Complex sequences are ubiquitous in human mental life, structuring representations within many different cognitive domains--natural language, music, mathematics, and logic, to name a few. However, the representational and computational machinery used to learn abstract grammars and process complex sequences is unknown. Here, we used an artificial…

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…