Evidently there is a bumper sticker on cars in California which says‘Philosophy is a game with objectives and no rules – mathematics is a game with rules and no objectives.’
If this is taken at face value it might be concluded that either philosophy and mathematics have nothing at all in common, or that they would usefully complement each other. This article attempts to show the latter, with particular reference to a practice known as Philosophy for Children (P4C). I will argue that good thinking and facilitation of thinking is similar in both a P4C community of enquiry and in a mathematics lesson designed to develop what Richard Skemp (1976) would call ‘relational understanding’.
I will also argue that thinking and learning develops more effectively if these skills and strategies are made explicit and brought to the attention of both pupils and teachers, which a combination of P4C and exploratory mathematics sessions can do. I will attempt to give examples to demonstrate that cross-fertilisation of P4C and mathematics practice can broaden learning and teaching across the curriculum by providing mutual support for such skills.
Contexts for learning in mathematics
Richard Skemp (1976) refers to ‘relational’ and ‘instrumental’ understanding in mathematics. The first could be classed as deep understanding and is a function of the number of links made within the field of mathematics, the second an ability to follow a rule. An important part of achieving relational understanding is that learners’ present thinking is challenged. John Mason (2004) refers to the Festinger idea of ‘cognitive dissonance’.