Although hypothetical learning trajectories (HLTs) are often viewed as a valuable instructional tool, little research has directly evaluated their value. A basic assumption of HLTs is that ordering instructional activities by developmental difficulty enhances learning. A randomized control trial (RCT) served to evaluate this assumption with a…

Although basing instruction on a learning trajectory (LT) is often recommended, there is little direct evidence to support the premise of a "LT approach"--that to be maximally meaningful, engaging, and effective, instruction is best presented one LT level beyond a child's present level of thinking. The present report serves to address…

Although basing instruction on learning trajectories (LTs) is often recommended, there is little direct evidence regarding the premise of an LT approach--that instruction should be presented (only) one LT level beyond a child's present level. We evaluated this hypothesis in the domain of early shape composition. One group of preschoolers, who were…

How should a wide variety of educational activities be sequenced to maximize student learning? Although some experimental studies have addressed this question, educational data mining methods may be able to evaluate a wider range of possibilities and better handle many simultaneous sequencing constraints. We introduce Sequencing Constraint…

In this paper, we describe our learning progressions approach to early algebra research that involves the coordination of a curricular framework, an instructional sequence, written assessments, and levels of sophistication describing the development of students' thinking. We focus in particular on what we have learning through this approach about…