Early Awareness of Mathematical Pattern and Structure

Abstract

This chapter provides an overview of the Australian Pattern and Structure Project, which aims to provide new insights into how young students can abstract and generalize mathematical ideas much earlier, and in more complex ways, than previously considered. A suite of studies with 4- to 8-year old students has shown that an awareness of mathematical pattern and structure is both critical and salient to mathematical development among young students. We provide a rationale for the construct, Awareness of Mathematical Pattern and Structure (AMPS), which our studies have shown generalizes across early mathematical concepts, can be reliably measured, and is correlated with mathematical understanding. A study of Grade 1 students and follow up case studies enabled us to reliably classify structural development in terms of a five structural levels. Using a Pattern and Structure Assessment (PASA) interview involving 39 tasks, students identified, visualized, represented, or replicated elements of pattern and structure. Students with high AMPS are likely to have a better understanding of Big Ideas in mathematics than those with low AMPS. They are likely to look for, remember and apply spatial and numerical generalizations and in particular are likely to grasp the multiplicative relationships that underlie the majority of the concepts in the elementary mathematics curriculum.