The Evolution of Mathematics

This chapter discusses at a more historical level how our conceptions of mathematics and of ourselves as researchers, teacher educators, teachers and students have been transformed through mathematical activity being viewed through the apparatus of schooling and international comparative filters. This model provides an example of how changing practices impact on the social construction of mathematics itself. The chapter argues that the fields of psychology and mathematics each describe realities that are consequential to past human endeavours or conceptualisations. Neither of these fields depicts stable truths. Mathematical concepts and the ways in which we relate to them never finally settle in relation to each other nor do the theories we introduce. Their final form always stays out of reach. The building of mathematics then reflects the image we have of ourselves and becomes part of those selves that it reflects. Whilst the truth of mathematics can sometimes be used to underwrite its ideologically motivated manifestations, we need to trouble the “truths” that are presented to us, towards encountering the spaces beyond and the hold they have on us.