Rationality and belief in learning mathematics

This paper argues that rationality and belief are mutually formative dimensions of school mathematics, where each term is more politically embedded than often depicted in the field of mathematics education research. School mathematics then presents not so much rational mathematical thought distorted by irrational beliefs but rather a particular mode of activity referenced to the performance of certain substitute skills and procedures that have come to represent mathematics in the school context as a result of social management. The paper considers alternative modes of apprehending mathematical objects. Firstly, 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 enculturation. This comparison then underpins a discussion of how mathematics is produced as entities to be acquired according to certain ideological schema. The resulting cartographic definition of mathematics steers the production then selection of learners according to arbitrary curriculum or assessment criteria. Secondly, some trainee teachers report on shared experience in a spatial awareness exercise concerned with exploring alternative apprehensions of geometric objects. This provides an account of my own teaching and explains why I find teaching mathematics so exciting if it can be linked to the generation of multiple perspectives. The paper’s central argument is that rational mathematical thought necessarily rests on beliefs set within a play of ideological framings that within school often partition people in terms of their proxy interface with mathematics. The challenge is to loosen this administrative grip to allow both students and teachers to release their own powers to generate diversity in their mathematical insights rather than conformity.