Gilles Aldon

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.

Didactic Incidents: A Way to Improve the Professional Development of Mathematics Teachers

In this chapter the professional development of teachers is observed through the joint work of researchers and teachers. In the particular context of the European project EdUmatics, which focuses on mathematics education in a computer environment, the collaboration between researchers and teachers has helped both to build innovative situations and also to better understand the difficulties involved in the introduction of technology in classrooms. The theoretical framework of the theory of didactic situations, didactic incidents and documentational genesis allows the construction of analyses in order to better understand the students’ and teacher’s joint action and so to enhance teachers’ professional development. We highlight both the consistency of the framework and the contributions of our findings to the professional development of teachers.

Technology and Education: Frameworks to Think Mathematics Education in the Twenty-First Century

Improving the quality of teaching and learning by effective use of technology is a common goal that brings together teachers, researchers, students and, more widely, other citizens. However, the roads leading to this goal are often quite different. What are the main changes, for teachers, for students and in the interactions between students and teachers? Different theoretical frameworks provide tools to analyse and understand what happens in the classroom: multirepresentation and multimodality; instrumental and documentational genesis; role of technology in an experimental part of mathematics, didactical incidents. Starting from experiments, this chapter shows how these frameworks can be combined to analyse the role of technology, the difficulties and some success in mathematics education.

Problems Promoting the Devolution of the Process of Mathematisation: An Example in Number Theory and a Realistic Fiction

Modelling is a complex and difficult process when studying phenomena from real-life situations. However, it is an important part of the work of mathematicians that needs to be addressed in the teaching of mathematics. We have studied two different types of problems, the first within mathematics and the second in the form of “realistic fictions”, that is to say, a problem inserted into a fictional context allowing a modelling process. We hypothesize that the solving of both of these types of problem requires constructing meta-mathematical skills as well as using mathematical knowledge. In both cases, we stress the different roles of technology as a medium of communication and in providing a dynamic environment.