ABSTRACT
One of the most salient characteristics of mathematics is its logical structure; one would therefore expect mathematics to be a subject that is easy to teach. Reality, however, shows that this is not the case. Mathematics proves to be hard to learn for many students. A common explanation is that mathematics is too abstract. Sfard (1991) offers a deeper explanation by showing that there is more to mathematics than just the rules of logic. She points to the epistemological nature of mathematical knowledge. Reflecting upon the history of mathematics, she construes a dual nature of mathematical conceptions: a structural conception, and an operational conception.1 The first concerns mathematical objects, the latter mathematical processes. We may start by elucidating the structural conception that encompasses the notion of mathematical objects. Sfard (1991) observes that, although it is commonplace to speak of ‘a function such that . . .’ in a similar manner as a physicist speaks about the existence of certain subatomic particles, mathematical objects are very different from physical or material objects. Mathematical constructs such as functions are inaccessible to our senses.
