Undergraduate students' difficulties with boundary conditions for the diffusion equation

Sofie Van den Eynde*, Johan Deprez, Martin Goedhart, Mieke De Cock

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

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Combining mathematical and physical understanding in reasoning is difficult, and a growing body of research shows that students experience problems with the combination of physics and mathematics in reasoning beyond the introductory level. We investigated students' reasoning about boundary conditions (BCs) for the diffusion equation by conducting exploratory task-based, think-aloud interviews with twelve undergraduate students majoring in physics or mathematics. We identified several difficulties students experienced while solving the interview task and categorized them using the conceptual blending framework. This framework states that in reasoning, people draw from separate input spaces, in this case the mathematics and the physics input space, to form a blended space, where they make connections between elements from these spaces. To identify difficulties, we used open coding techniques. We observed few difficulties in the physics space. In the mathematics space, we identified several difficulties that we clustered in two main groups: findings about the mathematical meaning of BCs, and findings about reasoning with functions of two variables. Lastly, we identified four ways in which blending failed. Starting from our findings, we formulate recommendations for teaching and future research.

Original languageEnglish
Pages (from-to)2176-2198
Number of pages23
JournalInternational Journal of Mathematical Education in Science and Technology
Issue number8
Early online date21-Jan-2021
Publication statusPublished - 2022


  • boundary conditions
  • conceptual blending
  • Mathematics
  • partial differential equations
  • physics
  • student difficulties

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