This study investigates when and how university students in first-semester introductory calculus interpret multiple representations of the same function. Specifically, it focuses on three tasks. The first task has students give their definitions of 'function sameness', the results of which suggests that many students understand a function as being…

This study explores calculus students' opportunities to learn the concepts of integral by examining one mathematician's videotaped lessons and the textbook. Results show that both lessons and the textbook introduce important cognitive resources briefly and focus on other units of knowledge. Implications to these results are also discussed.

The topic of this research study is mastery learning, an educational theory that began with the work of John Carrol in 1963. The core principle of this theory is that all students can achieve uniform learning outcomes, but it will take some students longer than others to reach the same performance goals. The problem that this research study…

This research study examined inclusive teaching practices, class policies, and course structures in active learning Calculus classes. Analyzing interview data, along with focus group discussions and classroom observations, obtained from 23 students and 4 instructors, themes were extracted through open-coding methodology, employing scholarly…

Note-taking is one of the most pervasive activities of students in college courses, so it has been the subject of educational research for quite some time. Yet despite the large body research, little is known about the characteristics of note-taking in mathematics. For this reason, this exploratory study examined the note-taking habits of seven…

This keynote address explores the history and role of college math requirements with a focus on ensuring math courses serve to expand students' horizons, rather than serve as gatekeepers. It discusses the advent of general education math courses, which brought more students into math departments, which ultimately contributed to broadening the…

This article reports on a study of Kuwaiti college students' knowledge about the concept of functions. It also shows the connections these students make between different representations of functions. The results indicated that most students (96%) were unable to provide a definition of a function and only a third could provide examples of a…

This study explored the lived experiences of eleven transfer students as they described their experiences in Calculus 2 at very high research land grant institutions (R1). This qualitative investigation focused on the psychological phenomenon of transition as the transfer students perceived, reflected, made sense, and understood their transition…

This study investigates the embodied, symbolic, and formal reasoning of two fourth-year university students while exploring geometric reasoning about the Cauchy-Riemann equations with the aid of "Geometer's Sketchpad (GSP)." These students participated in a teaching activity designed to encourage shifts between embodied, symbolic, and…

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…

University Calculus I courses serve as a means of access into high demand STEM fields and large lecture style passive calculus courses can be difficult for students. A mixed methods research design was used to compare a flipped instructional approach to a traditional lecture approach in large section Calculus I courses. The flipped lecture model…

This article shows results on the simulation of partial differential equations such as the heat equation, the Laplace equation and the wave equation in a course called mathematical methods at a university in Bogotá Colombia. In this course, the concept of partial differential equations and different solution methods were explained to them, both in…

Learning centers offer academic resources to postsecondary students to aid in their success. Despite deep work examining the efficiency of these learning centers, the field still does not know enough about students' experiences with these learning centers' resources. By understanding the mechanisms and experiences of students as they learn about,…

Adolescent and children's concepts of multiplication and fractions have been linked to differences in the number of levels of units they coordinate. In this paper, we discuss relationships between adult students' conceptual structures for coordinating units and their pre-calculus understandings. We conducted interviews and calculus readiness…

The ability to solve mathematical problems has been an interesting research topic for several decades. Intuition is considered a part of higher-level thinking that can help improve mathematical problem-solving abilities. Although many studies have been conducted on mathematical problem-solving, research on intuition as a bridge in mathematical…