We have investigated the temporal patterns of algebra (N = 606) and calculus (N = 507) introductory physics students practicing multiple basic physics topics several times throughout the semester using an online mastery homework application called science, technology, engineering, and mathematics (STEM) fluency aimed at improving basic physics…

Students often struggle in the transition from high school to college. One component of this struggle is adjusting study habits to navigate new academic expectations. Another is establishing new relationships in college that can support their emotional well-being and academic success. We administered surveys consisting primarily of open-ended…

Relating mathematics learned in the classroom to real situations increases student motivation and enhances learning. In this paper, we provide an example of a classroom application of calculus to physiology in two courses: "Differential Equations" and "Calculus I for Biology and Medicine." We designed and implemented a project…

The Force Concept Inventory (FCI) can serve as a summative assessment of students' conceptual knowledge at the end of introductory physics, but previous work has suggested that the knowledge measured by this instrument is not a unitary construct. In this article, we consider the idea that FCI performance may reflect a number of student attributes…

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…

Responsive instruction--or instruction that foregrounds and takes up the disciplinary substance of student thinking--is both a hallmark of recent STEM education reforms and challenging to enact. This kind of instruction may be especially challenging in instructional contexts that mandate or rely on curriculum with set, structured learning…

In the context of introductory physics, we study student conceptual understanding of differentials, differential products, and integrals and possible pathways to understanding these quantities. We developed a multiple choice conceptual assessment employing a variety of physical contexts probing physical understanding of these three quantities and…

This paper reports the results of a research exploring the mathematical connections of pre-university students while they solving tasks which involving rates of change. We assume mathematical connections as a cognitive process through which a person finds real relationships between two or more ideas, concepts, definitions, theorems, procedures,…

Students' intentions to persevere and their career choices in science, technology, engineering, and math fields can be impacted by their physics identities. Women are severely underrepresented at all levels in physics and engineering. Physics in particular has stereotypes about being a discipline for brilliant men. Therefore, it is particularly…

Homework in introductory physics represents an important part of a student's learning experience; therefore, choosing the manner in which homework is presented merits investigation. We performed three rounds of clinical trials comparing the effects of mastery-style homework vs. traditional-style homework with students in both algebra-based and…

A critical component of scientific reasoning is the consideration of alternative explanations. Recognizing that decades of cognitive psychology research have demonstrated that relative cognitive accessibility, or "what comes to mind," strongly affects how people reason in a given context, we articulate a simple "cognitive…

Understanding Maxwell's equations in differential form is of great importance when studying the electrodynamic phenomena discussed in advanced electromagnetism courses. It is therefore necessary that students master the use of vector calculus in physical situations. In this light we investigated the difficulties second year students at KU Leuven…