Unpacking students’ use of mathematics in upper-division physics: where do we go from here?

In this article, we discuss the development and the administration of a multiple-choice test, which we named Test of Calculus and Vectors in Mathematics and Physics (TCV-MP), aimed at comparing students' ability to answer questions on derivatives, integrals, and vectors in a purely mathematical context and in the context of physics. The comparison between the two contexts was achieved by using parallel (isomorphic) questions in mathematics and physics. The final version of the test contains 34 items (17 in a purely mathematical context and 17 in the context of physics) involving different representations (graphs, words, numbers, and formal expressions) of the concepts covered by the test. The test was administered in Spring 2018 to 1252 first-year students enrolled in 23 different degree programs of the School of Science and the School of Engineering of the University of Padua. We assessed the validity, reliability, and discriminatory power of the test both as a whole and at the single-item level, obtaining values within the desired ranges. The analysis of students' answers to individual items and the comparison between parallel mathematics and physics items provides insights into the factors that affect students' ability to use derivatives, integrals, and vectors in the context of introductory physics. We believe that the instrument we have developed can be useful not only for research purposes, but also for instructors and for students.

Section: Context and Motivation For The Studymentioning

confidence: 99%

Testing students ability to use derivatives, integrals, and vectors in a purely mathematical context and in a physical context

Carli

Lippiello

Perona³

et al. 2020

“…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

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.

“…However, education research has shown that many students struggle to apply their acquired mathematical skills in physics contexts [1][2][3][4][5][6][7][8][9][10][11]. Consequently, the investigation of how physics students use mathematics has been a prominent topic in recent literature [12][13][14][15][16][17][18][19][20][21][22][23][24][25]. It is also well established that students have difficulty coordinating information drawn from texts, equations, symbols, graphs, and figures when formulating a solution to a given problem.…”

Section: Introductionmentioning

confidence: 99%

Qualitative investigation into students’ use of divergence and curl in electromagnetism

Bollen

Kampen

Baily

et al. 2016

Many students struggle with the use of mathematics in physics courses. Although typically well trained in rote mathematical calculation, they often lack the ability to apply their acquired skills to physical contexts. Such student difficulties are particularly apparent in undergraduate electrodynamics, which relies heavily on the use of vector calculus. To gain insight into student reasoning when solving problems involving divergence and curl, we conducted eight semistructured individual student interviews. During these interviews, students discussed the divergence and curl of electromagnetic fields using graphical representations, mathematical calculations, and the differential form of Maxwell's equations. We observed that while many students attempt to clarify the problem by making a sketch of the electromagnetic field, they struggle to interpret graphical representations of vector fields in terms of divergence and curl. In addition, some students confuse the characteristics of field line diagrams and field vector plots. By interpreting our results within the conceptual blending framework, we show how a lack of conceptual understanding of the vector operators and difficulties with graphical representations can account for an improper understanding of Maxwell's equations in differential form. Consequently, specific learning materials based on a multiple representation approach are required to clarify Maxwell's equations.