The University Entrance Exam (UEE) has an important impact on how math instructors teach mathematics to prepare students for this exam as well as how their students learn mathematics. Since the UEE is like a bridge between high school and university, its importance becomes twofold. However, research regarding this issue is very limited in…

Income inequality is a central social justice concern, and hence excellent motivation for real-world applications in mathematics classrooms at every level. We describe the "Mathematics for Social Justice" course at Saint Michael's College, giving a specific example of one of the typical social justice projects for the course, and showing…

We present our experience with an open-ended lab activity that we designed for students with a Calculus 1 background. With the goal of learning how scientists study transport in streams, the students collected data on how a pulse of leaves travels down a nearby stream. Students who had little to no experience with data with two independent…

Project-based learning supports unique and authentic problems in differential equations courses. An intuitive, interesting and deep differential equations project is described. The description illustrates a case study of guiding students through a complex project and the technical and personal rewards gained from it. Valuable advice is provided to…

Previous studies have explored students' understanding of the relationship between definite integrals and areas under curves, but not their metacognitive experiences and skills while solving such problems. This paper explores students' mathematical performance, metacognitive experiences and metacognitive skills when solving integral-area tasks by…

This study explored the mathematics beliefs of students enrolled in a first year calculus class at a Midwestern university in the United States. The Indiana Mathematics Belief Scale was administered to 162 students enrolled in a first year calculus class during the first week of school. An exploratory factor analysis (EFA) was performed to examine…

A single laboratory exercise in introductory physics that includes a bit of calculus, a little programming, some breadboard wiring, and making mathematical connections between motion, net force, and power provides a nice STEM experience for students. If you can add in a biomechanics component you hopefully have something that overall can be an…

We discuss an investigation of the difficulties that students in a calculus-based university introductory physics course have with electric field and the superposition principle for the case of a continuous charge distribution and how that research was used as a guide in the development, validation, and evaluation of a tutorial on these topics to…

Vector calculus and multivariable coordinate systems play a large role in the understanding and calculation of much of the physics in upper-division electricity and magnetism. Differential vector elements represent one key mathematical piece of students' use of vector calculus. In an effort to examine students' understanding of non-Cartesian…

We outline the broad epistemic tendencies of Inuit and Qallunaaq1 teaching, in the context of a faculty member in the Mathematics department of a large, research-oriented Qallunaaq university. We argue that, against the recommendations of academic literature, historical support and personal experience, the South maintains a position of strong…

Previous studies indicated that calculus courses are considered 'weed-out' courses as a lot of students in STEM majors struggle to pass. Instructors and researchers explored various instructional methods to facilitate calculus learning, however, more tailored instructional strategies are still needed. Inventing Contrasting Case is a strategy that…

Researchers have been interested in students' transition to calculus since the early 1900s. One line of inquiry highlights students' understandings of high school mathematics as impeding or supporting their successful transition to university mathematics. This paper addresses an underlying question in this line of inquiry: does school mathematics…

In this paper we examine changes to the national calculus curriculum of South Korea, where mathematics performance often serves as the mark of academic excellence. We describe relevant cultural traditions of mathematics education in South Korea, including the history of curricular changes in calculus at the secondary level. We then investigate how…

We designed a rubric to assess free-response exam problems in order to compare thinking skills evidenced in exams in classes taught by different pedagogies. The rubric was designed based on Bloom's taxonomy and then used to code exam problems. We have analyzed historical and recent exam problems in both algebra-based and calculus-based exams. In…

One desired outcome of introductory physics instruction is that students will develop facility with reasoning quantitatively about physical phenomena. Little research has been done regarding how students develop the algebraic concepts and skills involved in reasoning productively about physics quantities, which is different from either…