Annalisa Cusi

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.

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.

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.

Formative Assessment: A Critical Component in the Teaching-Learning Process

This introductory paper to the volume contrasts formative assessment with summative assessment and describes the importance of formative assessment to classroom instruction. In particular, it argues that a task is formative to the extent that data from the task are used to enhance and inform further instruction rather than simply to provide an evaluation of a student or of instruction. The use of design research as a mechanism to develop sound classroom assessment is outlined because a design science framework provides a means to tie together varied exemplars of innovations in assessment. A cycle of task implementation and revision can lead to improved assessment practices.

Looking to the Future: Lessons Learned and Ideas for Further Research

This concluding paper to the volume highlights some lessons learned from the various papers relative to the issue of formative assessment and draws them together as a range of attempts to make students’ learning visible. In addition, possible avenues for further research related to this important topic are discussed, including formative assessment as an instrument or a process, the development of tools for assessment, and a more nuanced understanding of classroom assessment.

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

Mathematics Teachers Working and Learning Through Collaboration

The authors of this paper were tasked by ICME-13 organisers with conducting a survey on the topic “Mathematics Teachers Working and Learning through Collaboration”. Four research questions guided the survey, concerned with: the nature of collaborative working; the people who engage collaboratively; the methodological and theoretical perspectives used; what learning could be observed and how it related to collaboration? The resulting survey drew from a wide range of sources, identifying papers relevant to the topic—316 papers were identified, analysed against a set of criteria and organised into three major themes, each relating to one or more of our research questions: Different contexts and features of mathematics teachers working in collaboration; Theories and methodologies framing the studies; Outcomes of collaborations. In addition to the papers revealed by the survey, the team sought contributions from projects around the world which are not represented in the published literature. Members from these projects offered ‘narratives’ from the work of teachers in the projects. This paper reports on the nature of the projects revealed by the survey and the narratives, their theoretical and methodological focuses, and the range of findings they expressed. While we offer a significant range of factors and findings, resulting from a very considerable work, we are aware of limitations in our study: we missed relevant papers in journals outside our range; papers reviewed were usually not authored by teachers so the teachers’ voice was often missing; narratives came from projects with which we were familiar, so we missed others. The survey team is in the process of initiating an ICMI study which can take this work into these missing areas. This paper follows closely the presentation made by the survey team at the ICME-13 congress. In presenting findings from the survey, we have tried to provide examples from and make reference to the survey papers. Because the set of references would be too large to fit within our word limit, we have had to reduce the number of references made. However, readers can find a full set of references in a more detailed paper, Robutti et al. in (ZDM Mathematics Education, 48(5), 651–690, 2016).

“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.