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As part of an effort to examine student understanding of expressions for probability in an upper-division spins-first quantum mechanics (QM) context, clinical think-aloud interviews were conducted with students following relevant instruction. Students were given various tasks to showcase their conceptual understanding of the mathematics and physics underpinning these expressions. The symbolic forms framework was used as an analytical lens. Various symbol templates and conceptual schemata were identified, in Dirac and function notations, with multiple schemata paired with different templates. The overlapping linking suggests that defining strict template-schema pairs may not be feasible or productive for studying student interpretations of expressions for probability in upper-division QM courses.
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Making context explicit in equation construction and interpretation: Symbolic blending
Much of physics involves the construction and interpretation of equations. Research on physics students’ understanding and application of mathematics has employed Sherin’s symbolic forms or Fauconnier and Turner’s conceptual blending as analytical frameworks. However, previous symbolic forms analyses have commonly treated students’ in-context understanding as their conceptual schema, which was designed to represent the acontextual, mathematical justification of the symbol template (structure of the expression). Furthermore, most conceptual blending analyses in this area have not included a generic space to specify the underlying structure of a math-physics blend. We describe a conceptual blending model for equation construction and interpretation, which we call symbolic blending, that incorporates the components of symbolic forms with the conceptual schema as the generic space that structures the blend of a symbol template space with a contextual input space. This combination complements symbolic forms analysis with contextual meaning and provides an underlying structure for the analysis of student understanding of equations as a conceptual blend. We present this model in the context of student construction of non-Cartesian differential length vectors. We illustrate the affordances of such a model within this context and expand this approach to other contexts within our research. The model further allows us to reinterpret and extend literature that has used either symbolic forms or conceptual blending.
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- Award ID(s):
- 1912087
- PAR ID:
- 10535959
- Publisher / Repository:
- American Physical Society
- Date Published:
- Journal Name:
- Physical Review Physics Education Research
- Volume:
- 19
- Issue:
- 2
- ISSN:
- 2469-9896
- Page Range / eLocation ID:
- 020149
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1103/PhysRevPhysEducRes.19.020149
