F.D. Rivera has written an article called Visual templates in pattern generalization activity. The article was published online in Educational Studies in Mathematics last Thursday. The study, which is described in the article, was carried out in an eighth-grade Algebra 1 class in California. Four and a half months after a teaching experiment on pattern generalization, 11 students were interviewed (clinical interviews). Clinical interviews were also made with these students directly before and after the teaching experiment. The article reports on results from the analyses of these clinical interviews.

Here is the abstract of the article:

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 design-driven 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.