In this paper, a simple proof of the Morley's Trisector Theorem is presented which involves basic plane geometry only. The use of backward geometric approach, trigonometry or advanced mathematical techniques is not required. It is suitable for introducing to secondary or undergraduate students, as well as teachers or instructors for learning or…

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…

With a focus on related rates problems, the present study reports on quantitative and covariational reasoning opportunities provided by five widely used calculus textbooks in the United States. There are three major results from this study. First, quantitative reasoning opportunities are plentiful, while covariational reasoning opportunities are…

In this case study we explored how a mathematician's teaching of the Cauchy-Riemann (CR) equations actualized the virtual aspects of the equations. Using videotaped classroom data, we found that in a three-day period, this mathematician used embodiment to animate and bind formal aspects of the CR equations (including conformality), metaphors,…

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…

Exploring non-Euclidean geometries is a common way for College Geometry instructors to highlight subtleties in Euclidean geometry. The concept of congruence, going undefined or informally defined in multiple axiomatic systems, is particularly susceptible to conflation with the idea of "same measure." Taxicab geometry provides a context…

This paper discusses a project for linear algebra instructors interested in a concrete, geometric application of matrix diagonalization. The project provides a theorem concerning a nested sequence of tetrahedrons and scaffolded questions for students to work through a proof. Along the way students learn content from three-dimensional geometry and…

Despite growing recognition of the value of using technology in mathematics instruction and learning, preservice teachers consistently performed abysmally in college geometry. This study therefore examined the attitude of preservice teachers towards the integration of technology in the teaching and learning of College Geometry. Quantitative…

This paper shares a flexible activity for engaging people in mathematical inquiry that does not depend on fixed prior knowledge built on a famous property of Möbius strips. The discussion includes the implementation of the activity and its extensions, facilitator moves and common participant thinking, suggestions for adaptation and integration…

The current research trend of metacognitive regulation has shifted from an individual to a social context. One such social context is collaborative problem-solving. Interaction between group members is an essential factor in completing collaborative problems. Metacognitive regulation is divided into four forms based on the interaction in…

The aim of this study is to characterize ways of reasoning and arguing that first year university mathematics students exhibit in problem-solving activities from a course that emphasizes the importance of formulating conjectures and the search for different ways to support or validate them. The use of a Dynamic Geometry System in the…

This paper explains teaching modern geometry for schools using software called Surfer and converting the algebraic surfaces into Batik motifs as one example of teaching mathematics with the integration of STEAM. Typical algebraic surfaces known in schools were, for example, cylinders and spheres which are identified as traditional geometry in this…

This article describes an instructional sequence used with inservice secondary mathematics teachers as part of a graduate course. The instructional sequence focused on designing tasks using Interactive Geometry Software (IGS). This study answers a call for replication studies to investigate the use of an established instructional sequence. Results…

This study explored pre-service teachers' perceptions of a 3D printing integrated science, technology, engineering, and mathematics (STEM) module within a college-level mathematics content course. Data from surveys and reflections collected from nineteen participants were analyzed. Results indicated that the pre-service teachers perceived…

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…