L.V. Zankov (1901-1977), a student and colleague of Vygotsky, developed a system of developmental education for elementary education through 20 years of extensive research. Since 2009, a number of Norwegian schools have been using textbooks in mathematics based on Zankov's system. In this article, we present and discuss the experiences of some…

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…

What is the paradigmatic direction of teaching and learning mathematics? According to Yves Chevallard, father of the anthropological theory of the didactic, the current paradigm is characterized by an obsolescent form of monumentalism. But is a new paradigm possibly on the rise? And what is the role of powerful organizations such as the OECD? We…

Our planet is facing a biodiversity crisis and mathematics is involved. In this article, I focus on reports of a wolf hunt to examine different ways in which mathematics contributes to this crisis, shapes our understanding of the ecosystem and guides future actions. My examination contributes to understanding the ethical dimension of mathematics…

This meditation on subjectivity draws on mundane and explicitly political contexts to argue for mathematics education practices that help us understand how people use mathematics to shape our world. I use two contexts to consider how to develop citizens who understand how we are subjugated by mathematical systems (designed and sustained by…

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…

This paper seeks to integrate a scholarship of "ritual" with a scholarship of "improvisation" and relate the intersection thereof with mathematics teaching and learning and with mathematics education research. Drawing on their experiences as classroom teachers, as practicing improvisers, and as current education researchers,…

Many predominantly English-speaking countries have problems understanding the notion of "didactics" as it is used in many European and other countries. The term appears almost exclusively in the UK as a description of a form of teaching which in recent decades has been seen pejoratively. Didactic teaching is taken to mean teaching with…

Research in mathematics education constantly oscillates between theoretical or 'Is' questions and practical or 'Ought' questions: Researchers are not only pursuing theoretical questions by investigating what those involved in the teaching and learning of mathematics do, but they are also working on practical recommendations for what they ought to…

Drawing on the work of Gattegno, it is suggested that a powerful way of teaching mathematics is to introduce symbols as relationships between visible or tangible resources. The symbols are abstract (formal) from the beginning and yet there are concrete resources to support their use. Drawing on data from a research project in primary schools in…

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…

In this article, which was first published in 1991, the late Sandy Dawson, discusses aspects of a Lakatosian approach to mathematics teaching. The ideas are illustrated with examples from three teaching situations: making conjectures about the next number in a sequence; making conjectures about the internal angles in a triangle using Logo; and…

This paper focuses on the design of tasks that situate teachers in the work of mathematics teaching. We examine a simple, yet fundamental feature of pedagogical content knowledge tasks: the extent to which pedagogical warrants are necessitated by the pedagogical context. We argue that this feature has implications for the design of tasks, as well…

In this article, we consider the potential influences of the study of proofs in advanced mathematics on secondary mathematics teaching. Thus far, the literature has highlighted the benefits of applying the conclusions of particular proofs to secondary content and of developing a more general sense of disciplinary practices in mathematics in…

We examine different definitions presented in textbooks and other mathematical sources for "continuity of a function at a point" and "continuous function" in the context of introductory level Calculus. We then identify problematic issues related to definitions of continuity and discontinuity: inconsistency and absence of…