Didactic-mathematical knowledge on proportionality in prospective elementary school teachers

This paper describes the design, implementation, and retrospective analysis of a formative action with primary school prospective teachers, whose objective is to evaluate the knowledge about proportionality and the degree of development of two relevant aspects of didactic-mathematical knowledge of such content: the analysis of objects and meanings put into play in the mathematical practices and the study of algebraization levels involved in different solutions to proportionality tasks. The training experience has been carried out with a group of 35 students within the framework of a course on design and development of the curriculum in elementary grade-level in which a relevant role is attributed to team working. The results indicate that the students' specialized knowledge and competence on proportionality present specific gaps that may hinder the teaching of this subject. Students have achieved competence to identify the system of elementary practices in the resolution of tasks and recognize the levels of algebraization put into play there. However, more time is required for future teachers to be able to identify the different objects that intervene in mathematical practices and to enunciate meaningful variants of a given problem.