Dialogue between the Anthropological Theory of Didactics and the Onto-semiotic Approach in Mathematics Education on the notions of value judgement, praxeology and didactic paradigm

Abstract

The application of results of scientific and technological research to the teaching practice is conflictive, due to its descriptive, explanatory, and predictive nature and the demands of avoiding subjective value judgements in scientific and technological research. Educational practice requires, however, making decisions about the type of actions to be taken to improve teaching and learning processes, which implies the adoption of value judgements. The way in which this dilemma is approached depends on how Didactics is conceived, the theoretical frameworks used in research and the different research paradigms on which they are based. In this paper, I reflect on this problematic by discussing the role of value judgements in basic and applied science, as well as the notions of praxeology and didactic paradigm of reference introduced in the Anthropological Theory of Didactics. I also suggest the need to establish an interface between scientific-technological research and the reflective practice by identifying criteria of suitability that synthesise and structure the results of such research, as proposed by the Onto-semiotic Approach in mathematics education.