Cristina Sabena

Meta-Didactical Transposition: A Theoretical Model for Teacher Education Programmes

We propose a new model for framing teacher education projects that takes both the research and the institutional dimensions into account. The model, which we call Meta-didactical Transposition, is based on Chevallard’s anthropological theory and is complemented by relevant elements that focus on the specificity of both researchers’ and teachers’ roles, while enabling a description of the evolution of their praxeologies over time. The model is illustrated with examples from different Italian projects, and it is discussed in light of current major research studies in mathematics teacher education.

The Question of Method in a Vygotskian Semiotic Approach

In this chapter we present the main ideas of an educational Vygotskian semiotic approach, emphasizing in particular some crucial questions about its methods of inquiry. We resort, on the one hand, to Leont’ev’s (1978) work on activity, and, on the other hand, to Vygotsky’s cultural psychology. Considering a theory as an interrelated triplet of “components” (P, M, Q), where P stands for principles, M stands for methodology, and Q for research questions, in the first part of the chapter we present a brief sketch of the Vygotskian semiotic approach through the lenses of the aforementioned components. We refer in particular to two methodological constructs that have been built to account for multimodal sensuous actions: the semiotic node and the semiotic bundle. To illustrate the semiotic approach, in the second part of the chapter we discuss an example from a classroom activity concerning pattern generalization. This example constituted an important step in developing the semiotic approach under consideration. The example is about the role of words, gestures, and rhythm in the students’ process of objectifying (i.e., noticing or becoming aware of) mathematical relationships. We discuss how a “crude fact” that was not anticipated led to a transformation of the theory, and in particular its methods and research questions.

Formative assessment and technology: reflections developed through the collaboration between teachers and researchers

In this work, we present the analysis of the ways in which formative assessment processes can be developed, by the teacher and the students, thanks to the support given by technology. The analysis is carried out focusing on two case studies developed in France and Italy within the European Project FaSMEd, with two main aims: (1) highlighting how the different functionalities of technology could support formative assessment strategies at the teacher’s, the students’ and the peers’ levels; and (2) characterising the dynamics that intervene within programs involving a strict collaboration between teachers and researchers. Through the analysis of the two case studies we discuss, on one side, the effectiveness of the adopted theoretical tools, and, on the other side, the contribution, in terms of professional development, of the collaborative work developed within the project.

Participation in Mathematics Problem-Solving Through Gestures and Narration

On the one hand, recent results in neuroscience and communication bring the role of multimodal resources in cognitive and communicative processes to the fore. On the other hand, Bruner highlights the different role of narrative and logical thinking in human understanding. Before this background, we investigate the teaching and learning processes when children are introduced to the mathematical meanings by the use of narrative context and multimodality. We focus on a narratively-based problem-solving activity in the first year of primary school. We analyse the teacher-students multimodal interaction and discuss the potential and limits of what we call the “semiotic game” between teacher and students. The importance of the teacher being conscious of the multimodal aspects of teaching and learning mathematics, and of the complexity of narratively-based contexts comes to the fore.

Early child spatial development: a teaching experiment with programmable robots

This contribution addresses young children development of spatial competences, and investigates the didactic potentialities offered by a programmable robot. The theoretical framework addresses the delicate relationship between space as lived in everyday experience versus space as a mathematical notion, and takes a multimodal perspective on mathematics teaching and learning. An experimental study has been conducted in kindergarten school. The qualitative data analysis of video-recordings constitutes the background against which children spatial development is discussed.

Starting Points for Dealing with the Diversity of Theories

This chapter presents the main ideas and constructs of the book and uses the triplet (system of principles, methodologies, set of paradigmatic questions) for describing the theories involved. In Part II (Chaps. 3, 4, 5, 6, and 7), the diversity of five theoretical approaches is presented; these approaches are compared and systematically put into a dialogue throughout the book. In Part III (Chaps. 9, 10, 11, and 12), four case studies of networking practices between these approaches show how this dialogue can take place. Chapter 8 and Part IV (Chaps. 13, 14, 15, 16, and 17) provide methodological discussions and reflections on the presented networking practices.

The Use of Digital Technologies to Enhance Formative Assessment Processes

We focus on formative assessment processes carried out, by the teacher and the students, through the use of digital technologies. The research is situated within the European Project FaSMEd, in which a new model connecting the role of technology to classical views on formative assessment is proposed. Through data analysis from teaching experiments in Italian schools using connected classroom technology, we highlight how the specific choices concerning the use of technology and the design of the activities can enable the enactment of formative assessment strategies at the teacher’s, the students’, and the peers’ levels.

Exploring the Contribution of Gestures to Mathematical Argumentation Processes from a Semiotic Perspective

A multimodal perspective on mathematics thinking processes is addressed through the semiotic bundle lens and considering a wide notion of sign drawing from Vygotsky’s works. Within this frame, the paper focuses on the role of gestures in their interaction with the other signs (speech, in particular) and investigates the support they can provide to mathematical argumentation processes. A case study in primary school in the context of strategic interaction games provides data to show that gestures can support students in developing argumentations that depart from empirical stances and shift to a hypothetical plane in which generality is addressed. In this regard, by combining synchronic and diachronic analysis of the semiotic bundle, specific features of gestures are pointed out and discussed: the semiotic contraction, the condensing character of gestures, and the use of gesture space in a metaphorical sense.

Promuovere strategie di valutazione formativa in Matematica con le nuove tecnologie: l’esperienza del progetto FaSMEd

Abstract – This contribution describes a research work within the European project FaSMEd (Improving Progress through Formative Assessment in Science and Mathematics Education) aimed at investigating, through a design-based research approach, the use of technology to foster formative assessment strategies in primary and lower secondary school. The project (2014-2016) was carried out by eight European universities (for Italy, the University of Turin) and one university from South Africa. The theoretical framework refers to formative assessment, with a specific focus on different levels of feedback. By analyzing data from our teaching experiments, we identify strategies employed by the teacher to provide feedback during class discussion and investigate the effect of such strategies on the enactment of formative assessment. Riassunto – In questo contributo si presentano e discutono le metodologie didattiche sviluppate attraverso una ricerca design-based sull’utilizzo delle nuove tecnologie per promuovere strategie di valutazione formativa in matematica in classi di scuola primaria e secondaria di primo grado. La ricerca si situa all’interno di un progetto finanziato dall’Unione Europea denominato FaSMEd (Improving Progress through Formative Assessment in Science and Mathematics Education), che nel triennio 2014-2016 ha coinvolto otto Universita dell’Unione (per l’Italia l’Universita di Torino) e il Sudafrica. Facendo riferimento a un quadro teorico centrato sulle strategie di valutazione formativa e sui diversi livelli di feedback che possono essere forniti durante discussioni di classe su attivita matematiche ad alto contenuto argomentativo, proponiamo una classificazione di possibili azioni didattiche dell’insegnante, mettendo in luce gli effetti di tali azioni rispetto all’attivazione di strategie di valutazione formativa. Parole chiave – matematica, valutazione formativa, strategie di feedback, nuove tecnologie, ruolo dell’insegnante Keywords – mathematics, formative assessment, feedback strategies, new technologies, role of the teacher

“Every Time I Fell Down (Made a Mistake), I Could Get Up (Correct)”: Affective Factors in Formative Assessment Practices with Classroom Connected Technologies

In this contribution we analyse data coming from the research project FaSMEd, which aims at investigating the role of technologically enhanced formative assessment methods in raising the attainment levels of low-achieving students. Our working hypothesis is that low attainment is also linked to affective factors and that, consequently, these factors should be taken into account when planning interventions and when evaluating their effectiveness. We report our first steps towards the analysis of the experiments in terms of affect, drawing some preliminary conclusions on the students’ attitude towards the project and outlining further research developments.