Polyphony on Lesson Study in the Italian Context

Polyphony on Lesson Study in the Italian Context

Roberto Capone (Univertity of Salerno)

Carola Manolino, Riccardo Minisola (University of Turin)

In the last 20 years, Lesson Study (LS) has become an important theme in the discussion on mathematics Teachers’ Professional Development (TPD); nevertheless, LS is not much known in the Italian context. The three LS experiences presented in the symposium are rooted in such studies, each of them with its theoretical background and proper school level: semiotic of cultures for primary school; semiotic mediation for secondary school; boundary objects and meta-didactical transposition for the university. The three experiences, in spite of their differences, share the tools used for planning and observing, and especially the attention on the cultural transposition of the methodology. We will show how the intertwinement of such different points of view may reveal traits of the cultural issue that characterize each of them in its specific traits.

Summary (max 500 words)

This symposium will be chaired by Stéphane Clivaz and discussed by João Pedro Da Ponte.

This symposium connects three LS experiences in Italy, two at the University of Turin and one at the University of Salerno. These experiences share similar research questions, but each of them has its own peculiarities due to the specific institutional context. The Italian LS may be introduced in the Italian institution as an answer to institutional and teachers’ communities’ queries on TPD: on the one side, Italian law defines TPD as “mandatory, permanent and strategic” asking for “the establishment of adequate networks for professional collaboration”; on the other side, teachers ask for the opportunity to reflect on their own practices together. The symposium discusses the issue of cultural transposition (Mellone et al., 2018) using different theoretical backgrounds: paper 1 refers to semiotic of cultures (Lotman, 1990; Radford, 2008); paper 2 to semiotic mediation (Bartolini & Mariotti, 2008); paper 3 to boundary objects (Star, 2010) and meta-didactical transposition (Arzarello et al., 2014). We wonder how cultural transposition can contribute, as an opportunity to look at didactical methodologies from different cultures and societies, to a rethinking of Italian teachers’ practices and beliefs. Getting closer to answering Italian teachers’ everyday needs might lead to a new starting point: how much can LS contribute to an improvement of the teaching/learning processes, especially referring to time management? The three experiments were set up to discuss these research questions, and LS activities were carried out in three different schooling segments: paper 1 focuses on primary school teachers, paper 2 on high school teachers, paper 3 on university students (in their programmes as prospective teachers). The three experiences started with the long-term programming of learning aims typical of the Italian school and led to research lessons (lasting 1 hour in elementary and high schools, 20 minutes at the university). Specifically, the elementary teachers worked on the institutionalization of the + sign, high-school teachers worked on a project on art and geometry, the university students worked on continued fractions. The working groups all co-projected, implemented and discussed their research lessons, followed by a moment of meta-didactical reflection on the observed lessons. The initial results of all three experiments show an increased appreciation for peer-confrontation with colleagues, and attention on the detailed planning of the lesson: one of the most appreciated aspects of LS is a better understanding of time management for both the lesson and the teaching unit. Most teachers observe that thanks to LS they feel more in control of their own lessons. Moreover, they also note how meeting with others’ practices is an opportunity to observe and reflect on their own practices according to different paradigms. Finally, LS offers a tool for a micro-analysis of the lesson in a context in which long-term planning and analysis are more common. Furthermore, the researchers have a chance, thanks the introduction of a foreign tool, to make explicit (and, thus, reflect on and improve) some unintended in the relationship with the school community.

Symposium paper n.1 (max 200 words) – Carola

We are going to see the implementation of Lesson Study in a primary school in the district of Turin. We chose, as a fundamental element of the study, to address the need for professional development of a group of teachers working together: we proposed Lesson Study as a methodology for dialogue and exchange, an encounter between people and cultures. We envision a continuous process of didactical de-construction, which is the critical observation of strata composing the reality sphere into which the protagonists of the lesson move. The topic of the lesson is the introduction of the + sign and its institutionalization in grade 1. The challenge was to understand how to put the local needs for dialogue, time and malleability, together with Lesson Study, an unusual and, for this group of teachers, “firm” methodology. We observe this pilot experiment as a first development of design and observation tools, adapted to this specific context and born from the meeting between the Lotman’s semiotics of cultures and the ontosemiotic approach (Godino, Batanero & Font, 2007).

Symposium paper n.2 (max 200 words) – Roberto

The LS experiment in Salerno involved 4 teachers – from 4 different schools in the districts of Naples, Salerno, Avellino and Caserta – and 3 researchers from the mathematics department at the University of Salerno. The experiment is connected with the steady tradition in designing teaching units and activities in the Liceo Matematico (Mathematical High School) project. In the project, groups of teachers systematically meet with peers and researchers to collectively ex ante plan didactical activities and ex post analyse learning processes. Bringing LS in high schools can produce a stimulus towards improving teaching, thanks to the synergy between different institutional role of people operating in different school segments. It is an occasion for teachers to reflect on their own beliefs and choices in/on a competence-oriented didactic. The LS experiment has been introduced in the “art in geometry” teaching unit, particularly on the “tessellation” theme intertwined with science and art. Semiotic mediation is the theoretical background that shaped the experiment.

Symposium paper n.3 (max 200 words) – Riccardo

The experiment took place with 29 master students in Mathematics at the University of Turin, preparing to be teachers. They had little theoretical preparation on didactics and no teaching experience. They worked in small groups, each creating a Lesson Plan for a 20-minute lesson on continued fractions, to be performed (by one of each group, with the role of teacher) in front of their colleagues (with the role of students). The experiment aim was to choose tools for data collection and analysis, but other questions arose through the cultural transposition process: may we interpret LS a Boundary Object across different cultures? If yes, what kind of Boundary Crossing (Akkerman & Bakker, 2011) processes does it enable? Which are the elements that cross the boundary? Answering these questions in fundamental as, In Japan, LS is carried out from the teachers in the institutions, while in Italy LS has been introduced in a top-down way (from the researchers). Thus, it has to be discussed with the teachers’ communities and adapted to their needs, yet without losing its identity.

References

Akkerman, S. F., & Bakker, A. (2011). Boundary crossing and boundary objects. Review of educational research, 81(2), 132-169.

Arzarello, F., Robutti, O., Sabena, C., Cusi, A., Garuti, R., Malara, N., & Martignone, F. (2014). Meta-Didactical Transposition: A Theoretical Model for Teacher Education Programmes. In: Clark-Wilson A., Robutti O., Sinclair N. (eds). The Mathematics Teacher in the Digital Era. Mathematics Education in the Digital Era, vol 2. Springer, Dordrecht.

Bartolini Bussi, M., & Mariotti, M. A. (2008). Semiotic mediation in the mathematics classroom: Artifacts and signs after a Vygotskian perspective. Handbook of international research in mathematics education, New York, 746-783.

Godino, J. D., Batanero, C., & Font, V. (2007). The onto-semiotic approach to research in mathematics education. ZDM. The International Journal on Mathematics Education, 39(1), 127-135.

Lotman, Y. (1990). Universe of the mind. A semiotic theory of culture. London: I. B. Taurus.

Mellone, M., Ramploud, A., Di Paola, B., & Martignone, F. (2018). Cultural transposition: Italian didactic experiences inspired by Chinese and Russian perspectives on whole number arithmetic. ZDM, 1-14.

Radford, L. (2008). Connecting theories in mathematics education: Challenges and possibilities. ZDM,

40(2), 317-327.

Star, S. L. (2010). This is not a boundary object: Reflections on the origin of a concept. Science, Technology, & Human Values, 35(5), 601-617.