Editorial: Focused Collection: PER in Upper-Division Physics Courses

Loverude, Michael E.; Ambrose, Bradley S.

doi:10.1103/physrevstper.11.020002

Cited by 12 publications

(5 citation statements)

References 83 publications

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“…Using non-Cartesian coordinate systems continues to be difficult for undergraduate physics students [1][2][3] even in upper-division physics courses (e.g., classical mechanics, electromagnetism, thermodynamics, quantum mechanics, statistical mechanics) where application of these mathematical ideas plays a more significant role [4][5][6][7]. As part of a larger initiative into exploring the math-physics interface in upper-division physics courses [8,9], our current collaboration has initiated the development of a research-based curriculum for a mathematical methods course for undergraduate physics majors. This paper discusses a portion of that effort by focusing on the identification of cognitive resources students activate in the context of basis unit vectors, position vectors, and velocity vectors in plane polar and spherical polar coordinate systems.…”

Section: A Background and Purposementioning

confidence: 99%

Mapping activation of resources among upper division physics students in non-Cartesian coordinate systems: A case study

Farlow

Vega

Loverude

et al. 2019

Phys. Rev. Phys. Educ. Res.

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An essential skill for success in upper-division physics curricula is the ability to work with and apply mathematical and physical concepts through Cartesian and non-Cartesian coordinate systems. These skills are most notably necessary in electricity and magnetism, wherein students must build and solve integrals and perform vector derivatives in Cartesian, spherical, and cylindrical coordinate systems. While limited in scope, early investigations into students understanding of coordinate systems has shown that students have considerable difficulty. Through the analysis of four one-on-one semistructured interviews, students were observed to activate numerous productive resources, despite frequently incorrect answers. This paper will revisit our previously identified student resource clusters for unit vectors. We also identify additional resources that cast additional light on students' thinking about position vectors, and velocity vectors in non-Cartesian coordinate systems. Through detailed analysis of a single student, we identify several groupings of resources that will serve as a baseline for future analysis of additional students and provide initial insight into potential curriculum development.

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Section: A Background and Purposementioning

confidence: 99%

Mapping activation of resources among upper division physics students in non-Cartesian coordinate systems: A case study

Farlow

Vega

Loverude

et al. 2019

Phys. Rev. Phys. Educ. Res.

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“…While PER has primarily focused on introductory-level courses, there are increasing efforts to expand into the upper division [2]. Upper division physics courses such as Mechanics and Electricity and Magnetism require a considerable understanding of challenging mathematical concepts.…”

Section: Introductionmentioning

confidence: 99%

Student understanding of unit vectors and coordinate systems beyond cartesian coordinates in upper division physics courses

Vega¹,

Christensen²,

Farlow³

et al. 2016

2016 Physics Education Research Conference Proceedings

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In upper division physics courses students are required to work with various coordinate systems. This skill becomes particularly important when learning Electricity and Magnetism, where the most appropriate coordinate system will often depend on the geometry and symmetry of a problem. This study aims to identify and describe "resources" used by students when answering physics questions regarding unit vectors in non-Cartesian coordinate systems, specifically polar coordinates [1]. Data were collected in the form of written responses and interviews in upper division physics courses at two universities. After deeper analysis we identified several resources that students use in ways that can be productive and unproductive.

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“…This myriad of factors informs research efforts to consider students' understanding and employment of mathematics at the upper-division level in physics. Therefore, within both a broader call for additional educational research to be conducted at the upper-division in physics [17] and a larger effort to study students use and understanding of math in the upper-division [18], an effort is underway to develop a research-informed curriculum for a mathematical methods course for undergraduate physics majors. This paper focuses on a preliminary portion of that effort by investigating Calculus textbooks for the prevalence of non-cartesian coordinates and unit vector content.…”

Section: Motivation and Literature Reviewmentioning

confidence: 99%

Multivariable calculus textbook representation of non-cartesian coordinates: a misalignment between multivariable calculus textbook content and upper-division physics application

Dalton,

Farlow,

Christensen

2024

Eur. J. Phys.

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Upper-division undergraduate physics coursework necessitates a ﬁrm grasp on and ﬂuid use of mathematical knowledge, including an understanding of non-Cartesian (speciﬁcally polar, spherical and cylindrical) coordinates and how to use them. A limited body of research into physics students’ thinking about coordinate systems suggests that even for upper-division students, understanding of coordinate system concepts is emergent. To more fully grasp upper-division physics students’ incoming understanding of non-Cartesian coordinates, the prevalence of non-Cartesian content in seven popular Calculus textbooks was studied. Using content analysis techniques, a coding scheme was developed to gain insight into the presentation of coordinate system content both quantitatively and qualitatively. An initial ﬁnding was that non-Cartesian basis unit vectors were absent in all but one book. A deeper analysis of three of the calculus textbooks showed that Cartesian coordinates comprise an overwhelming proportion of the textbooks’ content and that qualitatively the Cartesian coordinate system is presented as the default coordinate system. Quantitative and qualitative results are presented with implications for how these results might impact physics teaching and research at the middle- and upper-division.

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Editorial: Focused Collection: PER in Upper-Division Physics Courses

Cited by 12 publications

References 83 publications

Mapping activation of resources among upper division physics students in non-Cartesian coordinate systems: A case study

Mapping activation of resources among upper division physics students in non-Cartesian coordinate systems: A case study

Student understanding of unit vectors and coordinate systems beyond cartesian coordinates in upper division physics courses

Multivariable calculus textbook representation of non-cartesian coordinates: a misalignment between multivariable calculus textbook content and upper-division physics application

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