Mathematics majors, including future secondary teachers, should understand the work of pure mathematicians and the crucial role proof plays for the discipline of mathematics. Beyond the textbook proofs seen in most transition-to-proof courses, we conjectured that students might develop a deeper understanding of the discipline of mathematics and proof if they had the opportunity to do mathematical research--to try and prove an unsolved conjecture. As an added component of our transition-to-proof course, we designed an intervention so that students researched the Twin Primes conjecture or the Collatz conjecture. Students wrote reflections about their research and described how their perceptions of mathematics were influenced by the research. We analyzed the reflections and sought to understand how the students' views of mathematics and proof were enriched, if at all, through research on unsolved conjectures. [For the complete proceedings, see ED629884.]