This study aimed to examine the collaborative design of an interdisciplinary STEAM activity conducted by lower-secondary school teachers of different disciplines. We adopted an approach based on a case study involving four teachers (art, music, technology, and mathematics/science teachers) designing an activity focused on the concept of symmetry. We gathered data through oral, semi-structured interviews with the teachers and through schematic representations of resource systems provided by the teachers themselves. Data analysis aimed to identify the different kinds of resources the teachers relied on, their utilization schemes, and the overarching meta-didactical praxeology adopted by the teachers for their collaborative design work. The theoretical model adopted for data analysis was a combination of the Documentational Approach to Didactics and the Meta-Didactical Transposition frameworks, originally introduced to study the work of researchers in the context of teacher professional development. An application of this model to the collaborative design work of teachers can provide a fresh insight into the relationship between teachers’ documentation work for the design of a STEAM activity, the practices that they adopt to address this shared task (praxis), and the shared justifying discourses (logos) for their praxis.

This study investigates teachers’ beliefs about the inquiry-based learning approach in mathematics. In particular, as the first research problem, it addresses teachers’ beliefs about the appropriateness of inquiry activities for all students, after three years of attendance in a professional development programme, focused on inquiry. As a second research problem, it studies the evolution of teachers’ beliefs and practices, during their fourth year of attendance of the programme. The results show that, at the beginning of the fourth year, the teachers, despite thinking that inquiry activities in mathematics have several valuable aspects, held the belief that they are not appropriate for all the students, but only for the high-achieving ones. The two case studies, analysed to address the second problem, refer to two teachers with different outcomes of their developmental paths. During the fourth year, in which the teachers have been invited to experiment with inquiry activities in their whole classes, one of them accepted the challenge and, as a consequence, had the opportunity to change both her practices and her beliefs. The second teacher, instead, continued to propose inquiry activities only to her high-achieving students and, consequently, showed no signs of change, either in her practices, nor in her 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.

This study is aimed to understand the connections between didacticians’ meta-didactical praxeologies for the design and implementation of a teacher professional development program and their documentation work for the program itself. Didacticians are mathematics education researchers with the role of teacher educators. Data presents a case study, in which two didacticians (the authors) generate documents for the work with seventeen in-service mathematics teachers working at the lower secondary level, on inquiry mathematics tasks. The results reveal relationships, not yet fully addressed in research, between the intertwining evolution processes of the didacticians’ meta-didactical praxeologies and their documentation work, nurtured by the collaboration with the teachers. The whole process is led by the evolving goal of the professional development program, from the promotion of the classroom implementation of inquiry mathematics tasks to the broader goal of building an inquiry community with the teachers. This study could contribute to the introduction of an interpretative model for the didacticians’ work for the design and implementation of a teacher professional development program, based on the combination of Meta-Didactical Transposition and Documentational Approach to Didactics frameworks.

The research presented in this paper aims to shed light on the complex role of mathematics teacher educators who led courses for prospective mathematics teachers. Theoretically, the research combines the documentational approach to didactics and the meta-didactical transposition frameworks, complementing the study with the analysis of the teacher educators’ beliefs about the prospective teachers’ needs. The methodology entails a comparative case study related to two courses, taking place in quite different contexts, led by the two authors independently, and a collaborative self-study of teacher education approach, based on eight reciprocal semi-structured interviews between the authors. The result is a holistic model of mathematics teacher educators’ work that takes into account their practices, including the design of teaching materials based on a variety of resources, justifying discourses and personal beliefs. This can deepen our insight into the expertise of mathematics teacher educators and, prospectively, can be fruitful for their professional development.