues. Instead, the focus is on structural issues such as whether students recognize when solving Laplace’s equation would be an effective approach to finding the potential and set up the problems correctly, and whether they can draw the electric field lines and equipotential surfaces in a given situation. Although many prior investigations have shed light on student sensemaking in introductory physics contexts, very few investigations have focused on graduate student sensemaking while solving advanced physics problems. We present the findings of our research, which was conducted through the lens of the epistemic game framework proposed by Tuminaro and Redish. We observe different nested epistemic games played by students.

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References (94)

  1. Á. Suárez, A. C. Marti, K. Zuza, and J. Guisasola, Learning difficulties among students when applying Ampére-Maxwell’s law and its implications for teaching, Phys. Rev. Phys. Educ. Res. 20, 010143 (2024).
  2. D.-H. Nguyen and N. S. Rebello, Students’ difficulties with integration in electricity, Phys. Rev. ST Phys. Educ. Res. 7, 010113 (2011).
  3. E. Campos, G. Zavala, K. Zuza, and J. Guisasola, Students’ understanding of the concept of the electric field through conversions of multiple representations, Phys. Rev. Phys. Educ. Res. 16, 010135 (2020).
  4. E. Campos, G. Zavala, K. Zuza, and Jenaro Guisasola, Electric field lines: The implications of students’ interpretation on their understanding of the concept of electric field and of the superposition principle, Am. J. Phys. 87, 660 (2019).
  5. J. Li and C. Singh, Investigating and improving introductory physics students’ understanding of the electric field and superposition principle, Eur. J. Phys. 38, 055702 (2017).
  6. J. Li and C. Singh, Investigating and improving introductory physics students’ understanding of electric flux, Eur. J. Phys. 39, 045711 (2018).
  7. J. Li and C. Singh, Investigating and improving introductory physics students’ understanding of electric field and the superposition principle: The case of a continuous charge distribution, Phys. Rev. Phys. Educ. Res. 15, 010116 (2019).
  8. I. Garzón, M. De Cock, K. Zuza, P. van Kampen, and J. Guisasola, Probing university students’ understanding of electromotive force in electricity, Am. J. Phys. 82, 72 (2014).
  9. K. Zuza, J. Guisasola, M. Michelini, and L. Santi, Rethinking Faraday’s law for teaching motional electromotive force, Eur. J. Phys. 33, 397 (2012).
  10. K. Zuza, M. De Cock, P. van Kampen, L. Bollen, and J. Guisasola, University students’ understanding of the electromotive force concept in the context of electromagnetic induction, Eur. J. Phys. 37, 065709 (2016).
  11. K. Zuza, J.-M. Almudí, A. Leniz, and J. Guisasola, Addressing students’ difficulties with Faraday’s law: A guided problem solving approach, Phys. Rev. ST Phys. Educ. Res. 10, 010122 (2014).
  12. J. Li, A. Maries, and C. Singh, Helping students apply superposition principle in problems involving spherical, cylindrical, and planar charge distributions, Am. J. Phys. 91, 613 (2023).
  13. A. Maries, S.-Y. Lin, and C. Singh, Challenges in designing appropriate scaffolding to improve students’ representational consistency: The case of a Gauss’s law problem, Phys. Rev. Phys. Educ. Res. 13, 020103 (2017).
  14. E. Campos, E. Hernandez, P. Barniol, and Genaro Zavala, Phenomenographic analysis and comparison of students’ conceptual understanding of electric and magnetic fields and the principle of superposition, Phys. Rev. Phys. Educ. Res. 17, 020117 (2021).
  15. J. Guisasola, J. L. Zubimendi, and K. Zuza, How much have students learned? Research-based teaching on electrical capacitance, Phys. Rev. ST Phys. Educ. Res. 6, 020102 (2010).
  16. P. van Kampen, Students’ Understanding of Electricity and Magnetism (AIP Publishing LLC, Melville, NY, 2023).
  17. L. Doughty, E. McLoughlin, and P. van Kampen, What integration cues, and what cues integration in intermediate electromagnetism, Am. J. Phys. 82, 1093 (2014).
  18. B. S. Eylon and U. Ganiel, Macro-micro relationships: The missing link between electrostatics and electrodynamics in students’ reasoning, Int. J. Sci. Educ. 12, 79 (1990).
  19. B. A. Thacker, U. Ganiel, and D. Boys, Macroscopic phenomena and microscopic processes: Student understanding of transients in direct current electric circuits, Am. J. Phys. 67, S25 (1999).
  20. C. Singh, Student understanding of symmetry and Gauss’s law of electricity, Am. J. Phys. 74, 923 (2006).
  21. J. Bilak and C. Singh, Improving students’ conceptual understanding of conductors and insulators, AIP Conf. Proc. 951, 49 (2007).
  22. E. Gire and E. Price, Graphical representations of vector functions in upper-division E&M, AIP Conf. Proc. 1413, 27 (2012).
  23. S. V. Chasteen, S. J. Pollock, R. E. Pepper, and K. K. Perkins, Transforming the junior level: Outcomes from instruction and research in E&M, Phys. Rev. ST Phys. Educ. Res. 8, 020107 (2012).
  24. S. V. Chasteen, R. E. Pepper, M. D. Caballero, S. J. Pollock, and K. K. Perkins, Colorado upper-division electrostatics diagnostic: A conceptual assessment for the junior level, Phys. Rev. ST Phys. Educ. Res. 8, 020108 (2012).
  25. J. P. Zwolak and C. A. Manogue, Assessing student reasoning in upper-division electricity and magnetism at Oregon State University, Phys. Rev. ST Phys. Educ. Res. 11, 020125 (2015).
  26. 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).
  27. B. R. Wilcox and S. J. Pollock, Upper-division student difficulties with separation of variables, Phys. Rev. ST Phys. Educ. Res. 11, 020131 (2015).
  28. Q. X. Ryan, B. R. Wilcox, and S. J. Pollock, Student difficulties with boundary conditions in the context of electromagnetic waves, Phys. Rev. Phys. Educ. Res. 14, 020126 (2018).
  29. B. R. Wilcox and G. Corsiglia, Cross-context look at upper-division student difficulties with integration, Phys. Rev. Phys. Educ. Res. 15, 020136 (2019).
  30. 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).
  31. 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).
  32. L. Bollen, P. van Kampen, C. Baily, M. Kelly, and M. De Cock, Student difficulties regarding symbolic and graphical representations of vector fields, Phys. Rev. Phys. Educ. Res. 13, 020109 (2017).
  33. L. Bollen, P. van Kampen, and M. De Cock, Development, implementation, and assessment of a guided-inquiry teaching-learning sequence on vector calculus in electrodynamics, Phys. Rev. Phys. Educ. Res. 14, 020115 (2018).
  34. C. Singh and A. Maries, Core graduate courses: A missed learning opportunity?, AIP Conf. Proc 1513, 382 (2013).
  35. A. J. Mason, J. M. McCardell, P. A. White, and J. S. Colton, Improving performance in upper-division electricity and magnetism with explicit incentives to correct mistakes, Phys. Rev. Phys. Educ. Res. 19, 020104 (2023).
  36. B. Brown, A. Mason, and C. Singh, Improving performance in quantum mechanics with explicit incentives to correct mistakes, Phys Rev Phys. Educ. Res. 12, 010121 (2016).
  37. O. Uhden, R. Karam, M. Pietrocola, and G. Pospiech, Modelling mathematical reasoning in physics education, Sci. Educ. 21, 485 (2012).
  38. C. Tzanakis, Mathematics & physics: An innermost relationship, in Didactical Implications for their Teaching Learning, Conference Proceedings, edited by L. Radford, F. Furinghetti, and T. Hausberger (2016), https://hal.science/hal-01349231/document.
  39. R. Karam, Framing the structural role of mathematics in physics lectures: A case study on electromagnetism, Phys. Rev. ST Phys. Educ. Res. 10, 010119 (2014).
  40. R. Karam, Introduction of the thematic issue on the interplay of physics and mathematics, Sci. Educ. 24, 487 (2015).
  41. D. Hu and N. S. Rebello, Using conceptual blending to describe how students use mathematical integrals in physics, Phys. Rev. ST Phys. Educ. Res. 9, 020118 (2013).
  42. L. Branchetti, A. Cattabriga, and O. Levrini, Interplay between mathematics and physics to catch the nature of a scientific breakthrough: The case of the blackbody, Phys. Rev. Phys. Educ. Res. 15, 020130 (2019).
  43. E. F. Redish, Using math in physics: Overview, Phys. Teach. 59, 314 (2021).
  44. E. F. Redish, Varenna Summer school, in Research on Physics Education: Proceedings of the International School of Physics “Enrico Fermi” Course CLVI, edited by E. Redish and M. Vicentini (IOS Press, Amsterdam 2004), pp. 341–350.
  45. E. F. Redish and E. Kuo, Language of physics, language of math: Disciplinary culture and dynamic epistemology, Sci. Educ. 24, 561 (2015).
  46. T. J. Bing and E. F. Redish, The cognitive blending of mathematics and physics knowledge, AIP Conf. Proc. 883, 26 (2007).
  47. 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).
  48. D. Hu and N. S. Rebello, Understanding student use of differentials in physics integration problems, Phys. Rev. ST Phys. Educ. Res. 9, 020108 (2013).
  49. T. Tu, C.-F. Li, Z.-Q. Zhou, and G.-C. Guo, Students’ difficulties with partial differential equations in quantum mechanics, Phys. Rev. Phys. Educ. Res. 16, 020163 (2020).
  50. C. Keebaugh, E. Marshman, and C. Singh, Challenges in sensemaking and reasoning in the context of degenerate perturbation theory in quantum mechanics, Phys. Rev. Phys. Educ. Res. 20, 020139 (2024).
  51. A. Sirnoorkar, P. D. O. Bergeron, and J. T. Laverty, Sensemaking and scientific modeling: Intertwined processes analyzed in the context of physics problem solving, Phys. Rev. Phys. Educ. Res. 19, 010118 (2023).
  52. A. A. diSessa, Knowledge in pieces, in Constructivism in the Computer Age, edited by G. Forman and P. Pufall (Lawrence Erlbaum, Hillsdale, NJ, 1988), pp. 49–70.
  53. T. J. Bing and E. F. Redish, Analyzing problem solving using math in physics: Epistemological framing via warrants, Phys. Rev. ST Phys. Educ. Res. 5, 020108 (2009).
  54. T. J. Bing and E. F. Redish, Epistemic complexity and the journeyman-expert transition, Phys. Rev. ST Phys. Educ. Res. 8, 010105 (2012).
  55. B. W. Dreyfus, A. Elby, A. Gupta, and E. R. Sohr, Mathematical sense-making in quantum mechanics: An initial peek, Phys. Rev. Phys. Educ. Res. 13, 020141 (2017).
  56. C. Singh, When physical intuition fails, Am. J. Phys. 70, 1103 (2002).
  57. D. Hu and N. S. Rebello, Shifting college students’ epistemological framing using hypothetical debate problems, Phys. Rev. ST Phys. Educ. Res. 10, 010117 (2014).
  58. G. Wake, Making sense of and with mathematics: The interface between academic mathematics and mathematics in practice, Educ. Stud. Math. 86, 271 (2014).
  59. T. O. B. Odden and R. S. Russ, Sensemaking epistemic game: A model of student sensemaking processes in introductory physics, Phys. Rev. Phys. Educ. Res. 14, 020122 (2018).
  60. R. S. Russ and T. O. B. Odden, Intertwining evidence- and model-based reasoning in physics sensemaking: An example from electrostatics, Phys. Rev. Phys. Educ. Res. 13, 020105 (2017).
  61. D. Hu and N. S. Rebello, Using conceptual blending to describe how students use mathematical integrals in physics, Phys. Rev. ST Phys. Educ. Res. 9, 020118 (2013).
  62. D. Hammer, Epistemological beliefs in introductory physics, Cognit. Instr. 12, 151 (1994).
  63. J. Tuminaro and E. F. Redish, Elements of a cognitive model of physics problem solving: Epistemic games, Phys. Rev. ST Phys. Educ. Res. 3, 020101 (2007).
  64. F. Reif, Teaching problem solving—A scientific approach, Phys. Teach. 19, 310 (1981).
  65. F. Reif, Millikan lecture 1994: Understanding and teaching important scientific thought processes, Am. J. Phys. 63, 17 (1995).
  66. F. Reif, Scientific approaches to science education, Phys. Today 39, No. 11, 48 (2008).
  67. C. Singh, Problem solving and learning, AIP Conf. Proc. 1140, 183 (2009).
  68. C. Singh et al., Instructional strategies that foster effective problem-solving, in The International Handbook of Physics Education Research: Learning Physics (AIP Publishing, Melville NY, 2023), 10.1063/9780735425477_017.
  69. A. Maries and C. Singh, Helping students become proficient problem solvers part I: A brief review, Educ. Sci. 13, 138 (2023).
  70. A. A. diSessa, Toward an epistemology of physics, Cognit. Instr. 10, 105 (1993).
  71. A. Elby, Helping physics students learn how to learn, Am. J. Phys. 69, S54 (2001).
  72. V. Dini and D. Hammer, Case study of a successful learner’s epistemological framings of quantum mechanics, Phys. Rev. Phys. Educ. Res. 13, 010124 (2017).
  73. M. Lenz et al., Student perspective of and experience with sense-making: A case study, presented at PER Conf. 2017, Cincinnati, OH, 10.1119/perc.2017.pr.055.
  74. E. Gire and C. Manogue, Making sense of quantum operators, eigenstates and quantum measurements, AIP Conf. Proc. 1413, 195 (2012).
  75. P. Hu, Y. Li, and C. Singh, Investigating and improving student understanding of the basics of quantum computing, Phys. Rev. Phys. Educ. Res. 20, 020108 (2024).
  76. B. Modir, J. D. Thompson, and E. C. Sayre, Framing difficulties in quantum mechanics, Phys. Rev. Phys. Educ. Res. 15, 020146 (2019).
  77. J. D. Gifford and N. D. Finkelstein, Categorical framework for mathematical sense making in physics, Phys. Rev. Phys. Educ. Res. 16, 020121 (2020).

  78. Using analogical reasoning with the addition of angular momentum for electron and positron spins, if physical reasoning is like electron spin and mathematical reasoning is like positron spin, then understanding physical and mathematical entities is like up and down spin modes of electron and positron. In this analogy, considering physical and mathematical reasoning as entangled in sensemaking is akin to being in the coupled representation in the entangled (singlet or triplet) states of electron and positron spin.

  79. D. Hu, K. Chen, A. E. Leak, N. T. Young, B. Santangelo, B. M. Zwickl, and K. Norris Martin, Characterizing mathematical problem solving in physics-related workplaces using epistemic games, Phys. Rev. Phys. Educ. Res. 15, 020131 (2019).
  80. A. Gupta and A. Elby, Beyond epistemological deficits: Dynamic explanations of engineering students’ difficulties with mathematical sense-making, Int. J. Sci. Educ. 33, 2463 (2011).
  81. R. R. Bajracharya and J. R. Thompson, Analytical derivation: An epistemic game for solving mathematically based physics problems, Phys. Rev. Phys. Educ. Res. 12, 010124 (2016).
  82. Y. Chen, P. W. Irving, and E. C. Sayre, Epistemic game for answer making in learning about hydrostatics, Phys. Rev. ST Phys. Educ. Res. 9, 010108 (2013).
  83. H. Sevian and S. Couture, Epistemic games in substance characterization, Chem. Educ. Res. Pract. 19, 1029 (2018).
  84. A. Collins and W. Ferguson, Epistemic forms and epistemic games: Structures and strategies to guide inquiry, Educ. Psychol. 28, 25 (1993).
  85. D. P. Maloney, An overview of physics education research on problem solving, presented at PER Conf., 2011, 10.1119/RevPERv2.2.2.
  86. D. H. Jonassen, Toward a design theory of problem solving, Educ. Technol. Res. Dev. 48, 63 (2000).
  87. W. K. Adams and C. E. Wieman, Analyzing the many skills involved in solving complex physics problems, Am. J. Phys. 83, 459 (2015).
  88. E. F. Redish, Problem solving and the use of math in physics courses, arXiv:physics/0608268.
  89. L. D. Bendixen and F. C. Feucht, Personal Epistemology in the Classroom: Theory, Research, and Implications for Practice (Cambridge University Press, Cambridge, England, 2010).
  90. D. J. Griffiths, Introduction to Electrodynamics, 4th ed. (Cambridge University Press, Cambridge, England, 2017).
  91. B. L. Sherin, How students understand physics equations, Cognit. Instr. 19, 479 (2001).
  92. K. McLellan-Lemal and E. MacQueen, Team-based codebook development: Structure, process, and agreement, in Handbook for Team-Based Qualitative Research (Altamira, Lanham, MD, 2008), p. 119.
  93. J. T. Stuckey and G. M. Quan, Student understanding of divergence and curl in upper-division electricity and magnetism, presented at PER Conf. 2024, 10.1119/perc.2024.pr.Stuckey.
  94. J. S. Kashyap and C. Singh, Students’ sensemaking using pictorial analysis game in upper-level electrostatics, presented at PER Conf. 2024, Boston, MA, 10.1119/perc.2024.pr.Kashyap.

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Phys. Rev. Phys. Educ. Res. 21, 020125– Published 10 September, 2025
  • Received 9 January 2025
  • Accepted 12 August 2025
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