Chapter 6: Exploring the Relationship Between Learning Trajectories and Curriculum: A Content Analysis of Rational Number Reasoning in Connected Mathematics and UCSMP Transition Mathematics

This chapter considers the relationship between learning trajectories and curriculum through an analysis of the rational number reasoning content of two middle school mathematics curricula (Connected Mathematics and UCSMP Transition Mathematics) using a learning trajectories perspective. The content analysis revealed that the two curricula approached rational number reasoning differently. Connected Mathematics tended toward a “many-to-one” approach where rational number was developed as ratio, while Transition Mathematics tended toward a many-to-one approach where rational number was developed as a point on the number line. Neither curriculum included a full learning trajectories development of rational number as defined by Confrey’s (2008) construct map of rational number understanding. Based on the content analysis, an argument is made that research-based learning trajectories are a useful mediational tool that can reveal gaps within a curriculum. Practically, learning trajectories can thus assist teachers to modify their written curriculum to include the missing content, address common misconceptions, and bridge to new content consistent with research in the field of mathematics education.