of the 100th Anniversary of ICMI

WORKING GROUP #4

Technology has long been a theme open for debate within the mathematics education community and has been reflected in the work of ICMI even prior to the first ICME (Lyon, 1969). More recently, information and communication technology (ICT) has played an increasing role in the events organized by ICMI.

Debates around ICT have brought to light the fact that other resources and technologies have been introduced over the last 100 years. This Working Group will deal with how artefacts and materials (e.g. paper and pencil, memorisation and calculators, Dienes blocks, mathematical machines, computers, software and digital learning objects etc.) have been used over the 100 years of ICMI's history.

**TECHNOLOGY AND ICMI:**

The integration of tools and technologies is an important and current theme today. Research in learning with technological tools has been showing much promise with respect to their use in the generation of learning environments where students have richer opportunities to construct mathematical meanings, to explore and experiment with mathematical ideas and to express these using a wealth of representations. However, actual use of these tools in real school environments is still very sparse despite the abundance of governmental funding and interest. The changes in classroom practices involved in the use of technology seem to pose a real challenge to administrators, curriculum designers, teachers and students.

It must be emphasized, however, that a deeper understanding of ICT may be reached only if viewed from an historical perspective. Euclid's *Elements* may be considered a modelling theory of geometrical drawing by means of ruler and compasses. The ancient abacus (in Roman area as well as in the far East) and the other devices used in pre-Columbian America can be seen as the roots of the modern positional system of number representation. More recently, the development of perspective drawing in Europe by means of instruments used in artists studios, has laid the foundations for modern development of projective geometry. Attention to these kinds of instruments has been held by the first president of ICMI, Felix Klein, who established a subject for university education of teachers (named *Elementary mathematics from an advanced standpoint*) where the use of ancient instruments was put in the perspective of the advances of mathematics of the 18th and 19th century.

The present technologies (ICT) are, in some respects, the heirs of this long tradition. A widespread misunderstanding is that, due to their effectiveness, they may replace the old instruments: why use abaci when pocket calculators are available? Why refer to ruler and compass construction when powerful software is available?

From time to time, in ICMI Studies, the issue of ancient and new instruments has been raised (ICMI Study on History e.g.). In national curricula (e.g. Italy), the integration of ancient and ICT technologies has been raised. Research has been presented at different ICME's that integrates artefacts and "computer artefacts". More recently, there has been an increase in research that includes digital objects, which opens up new possibilities for merging objects and "regular software" in virtual objects such as applets and video-stories.

Although this group should focus on different kinds of technology, we dedicate special time to the different facets of computer technology and its relation with other artefacts. Questions such as the following may be addressed:

- Is it different to use the graphing calculator or a function software in the classroom?
- What kind of change does the Internet bring to mathematics education?
- Do new technologies transform old ones or erase them?
- What is the relation between human thinking and the tools that have been developed throughout our history?
- How is the very notion of body affected by artefacts in general, and by computer technology in particular?
- Are representations of a given mathematics concept being transformed by the different technology we have experienced in these 100 years of ICMI?
- Is knowledge a product of units of humans-with-media as proposed by some authors?
- Has the notion of a problem in the mathematical classroom been affected by different technology?
- How has the classroom been affected by the Internet?
- Are teachers in a new "risk zone" as they need to deal with new uncertainties due to the availability of information and communication technology?

Although participants can bring issues from their experience, and in particular from their study of ICMI and ICME history, which may differ from the ones raised in this paper, we believe that the issues mentioned above represent a good starting point for the celebration of the centenial of ICMI.

*Deadline for applications:* February 28, 2007

**Co-chairs: Marcelo C. Borba (Brazil), Mariolina Bartolini Bussi (Italy)**

**PAPERS:**

- George L.Ekol Characterization of ICT activities in the teaching/learning institutions and the role of ICMI
- George Gadanidis Rare events: Technology throughout the history of ICMI
- Vince Geiger The emergence of social perspectives on the use of technology in mathematics education
- Paulus Gerdes Exploration of technologies, emerging from African cultural practices, in mathematics education
- Lulu Healy Charting the microworld territory: the placing of theoretical signposts
- Celia Hoyles & Jean-Baptiste Lagrange The seventeenth ICMI study: Technology revisited
- Masami Isoda Mathematization and mathematics activity: An appearance of ICMI and world mathematics reform movements in Japan before and after WWII
- Luckson Muganyizi Kaino Information and Communication Technology (ICT) developments, utilization and challenges in ICMI history
- Chronis Kynigos Half-baked mathematical microworlds as boundary objects in connected design
- Colette Laborde Technology as an instrument for teachers
- Zsolt Lavicza The examination of technology use in university-level mathematics teaching
- Thomas Lingefjärd Hundred years of technology in mathematics classrooms
- Richard Noss A brief note on a 'widespread misunderstanding'
- John Olive From Dienes’ blocks to JavaBars: A personal odyssey in the use of artifacts, materials and tools for learning and teaching mathematics
- Domingo Paola ICT throughout the history: the retrospective gaze of the crab
- F.D. Rivera Technology as experience: three instrumental-genetic issues
- Ornella Robutti Can we consider graphic calculators as an "old" technology, compared with a new one?
- Kenneth Ruthven Mathematical technologies as a vehicle for intuition and experiment: a foundational theme of the ICMI, and a continuing preoccupation
- Mamadou Souleymane Sangaré La machine de Sylvester: conception et réalisation de deux modèles à usage didactique
- Rudolf Strässer Learning with new technology – some aspects of a history of didactics of mathematics
- Daina Taimina Geometry and motion links mathematics and engineering in collections of 19th century kinematic models and their digital representation
- Luc Trouche & Michela Maschietto ICT, new insights on old problems
- Mónica E. Villarreal Some reflections about old and new media in mathematics education