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