Servizio Comunitario di Informazione in materia di Ricerca e Sviluppo - CORDIS

Final Activity Report Summary - CB_DIDACTIQUE (Using a computer environnement to improve the quality of algebra education at different school levels)

The main goal of our project was to investigate students' conceptions of elementary algebra relying on an international overview of the teaching and learning of this subject in different countries, along with its different cultures. We decided to tackle this question by choosing three countries which social, cultural and scholar systems differed, yet which presented commonalities tying them together. More precisely, our study focused on the examination of the Australian, French and Brazilian scholar systems. The methodology employed was meant to follow and extend the innovative methodology developed in our PhD research: we aimed to investigate the teaching and learning of algebra by bringing together three different (yet complementary) disciplines, namely didactics, epistemology and informatics.

Taking the informatics aspect of our work as a guide, we could say that our aim was two-folded.

First we intended to design tasks to assess student's algebraic skills relying on the French algebraic software prototype PETPITEST in the other two countries. Part of our work has therefore been devoted to develop both a Brazilian and an Australian version of the French software according to the scholar system and 'mathematical culture' specific to each country. In order to do so, we carried out didactical analyses of official texts and textbooks, working closely with students, teachers and maths educators (analysing teaching practices, interviewing teachers and students, etc.). This work enabled us to gather different points of view from the diverse agents of the scholar system and improve the preliminary versions of the software. By the end of our project, a final Brazilian and Australian versions were ready and have been experimented in several schools of both countries, providing us with data about students' algebraic skills. Grounded by an epistemological study, we finally carried out an analysis on the didactical implications of the designing and experimenting mathematic tasks in different countries that the study grounded on the overall process of translation the algebraic software revealed.

Also benefiting from the host (University of Melbourne) research on CAS we intended to develop new tasks with current educational mathematical software and study the potentiality for implementing these tasks in the different countries and especially examine the possibilities for integrating these tasks within the framework of the French software PEPITEST. Several tasks using with current mathematical educational software was then designed, implemented in several Victorian teachers and have now become part of Australian teaching resources.

More than producing Brazilian and Australian versions of an algebraic software and assessing students on elementary algebra taught nowadays, conducting this international work involving different schools and teachers in France, Brazil and Australia showed that designing and experimenting algebraic tasks in different countries is much more than just a matter of translation. Mathematics and more precisely algebra, which are often seen as universal languages unfolded in fact authentic mathematical and algebraic 'cultures' specific to each country. And such 'cultures', that we showed to be grounded on genuine historical and epistemological roots cannot be neglected when considering and eventually acting on the teaching and learning of mathematics. The present work is currently being extended, by taking into account new technologies recently released.

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