Mathematics Majors' Exploration of Famous Conjectures in a Transition-to-Proof Course.

For a semester within a transition-to-proof course, mathematics majors explored two famous conjectures: The Twin Primes Conjecture and the Collatz Conjecture. Students were scaffolded into exploring the conjectures through directed activities but were also expected to create their own methods of exploration. We documented students' experiences working on the conjectures in order to understand how their perceptions of the nature of mathematics (NOM) were enriched through the project. Some students learned about conjectures for the first time and, although it was challenging for students to create their own methods of exploration, most students productively engaged with the conjectures in creative ways. Students enjoyed exploring mathematics and thinking outside the box. They also came to better understand what goes on behind the scenes of mathematics and came to appreciate and identify with mathematicians. Overall, students had a deeper understanding of NOM after working on unsolved conjectures. [ABSTRACT FROM AUTHOR]