Temporal freedom in mathematical thought:A philosophical–empirical enquiry

摘要

This paper seeks to introduce and elaborate on the notion of 'temporal freedom' in thecontext of mathematical thinking.The intention is to merge a philosophical and empirical discussion on this topic, andfindings will be presented from a qualitative study in which 29 high-school students wereinvited to explore the symmetry group of a square during clinical interviews. The dataindicate how the interviewees – who were given the opportunity to freely explore an unseenmathematical system – repeatedly brought past and future together in a tangible presentduring their investigations. In doing so they were exceptionally successful in engaging withadvanced abstract algebra, far beyond what might have been expected at the outset.By using empirical data to exemplify an otherwise highly philosophical discussion, I hopeto draw explicit attention to the temporal aspect of the human mind in mathematical actionwhich instructional methods frequently fail to recognise, value and utilise.