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Physical Review Physics Education Research
written by Emily M. Smith, Justyna P. Zwolak, and Corinne A. Manogue
Mathematical reasoning with algebraic and geometric representations is essential for success in upper-division and graduate-level physics courses. Complex algebra requires student to fluently move between algebraic and geometric representations. By designing a task for middle-division physics students to translate a geometric representation to several algebraic representations, we identified students' facilities and difficulties with complex number algebra. Students were successful when they isolated approaches, which was characterized by students' use of circle trigonometry, triangle trigonometry, the Pythagorean theorem, and the square of the norm approaches. When students were not successful, they inappropriately mixed approaches to the problem, including failing to distinguish between triangle and circle trigonometry.
Physical Review Physics Education Research: Volume 15, Issue 1, Pages 010138
Subjects Levels Resource Types
Education Foundations
- Cognition
= Cognition Development
- Learning Theory
= Representations
- Problem Solving
= Frameworks
= Processes
= Representational Use
- Student Characteristics
= Skills
General Physics
- Physics Education Research
Mathematical Tools
- Algebra
- Problem-Solving Techniques
- Trig and Pre-cal
Other Sciences
- Mathematics
- Upper Undergraduate
- Lower Undergraduate
- Reference Material
= Research study
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Free access
License:
This material is released under a Creative Commons Attribution 3.0 license.
Rights Holder:
American Physical Society
DOI:
10.1103/PhysRevPhysEducRes.15.010138
NSF Number:
DUE-1323800
Keywords:
complex algebra, complex number algebra, math skills transfer
Record Creator:
Metadata instance created August 23, 2019 by Sam McKagan
Record Updated:
February 22, 2023 by Caroline Hall
Last Update
when Cataloged:
June 10, 2019
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AIP Format
E. Smith, J. Zwolak, and C. Manogue, , Phys. Rev. Phys. Educ. Res. 15 (1), 010138 (2019), WWW Document, (https://doi.org/10.1103/PhysRevPhysEducRes.15.010138).
AJP/PRST-PER
E. Smith, J. Zwolak, and C. Manogue, Isolating approaches: How middle-division physics students coordinate forms and representations in complex algebra, Phys. Rev. Phys. Educ. Res. 15 (1), 010138 (2019), <https://doi.org/10.1103/PhysRevPhysEducRes.15.010138>.
APA Format
Smith, E., Zwolak, J., & Manogue, C. (2019, June 10). Isolating approaches: How middle-division physics students coordinate forms and representations in complex algebra. Phys. Rev. Phys. Educ. Res., 15(1), 010138. Retrieved July 13, 2024, from https://doi.org/10.1103/PhysRevPhysEducRes.15.010138
Chicago Format
Smith, E, J. Zwolak, and C. Manogue. "Isolating approaches: How middle-division physics students coordinate forms and representations in complex algebra." Phys. Rev. Phys. Educ. Res. 15, no. 1, (June 10, 2019): 010138, https://doi.org/10.1103/PhysRevPhysEducRes.15.010138 (accessed 13 July 2024).
MLA Format
Smith, Emily M., Justyna Zwolak, and Corinne Manogue. "Isolating approaches: How middle-division physics students coordinate forms and representations in complex algebra." Phys. Rev. Phys. Educ. Res. 15.1 (2019): 010138. 13 July 2024 <https://doi.org/10.1103/PhysRevPhysEducRes.15.010138>.
BibTeX Export Format
@article{ Author = "Emily M. Smith and Justyna Zwolak and Corinne Manogue", Title = {Isolating approaches: How middle-division physics students coordinate forms and representations in complex algebra}, Journal = {Phys. Rev. Phys. Educ. Res.}, Volume = {15}, Number = {1}, Pages = {010138}, Month = {June}, Year = {2019} }
Refer Export Format

%A Emily M. Smith %A Justyna Zwolak %A Corinne Manogue %T Isolating approaches: How middle-division physics students coordinate forms and representations in complex algebra %J Phys. Rev. Phys. Educ. Res. %V 15 %N 1 %D June 10, 2019 %P 010138 %U https://doi.org/10.1103/PhysRevPhysEducRes.15.010138 %O application/pdf

EndNote Export Format

%0 Journal Article %A Smith, Emily M. %A Zwolak, Justyna %A Manogue, Corinne %D June 10, 2019 %T Isolating approaches: How middle-division physics students coordinate forms and representations in complex algebra %J Phys. Rev. Phys. Educ. Res. %V 15 %N 1 %P 010138 %8 June 10, 2019 %U https://doi.org/10.1103/PhysRevPhysEducRes.15.010138


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