Background: A strong calculus foundation is essential to undergraduate engineering success. However, some students may be self-selecting to begin their mathematics sequence in a lower-level calculus course than their prior achievement and aptitude would suggest is appropriate (i.e., undermatch). Purpose: This study examined (a) the relationship…

Many active learning practices highly depend on students' advance preparation for the class. However, reading Calculus can be a challenging task to students. We address this concern by assigning targeted pre-class readings in multiple Calculus courses. We report on our implementations, provide students' feedback, and discuss the lessons learned…

The purpose of this study was to investigate the gender differences in students' attitude toward mathematics and how attitude impacts achievement in the course. The sample consisted of 172 undergraduate health science students (123 women, 49 men) enrolled in mathematics courses at a University in the Midwestern United States. Data were collected…

In this dissertation, we propose a computer-supported method, called insightful learning systems, for tracking student progress that yields human actionable insights. We cover our theories, experiments and applications that aim to pave the way for more effective understanding of student progress, in key skills for a course, by looking at students…

It is well-known that the Lotka-Volterra predator-prey model has a family of periodic orbits, but does not possess limit cycles and therefore the model is said to be structurally unstable. The Lotka-Volterra model is a special case of a much larger group namely the quadratic population models and it can be shown that none of them can produce limit…

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…

This conceptual paper explores the pedagogical tension and potential synergy between teacher-centred and student-centred instructional approaches, particularly within the context of teaching abstract concepts in science and mathematics such as quantum mechanics and calculus. Grounded in the theoretical frameworks of essentialism and…

The typical trigonometry, precalculus, or calculus student might not agree that logarithms are hot stuff, but we drew motivation from chili peppers to help students get a better taste for logarithms. The Scoville scale, which ranges from 0 to 16,000,000, has been the sole quantitative metric to measure the pungency (spiciness) of peppers since its…

This paper examines the prevalence of rapid answer copying among university students completing online homework for an introductory level calculus-based physics course taught remotely during the COVID pandemic. We first compared the attempt duration distribution of 26 problems, between 42 students who self-reported as having completed the homework…

Given the importance of the ability to use variables flexibly in Calculus and students' difficulties related to various uses of variables, this study examined how variables are treated in calculus class. Data for this study came from graduate teaching assistants' (TAs') classroom teaching, which plays a crucial role in undergraduate students'…

Math classes do not usually offer students an opportunity to learn about the diversity within the field of mathematics. As a result, students tend to hold inaccurate, negative perspectives about diversity in the world of mathematics and many may not feel a sense of belonging in the classroom when they do not see themselves reflected in the…

As part of a departmental reform project, a large University converted a "Precalculus College Mathematics" lecture-based course for 97 students into an active learning flipped classroom for first-year engineering students. The curriculum was designed specifically to provide applications of pre-calculus in various engineering subjects.…

Textbooks have been the subject of research within and across disciplines, but have not yet been widely studied from a disciplinary literacy perspective. Readerly agency is also understudied in disciplinary literacy. The present paper aims to illuminate both of these areas by examining facets of agency that readers demonstrated during think-aloud…

In summer 2013, Manhattan College introduced an online summer "bridge to calculus" course for incoming first-year students in science, engineering, and mathematics education who marginally did not receive a calculus recommendation based on a mathematics placement test. In this paper, we describe the development of the bridge course and…

This work aims to analyze the responses of a group of engineering students related to problems about tangents in a teaching learning process of derivative in a differential calculus course. The methodological design, oriented to a group of 161 students from two Chilean universities, considers different onto-semiotic configurations in…