In 2020, the emergency due to the COVID-19 pandemic brought a drastic and sudden change in teaching practices, from the physical space of the classrooms to the virtual space of an e-environment. In this paper, through a qualitative analysis of 44 collected essays composed by Italian mathematics teachers from primary school to undergraduate level during the spring of 2020, we investigate how the Italian teachers perceived the changes due to the unexpected transition from a face-to-face setting to distance education. The analysis is carried out through a double theoretical lens, one concerning the whole didactic system where the knowledge at stake is mathematics and the other regarding affective aspects. The integration of the two theoretical perspectives allows us to identify key elements and their relations in the teachers’ narratives and to analyze how teachers have experienced and perceived the dramatic, drastic, and sudden change. The analysis shows the process going from the disruption of the educational setting to the teachers’ discovery of key aspects of the didactic system including the teacher’s roles, a reflection on mathematics and its teaching, and the attempt to reconstruct the didactic system in a new way.

Instructional design is an essential part of teaching practice: both researchers and teachers are engaged in finding strategies to deal with this complex work. We propose the use of storytelling as a skeleton to structure a long-lasting teaching unit, maintaining coherence and giving meaning to its various elements. We refer to an interpretation of storytelling for educational purposes as a role-playing game, drawing inspiration from the Digital Interactive Storytelling in Mathematics framework. Designing a learning unit based on storytelling means integrating every moment of the teaching–learning process within the narrative: the teacher and students are all part of the same story, which motivates every activity carried out in the unit and contextualizes the tasks performed. Moreover, the assessment is also integrated into the narrative flow. In this study, we designed an exemplary Storytelling Learning Unit (SLU) model for the study of light, promoting modelling and argumentation skills in mathematics and physics. This unit, intended for ninth-grade students in an Italian scientific high school, was co-designed by the teacher of the class in which it will be implemented. This work particularly focuses on the design process. From reflection on the specific unit developed, general design principles for creating a SLU were hypothesized.

In light of the recent interest in mathematical competencies and the ways in which students communicate their ideas, this study aims to explore how undergraduate students communicate their ideas about mathematical tasks through written texts. Forty-three first-year undergraduate students participated in this study. They were given a graph of a function and tangent line and were asked to estimate the value of the derivative at the tangent point justifying their answer. We analyzed the justification of students to the given task by referring to the cooperative principle and to the Anthropological Theory of the Didactic. For the former, we employed the four Grice maxims: Quantity, Quality, Relation and Manner. For the latter, we employed the main components of praxeologies: the type of task, the technique needed to solve the task, the technology as knowledge needed to explain the technique, and a theory as basis to justify the technology. A model of the students’ communication about mathematical ideas emerges and is described with reference to data analysis. The model sheds light on the relationship between the discourse of a student solving a mathematical task and how she performs the related problem-solving activity.