This paper provides some insights into the use of example-generating tasks in the design of a technology-rich learning environment to enhance students' mathematical thinking. The paper reports on an early stage of a design-based research project concerning the design of tasks and associated feedback utilising the affordances provided by a combined…

This quantitative correlational study examines school-level longitudinal outcomes of eighth-grade algebra universal acceleration in 15 U.S. school districts when compared with selective acceleration in 289 school districts. Universally accelerated school districts had higher enrollments, with large effect sizes, in geometry, algebra 2, and…

We believe that developing cultural competencies can help students learn mathematics and conversely that learning mathematical content can help students learn about themselves and others. Using frameworks introduced by Rendón (2009) and Gutiérrez (2018), we present a five-part bundle of activities for undergraduate differential equations course…

Purpose: Creating suitable learning conditions in university classrooms continues to be a topical issue in higher education. The above means that a continued search for innovative teaching and learning strategies in universities remains a priority issue. The study therefore investigated conditions that facilitate the effective implementation of…

This paper reports changes in the extent to which a group of Year 11 students used a Computer Algebra System (CAS), pen-and-paper (P&P), or a combination of both, when solving routine problems across seven months in four different topics. Comparing the frequency of CAS use across topics shows students made greater use of CAS in the topics of…

Educators are faced with the sudden infiltration of AI, including artificially intelligent tools that generate content far more sophisticated than any prior technological advancement. In this study, the researchers investigated the use of ChatGPT (currently the most used generative AI tool) as a means of learning Calculus. The study examined…

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…

Geometry, calculus and in particular integrals, are too often seen by young students as technical tools with no link to the reality. This fact generates a loss of interest in students with a consequent removal of motivation in the study of such topics and more widely in pursuing scientific curricula. With this note we put to the fore a simple…

We use Taylor's formula with Lagrange remainder to prove that functions with bounded second derivative are rectifiable in the case when polygonal paths are defined by interval subdivisions which are equally spaced. As a means for generating interesting examples of exact arc length calculations in calculus courses, we recall two large classes of…

The aim of this paper is to narrate a significant part of the experience of a professor over several semesters teaching fundamental ideas of the "Theory of Calculus." The narrative explains how his didactic and mathematical mentality evolved as he witnessed students' conceptual difficulties, as they were confronted with situations that…

In this paper, we investigate leadership related to the instruction of lower division undergraduate courses at five university mathematics departments with strong calculus programs. We use social network analysis to identify patterns of influence on instruction, using the relations: advice seeking, instructional material sharing, discussion of…

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…