This study investigated how students reason about the partial derivative and the directional derivative of a multivariable function at a given point, using different graphical representations for the function in the problem statement. Questions were formulated to be as isomorphic as possible in both mathematics and physics contexts and were given…

When learning physics, students need more than just an understanding of mathematical and physical concepts. Integrating the two fields is crucial, as research indicates that students often struggle even when they have a strong grasp of both. In this paper, we use the heat equation as an example from higher education. Given the importance of the…

Of the many disciplines that rely on calculus, physics is among those with the strongest connections to this branch of mathematics. For instance, the derivative--one of the key notions of calculus--is used to describe velocity and acceleration, which play a central role in mechanics. In post-secondary education, in particular at the college level,…

This paper is a continuation of an earlier discussion in this journal about adhering to principles of mathematics while presenting function graphs in physics. As in the previous paper, the importance of the vertical line test was examined, this paper delves more in-depth, and it pinpoints a need for presenting graphs with a continuous rate of…

Research has shown the majority of students who have completed a university calculus course reason about the definite integral primarily in terms of prototypical imagery or in purely algorithmic and non-quantitative ways. This dissertation draws on the framework of Emergent Quantitative Models to identify how calculus students might develop a…

Females are underrepresented in all levels of physics, while a simultaneous need exists to increase the physical science workforce pipeline. A review of current literature found exposure to more advanced pSTEM courses might influence students to pursue those career-fields, however enrollment in Advanced Placement (AP) Physics remains…

Mathematical reasoning skills are a desired outcome of many introductory physics courses, particularly calculus-based physics courses. Novices can struggle to understand the many roles signed numbers play in physics contexts, and recent evidence shows that unresolved struggle can carry over to subsequent physics courses. Positive and negative…

Many teachers of intermediate algebra or precalculus use an activity where balls are dropped from known heights and the heights of the bounces are recorded. The "bounce height" will be a roughly constant fraction of the "drop height." Then one can plot each bounce height against its bounce number, an exponential function can…

Previous work has looked at the relationship between high school preparation and student performance in calculus-based introductory mechanics (physics 1) courses. Here, we extend that work to look at performance in introductory calculus-based electricity and magnetism (physics 2), and we look at the significance of what college math courses have…

Theorising STEM Education in the 21st Century is a book that captures the essence of Science, Technology, Engineering and Mathematics and the intricacies of STEM education in the contemporary society. It explores STEM as an interdisciplinary field as well as the individual disciplines that make up STEM. This ensures the field of STEM as a whole is…

This study examined outcomes for AP® Calculus and AP Physics students on the 2015 Trends in International Math and Science Study (TIMSS) relative to other participating countries and other advanced math and science students in the United States. Compared to other countries in the study, AP Calculus BC and AP Physics C: EM students outperformed all…

One of the key steps when developing pathways between baccalaureate and diploma programs is comparing learning goals between the programs. This paper presents application of a seven-dimensional framework (cognitive process, transferability, depth of analysis, interdependence, question novelty, scaffolding and communication) to analyze the implicit…

"Inequitable Opportunity to Learn: Access to Advanced Mathematics and Science Courses" is the second in a series of Learning Policy Institute reports analyzing data primarily from the U.S. Department of Education's Civil Rights Data Collection (CRDC). This report uses the most recent CRDC data from 2017-18. The CRDC includes data on a…

By introducing the mathematical concept of orientation, the significance of the minus sign in Faraday's law may be made clear to students with some knowledge of vector calculus. For many students, however, the traditional approach of treating the law as a relationship between positive scalars and of relying on Lenz's law to provide the information…

This study describes the trends in course credit attainment (CCA) of high school students in required and non-required science and math courses and trends in registration in non-required science and math courses in Texas between 1997 and 2009. Using Texas Public Education Information Management System data between 1997 and 2009, it presents…