Authors of calculus texts often include graphs in the text with the intent that the graph depicts relationships described in theorems and formulas. Similarly, graphs are often utilized in classroom lectures and discussions for the same purpose. The author or instructor includes function graphs to represent quantitative relationships and how a pair…

We discuss student conceptions of improper integrals and infinity in the context of a second-semester calculus course (in a three-course sequence). Our observations stem from a sequence of activities used in an online course over a three-day period. Throughout the enactment of these activities, students are challenged to develop conceptions of…

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…

The concept of the limit is often experienced as a very abstract concept. In this study we explore the understanding of the concept of the limit with 74 students who are prospective high school mathematics teachers. The study is located within the first of three calculus courses which they study as part of their bachelor's degree in education at a…

3D-printing technology has become increasingly important in recent years, offering many possibilities for mathematics teaching and learning. From our point of view, the field of calculus seems to be particularly suitable for the use of 3D-printing. Using the example of 3D-printed graphs of functions, the use of this technology in calculus is…

The purpose of this research is to identify prospective mathematics teachers' conceptual structure about the concept of "Integral". In this research, phenomenology design, one of the qualitative research designs, was used. A total of 35 prospective mathematics teachers, studying at a state university, participated in the research. The…

Nowadays, mathematics teachers in K-12 strive to promote their students' mathematical knowledge and computational thinking (CT) skills. There is an increasing need for effective CT-embedded mathematics learning material and a better understanding of students' views toward them. In this work, we present the results of a research study, which…

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…

This study investigates prospective elementary and secondary school mathematics teachers' ways of reasoning about differentiability at a point and corner points while working on a mathematical modelling activity. Adopting a multiple-case study design, the participants of the study were 68 prospective elementary school mathematics teachers enrolled…

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…

Visual thinking plays an essential role in solving problems and in learning mathematics. Many students do not understand how to graphically or geometrically represent problems and solve algebra problems. Visual thinking is the ability, process, and results of creating, interpreting, using, and imagining images and diagrams on paper or with…

This dissertation report follows a three-paper format, with each paper having a different but related focus. In Paper 1 I discuss conceptual analysis of mathematical ideas relative to its place within cognitive learning theories and research studies. In particular, I highlight specific ways mathematics education research uses conceptual analysis…

Interest in understanding mathematics teaching and learning phenomena, and to develop new and effective methodologies to teach Differential Calculus and Linear Algebra led me to look for ways to dialogue between APOS Theory and other mathematics education theories. This enterprise has facilitated a better understanding of them. Bridges between…

With COVID-19 continuing to make meeting face-to-face impossible, the Canadian Mathematics Education Study Group/Groupe Canadien d'Étude en Didactique des Mathématiques (CMESG/GCEDM) executive decided that, for the first time, the CMESG/GCEDM meeting would be held virtually. By necessity, the program had to be much compressed with no topic…