Task as a pedagogical resource: an example in the context of proportionality at lower secondary

Abstract

Tasks are central elements in our professional practice. Its implementation requires teacher’s knowledge concerning their potentialities and limitations aimed at leading to students’ mathematical learning. Considering teachers’ knowledge as specialized – here, assuming the Mathematics Teacher’s Specialized Knowledge (MTSK) – leads to the need for an innovative approach in the way pedagogical resources are understood; the specialized knowledge involved in its use and the specialized set of indications for its implementation. In the work we developed at CIEspMat – Grupo de Pesquisa e Formação sobre o Conhecimento Interpretativo e Especializado do professor de e que ensina matemática – as part of the so-called Tasks for Teacher Education (TpF) – we present a conceptualization of tasks for students including a set of five dimensions corresponding to guidelines for the implementation, pursuing the mathematical learning associated to its conceptualization. Here, we focus on a task for students (perceived as a resource), focusing on the topic of proportionality, discussing the content of the five dimensions composing the specialized guidelines aimed at developing the students mathematical understanding.