Università di Genova , Genova , Italia
Title: Mathematics education today: Scientific advancements and societal needs
Abstract. In the last two decades, a contradiction gradually emerged in the field of mathematics education between: the accumulation of a great deal of research results concerning specific aspects of the teaching and learning of mathematics, the learners and the teachers; and the increasing difficulty of dealing, according to rigorous academic standards, with general, important questions deriving from the evolution of societal needs and policy decisions regarding mathematics instruction. Based on my personal experience of researcher and curriculum developer, in my lecture I will compare and discuss possible ways of addressing "big" cultural and social problems in a scientific way in the field of mathematics education. Through examples, I will advocate the necessity of: ad-hoc theoretical framings (including the necessity of reconsidering the meaning of mathematics literacy in today society and the variety of mathematical experiences in different cultures); suitable methodological assumptions and experimental settings (including the role of teachers as "participant observers" in long term experimental activities); re-interpreting and exploiting some available research results in the field of mathematics education (particularly those concerning the role of context and language in mathematical activities); referring to results, tools and perspectives provided by other disciplines (including epistemology and history of mathematics, anthropology and philosophy). Given the complexity of such enterprise, co-operative work should be enhanced, engaging different competencies and professional experiences.
Université Paris- Diderot, Paris, France
Title: Teaching and Learning Geometry and Beyond ...
Abstract. Geometry and its teaching have always been a problematic and exemplar issue regardless of the period. Torn between utilitarian and idealistic visions, the very nature of geometry has moved within very wide margins from regarding it as sacred to aiming at its disappearance. Regarding mathematics education, researches on geometry have raised the attention of most prominent researchers in the domain such as for instance Freudenthal and Brousseau. What are today the core items and the contributions of researches in the didactics of geometry, a domain in which the current development of specific software has caused quick changes? We will address this question in the light of the results of recent researches and also the rich discussions which have been occurring in the CERME Working Group on geometry from its beginning in 1999. We will also develop some ideas about the perspective of geometric paradigms and Geometric Work Spaces and show how it allows to describe and change the nature of geometric activity in different educational contexts. We will also consider how this approach can be extended to other mathematical domains.
University of London, London, UK
Title: Language and Mathematics: a field without boundaries?
Abstract. It is widely acknowledged within the field of mathematics education that language plays an important (or even essential) role in the learning, teaching and doing of mathematics. This is evident in the extent of participation in groups focusing on Language and Mathematics at CERME and other conferences as well as in a growing literature. However, general acceptance of the importance of language is not matched by agreement about what this role (or these roles) might be or even about what the term language itself encompasses. I propose to construct a map of the field, identifying the range of ways of conceiving of language and its relevance to mathematics education, the theoretical resources drawn upon to systematise these conceptions and the methodological approaches employed by researchers. Through this, I will identify some outstanding issues and questions and suggest some ways of building upon the diversity of the field in order to strengthen its coherence and the utility of its outcomes.