Antonella Montone

Synergy between manipulative and digital artefacts: a teaching experiment on axial symmetry at primary school

ABSTRACT This paper presents a study aimed at investigating the didactic potentiality of the combined use of two different kinds of artefacts for the purpose of constructing and conceptualizing mathematical meanings related to the notion of axial symmetry. In our view, the process of meanings construction can be fostered by the use of adequate artefacts, but it requires a teaching/learning model, which explicitly takes care of the evolution of meanings, from those personal, emerging through the activities, to the mathematical ones, aims of the teaching intervention. The main hypothesis of this study is that a potential synergy may occur between the use of different artefacts, synergy that can foster the integration of different and complementary meanings providing a rich support to the development of the expected mathematical meaning. The Theory of Semiotic Mediation offers the theoretical framework suitable to design the teaching sequence and to analyze the collected data. Specifically, the construct of semiotic potential provides the tool for describing the potentialities of the two artefacts, while that of didactic cycle offers a model for the organization of the different activities. The paper reports on a teaching sequence and its implementation in a teaching experiment, involving pupils at fourth grade level. We describe them, within the chosen theoretical framework, and provide the analysis of key episodes of the teaching sequence. We show evidence supporting our main hypothesis about the combined use of an artefact that can be manipulated (paper and pin), and a digital artefact (Dynamic Geometry Environment) in the development of the notion of axial symmetry and its properties: the combined, intentional and controlled use of the two artefacts may develop a synergy, so that each activity enhances the potential of the other.

The synergy between Manipulative and Digital Artefacts in a Mathematics Teaching Activity: a co-disciplinary perspective

This paper presents a teaching experiment aiming at constructing the meaning of axial symmetry through the mediation of a “duo of artefacts”, made up by a digital artefact and a manipulative one. The meaning of the term “mediation” is described and used from a dual perspective, joining General Didactics and Mathematics Education. Herein, we describe an interactive book, created in a Dynamic Geometry Environment and a teaching sequence, based on the use of such a digital artefact, combined with a manipulative one. The main potential of the interactive book is based on the possibility to drag geometric objects and observe the effects of the dragging. The sequence has been experimented with a 4th grade class and the activities have been videotaped and analysed. Results have been analysed through the cited dual perspective and reveal how the mediation of the duo of artefacts can foster the construction of the mathematical meaning. In this paper we show how the digital artefact, acting in synergy with the manipulative artefact, seems to exploit the potential of the sequence in terms of embodied involvement of the pupils in their cognitive process.

Introduction: Innovative Spaces for Mathematics Education with Technology

The idea of this book arose from research encounters occurred during a past ICTMT Conference: the International Conference on Technology in Mathematics Teaching. The ICTMT Conference, which is now moving to its 13th edition, has a strong commitment to promote technology in mathematics education for improving the quality of teaching and learning by effective use of technology. In recent years, international research in mathematics education has offered a range of theoretical perspectives that attempted to provide different and interrelated frames and viewpoints to the study of use and role of digital technologies in/for teaching and learning mathematics.

From Acorns to Oak Trees: Charting Innovation Within Technology in Mathematics Education

Technology has created an expectation in all levels of education that requires us to understand how we can harness its potential for improving the depth and quality of mathematical learning. It is highly unlikely that there is a universal recipe or formula for how technology should be used that would satisfy every context or culture, but there have been recurring trends in the process of designing and implementing such innovative environments. By considering the papers included in proceedings of the past International Conferences on Technology in Mathematics Teaching (ICTMT), this chapter aims to highlight how a few key innovations have been seeded and taken root within this community. We begin by describing the ways in which innovation has been presented at ICTMT conferences with a view to exploring this from the perspectives of technology designers, researchers and teachers/lecturers from all levels of education. Given the extensive literature on this topic, it is not feasible to carry out a comprehensive survey of the complete literature base, however it is anticipated that the analysis of key ICTMT papers will be sufficient to present an informative and insightful picture and highlight some important knowledge and experience that has been elicited and disseminated.