Anna Sfard Unit - Module 3

Mathematics as a discourse

In the last module (Module 2) I defined learning as a process of changing an activity and claimed that school learning aims at those activities that have been developed throughout history and are now prevalent in our society. In this module I focus on the question of “What is the activity that we change when learning mathematics?” The commognitive answer to this query echoes those given by postmodern thinkers such as Foucault, Lyotard, and Rorty. According to this definition, mathematics is a form of discourse, in which we create theories of mathematical objects, MOs. Here, the term discourse signifies a form of communication made distinct, among others, by its unique keywords, visual mediators, and routines. Theories of MOs are potentially useful stories about MOs that we gradually construct as we apply these discursive tools. After explaining what is meant by story, I specify the characteristics according to which a story can be considered as useful. Having done all this, we are left  with the task of defining what is meant by mathematical object. The clarification of this latter notion will be the aim of Module 4. For the summary of our recursive process of defining mathematics, see the diagram below.