Pre-service teachers’ mathematical work on a calculus task that connects school and university

This paper addresses the issue of the gap that exists between the mathematics studied in initial teacher training and the school mathematics that the in-service teacher must teach. We present empirical results on how pre-service teachers (PTs) activate and coordinate cognitive processes and epistemological aspects when solving a university mathematic task that can be solved in the calculus domain. This task can likewise be adapted to the school level. This study is based on the theory of mathematical working spaces (MWS). The results examine the differentiation of the MWS of the participants according to the dynamics present between the problem-solving processes used in the task. The study’s conclusion explores the possibilities offered by the task in terms of enriching the MWS of PTs and contributing to the shrinking of the mathematical gap that exists between the university and the school.