In this paper, we discuss our experience in collaborating with mathematicians to increase their use of active learning pedagogy in a proof-based linear algebra course. The mathematicians we worked with valued using active learning pedagogy to increase student engagement but were reluctant to use active learning pedagogy due to time constraints.…

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…

Mathematical induction is a powerful method of proof, taught in most undergraduate programs involving mathematics and in secondary schools in some countries. It is also commonly known to be complex and difficult to comprehend. During the last five decades, mathematics education research has produced numerous studies on the learning and teaching of…

The ability to apply mathematical knowledge to solve real-life problems is often considered one of the fundamental educational goals. However, more attention in mathematics education has been given to the development of abstract mathematical computations in symbolic form. The current investigation aims to disclose whether there are different…

A teacher of mathematics knows mathematics as a teacher and as a mathematician. Whilst the existing research on teacher knowledge contributes to our understanding of the ways of knowing mathematics as a teacher, little is known about ways of knowing mathematics as a mathematician. Guided by the conceptual framework of mathematical practices (MPs)…

"Epistemological justification" is a way of thinking that manifests itself through perturbation-resolution cycles revolving around the question "why and how was a piece of mathematical knowledge conceived?" The paper offers a conceptual framework for constituent elements of epistemological justification. The framework provides:…

Recent research in university mathematics education has moved beyond the traditional focus on the transition from secondary to tertiary education and students' understanding of introductory courses such as pre-calculus and calculus. There is growing interest in the challenges students face as they move into more advanced mathematics courses that…

For students taking higher level mathematics courses, the transition from computational to proof-based courses such as analysis and algebra not only introduces a new format of writing and communication, but also a new level of abstraction. This study examines the affordances of one particular tool to aid students in this transition: a proof…

While proof has been studied from different perspectives in the mathematics education literature for decades, students continue to struggle to build proof comprehension. Complicating this, the manner in which proof comprehension is assessed largely remains to be the definition-theorem-proof format in which students are asked to reproduce proofs or…

For over a decade, Which One Doesn't Belong? (WODB; Danielson, 2016) has been a beloved classroom routine that invites students to engage in mathematical decision-making and justification. In the WODB routine, four related figures are shown to students, and they are asked to decide which of them doesn't belong with the other three. The beauty of…

The short activity presented in this article continues a discussion related to the value of golden ratio explorations in secondary mathematics, and acts as a companion to the earlier paper in this journal (Crawley, 2023). Exploring meaningful ways in which teachers can elicit students' interest and engagement in mathematics is vital, and…

Diagrams and in general the use of visualization and manipulative material play an important role in mathematics teaching and learning processes. Although several authors warn that mathematics objects should be distinguished from their possible material representations, the relations between these objects are still conflictive both from an…

This research article is about "Introducing a Supportive Framework to Address Students' Misconceptions and Difficulties in Learning Mathematical proof techniques (MPT): A Case of Debark University". This study aims to develop, introduce, and implement a supportive framework to overcome students' misconceptions and difficulties in MPT.…

The ability to interpret mathematical symbols and understand how they capture contextual relationships is a critical element of algebraic thinking. More often than not, students see algebra as merely a list of rules for manipulating abstract symbols, with limited to no meaning. Instead, for students to see algebra as a powerful tool and rich way…

The mathematics curricula of Australia (ACARA, 2019), Scotland, England and America all require an understanding of proof by contradiction. Specifically, proof by contradiction is included as a Geometry topic in Specialist Mathematics (Version 8.4). In Specialist Mathematics, it is expected that students construct proofs in a variety of contexts…