Reflective Knowing in the Mathematics Classroom: The Potential of Philosophical Inquiry for Critical Mathematics Education

This chapter argues that critical mathematics education requires reflective knowledge, which often lies outside of mathematical and technological knowledge and which can be generated through philosophical inquiry in the classroom. I first examine the concept of reflective knowing more closely and suggest that philosophical inquiry in collaborative group settings may be an appropriate vehicle to facilitate critical reflection in the classroom focused on the understanding of mathematics as a tool, its role in society, and the implications of using mathematical and technological knowledge in addressing social problems. I then offer a brief description of the practice of communal philosophical inquiry, the context in which it is conducted, and a framework for practicing it in the mathematics classroom by engaging school students in collective encounters with contestable questions related to mathematics and its role in society. I claim that philosophical inquiry can offer a space for critique and reflection on mathematics and for the development of an epistemological approach that encourages an enriched, overarching view of mathematics and its connections to the other school disciplines, society, and self. It also offers space for the deconstruction and reconstruction of beliefs about mathematics as a form of knowledge, about the social value of mathematical practice, and beliefs about oneself as a mathematics learner/thinker.