Graded Pattern Generalization Processing of Elementary Students (Ages 6 Through 10 Years)

Abstract

In this chapter, we focus on pattern generalization studies that have been conducted with elementary school children from Grades 1 through 5 (ages 6 through 10 years) in different contexts. Our contribution to the current research based on elementary students’ understanding of patterns involves extrapolating the graded nature of their pattern generalization schemes on the basis of their constructed structures, incipient generalizations, and the use of various representational forms such as gestures, words, and arithmetical symbols in conveying their expressions of generality. The gradedness condition foregrounds the dynamic emergence of parallel types of pattern generalization processing that is sensitive to a complex of factors (cognitive, sociocultural, neural, constraints in curriculum content, nature and type of tasks, etc.), where progression is seen not in linear terms but as states that continually evolve based on more learning. In a graded pattern generalization processing view, there are no prescribed stages or fixed rules but only states of conceptual coalescences and coherent covariations that change with more experiences. The chapter addresses different aspects of pattern generalization processing that matter to elementary school children. We also explore approximate and exact pattern generalizations along three dimensions, namely: whole number knowledge, shape sensitivity, and figural competence. We further discuss the representational modes that elementary students oftentimes use to capture their emergent structures and incipient generalizations. These modes include gestural, pictorial, verbal, and numerical. In another section, we address grade-level appropriate use and understanding of variables via the notions of intuited and tacit variables. We close the section with an analysis of the relationship between elementary children’s structural incipient generalizations and the natural emergence of their understanding of functions.