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…

A productive understanding of rate of change concept is essential for constructing a robust understanding of derivatives. There is substantial evidence in the research that students enter and leave their Calculus courses with naive understandings of rate of change. Implementing a short unit on "what is rate of change" can address these…

The number of undergraduates placing into developmental or "remedial" coursework continues to increase. This rise is concerning because developmental or "remedial" coursework creates barriers for many students. This mixed method study examines a holistic approach to placement. After one-on-one interviews with mathematics…

This paper discusses several linear algebra activities designed to help enhance students' skills in collaborating, exploring mathematics, and linking together abstract and visual ways of approaching mathematics. Most of these activities are short, accessible, engaging, and easy to incorporate into any classroom. In addition, we discuss some…

Understanding the secondary--tertiary transition is not only an educational matter, but also an inclusion and equality matter as mathematics qualifications lead to better employment and better earning for students. Research on what causes the crisis associated to this transition has so far focused on the impact of cognitive and epistemological…

Creativity and problem solving are considered to be twenty-first-century competencies, therefore promoting mathematical creativity should be an important part of school mathematics. The study presented in this paper is inspired by the notion of mathematical creativity and the utilization of multiple solution tasks (MSTs) to investigate students'…

R is becoming the standard for teaching statistics due to its flexibility, and open-source nature, replacing software programs like Minitab and SPSS. The main driver for reform within Scottish statistical undergraduate programs is the creation of the Scottish Qualification Authority's Higher Applications of Mathematics course which has statistics…

This paper presents a semester-long bottle design project for an undergraduate Numerical Analysis course. Students implement numerical methods in MATLAB to design and 3D print a bottle. Employing mathematical methods to compute features of their designs enhances students' understanding of numerical techniques in design applications. Student…

This paper shares a flexible activity for engaging people in mathematical inquiry that does not depend on fixed prior knowledge built on a famous property of Möbius strips. The discussion includes the implementation of the activity and its extensions, facilitator moves and common participant thinking, suggestions for adaptation and integration…

Misconceptions are one of the biggest obstacles in learning mathematics. This study aimed to investigate students' common errors and misunderstandings they cause when defining the angle and the triangle. In addition, we investigated the metacognition/ drawing/ writing/ intervention (MDWI) strategy to change students' understanding of the wrong…

This paper describes a course designed to introduce students to mathematical thinking and a variety of lower level mathematics topics using baseball while satisfying the goals of quantitative reasoning. We give suggestions for sources, topics, techniques, and examples so any mathematics teacher can design such a course to fit their needs. The…

Infinite series are known to be challenging for Calculus II students, perhaps because they lack intellectual need for the content. In their analysis of Calculus textbooks found few instances of potential intellectual needs for infinite series. This study combines a textbook analysis with interviews of four professors and observations of their…

National studies continue to indicate that the graduating STEM student body is not representative of the diversity of the U.S. population. In addition to, or in the absence of, institutional change, instructors must learn how to implement equity-focused pedagogical changes in order to better support their students. This article describes my…

Point-set topology is among the most abstract branches of mathematics in that it lacks tangible notions of distance, length, magnitude, order, and size. There is no shape, no geometry, no algebra, and no direction. Everything we are used to visualizing is gone. In the teaching and learning of mathematics, this can present a conundrum. Yet, this…

This article describes an instructional sequence used with inservice secondary mathematics teachers as part of a graduate course. The instructional sequence focused on designing tasks using Interactive Geometry Software (IGS). This study answers a call for replication studies to investigate the use of an established instructional sequence. Results…