In this study, we present a mathematical analysis distinguishing two conceptions of equivalence: "proportional equivalence" and "unit equivalence." These two conceptions have distinct meanings in relation to equivalent fractions: one is grounded in proportionality, while the other is grounded in equal wholes. We argue that (a)…

This article recounts the life of mathematician Leonhard Euler and discusses the use of Graph Theory in student learning.

Getting the right answers in maths is only half the problem. Understanding why what you're doing works is the part that often stumps students and teachers alike. The essential guide for mathematics teachers and those training to teach, "Yes, but Why?" answers all your questions, and sheds light on the hidden connections between…

In this edition's Discovery, the problem of interpreting the term "mean" is discussed with examples of the different kinds of mean. Mathematics teachers should therefore use the term "arithmetic mean" when introducing measures of central tendency in statistics. Some various definitions of the term "average" and sports…

Why do honeycomb cells have hexagonal openings? This is a problem of antiquity. More than 2000 years ago, Greek scholars referred to "the geometrical forethought" of bees in constructing the most efficient structure to hold honey. In this article, the author determines the exact size of the trihedral angle, and provides insight as to why…

Incorporating technology into educational processes is increasingly necessary to address the complexities of contemporary learning environments. This study investigates the impact of Augmented Reality (AR) on the academic performance of third-grade students in the areas of graphs and geometry. A quasi-experimental design was employed, comparing a…

Mathematical spaces often reinforce and perpetuate whiteness. Despite efforts to decenter whiteness in secondary and post-secondary classrooms, equity-oriented strategies can still perpetuate whiteness. In this action research study, I turned the lens of whiteness upon my instructional practices and curriculum. Using an analytic framework for…

On the basis of a substantial, robust, and well-replicated cognitive science research literature, interleaving has been recommended across a range of professional pedagogical works as an evidence-based strategy for mathematics teachers. This report first notes the conflation of interleaving and spacing effects underpinning those recommendations…

There has been a notable number of respectable studies in mathematical creativity and its promotion in education with K-12 pupils. Nonetheless, when it comes to mathematics education in higher education, there is not a wide variety of studies. One can observe that the mathematics content in higher education is completely different from the K-12…

Argumentation is a key skill in most school subjects and academic disciplines, including mathematics and science. It is possible that similarities and differences between how argumentation is expressed in different subjects can contribute to, or disrupt, students' transferrable argumentation skills. The purpose of this study is therefore to…

Research has shown there are algebra concepts elementary teachers can introduce that help prepare elementary students for the eventual transition to algebra (e.g., the relational interpretation of the equal sign). "Early algebra" refers to the use of informal approaches to introduce such concepts to elementary students. "Strip…

Education 4.0 strongly promotes the development of communication, collaboration, critical thinking, and creativity (4C) skills among students. Consequently, it is crucial for mathematics teachers to integrate activities that facilitate the cultivation of these skills. However, the scarcity of resources, such as recommended instructional…

A controversial, equity-focused mathematics reform in the San Francisco Unified School District (SFUSD) featured delaying Algebra I until ninth grade for all students. This study examines student-level longitudinal data on mathematics course-taking across successive cohorts of SFUSD students who spanned the reform's implementation. We observe…

Studies show that supporting argumentation in mathematics classrooms is challenging for teachers. This study reports on the experience of seven elementary and middle-school mathematics teachers in an afterschool classroom-based program where they had the opportunity to facilitate research sessions on students' development of mathematical ideas and…

Successful adoption of proven effective practice strategies such as distributed practice may contribute to much-needed improvement in mathematics performance. However, it is not yet fully understood if distributed practice is beneficial for long-term retention of complex procedural knowledge and, if so, for which initial practice performance level…