La multimodalidad y el lente Semiotic Bundle: una resonancia constructiva con la teoría de la objetividad

The paper situates mathematics teaching-learning processes within a multimodal perspective and discusses a semiotic approach apt to seize this dimension, namely the Semiotic Bundle lens. This analytical tool considers the great variety of semiotic resources through which mathematical meanings emerge and evolve in the classroom, ranging from embodied ones such as gestures, to symbolic systems. In particular, the analysis considers them in a systemic and dynamic way. The theoretical account is illustrated by means of an example on children spatial conceptualization, carried out in kindergarten. The data analysis will constitute a background against which the connections with the Theory of Objectification will be highlighted, showing a constructive resonance between the two theories.El artículo sitúa los procesos de enseñanza-aprendizaje de las matemáticas dentro de una perspectiva multimodal y discute un enfoque semiótico apto para aprovechar esta dimensión llamada el lente Semiotic Bundle. Esta herramienta analítica tiene en cuenta la gran variedad de recursos semióticos a través de los cuales los significados matemáticos emergen y evolucionan en el aula, como los gestos hasta los sistemas simbólicos. En particular, el análisis los considera de forma sistémica y dinámica. La explicación teórica se ilustra mediante un ejemplo de conceptualización espacial de niños, llevado a cabo en el jardín de infantes. El análisis de datos constituirá un trasfondo contra el cual se resaltarán las conexiones con la teoría de la objetivación, mostrando una resonancia constructiva entre las dos teorías.Universidad de Granada. Grupo de Investigación Didáctica de la Matemática: Pensamiento Numérico (FQM-193

The role of the teacher in fostering students’ evolution across different layers of generalization by means of argumentation

We address students’ processes of generalization in early algebra and investigate how the teacher can support them in developing interpretations of non-canonical arithmetic representations, by means of argumentation. Data are constituted by grade 5 students written protocols and excerpts from video-recorded classroom discussions. The analysis is developed on qualitative base, referring to three main aspects: the layers of generalization that emerge in students’ semiotic activities, the argumentation, with reference to the criteria of correctness, clearness, and completeness, and the roles played by the teacher to foster students’ generalization and argumentation processes. Results point out three specific roles that revealed powerful for fostering students’ evolution across different layers of generalization, by means of argumentation: reflective guide, activator of reflective attitudes and activator of interpretative processes

Informal mathematics in teacher education: The teachers’ voice

Informal Mathematics Education is an emergent field of research in which out of school spaces become protagonist of intentional learning designs. In our research we exploit cultural spaces such as art and history museums to engage teachers in a challenging teacher education programme called “InformalMath”. In InformalMath teachers work in communities of practices to design informal mathematics workshops, with the support of teacher educators and museum experts. The paper presents the theoretical choices underpinning the design and implementation of InformalMath and gives voice to the enrolled teachers