Abstract Algebra Students' Representational Fluency during a Collapsing Structure Task

event Friday, May 7, 2021
access_time 9:00am (CDT)
room Zoom

Abstract: The quotient group concept is a difficult concept for many students getting started in abstract algebra (Dubinsky et al., 1994; Melhuish, Lew, Hicks, and Kandasamy, 2020). This Friday's talk uses a semiotic lens to explore three students' sign, interpretation, and signified object triangles as they work on a collapsing structure'' task (i.e., a quotient group task) across multiple registers: Cayley tables, group presentations, Cayley digraphs, Schreier coset digraphs, formal-symbolic mappings, and objects of symmetry. This work is part of a larger project that attempts to develop techniques that can be used to evaluate two intuition associated factors: representational fluency and example-based intuitions. My upcoming thesis talk in July will discuss progress related to the second factor and includes cluster models for the (partial) make-up of learner's example-based intuitions related to group actions. The (partial) make-up of a learner's intuition as a quantifiable object was defined in this thesis as a point viewed in R^17, 12 NCC variable values collected with the NCCFIS (Non-creative versus Creative Forms of Intuition Survey), 2 values for confidence in truth value, and 3 additional variables: error to non-error type, unique vs common within the sample, and network thinking. The revised Fuzzy C-Means Clustering Algorithm (FCM) by Bezdek et al. (1984) was used to classify the (partial) make-up of learners' reported intuitions into fuzzy sets based on attribute similarity.