The COVID-19 crisis has strongly affected the school system. In Italy, at-distance forms of didactics have been activated, changing the physiognomy of schools in terms of social interaction, practices and the identity of the individuals. In this paper, we address the issue of how teachers are facing the crisis: our focus is on assessment, as a key variable catalyzing personal history; beliefs; the interface between students; teachers and the school system. We study teachers’ beliefs as part of their identities and assessment as a fundamental variable of beliefs. A qualitative content analysis of the open-ended answers to an online questionnaire is carried out to understand the main characteristics associated with assessment by teachers and the obstacles to overcome in the context of long distance learning (LDL). The data show that teachers did not identify valid assessment methods for LDL during the lockdown, especially due to the lack of control over the students. A misconception emerges concerning the definition of formative assessment together with a new awareness of the possibilities offered by digital technologies regarding the individualization of didactics. This study helps to understand which teachers’ beliefs are related to assessment are and how they are shaped.

We report an example of a research approach aimed at gathering quantitative pieces of evidence of solid findings in mathematics education. The main goal of this project is to provide an additional perspective on solid findings in education, to be used by teachers and by researchers in their work. As a case study, we present a situation of “loss of meaning” in algebra, exploring it with data coming from a large-scale assessment interpreted by means of theoretical lenses. We are able to give information about the extent of the phenomenon and to highlight how the phenomenon is relevant also for high-level students. This approach can provide a link between large-scale assessment results, educational research, and teachers’ practices, and suggests further research issues.

In this paper we interpret pervasive difficulties with second degree inequalities as a macro-phenomenon emerging from Large Scale Assessment. In line with the theory of reification, we link common students’ difficulties to approaches they use that undermine the intertwining of processes and the ensuing emergent mathematical objects. To frame the movement from process to object, we network the theory of objectification with Duval’s semio-cognitive approach. We conclude that students’ difficulties can be traced back to a disruption of the dialectical movement between process and object. Thus, the students lose the link to meaning, rooted in mathematical activity, and handle semiotic transformations out of the object-sign relation. Such a phenomenon is conceived as a macro-phenomenon emerging from the Italian educational system.

Whole-class mathematical discussion in a problem-solving activity is recognized as a powerful pedagogical activity but also a challenge for teachers who must consider several difficulties that learners might face, particularly in terms of an overload of Working Memory and Executive Functions. This study investigates how the use of a digital platform (Padlet) can support participatory and inclusive mathematical classroom discussion. We proposed a teaching experiment based on graphical tasks anticipating integral calculus to grade 13 students, and we examined how the use of the digital platform plays a role in the construction and interpretation of new mathematical objects emerging from the activity. The use of Instrumental Genesis and Double Instrumental Genesis frameworks allowed us to make the affordances of the tool emerge. As a result, we got evidence of how mathematical discussion may develop as a network of interactions, feedback, and connection of input and discuss examples of how active participation and inclusion are enhanced by the tool affordances. Indeed, the digital platform allowed easy interaction, with many ways to represent and express the ongoing evolution of personal and shared meanings and the possibility to manage the time of the activity. This fostered students’ participation and students which did not participate in previous discussions were actively engaged in it.