ANTHROPOLOGICAL THEORY OF THE DIDACTIC (ATD) A NEW RESEARCH PERSPECTIVE ON DIDACTIC MATHEMATICS IN INDONESIA

Abstract

Théorie Anthropologique du Didactique/Anthropological Theory of the Didactic (ATD) is a new theory on didactic mathematics that was introduced by a French mathematician, Chevellard [1], in 1991. The ATD is an epistemological model of mathematical knowledge that can be applied to investigate human mathematical activities. Chevallard [1] identified two aspects of a human mathematical activity that are a practical block and a knowledge block. Both are the main component of praxeologies.The practical block consists of a type of task (T) and a technique (τ). The type of task (T) is a task given to pupils, and they need a technique (τ) to solve it. Meanwhile, the theoretical block consists of a technology (θ) to explain the practical block, and a theory (Θ) is used to justify the technology (θ). The four elements (T, τ, θ, Θ) are connected. In this paper, we try to describe two cases based on ATD especially praxeologies. The first case is a research by Putra [3] about elementary teachers’ knowledge in designing contextual problems related to multiplication of fractions. This study focused on the analysis of didacticalpraxeologiesbecause it gave more attention to mathematical didactics of teachers’ representations from abstract to contextual problems. The second case is a study done by Wijayanti [2]. She analysed how ratio and proportion present on Indonesian mathematical textbooks. She tried to describe mathematicalpraxeologiesof ratio and proportion of arithmetic and geometry. Implication of both studies is that the ATD especially praxeologiescan be a model to analyse both mathematical and didactical knowledge. Therefore, we suggest researchers to apply this model as an alternative method to study teachers’ knowledge and analysis mathematical textbooks.