Reason to Believe in Mathematics

Abstract

This chapter provides a theoretical discussion of how we understand mathematical knowledge. The theory presents rationality and belief as mutually formative dimensions of mathematics, where each term is more politically and socially embedded than sometimes depicted in the field of mathematics education research. The chapter considers alternative modes of apprehending mathematical objects derived as they are from this socially defined space. Two accounts of how a young child might learn to point at mathematical entities are presented, where alternative interpretations of this act of pointing are linked to conceptions of sharing understandings. This comparison then underpins a discussion of how mathematics is produced as entities to be acquired according to certain shared ideological schema that also shapes who we are. The chapter’s central argument is that rational mathematical thought necessarily rests on beliefs set within a play of ideological framings that partition people in terms of their proxy interface with mathematics. The challenge is then seen as being to loosen this administrative grip to allow individuals to release their own powers to generate diversity in their shared mathematical insights rather than being guided by conformity.