Learning progressions detail the incremental steps that students take as they learn to master a skill. These progressions are based on developmental research about how students learn and how their thinking develops as a result of instruction. A typical progression not only describes the stages that students must master, but it also shows what…

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…

This article promotes the use of mathematically appropriate, engaging and challenging tasks to support learning that is worthwhile. The authors share insights from a three-lesson design experiment and the three tasks along with the results from their implementation are explored.

This annotated bibliography is a compilation of the research on programed instruction conducted in the United States since 1954. The introduction describes the field; looks back over the research and reviews some of its conclusions; answers the question whether students learn from programmed instruction; explains the characteristic variables; and…