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On a New Requirement in Teacher Education Remember Y2K? Back in those days, important changes took place in the way universities in Quebec were to conceive teacher education: "professional competencies" were supposed to become the backbone of our programs (see Lajoie & Pallascio, 2001). One key idea we have drawn from this requirement is the concept of "knowing how to act in the moment." How could student-teachers be prepared to know how to deal with the unexpected? And not only to "know how", but indeed develop know-how, competencies to actually act in the moment and make the best-in terms of the subject matter-of surprising, unforeseen, startling events that sparkle in the everyday of teaching and learning? Even more: how can this "know how"be made part of "formal," intra muros, teacher education, and not only fall on the charge of practicum? Our answer: improvisation! On Improvisation and Role Play Placing improvisation at the heart of an undergraduate course in mathematics education is not the easiest thing to do. Our students themselves are quite puzzled when they

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mise au jour d'un contrat réflexif comme régulateur de démarches de recherche participative : le cas d'une recherche-action et d'une recherche collaborative », Recherches en éducation [

The notion of emergence has considerable currency in mathematics education. However, the notion tends to be used in a descriptive way rather than being theorized and developed as a phenomenon sui generis. The purpose of this article is to contribute to building a theory of emergence. After providing an exemplifying description and analysis of an episode from a second-grade mathematics classroom studying three-dimensional geometry, we discuss implications for theoretical and classroom praxis in mathematics education, especially for the curriculum planning and the preparation, training, and enhancement of teachers of mathematics.Keywords Emergence . Indeterminacy . Witness . Intention . Intuition . Excess . SocialityWithout emergence there are no distinguishable events thanks to which time emerges. (Mead 1932, p. 49) Th[e] present is the scene of that emergence which gives always new heavens and a new earth, and its sociality is the very structure of our minds. (Mead 1932, p. 90) Mathematical lesson plans and assessment that evaluates classroom events in terms of what the lesson plans have stated presuppose the idea that whatever is contained in the planned curriculum specifies, more or less accurately, what will actually happen in a lesson. Such presuppositions, however, contradict empirical findings showing that even the most highly trained professionals (e.g., engineers and scientists) cannot with any certainty anticipate their own always contingent, practical actions, which leads to the fact that there is a permanent gulf between plans and situated actions (Roth 2009;Suchman 2007). In mathematics education, this is viewed, for example, as a conceptual shift away from mathematics as content, where the notion of mathematics placed in the container of curriculum dominates, Math Ed Res J (2014) 26:325-352