@article{confrey_gianopulos_mcgowan_shah_belcher_2017, title={Scaffolding learner-centered curricular coherence using learning maps and diagnostic assessments designed around mathematics learning trajectories}, volume={49}, ISSN={["1863-9704"]}, DOI={10.1007/s11858-017-0869-1}, number={5}, journal={ZDM-MATHEMATICS EDUCATION}, author={Confrey, Jere and Gianopulos, Garron and McGowan, William and Shah, Meetal and Belcher, Michael}, year={2017}, month={Oct}, pages={717–734} }
 @article{confrey_maloney_gianopulos_2017, title={Untangling the "Messy Middle" in Learning Trajectories}, volume={15}, ISSN={["1536-6359"]}, DOI={10.1080/15366367.2017.1404370}, abstractNote={In “Tracing the Assessment TriangleWith Learning Progression-Aligned Assessments in Mathematics,” Lai, Kobrin, and DiCerbo present a learning trajectory on the measurement of area, a topic typically introduced in third and fourth grades. Proposing a five-level progression, they investigated student behavior and thinking in two studies: (1) cognitive think-aloud interviews using paper and pencil tasks and response-pattern coding and (2) computer-based tasks, digital data collection, and latent class analysis. Overall, the researchers find a reasonable degree of confirmation for the first and fifth levels of their LP, and support for the relevance, but nonrigid sequencing, of the middle levels. We commend the authors on the clear conceptualization of their ambitious scope of work. The well-organized and systematic report balances confirmatory and contrary evidence. Based on their conceptualization of the LP, they cleverly used digital-environment affordances to design data gathering on the underlying processes. We comment on two fundamental themes from LP research: (1) the structure of an LP relative to the “messy middle” and (2) the interaction of grain size and cognitive goals.}, number={3-4}, journal={MEASUREMENT-INTERDISCIPLINARY RESEARCH AND PERSPECTIVES}, author={Confrey, Jere and Maloney, Alan and Gianopulos, Garron}, year={2017}, pages={168–171} }