Teacher's reflections on their knowledge and practice of teaching high school functions

We report a characterization of the reflections made by high school mathematics teachers when discussing their resolutions of three numerical tasks related to the concept of function understood as a mathematical procept. Thematic analysis was used to code and categorize the reflections. Six teachers with at least 5 years of professional experience and an average age of 30 years participated. The results show that the teachers reflected on their actions in the tasks; their content knowledge; their teaching practice; and their professional training. As a result of these reflections, they recognized the need to improve their knowledge and practice of teaching functions in a more proceptual sense. The results contribute to deepen in how to make teachers reflect and incorporate a much more structural vision of functions in their teaching practices and, at the same time, incorporate the importance and role of their professional training in their reflections.