Patterns that support early algebraic thinking in the elementary school

Over a period of three years, the authors conducted an extensive longitudinal study in Australia aimed at ascertaining teachers' actions, activities, questions, and conversations that support the development of early algebraic thinking in the elementary (primary) school classroom. The study was conducted in five classrooms and consisted of teaching experiments focused on the development of an understanding of equivalence and equations, functional thinking, patterning, and generalised arithmetic. In this article, they report on one of those experiments involving repeating patterns and geometric growing patterns. As the authors began their work, they were aware that students spend a great deal of time in their early years in school investigating repeating patterns, but they have little experience with geometric growing patterns. There are three major reasons for exploring geometric growing patterns in the elementary school classroom: (1) they are visual representations of number patterns, (2) they can be used as an informal introduction to the concept of a variable, and (3) they can be used to generate equivalent expressions. The specific purpose of the study was to identify and characterise activities that help elementary school students distinguish repeating patterns from growing patterns, to establish relationships between data sets, to extend patterns, and to develop an awareness of the synergy between patterns and tables of values. The article is organised by mathematical idea and illustrated with activities and students' work. They begin by describing how they distinguished repeating patterns from growing patterns.