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…

Drawing on research in the context of Swedish school-age educare and adopting a post-humanist theoretical--methodological approach, we put forward the notion of mathemat-ing to conceptualise mathematical events that emerge in out-of-school configurations of practice. In them, ethical sensibilities as affects of engagement and rejection may be…

We explore how the concept of abstraction, which is central to mathematical activity, can lead to detachment or attachment to land, nature, culture, language, and heritage in Indigenous contexts. We wonder if students detach themselves from mathematics because they feel mathematics asking them to detach themselves from people and places to whom…

Covariational reasoning, essential for understanding functions and modeling dynamic situations, is traditionally introduced in secondary education. This paper proposes introducing covariational reasoning in primary school settings through an artifact, the Tracer. Previous studies investigate a covariational approach to functions with younger…

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…

This paper highlights the pedagogical importance of gaps in mathematical proofs to foster students' learning of proofs. We use the notion of 'gap-filling' (Perry & Sternberg, 1986) from literary theory to analyze a task based on a Proof Without Words, which epitomizes the notion of gaps. We demonstrate how students fill in gaps in this…

The purpose of this article is to explore the use of didactical phenomenology as an instructional design heuristic. In doing so, I will articulate ways in which didactical phenomenology can be used in conjunction with the guided reinvention and emergent models heuristics to support instructional design. This discussion will be supported by…

We hypothesize that one thing that has been holding the field back from recognizing the algebraic potential of young children's early experiences is an emphasis on specific definitions of what counts as algebra-relevant knowledge. In this article, we seek to develop a perspective on algebraic thinking that foregrounds the algebraic potential of…

We aim to open up discussion about the intertwined roles of teachers and tasks that involve students communicating about mathematics when working in groups. Over many years we have observed, researched and ourselves have taught students working on mathematics in groups and find that it is often easier to pay attention to the forms of communication…

Our aim is to discuss some choices of communicational artifacts made by Maxakali Brazilian Indigenous students to register and operate with numbers in a mathematics education course, and how these choices reflect in the ongoing classroom activity. We rely on Activity Theory to analyze an activity involving them and discuss how the choice of…

Described are the background, structure, themes, methodology, projects, and assessment for the course. A list of themes is provided. Results of the piloting of the course are discussed. (CW)

Explores the use of dialogue and dramatization to reconstruct the formation of mathematical concepts. An appendix provides the synopsis of a 6-scene play that portrays the rise of negative numbers over a period of 300 years. (MDH)

Describes an exploratory investigation of how children reacted to problems with missing, surplus or contradictory data. It was found that the majority of children gave unsatisfactory answers to such problems. (PK)

Presents the concept of "Fuzzy Sets" and gives some ideas for its potential interest in mathematics education. Defines what a Fuzzy Set is, describes why we need to teach fuzziness, gives some examples of fuzzy questions, and offers some examples of activities related to fuzzy sets. (MDH)

Describes a classroom experience in which the teacher experiments with integrating mathematics history into a calculus class by presenting a historical problem taken from L'Hopital to be solved by the students. Extracts the role that history can play in teaching mathematics from the experience. (MDH)