Historical-dialectical approach to concepts in the the organization of mathematics teaching

Abstract

Based on the Vygotskian proposal of the dialectical unity between ontogenesis and phylogenesis as the driving force of cultural development in human activity, we discuss aspects of the organization of mathematics teaching, basing the relationship between human activity, social practice and history of concepts in the historical-cultural perspective. In this sense, we argue that it is also possible to understand that the unity between the logical and historical aspects of the object of knowing are objectified for the knowing being through human collective activity. Thus, the awareness of historical concepts takes place in human activities and results from the critical production of sense of the historical concepts at stake, their motives and needs, emerging the importance of studying the concepts in their production process, together with the cultural meanings intrinsic to the culture in which they are embedded. As a result, the proposition of problems based on the history of mathematics, as we understand it, can only trigger learning through joint work with the teacher. In this sense, the history of mathematics is illuminating both by inspiring activities imbued with human needs of the concept, and by allowing the teacher to understand the limits of mathematical problems that can be formulated, as well as the necessary mediation for students to become creatively aware of the theoretical ways of thinking mathematically.

Keywords
Teaching organization; Cultural-historical theory; History of mathematics; Ontogenesis; Phylogenesis