Background and Context: We explored how learning trajectories (LTs) might be used to design variables instruction. Objective: We aimed to develop an LT for variables and use it to guide curriculum development for fourth graders working in Scratch in an integrated mathematics+CS curriculum. Method: We synthesized learning goals (LGs) and levels of…

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…