This study investigates when and how university students in first-semester introductory calculus interpret multiple representations of the same function. Specifically, it focuses on three tasks. The first task has students give their definitions of 'function sameness', the results of which suggests that many students understand a function as being…

In spring 2018, an inquiry-oriented differential equations course was offered at the Lebanese American University. This paper highlights students' comprehension of some qualitative aspects of differential equations, namely their understanding of the equations and their solutions. It also explores the students' success in moving between the…

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…

In introductory level math classes, writing prompts can be used as part of weekly homework assignments to encourage students to think more deeply about the subject at hand. These writing prompts present scenarios related to recently learned material in a new context and require students to submit a short written response online. Writing prompts…

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…

The Mathematical Association of America's "Precalculus to Calculus: Insights and Innovations Conference" brought together representatives of mathematics departments from across the country with members of two national research projects to share and discuss both research findings and on-the-ground concerns of faculty. In this article, we…

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…

Undergraduate mathematics education can be experienced in discouraging and marginalizing ways among Black students, Latin* students, and white women. Precalculus and calculus courses, in particular, operate as gatekeepers that contribute to racialized and gendered attrition in persistence with mathematics coursework and pursuits in STEM (science,…

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…

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…

Foundational undergraduate courses in chemistry and mathematics are gateways to a number of lucrative majors and pre-professional programs. Historically, however, students often struggle with these disciplines and can benefit from alternate approaches to examining their learning strategies. This article describes the use of exam…

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…