Scenarios of students using manipulatives to explore and justify mathematical ideas show how they are poised to generate effective proofs.
Kristen N. Bieda, email@example.com, teaches at Michigan State University in East Lansing. Her interests include supporting middle school teachers in enacting core mathematical practices with their students, in particular, the practices of justifying and proving. The ideas presented in this article come directly from results of a study that examined the implementation of problems from the Connected Mathematics Project (CMP) curriculum (Lappan et al. 2002), designed to develop students' competencies to justify and prove their conjectures.