Our research is concerned with teacher's knowledge, and especially with teacher's processes of learning, in the classroom, from observing and interacting with students' work. In the first part of the paper, we outline the theoretical framework of our study and distinguish it from some other perspectives. We argue for the importance of distinguishing a kind of teacher's knowledge, which we call didactic knowledge. In this paper, we concentrate on a subcategory of this knowledge, namely observational didactic knowledge, which grows from teacher's observation and reflection upon students' mathematical activity in the classroom. In modeling the processes of evolution of this particular knowledge in teachers, we are inspired, among others, by some general aspects of the theory of didactic situations. In the second part of the paper, the model is applied in two case studies of teachers conducting ordinary lessons. In conclusion, we will discuss what seems to be taken into account by teachers as they observe students' activity, and how in-service teacher training can play a role in modifying their knowledge about students' ways of dealing with mathematical problems.KEY WORDS: case study, didactic knowledge, didactique of mathematics, ordinary mathematics lesson, theory of didactic situations, teacher's activity, teacher's knowledge Educational Studies in Mathematics (2005) 59: 205-234

Previous research on the development of educational inequalities in mathematics lead me to focus on the institutionalization and the role of language in this process, as they determine the students’visibility of mathematical knowledge. The concept of secondarization seems to contribute in studying the role of language practices in the institutionalization of mathematical knowledge. To illustrate this crucial point of my research, I present a case study which is an ordinary teaching situation of geometry, observed in a CM2 classroom (10-11 years). The results of this study reveal various phenomena. I consider some of them as dysfunctions of the secondarization of language practices and of the institutionalization of geometrical knowledge. I assume that inequalities in students’learning of mathematics are partly due to such dysfunctioning. I therefore point out new issues of research which may help analyze these educational-linguistic phenomena related to teaching and learning of mathematics in school.

PurposeIn March 2020, with only two working days’notice the French national education system went online due to the coronavirus pandemic. This study explores the relationship between the move to distance learning, the teaching practices employed and the socio-economic context of the learners in French schools during this period. We ask how far the changes in teaching practices during the coronavirus crisis were influenced by the social context of teaching. And to what extent this context influenced the focus of the pedagogical continuity those teachers set up.Design/methodology/approachA review of the literature situates the study within the field of mathematics teaching practices. The study was carried out through a multidimensional analysis using multiple correspondences of the responses of 368 French secondary school mathematics teachers to an online questionnaire.FindingsWe found that the unprepared move to distance learning impeded the employment of dialogic practices. The socio-economic situation of the teaching was identified as a determining factor in the teachers' different interpretations of the term pedagogical continuity. Whilst those working in more deprived areas tended towards practices which focused on maintaining pupils' links with school, consolidation of knowledge and providing social/affective support, those teaching a more privileged public favoured tools and practices which allowed them to focus on the disciplinary content of their teaching.Practical implicationsThe challenge of maintaining dialogic activities – teacher education to combat inequalities.Originality/valueA quantitative study of mathematics teachers providing pedagogical continuity through distance learning for the duration of the crisis.

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