Learning Trajectory Based Instruction: Toward a Theory of Teaching

In this article, we propose a theoretical connection between research on learning and research on teaching through recent research on students' learning trajectories (LTs). We define learning trajectory based instruction (LTBI) as teaching that uses students' LTs as the basis for instructional decisions. We use mathematics as the context for our argument, first examining current research on LTs and then examining emerging research on how mathematics teachers use LTs to support their teaching. We consider how LTs provide specificity to four highly used frameworks for examining mathematics teaching, namely mathematical knowledge for teaching, task analysis, discourse facilitation practices, and formative assessment. We contend that by unifying various teaching frameworks around the science of LTs, LTBI begins to define a theory of teaching organized around and grounded in research on student learning. Thus, moving from the accumulation of various frameworks into a reorganization of the frameworks, LTBI provides an integrated explanatory framework for teaching.