To invest in the future of mathematics education is to invest in our future teachers. Equipping such individuals should be the utmost priority, for they will communicate mathematics to our students. Research shows that the way we work with and explain mathematics is consequential to our proof scheme; that is, the proof schemes we hold are the proof schemes we will inevitably teach. This study explores the possible proof schemes and mindsets held by ten university students studying mathematics education at Lee University--six enrolled in a geometry course and four in an algebra course. Through interviews and critical thinking exercises, we analyzed the future students\u27 proof schemes and views on mathematics. Our analysis found that participants who had encountered proof-based mathematics courses had a tendency to approach problems analytically, which implied the existence of an association between their definitions of proof and methods of problem-solving. This relationship perhaps has implications about teacher preparation and development prior to entering the classroom, thus revealing its significance to student success
