An organization of teaching-learning systems of linear equations in high school, from a developmental perspective:

a didactic-training experiment

Abstract

When considering the scenario of Brazilian education, at the beginning of the 21st Century, marked by the utilitarian value of school content, and, taking into account the need to define a specific mathematics of teacher action, the research question presented is: How to organize the teaching-learning of Systems of Linear Equations in High School, from a developmental perspective, based on principles of the Historical-Cultural Theory (Vygotsky, 1896-1934) and Study Activity Theory (Davydov, 1930-1968),  so as to create conditions for the development of  students’ theoretical thinking? To this end, this article presents discussions on the conception and execution of a Task, which comprised a didactic proposal, in the context of a didactic-training experiment, with the objective of proposing an organization of the teaching-learning process of Systems of Linear equations, with 2nd year high school students, aiming to develop theoretical thinking. Three Study Tasks were created, which constitute the basic unit (cell) of the Study Activity. It is concluded that: 1) the organization of teaching required consistent knowledge of the theoretical assumptions of the Study Activity Theory and the logical and historical aspects of Systems of Linear Equations, fertile theorizations to discuss mathematical knowledge for teaching; 2) the teacher plays a fundamental role in the process as an organizer of teaching and as being responsible for mediation, working in the Zone of Proximal Development – ZDP, which requires teaching-specific mathematical knowledge ; 3) concern with the development of theoretical thinking can lead to the appropriation of concepts, in essence.