Take a family of independent events. If some of these events, or all of them, are replaced by their complements, then independence still holds. This fact, which is agreed upon by the members of the statistical/probability communities, is tremendously well known, is fairly intuitive and has always been frequently used for easing probability…

In this paper we discuss the important Abel's summation formula, which is a very powerful tool for analysing series of real or complex numbers. We derive from it an integral test which may be useful in cases where the classical integral test may not be applied. We also discuss how this new integral test may be used when one is dealing with…

Neoliberal logics, a form of racial capitalism, adjudicate children as smart, able, and desirable (or not) in schools. I explore the social processes and structural arrangements by which such logics position a Latina mathematics student as "undesirable" in her class. Drawing on data collected over a year, the analysis lays bare how…

This paper walks the reader through a simple mathematical characterization of the popular children's game, "Chutes and Ladders," focusing primarily on Monte Carlo simulation. The focus is then shifted to the board game "No Te Enojes" in order to analyze the implications of the introduction of strategy. The presence of strategy…

This paper presents a qualitative study developed with a group of 16-year-old students who were asked to estimate large numbers of elements on a bounded surface. Taking the realistic mathematics education framework as a reference, we presented the students with an activity sequence comprised of four different tasks--each one with a different…

The contribution aims at subject-specific analyses of student solutions of an exercise from an electrical engineering signal theory course. The basis for the analyses is provided by praxeological studies (in the sense of the Anthropological Theory of Didactics) and the identification of two institutional mathematical discourses, one related to…

Calculus is a required course in most engineering programmes and is intended to provide students with tools they will use throughout the rest of their training. However, research seems to indicate that calculus is not very prevalent in the engineering workplace or in university engineering courses. To shed some light on how calculus is actually…

The purpose of this article is to provide an explicit formula for the bounds of integration of the regular simplex centred at the origin. Furthermore, this article rigorously proves that these integration bounds recover the volume of the regular simplex. To the authors' knowledge, this is the first time that such integration bounds have been…

The objective of this study was to characterise prospective kindergarten teachers' development of noticing children's thinking about length and its measurement. We used the concepts of instrumental genesis and learning trajectories to identify the ways in which prospective kindergarten teachers used a learning trajectory to learn to notice…

In this study we aimed to understand teaching mathematics through problem posing based on an analysis of 22 teaching cases. Teaching mathematics through problem posing starts with problem-posing tasks. This study provides not only specific examples of problem-posing tasks used in classrooms but also related task variables to consider when…

As a Canadian mathematics educator, I have a vested interest in Canadian mathematics education matters. After all, to me, Canadian mathematics education matters. Knowing this little factoid, imagine my horror when it recently dawned on me that, no matter where I looked during this COVID-19 pandemic, all I saw was flippant treatment towards the…

In order to describe the velocity of two bodies after they collide, Newton developed a phenomenological equation known as 'Newton's experimental law' (NEL). In this way, he was able to practically bypass the complication involving the details of the force that occurs during the collision of the two bodies. Today, we use NEL together with momentum…

In this paper, the authors propose a novel forwarding strategy based on deep learning that can adaptively route interests/data packets through ethernet links without relying on the FIB table. The experiment was conducted as a proof of concept. They developed an approach and an algorithm that leverage existing intelligent forwarding approaches in…

The author believes that in mathematics education, with ourselves AND with students or learners, people need to embrace failure as a beautiful thing -- an incredibly wonderful opportunity to learn more about the math or the tool or the people. The five characteristics of provocative objects can help to understand how to design such lovely failure,…

In mathematics education, assessment is increasingly conducted using computer- or tablet-based technologies as alternatives to the traditional paper-and-pencil format. Several studies have examined the impact of test mode (computer vs. paper) on test performance in mathematics, but these studies have produced mixed results and few studies…