Roberta Mura

Images of mathematics held by university teachers of mathematics education

This article presents data about views of mathematics collected through a national survey of teachers of mathematics education in Canadian universities. The results are compared to those obtained through a similar survey of university teachers of mathematical sciences carried out earlier.

What is Mathematics Education? A Survey of Mathematics Educators in Canada

This chapter is about some results from a survey of mathematics educators in Canadian universities that was conducted in 1993. The aim of the survey was to collect information about their social backgrounds, education, careers and views about mathematics and mathematics education, in order to gain a sense of the identity of this professional community. The results presented here are mainly those concerning the views about mathematics education. The remaining results are discussed in Mura (1995a, 1995b).

L'Épaisseur d'un décimètre carré 1

RésuméLe présent article illustre les difficultés qui peuvent surgir lorsque la distinction entre les notions mathématiques et leurs modèles issus du monde physique n’est pas bien comprise. Les exemples fournis touchent divers ordres d’enseignement, notamment celui de la formation des enseignantes et des enseignants pour le primaire.Executive SummaryIn spite of great diversity in epistemological theories, hardly anybody denies that the physical world, or our perception of it, plays some role in the origin of mathematical ideas. Advanced concepts may be built on elementary ones, but there is general agreement that the latter are prompted by or abstracted from physical experience. It is difficult to imagine learning the concept of numeracy without some previous experience of counting objects, learning the arithmetical operations without familiarity with corresponding material situations, or learning about circles and squares without having observed similar shapes in the natural or artificial environment. However, the mathematical is distinct from the material. There is a correspondence between the two, but never identity. The mathematical concept of number is not a handful of counters, the arithmetical operation of division is not the action of sharing candies, and geometrical figures are neither plastic toys nor drawings.When the distinction between mathematical ideas and their physical models is not well understood, various difficulties may arise. For instance, physical models may lead learners to attribute to a mathematical concept properties that it does not generally have or prevent recognition of properties that it does have. The present article offers several illustrations of such difficulties. The examples are drawn from the literature and from the author’s research and practice. They concern people at various levels of mathematical education, from children to experts, most particularly pre-service elementary teachers, and they touch on diverse mathematical subjects, including arithmetic, geometry, and measurement.The following are among the difficulties discussed: •conceiving the number zero as ‘nothing’ and identifying arithmetical operations with ‘actions’ may hinder understanding of multiplication and division by zero•thinking of translations and rotations as movements may lead to confusion about geometric transformations•Using manipulatives may induce the belief that square decimetres have thickness and that 10 of them make up a cubic decimetre.