Student Experiences of Graph Theory Research in a Transition-to-Proofs Course

In this study, we report on a pure mathematics Course-Based Undergraduate Research Experience (CURE) implemented within a transition-to-proof course where students learned about graph theory research. Through the CURE, students worked independently and collaboratively as they learned about fundamental concepts of graph theory, watched videos of graph theorists discussing their work, and made sense of a theorem from published research papers. Seventeen students agreed to participate in a research study designed to understand students’ CURE experiences and the impact of the CURE on their understandings of the nature of mathematics. Through qualitative research methods such as coding and thematic analysis, the researchers found that participants learned about the practices of mathematicians, were impressed with the time and effort mathematicians put into proving the conjectures, and believed they developed skills and confidence to pursue advanced mathematics. While CUREs offer novel learning opportunities, they also present varying challenges for students who will respond according to their backgrounds, beliefs, and aspirations. In conclusion, we suggest that definitions of CURE in mathematics education should be revised to be inclusive rather than restrictive, so that the greatest number of students can learn about and experience mathematical research.