This paper describes a professional development experience designed to help teachers support their students to make, represent, and justify generalizations about the behavior of the operations. We report on the pre- and post-assessments of 36 teachers who participated in an online course and implemented what they were learning in their classrooms across a full school year, and of the 600 students in their classrooms versus a comparison group. Participating teachers improved significantly in articulating general claims about the operations, representing mathematical ideas, and using mathematical language and notation. Their students, particularly those in grades 3-5, provided significantly more relational explanations on post-assessment items than comparison students. We consider what characteristics of the professional development may account for these results.

This paper is based on work from the project, Foundations of Algebra in the Elementary and Middle Grades: Supporting Students to Make, Represent, and Justify General Claims about Operations, supported in part by the National Science Foundation under Grant ESI-0550176. Any opinions, findings, and conclusions or recommendations expressed in this paper are those of the authors and do not necessarily reflect the views of the National Science Foundation.