Taylor series play a ubiquitous role in calculus courses, and their applications as approximants to functions are widely taught and used everywhere. However, it is not common to present the students with other types of approximations besides Taylor polynomials. These notes show that polynomials construed to satisfy certain boundary conditions at…

Differential equations are an important mathematical concept used to model processes in many disciplines. However, the literature shows that students experience many difficulties when studying this topic. We investigate the effect of using context while teaching differential equations on engineering students' ability to construct and interpret…

Researchers have demonstrated a much-needed shift in pedagogical practices to incorporate literacy strategies. This dissertation provides additional empirical evidence to expand the body of research by utilizing a comparative readability analysis that examines the academic language of a popular calculus textbook. A sample from the published…

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…

College calculus plays an important role in STEM students' degree and career aspirations. One of the key factors considered in assessing a student's ability to be successful in calculus is their proficiency in topics from prior mathematics courses such as algebra and precalculus. This study set out to examine the impact of students' precalculus…

The postsecondary Calculus series poses an ongoing challenge for students and instructors. With the rapid growth of STEM careers and the traditional role of calculus as a gatekeeper to higher mathematics, it is urgent that students develop a stronger skillset with regard to calculus topics. The current availability of technology allows instructors…

Though the curriculum reform movement that began in 1989 has had a significant impact on calculus pedagogy and content (Windham, 2008), the question remains to what extent reform-based calculus textbooks reflect these reforms. This paper explores this question by analyzing the mathematical content and pedagogical approach of the chapter on…

This research explores the use of guided notes in a post-secondary calculus course and the extent to which use enhanced students' success in a first year calculus course. Guided notes have been previously shown to be perceived as helpful to learning by students, and one study showed that the use of guided notes improved pass rates in a first year…

In this university study, sections of an integral calculus course were randomly assigned to either a control or treatment group for a lesson on volumes of revolution. Both groups were given similar collaborative tasks, but only the students in the treatment group were given access to a set of 3D manipulatives. Pre- and post-assessments were…

Digital Game-Based Learning (DGBL) demonstrated a positive impact on students' motivation, engagement, knowledge acquisition, and many other areas. However, all the benefits DGBL can offer for the classroom do not seem to be enticing enough to persuade classroom instructors to implement DGBL in their classroom. There is a disconnect between…

This paper presents a case study conducted by two universities seeking to explore Open Education Resources (OER) in their precalculus course. Students not only gained access to their textbook for free on the first day of class, but also Lumen OHM, an online mathematics assessment platform. The majority of students involved in the study were…

The goal of the present study is to investigate the impact of procedural and conceptual teaching on students' mathematical performance over time. For this purpose, implicit differentiation and integration by parts were taught in two different ways to first-year university students of two different calculus courses: one course with Conceptual…

"Vicarious learning" research is a burgeoning area of inquiry, which examines the learning of students who observe and are engaged with video- or audio-taped presentations of other people engaged in learning (Chi et al., 2008). In such studies, the students or "vicarious learners" (VLs) are positioned as indirect participants…

"Vicarious learning" research is a burgeoning area of inquiry, which examines the learning of students who observe and are engaged with video- or audio-taped presentations of other people engaged in learning (Chi et al., 2008). In such studies, the students or "vicarious learners" (VLs) are positioned as indirect participants…

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…