Abstract

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.

中文翻译：

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教师和研究人员设计探究数学任务的行为学的演变：教师信念的作用

摘要

本文重点关注两个群体（一名教师和一名研究人员）在针对初中在职数学教师的数学探究式学习方法的教师专业发展计划期间的协作工作。我们将探究数学任务的设计概念化为两个社区协作工作的边界对象。我们的目标是利用元教学换位框架，研究教师和研究人员用于设计探究数学任务的元教学行为学的演变，以了解他们的合作是否以及如何有利于他们向最终元教学行为学的共享组成部分趋同。在结果中，我们表明，这种收敛的实现要归功于用于设计探究数学任务的人类行为学成分的内化过程，这是边界对象上的共同工作激活的学习机制的结果。在本文中，我们还解决了理解教师对探究数学任务的信念与教师和研究人员的元教学行为学之间复杂关系的问题。因此，我们提出了一个模型，在该模型中，教师信念的演变既被视为教师专业发展计划所涉及的两个社区的元教学行为学演变的推动者，又被视为其结果。