Network-Based Trajectory Analysis of a Precalculus Course

We employ a network theory mediated analysis to investigate the affordances of a precalculus curriculum, exemplified by the Pathways precalculus textbook and, in particular, its alignment with the research-based Algebra and Precalculus Concept Readiness Taxonomy (referred to as APCR). A network perspective of the precalculus curriculum has been helpful in identifying key features of the subject as they appear in several precalculus texts including the one being studied here by Carlson et al. Of these, “hubs” have been particularly useful in mapping the alignment between the preset goals of the precalculus course, as identified in the previous literature, and its execution. Probabilistic tools, such as cumulative distribution functions, prove to be effective in analyzing the distribution and accumulation of precalculus content throughout the APCR and CCR. At the same time, this analysis has also been valuable in identifying the trajectory of the textbook curriculum in adequately preparing students for success in calculus.