The research on mathematical argumentation has mainly adopted a dialectic lens which focuses on understanding the abstract and logical development of reasoning in argumentation. However, this approach may have overlooked other key aspects of mathematical argumentation, including the unfolding of the meaning-making experience and process during…

When a Year 7 student physically reacted to a prompt of another student by anxiously drumming the desk with his ruler, exclaiming "uuuuhh", the initial thought of the observing researcher, Laura, was: "this is an interesting account". This started a reflective journey of first applying robust research methodologies to the…

The observation that the human mind operates in two distinct thinking modes--intuitive and analytical- have occupied psychological and educational researchers for several decades now. Much of this research has focused on the explanatory power of intuitive thinking as source of errors and misconceptions, but in this article, in contrast, we view…

One of the challenges of learning ratio concepts is that it involves intensive quantities, a type of quantity that is more conceptually demanding than those that are evaluated by counting or measuring (extensive quantities). In this paper, we engage in an exploration of the possibility of developing reasoning about intensive quantities during the…

We report on an experiment conducted with pre-service teachers in France and in Quebec. They were submitted to a classroom situation involving regular polyhedra. We expected that through the activities of defining, of exploring and experimenting via concrete constructions and manipulation, students would reflect on the link face angle--dihedral…

The ideas of Kuhn and Lakatos are used to study four issues in mathematics education related to values, units of analysis, theory of mind, and nature of mathematical entities. The goal is to determine whether differences between the assumptions are best understood in Kuhnian or Lakatosian terms. (MNS)