In this article, we consider the phenomenon of improvisation by small groups of middle years students while engaged in rich mathematical tasks in a classroom setting. Working from the premise that improvisation comprises a spectrum of behaviour, we propose that there is a range of improvisational behaviours that may be observed as the students…

Children in a first-grade class who were taking their first steps in formal mathematical knowledge were given a sequence of five modelling tasks during their regular mathematics lessons. These tasks were different in nature from the problems they encountered in their textbooks. They are more complex and challenging, requiring analysis of the…

To what extent can instructional design be based on principles for instilling a culture of problem solving and conceptual learning? This is the main focus of the study described in this paper, in which third grade students participated in a one-year course designed to foster problem solving and mathematical reasoning. The design relied on five…