The Mathematical Work of Chilean Secondary Teachers in the Domain of Probability

The objective of this qualitative research is to study the mathematical work when solving a mathematical task in the domain of probability presented by Chilean high school mathematics teachers in pre-service and in-service training. We consider as theoretical support the Mathematical Working Space model and methodological design of a collective case study, comprising of five teachers in pre-service training and eight teachers in in-service training. This research design allows us to analyze mathematical objects under semiotic, instrumental, and discursive dimensions, identifying privileged vertical planes, the paradigm applied, and the different strategies used by teachers. The task presented to the participants allows two different correct answers depending on the interpretation of the random experiment in question. Since the definition of the random experiment involved in the task is of utmost importance, according to our results, this notion was not evident in all the productions analyzed, which issue poses a challenge for the teaching and learning of probability.