As universities contend with high rates of student attrition from intended STEM majors, due to many students' difficulty in passing entry-level mathematics courses, they must examine the systems they have in place and determine how best to support these students. Historically, graduate teaching assistants (GTAs) are assigned to introductory…

Much of the education research on implicit differentiation and related rates treats the topic of differentiating equations as an unproblematic application of the chain rule. This paper instead problematizes the legitimacy of this procedure. It develops a conceptual analysis aimed at exploring how a student might come to understand when and why one…

One of the memories of my freshman year at Amherst was a lecture in the required physics/calculus course in which Arnold Arons quoted Isaac Newton on standing on the shoulders of giants. Now that I have spent my physics career, I still use the same quote, but now apply it to the eponymous apparatus that has been designed by the giants in our field.

We reflect on the limitations of our research group's prior methods for assessing covariational reasoning which primarily used graphical tasks found in extant literature. Graphical tasks dominate the literature on covariational reasoning, and through our use of these tasks we came to question the heavy reliance on them. Our concerns led us to ask…

Mathematical objects are the outcomes of human discourse and come to life through the process of objectification. Primary and concrete discursive objects (d-objects) play an important role in this process, forming different realizations through the objectification process. In the present study, we analyze the written discourses about the…

We examined widely used popular calculus textbooks to explore opportunities to learn the limit concept. Definitions, worked problems, and exercise problems were coded to examine if these tasks allow students to use informal thinking to coordinate domain and range processes to understand the infinite process of limit. Results revealed many exercise…

We present a free student-facing tool for creating 3D plots and smartphone-based virtual reality (VR) visualizations for STEM courses. Visualizations are created through an in-browser interface using simple plotting commands. Then QR codes are generated, which can be interpreted with a free smartphone app, requiring only an inexpensive Google…

A recent review of literature in topic of rate of change mostly highlighted students and teachers' difficulties in handling conceptual questions. This initiated the researcher to investigate the Malaysian pre-service mathematics teacher's subject matter knowledge in rate of change through a case study design. A task-based interview was conducted…

In this paper, we study how well SAT scores, high school GPA, and undergraduate precalculus grades relate to undergraduate calculus grades at a 4-year private nonprofit university that does not have a placement exam. In addition, we compare the success in calculus of two groups of students, both of whom require two semesters to pass calculus. The…

This study aims to examine the effectiveness of the STEMDISLEARN module on students' critical thinking skills in the DE Course. This research design employed a quasi-experimental non-equivalent pre-test and post-test group. The samples amounted to 123 students, consisting of 64 students in the experimental group and 59 students in the control…

Mathematical notations not only contribute to but also confound the development of the understanding of mathematical concepts (Leinhardt, Zaslavsky & Stein,1990). Inaccurate use of calculus notations is likely to have a significant influence on student conceptual understanding and student assessment scores in the Calculus 1 course. This…

Why do people shift their strategies for solving problems? Past work has focused on the roles of contextual and individual factors in explaining whether people adopt new strategies when they are exposed to them. In this study, we examined a factor not considered in prior work: people's evaluations of the strategies themselves. We presented…

This study is concerned with the analysis of mathematical textbook tasks at the second-level in Ireland, in the context of the introduction of the revised curriculum entitled 'Project Maths'. A total of 7635 tasks on the topics of Pattern, Sequences and Series, and Differential Calculus were analysed; these tasks were selected from editions of…

The aim of this research was to explore the mathematical connections that pre-university students make when they sketch the graph of a derivative function and an antiderivative function. Also, we tried to explain the origin of the mathematical connections identified. We assume mathematical connections as a cognitive process through which a person…

This article presents the results of our analysis of a sample of 254 Calculus I final exams (collectively containing 4,167 individual items) administered at U.S. colleges and universities. We characterize the specific meanings of foundational concepts the exams assessed, identify features of exam items that assess productive meanings, distinguish…