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 attend to epistemological potentials of multilingual language use and mathematics in connection to the 'language-as-resource' idea and how the idea is actualised in Swedish mathematics education contexts. In this paper we develop and propose a framework for considering different epistemological potentials for multilingual…

How might a 4-year-old pupil come to conceive a line, created by himself with a continuous gesture, as constituted by a series of points? In this paper, we theoretically introduce and discuss a design study of the educational path in which this possibility emerged. The path aimed at leading pupils to "experience," in the sense of the…

As members of a research group taking initial steps for creating mathematics curriculum in an Indigenous language (Yakama Ichishkíin), we engaged with an unanticipated outcome: the ways Indigenous identities and homelands are fractionated, as part of ongoing colonizing harm. Our work centers on how mathematics instruction can help heal, by…

Within a study of student reasoning in abstract algebra, we encountered the claim "division and multiplication are the same operation." What might prompt a student to make this claim? What kind of influence might believing it have on their mathematical development? We explored the philosophical roots of "sameness" claims to…

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…

Critical to constructing and interpreting graphs is an individual's understanding of the underlying coordinate systems, yet coordinate systems are often overlooked or taken-for-granted in both mathematics education research and curricula. In this paper, we foreground coordinate systems and present a distinction between two uses of coordinate…

Dialogue has been characterised as a communicative pattern that supports critical learning in education. Seeking to analyse this relationship, we investigated the interaction between teachers and students in two classes, a Third Grade and a Fifth Grade of São Paulo State public school. During the interaction, we identified a variety of dialogic…

Mathematical argumentation, justification, and proof are practices at the heart of mathematics. Yet mathematics teachers generally operate without clear definitions of these practices making it difficult to communicate expectations, decide what to accept or expect from students at different grade levels, and distinguish these activities from…

Literature has already shown that gestures play a relevant role in classroom interactions between students and teacher. We integrate the perspective of Theory of Semiotic Mediation with the notion of Semiotic Bundle to illustrate how gestures can be used as "pivot signs" in semiotic chains. This means that gestures can be performed by…

The article identifies three narratives about mathematics education. The first claims that mathematics is a wonderful subject, which provides a true foundation for human knowledge and progress. The second presents mathematics as a suspicious subject, which serves functions of oppression. The third highlights that mathematics has critical…

Mathematics in its nature is exploratory, giving learners a chance to view it from different perspectives. However, during most of their schooling, South African learners are rarely exposed to mathematical explorations, either because of the lack of resources or the nature of the curriculum in use. Perhaps, this is due to teachers' inability to…

The aim of this article is to advise readers that natural numbers may be introduced as ordinal numbers or cardinal numbers and that there is an ongoing discussion about which come first. In addition, through several examples, the authors demonstrate that in the process of answering the question "How many?" one may, if convenient, use…

The purpose of this paper is to discuss a phenomenon that has evolved in mathematics education research journal articles during the last three decades, namely the 'ideal-typical' research paper. By not reflecting today's multi-faceted reality of the field, the ideal-typical research paper represents a far too narrow and rigid understanding of…

The application of ethnomathematics and mathematical modelling allow us to see a different reality and give us insight into mathematics accomplished holistically. In this context, a pedagogical action that connects ethnomathematics and the cultural aspects of mathematical modelling with its academic features is referred to as ethnomodelling. This…