It is easy to dismiss the work of "teaching students to apply formula" as a low-order priority and thus trivialises the professional knowledge associated with this practice. Our encounter with an experienced teacher--through the examination of her practices and elaborations--challenges this simplistic assumption. There are layers of…

This study investigated the effectiveness of using a sequence of worked examples as part of the feedback cycle. Worked examples were either presented as full worked examples or partial worked examples (single-step and completion formats). In two experiments, grade 8 students completed a learning phase on a mathematics topic, which was immediately…

In this article we advance characterizations of and supports for elementary students' progress in generalizing and representing functional relationships as part of a comprehensive approach to early algebra. Our learning progressions approach to early algebra research involves the coordination of a curricular framework and progression, an…