\input zb-basic \input zb-matheduc \iteman{ZMATH 2011d.00315} \itemau{Moreno-Armella, Luis; Sriraman, Bharath} \itemti{Symbols and mediation in mathematics education.} \itemso{Sriraman, Bharath (ed.) et al., Theories of mathematics education. Seeking new frontiers. Berlin: Springer (ISBN 978-3-642-00741-5/hbk; 978-3-642-00742-2/ebook). Advances in Mathematics Education, 213-232 (2010).} \itemab Summary: 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. This paper is dedicated to Jim Kaput (1942-2005), whose work on representations and technology is an inspiration to us all. \itemrv{~} \itemcc{D20} \itemut{concept formation; thinking; learning; semiotics; mathematics teaching and computers} \itemli{doi:10.1007/978-3-642-00742-2\_22} \end