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 contributes to Action, Process, Object, Schema (APOS) theory research by showing two approaches used by advanced mathematics students to construct relations between higher-order derivatives to solve complex problems. We show evidence of students' ability to perform Actions on their graphing derivative Schema, that is, of its…

Psychological interventions offer a unique approach to enhancing the educational experience for university students. Unlike traditional teaching methods, these interventions directly address cognitive, emotional, and behavioural factors without requiring changes to course content, delivery methods, or involvement from the teaching team. This…

The purpose of this comparative study was to determine if and to what extent there was a statistically significance difference in college students' motivation--amotivation, external regulation, introjection, identification, intrinsic motivation--to learn Algebra I between in-person instruction and online instruction in Central Arizona. The theory…

In this study, we explored the effect of delayed enrollment in college-level mathematics upon entry into a 4-year university for students who were not placed into remedial mathematics (i.e. college ready). For students who attempted a mathematics course, delayed enrollment in mathematics did not have an effect on GPA, graduating within 6-years or…

Action-Process-Object-Schema (APOS) theory and the triad of schema development are used as the framework in this study to investigate students' understanding of the concept of "circle." In this report, results are presented from the data analysis of responses to questions in semi-structured interviews of 15 students enrolled in a college…

This paper reports on university students' responses to an inverse proportion question. The authors conclude that inverse proportion is a difficult concept that requires constant reinforcement, using approaches to teaching that facilitate deeper conceptual understanding.

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.

We present a detailed description of a Cryptography and Computer Security course that has been offered at Knox College for the last 15 years. While the course is roughly divided into two sections, Cryptology and Computer Security, our emphasis here is on the Cryptology section. The course puts the cryptologic material into its historical context…

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…

Typically, departments and universities evaluate and/or provide feedback to college mathematics instructors on their teaching by conducting classroom observations. When these observations are guided by an observation protocol, the protocol provides a particular lens that focuses the observer's attention on certain aspects of instruction. To…

From the socio-critical perspective of mathematical modeling, reflexive discussions about the nature, criteria, and consequences of mathematical models are not a natural consequence of modeling in school. This report is part of a larger study focused on stimulating reflexive discussions in practice employing constructivist grounded theory as a…

That the manifestation of cheating varies between disciplines is rarely discussed, an unspoken assumption being that assessment takes the form of written prose supported by a bibliography. Students and academics from disciplines, such as mathematics, not fitting this model can feel that their work is regarded as an aberration. 'Plagiarism' is not…

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…

The purpose of this study is to examine the performances of university students' using dynamic mathematics software GeoGebra in argumentations and proving processes. A task related to the limit involving "sinx/x" was designed and 18 university students worked on the task during the collaborative learning, scientific debate, and…