Emerging mathematics education researchers in the United States need to be better equipped to attend to the philosophical backgrounds of theories used in research. Thus, doctoral programs must provide students with sustained space to reflect on the philosophical backgrounds of theories and attend to their worldviews to ensure students are well…

Learning mathematics is often justified as supporting students to make rational decisions, an important goal given the misinformation spread through social media every day. However, when asking preservice teachers to engage in a critical mathematics education activity in which they had to produce an argumentation that would persuade people to…

In this article, we analyse a script of an imagined classroom interaction from the perspectives of politeness and positioning. The script was written by a prospective teacher, Cara, as part of her Lesson Play. The Lesson Play was prompted by her reflection on how the needs of students who are disaffected with mathematics might be met, an issue…

Many universities throughout the world apply student-centered approaches. Common to these is that projects, problems, challenges etc. stem from "real life". Mathematics is an effective tool to solve problems, but in this paper, we discuss how we reconcile the fact that mathematics is both a pure and an applied discipline with…

Analogical reasoning has played an important role in the development of modern mathematics. However, there has been critique of analogies for the purpose of learning new mathematics. In this article, I counter that students can productively reason by analogy to learn new mathematics and even develop new mathematics themselves. I display examples…

Not-knowing is an underexplored concept defined as an individual's ability to be aware of what they do not know to plan and effectively face complex situations. This paper focuses on analyzing students' articulation of not-knowing while completing geometric reasoning tasks. Results of this study revealed that not-knowing is a more cognitively…

This paper is about the role and the potential of the history of mathematics in mathematics education. We report a discussion that we had about theoretical issues in this context, particularly about the notion of Otherness as developed by the French philosopher Emmanuel Levinas. The focus is on the reading of historical texts, both in the context…

Research in mathematics education suggests that learning to solve a problem should involve modelling and visual representation (e.g., Lesh & Zawojewski, 2007). According to researchers, transforming a mental representation of a situation into a visual representation of mathematical relationships between quantities enhances students'…

In this paper we analyze common solutions that students often produce to isomorphic tasks involving proportional situations. We highlight some key distinctions across the tasks and between the different equations students write within each task to help elaborate the different interpretations of equivalence at play: numerical, transformational, and…

This article is a celebration of the pleasure inherent in the teaching of mathematics, with a particular focus on a university undergraduate context, and a taught course in the Theory of Numbers. The paper describes a conscious effort by one lecturer to respect the 'genetic sequence', whereby students are encouraged and enabled to investigate the…

The paper argues that there is a need for new approaches to teaching proof with newly-available technology. It contributes to filling this need by opening a discussion on digital proof assistants, programs that allow one to do mathematics with the aid of a computer, construct proofs, and check their correctness. The paper starts by exploring such…

In this paper, we propose a potential interactional explanation of tertiary-to-secondary (dis)continuity: that of authority relations. Using secondary mathematics teachers' proof validations across two contexts, we suggest that secondary teachers' conceptions of authority shape their capacity to reconcile their positions as former mathematics…

Students who are labelled as low attaining in mathematics are often seen as a homogeneous group and as such can be assigned learning attributes by others that observe their identity work in the classroom. Rachel Helme argues that by giving attention to an otherwise marginalised voice, it may be possible to challenge the discourse of deficiency,…

We reflect on the evolution of an instrument designed to gather data about student actions with dynamic textbooks in university mathematics in a large-scale project. We also discuss the evolution of our understanding of the mediating role of this instrument in gathering data remotely that allow us to access student use and reconstruct their…

In this paper, we discuss the relationship between rhetoric and mathematics, focusing on mathematical proofs. We offer a theoretical framework based on Perelman's New Rhetoric for analyzing the teaching of proof, taking into account rhetorical aspects. We illustrate the practicality and applicability of the proposed framework and methodology by…