RUME 28
2026
Alexandria, Virginia
Conceptual Blending as a Problem-Solving Tool in Topology
Page: 617
The topic of topology is an important and unique course in advanced mathematics that carries two simultaneous complexities: logical proof and spatial reasoning. While proof and problem-solving are two areas that are well documented in mathematics education research, topology itself is a fairly rare topic to appear in the literature of mathematics education written in English. To address the gap in the literature, this paper analyzes a study in which two students attempt a topology question in order to understand their problem-solving techniques and how they leverage their various forms of thinking. We networked the theories of Tall’s Three Worlds of Mathematical Thinking and Cognitive Blending to describe the participants’ behaviors. The results showed that students leveraged a blend of their thinking to progress through the proof.