Evolution of teachers' and researchers' praxeologies for designing inquiry mathematics tasks: the role of teachers' beliefs

This paper is focused on the collaborative work of two communities, one of teachers and one of researchers, during a teacher professional development program on the inquiry-based learning approach in mathematics, addressed to lower secondary school in-service mathematics teachers. We conceptualize the design of inquiry mathematics task as the boundary object on which the two communities work collaboratively. We aim to study the evolution of teachers’ and researchers’ meta-didactical praxeologies for designing inquiry mathematics tasks, with the Meta-Didactical Transposition framework, to understand if and how their collaboration favors their convergence toward shared components of final meta-didactical praxeologies. In the results, we show that this convergence is reached thanks to internalization processes of praxeological components for designing inquiry mathematics tasks, as a consequence of the learning mechanisms activated by the common work on the boundary object. In this paper, we address also the issue of understanding the complex relationship between teachers’ beliefs on inquiry mathematics tasks and the meta-didactical praxeologies of teachers and researchers. As a result, we propose a model in which the evolution of teachers’ beliefs is taken into account both as an agent and a consequence of the evolution of the meta-didactical praxeologies of the two communities involved in the teacher professional development program.