Impact of practices teachers on the conceptualization of lines and planes in space: a case study ; Impact des pratiques enseignantes sur la conceptualisation des droites et des plans dans l'espace : une étude de cas

Our research focuses on the teaching of the lines and planes in space in Belgium. Research on this subject (Lebeau & Schneider, 2009; Cerclé, Chesnais, Gosselin, Leberre, & Nyssen, 2015; Maurel, 2001) has highlighted recurrent difficulties among students. However, few works on the teaching of these contents deal with the impact of practices teachers have on students' conceptualization. In a context where new official documents have been implemented since 2018, our work aims at a detailed analysis of teaching practices in order to study the links between teaching and learning for these contents. One of our objectives is to propose alternatives that would make it possible to overcome some of the difficulties identified among students. Based on cognitive studies (student difficulties), historical and epistemological studies (specificities of concepts) and curricular studies (programs and textbooks), we have highlighted (in the sense of Pariès, Pouyanne, Robert, Roditi & Rogalski, 2007) the concepts to be taught. This first part of the work constitutes our reference for future didactic analyses. Our questioning of the impact of teaching practices on student learning leads us to study student activities in the classroom in relation to the teachers' discourse. Our choice of theoretical framework is that of the dual didactic and ergonomic approach of teaching practices (Robert & Rogalski, 2002), derived from activity theory and contextualized to the teaching of mathematics (Vandebrouck, 2008). Our methodology is based on a study in which five teachers and their fifth grade students are involved. To study the teachers' discourse during moments of knowledge exposure (in the sense of Bridoux, Grenier-Boley, Hache, & Robert, 2016), we used the proximity tool (Robert & Vandebrouck, 2014). The study of procedural and constructive aids (in the sense of Pariès, Robert, & Rogalski, 2008) provided by the teachers made it possible to analyze their discourse during the exercise phases. This second part ...