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…

The main aim of this paper is to propose a critical view of the application of Toulmin's model of argument to mathematics education, focusing on aspects that have strong teaching implications. It is claimed that Toulmin's description of arguments in mathematics, in particular as regards the relations between form and meaning, is misleading and out…

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…

We live in an increasingly worrying future, where researchers are looking at how we can create education for a sustainable world. In this study we investigate what such education could look like, especially for young students, reinforcing hope and an ability to act and come up with ideas of sustainable solutions with no obvious 'good' solution.…

Planning lessons and in-the-moment improvising during enactment of the plan are two central activities inherent to the practice of teaching. To what extent are these pursuits conflicting or inconsistent? What are the characteristics of improvisation during teaching and what are teachers' possible stances on it? We discuss these questions based on…

The author has been influenced throughout his time in mathematics education by the work of Caleb Gattegno. Gattegno made extensive use of the word awareness whereas much educational literature from a psychological perspective talks about memory (for example, Justicia-Galiano, MartÌn-Puga, Linares & Pelegrina, 2017). This has, amongst other…

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…

Years of failed attempts to engage my mathematics teacher students in exploration and co-creation led me to radically change my teaching approach. Inspired by literature that uses the jazz improv metaphor for teaching, I derived three tenets based on principles from jazz improv. First, I would bring no more than a single problem-solving task to…

The aim of this study is to explore the possibility of introducing the general notions of function and inverse function through a mathematical activity on linear functions, focusing on the quantitative meaning associated to the connection between a relation and its inverse. We present a genetic decomposition, that is, a viable cognitive path for…