In this paper, we explore how the typical second year undergraduate topic of matrix diagonalisation can be applied to solve a geometric problem which arises frequently in Vector Calculus: to find the curve of intersection of a plane and a surface. We use GeoGebra, which offers a cost-free and dynamic interface, to explore a specific variant of…

College algebra is regarded as a gatekeeper course for attaining degrees, higher paying jobs, and overall individual empowerment. Educational stakeholders have reconsidered alternative instructional approaches such as computer-assisted instruction (CAI) to curb high failure rates and increase retention rates among college algebra students. One…

Universities have drawn on an assortment of strategies to address the learning challenges and high attrition rates of developmental mathematics students. One of those strategies has been utilizing computer adaptive instruction (CAI) mathematics software. Reports about the efficacy of CAI vary from glowing to unfavorable. This article presents an…

In this paper a class of regular surfaces, generated by rotation and twist of a rigid line segment, is considered. Firstly a complete description of those surfaces by means of local charts is obtained and then its orientability is characterized in terms of the number of half-twists, taking into account their direction (clockwise or…

Almost all finite groups encountered by undergraduates can be represented as multiplicative groups of concise block-diagonal binary matrices. Such representations provide simple examples for beginning a group theory course. More importantly, these representations provide concrete models for "abstract" concepts. We describe Maple lab…

Answering a call by the "Common Vision" for instructional material to "establish stronger connections with other disciplines" and "work with professional-level technology tools," the present article shows how various aspects of fitting circles to data fit in existing courses from basic calculus to advanced calculus.

This paper analyses student views on an e-learning intervention that incorporated a content development tool and computer algebra systems, aimed at improving performance and applicability of mathematics knowledge. The study deliberately relied on open source tools, with high usability both online and offline, that can be customized to address the…

As soon as a new technology emerges, the education community explores its affordances and the possibilities to apply it in education. In this article, we analyze sessions with ChatGPT around topics in basic linear algebra. We reflect on the affordances and changes between two versions of ChatGPT since its worldwide publication in our area of…

The widespread of online education is clear and the demand for online education is increasing rapidly, so the quality of offered online courses is urging. During COVID-19 restrictions, unprepared institutions, instructors, and students for online education were clear, especially in STEM. So there is a need for more research on online mathematics…

MathCheck is a relatively new online tool that gives students feedback on their solutions to elementary university mathematics and theoretical computer science exercises. MathCheck was designed with constructivism learning theory in mind and it differs from other online tools as it checks the solutions step by step and shows a counter-example if…

Remedial/developmental and introductory university mathematics courses have a long history of high attrition rates. Recently, university administration and mathematics departments have been considering technological solutions, and one such solution is computer-adaptive-instruction (CAI). In fact, CAI has been touted as a "silver bullet"…

The purpose of this research study was to understand how mathematics majors make sense of similar matrices, a linear algebra topic that is rich in internal and external connections, in a series of in-depth qualitative interviews in a technology-assisted (MATLAB) learning environment. The study was also an attempt to develop a cognitive theory in…

Scaffolding is defined as help that can assist students to solve problems or understand concepts that were not able to complete independently. In modern times, the concept of technology-based Scaffolding in learning has developed. In this study an educational game called "Telolet" was designed with the aim of providing Scaffolding to…

A personal overview about the use of new technologies for teaching and learning mathematics is given in this paper. We analyse the introduction of Computer Algebra Systems with learning purposes, reviewing different frameworks and didactical resources, some of them generated according the philosophy of the European Area of Higher Education.…

Approximately 30% of students entering West Virginia University (WVU) are not ready for college mathematics. The WVU Department of Mathematics has been tasked with remediating these students and has worked over the last decade to find the most efficient way to teach the Pre-College Algebra Workshop; the prerequisite course students must complete…