We present data from a between-student study on student response to questions on Newton's third law given in two introductory calculus-based physics classes (Mechanics and Electromagnetism) at a large northeastern university. Construction of a response curve reveals subtle dynamics in student learning not capturable by pretesting and post-testing.…

University mathematics education (UME) is considered, in this paper, as a kind of "didactic practice"--characterised by institutional settings and by the purpose of inducting students into "mathematical practices." We present a research programme -- the anthropological theory of the didactic (ATD)--in which this rough…

Although most calculus students are comfortable with the Cartesian equations of curves and surfaces, they struggle with the concept of parameters. A multivariable calculus course is really the time to nail this concept down, once and for all, since it provides an easy way to represent many beautiful and useful surfaces, and graph them using a…

This paper describes a collaboration between a mathematician and a compositionist who developed a sequence of collaborative writing assignments for calculus. This sequence of developmentally appropriate assignments presents peer review as a collaborative process that promotes reflection, deepens understanding, and improves exposition. First, we…

In this paper, we report a pilot study on engaging a group of undergraduate students to explore the limits of sin(x)/x and tan(x)/x as x approaches to 0, with the use of non-graphic scientific calculators. By comparing the results in the pretest and the post-test, we found that the students had improvements in the tested items, which involved the…

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…

Logarithms continue to play an important role in mathematics (most significantly in calculus), science, and engineering. It is therefore important for students to understand logarithms as real numbers as well as the characteristics of logarithmic functions. Exploration of challenges in understanding logarithms as real numbers and logarithmic…

This study considers tertiary calculus students' and instructors' conceptualizations of slope. Qualitative techniques were employed to classify responses to 5 items using conceptualizations of slope identified across various research settings. Students' responses suggest that they rely on procedurally based conceptualizations of…

This study examined student indicators for success in entry-level college calculus. An attitude toward mathematics inventory, course performance, readiness assessment, and student interviews were used to determine characteristics and behaviors of students who succeeded in the course. In addition to student indicators, difficult topics and…

The maximum power theorem is a useful extension to work on EMF and internal resistance at school level. Furthermore, a very simple physical collision model can be used to show equivalent mathematical patterns to those found with the maximum power theorem and to emphasize fundamental links to ideas of impedance matching. (Contains 2 tables and 6…

Continuity is a central concept in calculus. Yet very few students seem to understand the nature of continuity. The research described was conducted in two stages. Students were asked questions in multiple choice and true/false format regarding function, limit and continuity. These results were used to identify participants as strong, weak or…

Background: Engineering programs have high attrition rates, and once in college, students are unlikely to migrate to engineering from other majors. Factors that influence retention must be assessed. Purpose: This study investigated the relationships of aptitude and personality traits in predicting retention for persisting students, those leaving…

In this article we examine how secondary school students think about functional relationships. More specifically, we examined seven students' intuitive knowledge in regards to representing two real-world situations with functions. We found students do not tend to represent functional relationships with coordinate graphs even though they are able…

This five-year study of the peer-led team learning (PLTL) paradigm examined its implementation in a Calculus I course at an all-male HBCU institution. For this study we set up a strong control group and measured the effect of PLTL in the teaching and learning of Calculus I through two points of measure: retention and success rates and learning…

Research over the past few decades points to ways precalculus and calculus courses can be strengthened to improve student learning in these courses. This research has informed the development of the Algebra and Precalculus Concept Readiness (APCR) and the Calculus Concept Readiness (CCR) assessments. In this article, the authors present three…