Reflections as a challenge

Abstract

Reflections on mathematics-based actions and practices bring an ethical dimension to the notion of reflection, and this is the aspect I consider and develop in this essay.

I elaborate on the notion of reflection by addressing eight different issues. (1)The necessity of reflection emerges from the observation that mathematics-based actions do not have any intrinsic link to progress by virtue of being mathematics-based. Such actions can be as complex and as questionable as any other actions. (2) Although reflections, from this perspective, are believed to be necessary, one could cite afunctionality of non-reflection. For example, non-reflection enables the school mathematics tradition to continue to ensure that the future labour force has particular competencies in the right measures to match the social order for which they are destined. (3) Reflections often presupposespecificity, as they include general as well as specific reconsiderations with respect to some knowledge, actions and practices. (4) I usecollectivity of reflections to refer to the observation that ethical considerations can be facilitated through interaction and communication. Often this presupposes that challenging questions be formulated in order to open up the ethical dimension with respect to mathematics in action. (5) Reflections presuppose directedness and involvement, and this brings me to analyse theintentionality of reflections. (6) Reflections can address very many different issues, which leads me to recognise thediversity of reflections. (7) It is easy to ignore or to obstruct reflections, and when reflections emerge, they can easily be eliminated from an educational context. We should never ignore thefragility of reflections. (8) This brings me to recognise theuncertainty of reflection. Reflections cannot rely on any solid foundation. Still, I find that reflections are necessary.