This paper focuses on pattern generalisation as a way to introduce young students to early algebra. We build on research on patterning activities that feature, in their work with algebraic thinking, both looking for sameness recursively in a pattern (especially figural patterns, but also numerical ones) and conjecturing about function-based…

This paper comments on the expanded repertoire of techniques, conceptual frameworks, and perspectives developed to study the phenomena of gesture, bodily action and other modalities as related to thinking, learning, acting, and speaking. Certain broad issues are considered, including (1) the distinction between "contextual" generalization of…

The transition from arithmetic to algebra in general, and the use of symbolic generalizations in particular, are a major challenge for beginning algebra students. In this article, we describe and analyze students' learning in a "computer intensive environment" designed ad hoc and implemented in two seventh grade classrooms throughout two…