This article revisits and expands upon a previous phenomenographic study characterising the qualitatively different ways in which South African undergraduate physics students may experience the use of +/- signs in one-dimensional kinematics (1DK). We find the original categorisation as applicable for interpreting Swedish university-level students'…

This paper demonstrates an experimental integrated lesson of physics and calculus in a topic of fluid force applying on different shapes of dams. This lesson was designed for the first year students in engineering program in an attempt to show them the connection between these two disciplines, as well as to introduce more advanced…

Thermodynamics challenges teachers and learners. Its pervasiveness about nature, mathematical abstractness, nonnumerical relations, and complexity in applications can inhibit understanding and usage, especially by undergraduates. Perspectives are given about these obstacles, and some suggestions are made to enhance comprehension of the discipline.

A central goal of physics education is to teach problem-solving competency, but the description of the nature of this competency is somewhat fragmentary and implicit in the literature. The present article uses recent historical scholarship on Arnold Sommerfeld and Enrico Fermi to identify and characterize two positions on the nature of physics…

Professional problem-solving practice in physics and engineering relies on mathematical sense making--reasoning that leverages coherence between formal mathematics and conceptual understanding. A key question for physics education is how well current instructional approaches develop students' mathematical sense making. We introduce an assessment…

This paper studies the cognitive obstacles related to one aspect of mathematization in physics problem-solving, namely, what might be called "structuring for mathematization," where the problem situation is structured in such a way that a translation to a mathematical universe can be done. We report the results of an analysis of four…

In this paper, we investigate which aspects are overriding in the concept images of monotonicity of Finnish tertiary mathematics students, i.e., on which aspects of monotonicity they base their argument in different types of exercises related to that concept. Further, we examine the relationship between the quality of principal aspects and the…

The aim of this paper is to present and discuss some of the evidence regarding the resources that students use when they establish relationships between a contextual situation and an ordinary differential equation (ODE). We present research results obtained from work by seven students in a graduate level course in mathematics education, where they…

Problem solving in the field of quantitative composition of solutions (QCS), expressed as mass share and molar concentration, is essential for chemistry students. Since successful chemistry education is based on different mathematical contents, it is important to be proficient in both mathematical and chemistry concepts as well as interconnections…

This study focuses on students' use of the mathematical concept of differentials in physics problem solving. For instance, in electrostatics, students need to set up an integral to find the electric field due to a charged bar, an activity that involves the application of mathematical differentials (e.g., "dr," "dq"). In this…

We discuss common difficulties in upper-division electricity and magnetism (E&M) in the areas of Gauss's law, vector calculus, and electric potential using both quantitative and qualitative evidence. We also show that many of these topical difficulties may be tied to student difficulties with mathematics. At the junior level, some students…

We propose an analytic solution to the problem of the mechanical paradox consisting of a sphere rolling upwards on two diverging inclined guides as devised by Gardner. The presence of an unstable equilibrium point is highlighted and the analytic solution is found by means of elementary calculus concepts. (Contains 4 figures and 3 footnotes.)

Writing plays an integral role in any disciplinary course setting. In the sciences, WAC and WID initiatives primarily focus on using writing to deepen student understanding of scientific concepts. Scholars, however, have paid less attention to how writing may facilitate an understanding of the link between concepts and their quantitative…

Helping students set up equations is one of the major goals of teaching a course in physics that contains elements of problem solving. Students must take the stories we present, interpret them, and turn them into physics; from there, they must turn that physical, idealized story into mathematics. How they do so and what problems lie along the way…

We study the turning point problem of a spherical pendulum. The special cases of the simple pendulum and the conical pendulum are noted. For simple initial conditions the solution to this problem involves the golden ratio, also called the golden section, or the golden number. This number often appears in mathematics where you least expect it. To…