Department of Mathematical Sciences

Technical report #9/2010

Symbols and mediation in mathematics education

**Luis Moreno-Armella**

Cinvestav-IPN

Mexico

&

**Bharath Sriraman**

Dept. of Mathematical Sciences

The University of Montana

**Abstract**

In this paper we discuss topics that are relevant for designing a theory of mathematics
education. More precisely, they are elements of a *pre-theory* of mathematics
education and consist of a set of interdisciplinary ideas which may lead to understand
what occurs in the *central nervous system*—our metaphor for the classroom, and
eventually, in larger educational settings. In particular, we highlight the crucial role of
representations, the mediation role of artifacts, symbols viewed from an evolutionary
perspective, and mathematics as symbolic technology.

**Keywords:** representation theory in philosophy; symbolic technology; digital media; philosophy of mathematics education

**AMS Subject Classification:** 97