Diseño de tareas en la formación inicial docente de matemáticas que involucran las representaciones de una función

Abstract

In this research we present the analyses associated with the design of tasks developed by prospective secondary mathematics teachers. To do so, we pay attention to the formative experiences of teachers and the demands established in the school curriculum that must be considered in the development of activities in initial teacher education (ITE). We present a cases study that characterises the mathematical work around tasks designed by future teachers, focusing on the concept of function and favouring the ability to represent declared in the Chilean curriculum. The study is carried out in ITE didactics courses at two universities. The analyses are based on the theory called Mathematical Working Spaces, which allows us to delve into epistemological and cognitive aspects of the expected mathematical work that the tasks promote. The results show difficulties associated with the tasks that teachers design and what they hope to promote in their teaching. We conclude with a discussion of possibilities for improvement in teacher training.