An Anarchist Approach to the Undergraduate Mathematics Curriculum

TL;DR

This paper explores applying anarchist principles to reform the undergraduate mathematics curriculum, emphasizing decentralization, diversity, and process over traditional hierarchical assessment methods.

Contribution

It introduces a philosophical framework based on anarchism to critique and suggest alternatives for current assessment and curriculum practices in undergraduate mathematics.

Findings

Highlights the potential for non-hierarchical assessment methods

Proposes process-oriented and inclusive curriculum approaches

Encourages incremental and large-scale reforms in teaching practices

Abstract

Contemporary anarchism centers around three tenets: (1) a constant challenge of and resistance to all forms of domination, (2) so-called "prefigurative politics", in which all decisions are made in a manner that is consistent with a set of non-hierarchical values such as equality, decentralization and voluntary cooperation, (3) a focus on diversity and open-endedness (Gordon, 2008). Within this philosophy the notion of end goals becomes moot; progress, then, is measured by process, in which the values of diversity, pluralism, cooperation, autonomy and experimentation are celebrated. In this perspective piece we propose anarchism as a philosophical framework to address the perceived cognitive dissonances of the current undergraduate mathematics curriculum. Are learning outcomes appropriate in an anarchist approach to education? How can we address the power dynamics of grading and assessment? How can assessment be done in the context of a process-based and horizontal approach that celebrates diversity and autonomy? Should grades be used, and if so, how could they be assigned non-hierarchically? At its core, anarchism aims at aligning thoughts and actions, and we argue that an anarchist viewpoint on undergraduate mathematics addresses the cognitive dissonances that currently plague our curriculum. We propose food for thought for individual instructors' practice, including ideas for incremental and large-scale changes.