Learning trajectories: a framework for connecting standards with curriculum

Abstract Educational Standards provide a statement of educational competency goals. How to integrate such goal statements with the instructional core, in ways that promote curricular and instructional coherence and continuity of student learning, is a perennial challenge. In the United States, the Common Core State Standards for Mathematics, or CCSS-M, have been widely adopted, and are claimed to be based on research on learning in general and on learning trajectories in particular. The relationships, however, are tacit and incompletely, and sometimes controversially, articulated. This paper describes a body of work that associates the first nine grades of Standards (K-8) to eighteen learning trajectories and, for each learning trajectory, unpacks, interprets, and fills in the relationships to standards with the goal of bringing the relevant research to teachers (TurnOnCCMath.net). The connections are made using a set of descriptor elements, comprised of conceptual principles, coherent structural links, student strategies, mathematical distinctions or models, and bridging standards. A more detailed description of the learning trajectory for equipartitioning (EQP) shows the detailed research base on student learning that underpins a particular learning trajectory. How curriculum materials for EQP are designed from the learning trajectory completes the analysis, illustrating the rich connections possible among standards, descriptors, an elaborated learning trajectory, and related curricular materials.