Abstract
Current research and professional organizations call for greater emphasis on reasoning and sense making in algebra (Chazan, 2000; Cuoco, Goldenberg, & Mark, 1996; Harel & Sowder, 2005; National Council of Teachers of Mathematics [NCTM], 2009, 2010). This paper illustrates how students in an Algebra II class had opportunities to develop their reasoning and sense making skills while discussing a problem about piecewise linear functions in small groups. In particular, students displayed a capacity for provoking each other to extend their prior knowledge, for making use of multiple representations, and for making connections with their non-mathematical prior experiences. We discuss the teacher’s work in encouraging specific reasoning skills to support individual groups’ work on the problem. We argue that a teacher’s implementation of tasks that allow students the autonomy to work productively and promote student discussions of a problem can provide an avenue through which students in algebra may develop their reasoning and sense making skills.
