Prospective primary teachers’ knowledge about the mathematical practice of defining

International audienceThis study concerns the knowledge of two prospective primary teachers about the mathematical practice of defining. Starting with their analysis of a video recording of a primary lesson on constructing a definition of a polygon, the trainees discussed what it means to define in mathematics. Through analysis of the content of this discussion, we identified what they considered to be the nature of this practice and the features they felt a good definition should embody. The findings demonstrate that students tend to consider demonstrations as the touchstone of mathematical practice, and that they do not consider the use of examples as a valid element of formal mathematics. At the same time, they recognize that definitions must meet the criteria of hierarchy and minimality but see no need for the criteria of existence and arbitrariness