Chapter 7: Articulated Learning Trajectories: A Framework for Mathematical Content Analyses

The research reported in this chapter is based on a mathematical content analysis using an articulated learning trajectory (ALT) framework, used here to identify the textual development of algebraic thinking concepts through instances of content involving patterning constructs in four middle-school textbook series—Connected Mathematics 2 (Lappan, Fey, Fitzgerald, Friel, & Phillips, 2009), Mathematics: Applications and Concepts (Bailey et al., 2006), MathThematics (Billstein & Williamson, 2008), and Saxon Math (Hake, 2007). The ALT framework is discussed and delineated as it pertains to this study, and key findings are presented. Differences were found in the number of instances involving patterning constructs and contexts, in the textual placement and emphasis of particular patterning constructs and contexts, and in the development of algebraic thinking concepts. Working visual models for ALTs are presented, and implications are discussed for studies and professional development regarding the implemented curriculum, learning trajectory-based studies of students’ knowledge development, alignment studies with respect to the learning trajectories within the Common Core State Standards for Mathematics, and the use of the ALT framework in mathematics teacher education programs.