Teachers’ professional development: a cultural matter. How to describe cultural contexts?

International audienceTeachers' professional development in collaborative contexts is a growing trend in Mathematics Education research. Particularly, Japanese Lesson Study has seen a great focus on its dissemination around the world. Research shows that Japanese culture is one of the main reasons that makes Lesson Study effective: understanding Lesson Study means understanding the cultural context in which it originated. We attempt to describe the Japanese and the Italian cultural contexts. Since there exists no consensus on what is essential to analyse in order to understand a cultural context, we present two approaches to this description, and consider some advantages and shortcomings. We hope to sprout discussion on the possibility to create guidelines for describing cultural contexts, shared by the community of researchers in Mathematics Education: awareness of beliefs, identity and practice is a sensitive element for successful mathematics teacher professional development

Semiotic bundle approach and Onto-Semiotic Approach: a dialogue between two theories on an arithmetic-algebraic problem

Esta pesquisa baseia-se na análise de uma tarefa matemática, sobre um problema aritmético-algébrico e sua solução, utilizando ferramentas teóricas de dois quadros de referência principais: a Abordagem Semiótica do Conjunto (SBA) e a Abordagem Onto-Semiótica (OSA). A atividade foi examinada por meio de duas gravações em vídeo originais do grupo composto por cinco alunos do ensino fundamental. Ao apresentar um caso empírico de rede de teorias, o objetivo é começar a dialogar com as duas abordagens, lendo as assimetrias presentes entre suas linguagens, com o objetivo de obter novos insights sobre o problema matemático. Enquanto o SBA, em uma abordagem sistemática, é particularmente apto a focar as relações entre os diferentes recursos semióticos multimodais usados pelos alunos nos curtos prazos da história em sala de aula (um foco cognitivo incorporado), o OSA incorpora um conjunto de ferramentas conceituais para abordam a análise das diferentes facetas que interagem em um processo de educação matemática. Principalmente a SBA descreve a importância do conjunto de signos (como gestos, palavras, signos escritos) para o pensamento matemático e a comunicação e sua multimodalidade, e a OSA favorece a descrição de objetos e processos que emergem das práticas matemáticas. Os resultados desta análise conjunta fornecem uma rica visão do fenômeno observado e ajudam a iniciar um diálogo entre as teorias em Educação Matemática, dentro de uma Semiosfera gerada pela articulação entre SBA e OSA.This research rests on the analysis of a mathematical task, concerning an arithmetic-algebraic problem and its solution, using theoretical tools from two main frames: the Semiotic Bundle Approach (SBA) and the Onto-Semiotic Approach (OSA). The activity has been examined by two original video recordings of the group consisting of five pupils of primary education. By presenting an empirical case of networking of theories, the objective is to begin a dialogue with the two approaches, reading the asymmetries found between their languages, with the aim of getting some new insights into the mathematical problem. Whereas the SBA, in a systematic approach, is particularly apt to focus on the relationships among the different multimodal semiotic resources used by the students in the short timescales of the classroom story (an embodied cognitive focus), the OSA incorporates a set of conceptual tools to address the analysis of the different facets that interact in a mathematical education process. Mainly the SBA describes the importance of the bundle of signs (like gestures, words, written signs) for mathematical thinking and communication and its multimodality, whereas the OSA favours the description of objects and processes that emerge from the mathematical practices. The results from this joint analysis provide a rich insight into the observed phenomenon and help initiate a dialogue between theories in Mathematics Education, within a Semiosphere generated by the networking between SBA and OSA

Articulación de teorías en torno al análisis de un episodio de clases: SBA y EOS

El estudio en torno a la posibilidad de articulación de teorías en educación matemática, conocida internacionalmente como “Networking of Theories”, es un tema que está ganando cada vez más interés en el área. Ee este póster se presentan los primeros resultados de una investigación que tiene como objetivo estudiar las similitudes y complementariedades de dos marcos teóricos: el enfoque de Semiotic Bundle (SBA), descrito en Arzarello, Paola, Robutti y Sabena (2009) y el Enfoque Ontosemiótico (EOS), descrito en Godino, Batanero y Font (2007)

Culturally crafted Lesson Study to improve teachers' professional development in mathematics: a case study in Italian secondary school

This paper describes a Lesson Study in which in-service mathematics secondary-school teachers, collaborating with researchers, involve grade 10 students in tessellation problems. The data are collected by an experiment carried out in the context of the “Liceo Matematico” project, with three volunteer teachers. The experiment goal was to craft a collaborative design of the research lesson between teachers and researchers. The research aim of the paper is to examine the use of Lesson Study in the institutional and cultural context of Italian secondary school with the use of Cultural Transposition as a theoretical framework. The research is qualitative with idiographic aims, based on video research. The educational aim of the research is to provide a solid basis for a revamped in-service teacher education first in the context of the project, then in curricular context. Semiotic mediation is used to provide, within Lesson Study, the conceptual framework for teachers and researchers collaborative design of the research lesson. The results show that Lesson Study, as a foreign practice, is an opportunity for teachers to confront their teaching practices, to enrich their professional development, resulting in more awareness on their didactical action in and outside the classroom