PROCEEDINGS OF THE 21ST ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2018
San Diego, California
Revisiting Reducing Abstraction in Abstract Algebra
Page: 1197
In this paper, we revisit Hazzan’s (1999) fundamental work on reducing abstraction in abstract algebra tasks. As we analyzed hundreds of students’ activity related to abstract algebra tasks, we identified many ways students reduced abstraction that did not align with the original framework. We leverage additional theories of abstraction to expand and refine Hazzan’s framework to reflect new aspects of familiarity, contextualization, complexity and connectedness, and formality. For each of the new categorizations, we provide illustrations of students engaged in the relevant reduction of abstraction. We conclude with consideration to how the expanded framework may highlight productive types of abstraction reduction.