In this paper we propose a comprehensive model, conceived as a heuristic to support a co-disciplinary approach to the design, development and analysis of the didactical system, in particular in the case of mathematical e-learning situations. It has been developed by expanding the classical didactical triangle into a tetrahedron, and including within it a mediatory sphere whose intersection points with the tetrahedron can shed some light on the impact of technology within the didactical system. We explain how the model could address the need to take into account, in a co-disciplinary mode, different theoretical and empirical perspectives, within and beyond mathematics education.

The aim of this contribution to the Topic Study Group work is to focus on the effectiveness of physical and technological manipulation in terms of meaningful geometric learning gain, presenting an on-going research involving pupils at 4th, 5th and 6th grades. The main idea is to verify if an integrated laboratorial approach, exploiting the potentialities of both physical and technological instrument, can attempt to afford the building of new geometric concept and a firm understanding of geometrical relationships. According to the early results of the experience it seems that, within authentic learning situations, the integrated use of paper, scissors, strings, straws, geo-board and of the Interactive Collection 123…Cabri could guide pupils towards a progressive geometric mathematization.

This paper describes an Italian experience in Adult Learning Mathematics carried out in a Territorial Permanent Centre (CTP), i.e. an institutional structure for Adult Education. The program, that has been developed over the last three years, aims to enhance personal competencies without awarding any credentials. The description of the experience includes: an explanation of the aims and of our choiches of content and methodologies; an outline of the context and the procedures and, finally, illustration and discussion of the results.

In this work we investigate the potentiality of carrying out synergic activities using manipulative and virtual artefacts for the purposes of constructing/conceptualizing axial symmetry and its properties. The research study is based on the design and implementation of a teaching sequence involving 4th grade students. Both the design and the analysis of data is framed by the Theory of Semiotic Mediation (Bartolini Bussi & Mariotti, 2008) According to the results of the study the combined, intentional and controlled use of manipulative and virtual artefacts seems to develop a synergy whereby each activity enhances the potential of the other.

L’azione didattica è un processo olistico in cui interagiscono la didattica generale (DG) e le didattiche disciplinari (DD). Ma come si relazionano? Nel passato sono emersi due modelli: separando l’intervento tra saperi ed educazioni o eliminando uno dei due poli. Il lavoro che presentiamo cerca di superare i due opposti modelli. Le due discipline, DG e DD, impattano sulla stessa azione didattica e ciascuna interviene su tutti gli aspetti, ma con prospettive differenti. Tale sinergia permette un’analisi plurale che altrimenti sarebbe zoppa. Per cogliere i problemi e le sinergie di un’analisi plurale, il contributo analizza la ricerca relativa a un percorso di didattica della matematica per la Scuola Primaria al cui sviluppo hanno partecipato ri- cercatori dei due settori disciplinari.

Our research aims to investigate on creativity and imagination as possible artifacts for maths learning. In particular, we aim to understand if fairy tales can be used as artifacts for trying to find out whether children had previous mathematical knowledge or not, and as tools for developing knowledge, skills and abilities in the creation of imaginary settings. In this paper we claim that there may be an edge between imagination and creation of a reality that can lead to achieve mathematical notions in a creative way.

The aim of this chapter is to stress the role of GeoGebra as a methodological resource. In particular, we contend that teachers need to become aware that an appropriate integration of GeoGebra within the classroom activities could foster the construction of mathematical knowledge. As a consequence, educators need to guide teachers to perceive GeoGebra as a methodological resource so that they would be able to effectively use it. As a theoretical framework we mainly refer to the “instrumental approach” and to the idea of “mathematics laboratory as a Renaissance workshop”. We also suggest that, when teachers are “immersed” in appropriate non-standard learning situations, they could experience by themselves that GeoGebra can be very useful for creating a meaningful mathematics learning environment.

The use of technology and other resources for mathematical learning is a current issue in the field of mathematics education and lags behind the rapid advances in Information and Communication Technology. Technological developments offer opportunities, which are not straightforward to exploit in regular teaching. In CERME10 TWG16, the recent research findings, issues and future questions have been explored and discussed in detail. In this introductory chapter, we will outline the scope and focus of the work, describe the results with respect to existing questions, and identify upcoming topics as well as missing topics that might set the agenda for future work in this domain.

This paper presents the early results of an on-going research project on the use of technology in the mathematics teaching and learning processes. A first aim of this project is to understand how deeply math teachers do perceive the opportunities technologies can bring about for change in pedagogical practice, in order to effectively use them for the students’ construction of mathematical meanings. Secondly, the research aims at verify if teachers realise that, in order to successfully deal with perturbation introduced by technologies, they have to keep themselves continuously up-to-date and to acquire not only a specific knowledge about powerful tools, but also a new didactical and professional knowledge emerging from the deep changes in teaching, learning and epistemological phenomena.

In questo articolo si vuol riflettere sulle opportunità offerte dall’utilizzo della LIM nell’insegnamento-apprendimento della matematica, focalizzando l’attenzione sul ruolo del docente e sulle competenze necessarie perché tali opportunità possano essere sfruttate nel migliore dei modi. A tale scopo risulta importante precisare in che termini un uso appropriato della LIM possa essere funzionale a sviluppare e potenziare negli studenti la costruzione di significati matematici.