We introduce, motivate, and exemplify a proposed theoretical construct guiding the design and facilitation of collaborative geometry activities, conceptually generative perspectival complementarity (CGPC). Participants in CGPC activities learn content by negotiating their respective perceptions of situated features they manipulate to accomplish…

We use a multi-dimensional identity theory to examine how children's picturebooks present discourses about what mathematics is and what doing mathematics means. In our critical content analysis of twenty-four picturebooks, we found four recurring hidden messages that frame mathematical ability as preternatural; as having a magic eye; as doing…

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…

Backward transfer refers to the influence on prior knowledge of the acquisition and generalisation of new knowledge. Studies of backward transfer of mathematical knowledge have focused on content that is closely related in time and in curricular sequencing. Employing the notion of thickening understanding, we describe instances of transfer that…

Shulman (1986) conceptualized pedagogical content knowledge (PCK) at the intersection of content knowledge and pedagogical knowledge. In this paper, I re-explore the intersection of content--in our case, mathematics--and pedagogy, not in terms of domains of knowledge, but in terms of domains of practice. I conceptualize, describe, and exemplify…

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…

In this paper, I wish to reply to the questions posed by Gascón & Nicolás (2017) about the (possibly) prescriptive nature of the research results in didactics of mathematics: To what extent, how, under which conditions can (or must), didactics set value judgments and normative prescriptions in order to provide criteria about how to organize…

An important issue in mathematics education in many countries has long been how to make use of students' daily life mathematics (informal mathematics) in teaching mathematics at school (formal mathematics). This communication proposes an alternative framework of mathematics education that bridges informal and formal mathematics using…

The crucial reason for the common dislike, fear, and even hatred of mathematics by students and others is probably not the nature of mathematics itself, but the way the subject is portrayed and taught. We propose that instead of a mathematics curriculum that focuses on concepts and techniques (which is often seen), it might be more productive if…

In this article I consider what critical mathematics education could mean for different groups of students. Much discussion and research has addressed students at social risk. My point, however, is that critical mathematics education concerns other groups as well: for example, students in comfortable positions, blind students, elderly students,…

Technological developments make it feasible to assess students' mathematics work automatically when students are working in rich digital environments and thus offer important affordances for assessment in the service of instruction. In this article, we illustrate how these technological advances might be harnessed to support the work of teachers…

Pairing the mid-century work of Ada Dietz (1882-ca. 1970) with two compelling contemporary projects from Sonya Clark (1967- ), this article considers the ways in which normative mathematical ideas are remade through their engagement with weaving practice. Highlighting recent efforts to further ethnomathematics' original decolonial intentions, I…

Popular culture casts mathematics and writing as opposites--a false dichotomy, which can be harmful for our discipline of mathematics education. Positioning writing outside the domain of the mathematician's abilities and cultivated skill set can create doubt in the mathematician wishing to write--not that one cannot be both writer and…

Ecological sustainability has not been a major focus of mathematics education research, even though it has attracted considerable attention in other areas of educational research in the past decade. The connections between mathematics education and ecological sustainability are not readily apparent. This paper explores how mathematics educators…

Abstraction is a key adaptive mechanism of human cognition and an essential process in the personal construction of mathematical knowledge. Based on the notion of abstraction, this paper aims to conceptualise a framework for analysing textbooks. First, I search for the meaning of abstraction from a constructive-empirical and a dialectic…