Historical roots of limit notion: Development of its representation registers and cognitive development
Canadian Journal of Science, Mathematics and Technology Education, (2003)Abstract
The influence of visualisation and of verbal and symbolic expressions of main infinitesimal methods upon didactics, and in particular its importance for the correct characterisation of concepts, is well known. In this paper different ideas and expressions of infinitesimal methods in the history and in mathematics education are investigated, with particular reference to the limit notion. Historical development of representation registers can lead to a parallel development of the notion in students minds, and this would make it possible to design new ways to overcome some obstacles and to develop students ability to use and to co-ordinate different registers; however explaining the problems encountered by mathematicians in history (who inhabited different paradigms with different social knowledge structures and different beliefs) does not necessarily help students with their difficulties. Our main contribution resides in showing that dynamic and static ideas of limit are encompassed by different semiotic registers.