Interacting with Algebra: Mathematicians, Mathematics Educators, and Teachers Making Sense of Algebra Content

Abstract

This dissertation examines the interactions of mathematicians, mathematics educators, and teachers with a set of 12 algebra problems. The data are from two Making Connections workshops (2006 and 2008) which included members of these three professional groups; each workshop was comprised of 13 participants. The primary analytical focus was a task in which each professional group separately discussed and categorized the 12 algebra problems; interviews were conducted with the participants from the 2008 workshop. The methods and analysis of this study were framed by research on the teaching and learning of algebra, on curriculum use as a participatory relationship, and on the dispositions and beliefs of members of the three professional groups.The study indicated that teachers, as compared to the other two groups, drew more heavily upon their knowledge of students as they made sense of the algebra problems. Teachers were at times concerned with the wording of questions as an obstacle for students. The mathematicians and mathematics educators put a greater focus on algebraic structure as they discussed the problems whereas the teachers put a greater focus on graphing. I connect these findings to the workshop participants' views of algebra.