The Many Faces of Mathematics: Do Mathematicians and Researchers in Mathematics Education Speak about the Same Thing?

If a mathematics educator studies mathematics, is it the same object for him or her as it is for a mathematician who studies mathematics?, ask the authors of the Discussion Document. The very fact that the problem was raised is the first indication of a difference between the mathematician’s and the mathematics education researcher’s approaches to mathematics. Indeed, while the question imposes itself on the latter, it is not very likely to be asked by the former. Mathematicians seem to have little doubts as to the nature and the identity of the subject they deal with on a daily basis. Most of them would claim that there is only one object that can be called Mathematics and anything that differs from this unique exemplar cannot be given the same name. More often than not, the working mathematician is a Platonist, even if only tacitly: his or her mathematics has an appearance of an ideal, well-defined body of knowledge, faithfully mirroring a certain mind-independent reality of abstract ideas.