Visual templates in pattern generalization activity

Abstract

In this research article, I present evidence of the existence of visual templates in pattern generalization activity. Such templates initially emerged from a 3-week designdriven classroom teaching experiment on pattern generalization involving linear figural patterns and were assessed for existence in a clinical interview that was conducted four and a half months after the teaching experiment using three tasks (one ambiguous, two well defined). Drawing on the clinical interviews conducted with 11 seventh- and eighth-grade students, I discuss how their visual templates have spawned at least six types of algebraic generalizations. A visual template model is also presented that illustrates the distributed and a dynamically embedded nature of pattern generalization involving the following factors: pattern goodness effect; knowledge/action effects; and the triad of stage-driven grouping, structural unit, and analogy. © 2009 Springer Science+Business Media B.V.