RUME 27
2025
Alexandria, Virginia
Reasoning Beyond Content-Specific Objects: A Case Study of One Student's Structural Thinking
Page: 1115
In all levels of mathematics, especially beginning at the undergraduate level, structural thinking is pivotal for deeper understanding or more complex reasoning about the relevant mathematical concepts. In this preliminary research study, we investigated the structural thinking of one advanced undergraduate mathematics student as he conjectured the definitions of various concepts in graph theory. We observed various affordances and obstacles to his structural thinking. Affordances included his attention to a general structural property and his use of analogical reasoning with corresponding structures in group theory and point-set topology. Obstacles included utilizing a constrained example space and relying on his familiarity with previously encountered mathematical concepts.