This paper reviews research on equity in mathematics education (excluding gender equity) for the period 2017-2022. From the publications identified, five themes were distilled: conceptualizations and framing of equity in mathematics education; research methodologies and researcher positionalities; equity-focused practices, pedagogies and teacher…

Two novel proofs show that the sum of a specific pair of normal random variables is not normal are established in this note. This is one of the most often misunderstood facts by first-year students in probability theory and statistics. The first proof is concise using the moment generating function. The second proof checks whether the moments of…

A premise of this article is that the current methods used in mathematics education research may be preventing researchers from adequately addressing the body and, in particular, the alignment of acting and knowing. Pursuing a non-dualistic and non-hierarchical approach to learning and knowing, I experiment with new methods that aim to increase…

The concept of function is critical in mathematics in general and abstract algebra in particular. We observe, however, that much of the research on functions in abstract algebra (1) reports widespread student difficulties, and (2) focuses on specific types of functions, including binary operation, homomorphism, and isomorphism. Direct, detailed…

In this paper we deal with a geometric machine that has gone somewhat unnoticed in mathematics education: the Perfect Compass. It allows conics to be drawn using a special two aperture compass, based on Apollonius' conic sections. Proposed in the 10th century, it seems that it was never built in medieval times--at least no archaeological remains…

Leading on from a paper published in the previous edition of the "AMEJ" (Kissane, 2023), which looked at scientific calculators and irrational numbers, Barry Kissane now turns his attention to the attributes of modern calculators as environments for learning about rational numbers.

In high school geometry, students are expected to deepen their understanding of geometric shapes and their properties, as well as construct formal mathematical proofs of theorems and geometric relationships. The process of helping students learn to construct a geometric proof can be challenging given the multiple competencies involved (Cirillo…

In this study, effects of asking participants to make different types of considerations when solving a realistic word problem were investigated. A two-factorial experiment with the factors "addressing realistic considerations" (with vs. without) and "addressing mathematical operations" (with vs. without) was conducted. It was…

Spatial skills can predict mathematics performance, with many researchers investigating how and why these skills are related. However, a literature review on spatial ability revealed a multiplicity of spatial taxonomies and analytical frameworks that lack convergence, presenting a confusing terrain for researchers to navigate. We expose two…

Mathematical Internet memes are examples of how the creative thrust characterising the Web 2.0 environment reaches the field of mathematics, translating mathematical statements into a new digital form endowed with an epistemic potential that is capable of initiating a process of mathematical argumentation. The research presented in this paper aims…

Inductive reasoning is used when generalizing from particular cases to a general theory. The purpose of this paper is to present some highlights in the history of the problem of induction through notes on a selection of writers from ancient Greece to modern times. These notes contribute to the argument that there is a fundamental problem with…

The relevance of the published research on the actualization of interdisciplinary integration at mathematics lessons is due to the need for conceptual clarification of what is included in the concept of an academic discipline, and, consequently, interdisciplinary integration. Currently, there is no uniformly consistent interdisciplinary…

This paper reports on students' conceptions of minima points. Written assignments and individual interviews uncovered salient, concept images, as well as erroneous "mis-out examples" that mistakenly regard examples as non-examples and "mis-in examples" that mistakenly grant non-examples the status of examples. We used Tall and…

Metacognition has been a subject of considerable interest in school settings, particularly its implications on learning and performance in mathematics. While metacognition has been widely studied as a multi-faceted construct comprising of metacognitive knowledge, regulation and experiences in various combinations, few have examined these three…

Number lines can benefit students in learning an array of mathematical concepts. An area of mathematics where number lines are visibly underused is in teaching measurement concepts. For students in upper elementary grades, accurate measurements require the use of mathematical precision and coordination, including skills in fractions and decimals,…