Maria Giuseppina Bartolini Bussi’s research while affiliated with Università degli Studi di Modena e Reggio Emilia and other places

This is a summary report of the ICME-13 survey on the theme of recent research in geometry education. Based on an analysis of the research literature published since 2008, the survey focuses on seven major research threads. These are the use of theories in geometry education research, the nature of visuospatial reasoning, the role of diagrams and gestures, the role of digital technologies, the teaching and learning of definitions, the teaching and learning of the proving process, and moves beyond traditional Euclidean approaches. Within each theme, there is commentary on promising future directions for research.

This survey on the theme of Geometry Education (including new technologies) focuses chiefly on the time span since 2008. Based on our review of the research literature published during this time span (in refereed journal articles, conference proceedings and edited books), we have jointly identified seven major threads of contributions that span from the early years of learning (pre-school and primary school) through to post-compulsory education and to the issue of mathematics teacher education for geometry. These threads are as follows: developments and trends in the use of theories; advances in the understanding of visuo spatial reasoning; the use and role of diagrams and gestures; advances in the understanding of the role of digital technologies; advances in the understanding of the teaching and learning of definitions; advances in the understanding of the teaching and learning of the proving process; and, moving beyond traditional Euclidean approaches. Within each theme, we identify relevant research and also offer commentary on future directions.

We present some fragments of a teaching experiment realized in a first grade classroom, to sow the seeds for a mathematical definition of rectangles that includes squares. Within the paradigm of semiotic mediation, we studied the emergence of pivot signs, which were exploited by the teacher to pave the way towards an inclusive definition of rectangles and squares. This was done to favor overcoming children's spontaneous distinction of these figures into distinct categories, reinforced by everyday language. The experiment is an example of an approach towards the theoretical dimension of mathematics in early childhood.

To contrast the phenomenon of false positives in the diagnoses of dyscalculia in Italy, among 3rd grade children, a 3-year project (2011-2014), built upon a collaboration between psychologists and mathematics educators, was carried out. Within the project specific teaching strategies for preventing and addressing learning difficulties in arithmetic arising at the beginning of primary school were designed and tested in schools nation wide. This paper presents the project’s background and the theoretical foundations of the didactical material designed, providing also some examples. In particular, prototypical examples will show how the activities, grounded within a kinesthetic-tactile and visual-spatial approach, are designed to lead to students’ interiorization of part-whole relations, and to their thinking about multiplication through structured diagrams. Qualitative data confirming effectiveness of the proposed didactical strategies will also be discussed.

In early years schooling it is becoming com- mon to propose activities that involve moving along paths, or programming robots to do so. In order to promote con- tinuity towards the introduction of geometry in primary school, we developed a long-term teaching experiment (with 15 sessions) carried out over 4 months in a first grade classroom in northern Italy. Students were asked to program a robot to move along paths, to pretend to act as robots and to represent the sequence of commands and the resulting paths. In particular, in this teaching experiment, an overarching mathematical aim was to sow the seeds for a mathematical definition of rectangles that includes squares. Within the paradigm of semiotic mediation, we intended to foster the students’ transition from a dynamic perception of paths to seeing paths also as static wholes, boundaries of figures with sets of geometric characteristics. The students’ situated productions were collected and analysed together with the specific actions of the adults involved, aimed at fostering processes of semiotic mediation. In this paper we analyse the development of the situated texts produced by the students in relation to the pivot signs that were the beginnings of an inclusive definition of rectangles.

We present some fragments of a teaching experiment realized in a first grade classroom, to sow the seeds for a mathematical definition of rectangles that includes squares. Within the paradigm of semiotic mediation, we studied the emergence of pivot signs, which were exploited by the teacher to pave the way towards an inclusive definition of rectangles and squares. This was done to favor overcoming children's spontaneous distinction of these figures into distinct categories, reinforced by everyday language. The experiment is an example of an approach towards the theoretical dimension of mathematics in early childhood.