According to the NCTM Standards (2000), conjecturing and proving should be central activities throughout students' mathematical education. However, the question of how we can help students generate proofs, especially the formal proofs expected at the high school level, is still a difficult one. In this article, we argue that one cause of students' troubles with proof is that they are not accustomed to making the important, but difficult, connections between their intuitive sensemaking and the formal proofs they are supposed to produce. Thus as teachers, we should provide opportunities for students to make these connections.
Manya Raman, firstname.lastname@example.org, is an assistant professor of mathematics and mathematics education at Rutgers University.
Keith Weber, email@example.com, is an assistant professor of mathematics education at Rutgers University. They are interested in describing the reasoning used in constructing proofs and having students engage in this reasoning in their classrooms.