One study compared the reading and learning strategies of successful and unsuccessful students. Successful students spend more time processing the definition by describing it in their own words and relating it to other concepts they are learned, understanding what a theorem is asserting prior to reading its proof, and understanding what a statement is asserting and why it is true prior to writing a proof. Less successful students are more likely to view the arguments they read as “templates” for solutions to be produced at a later time.
K. Weber, A. Brophy, and K. Lin (2008). How do Undergraduates Learn about Advanced Mathematical Concepts by Reading Text? In Proceedings of the 11th Conference for Research in Undergraduate Mathematics Education. (http://www.rume.org/crume2008/weber_long.pdf)
(This paper was awarded the honorable mention as the second best paper of the conference).
K. Weber (2009). Mathematics Majors' Evaluations of Mathematical Arguments and Their Conceptions of Proof. To Appear in Proceedings of the 12th Conference for Research in Undergraduate Mathematics Education.
K. Weber (2009). Proving is not Convincing. To Appear in Proceedings of the 12th Conference for Research in Undergraduate Mathematics Education.