Analysis of 5-6-year-olds' responses to repeating, growing and spatial patterning tasks

EARLI symposium: Supporting preschoolers’ patterning competences: teaching practices and professional development

Mathematical patterns and structural thinking have been shown to co-develop, but the complexity of different forms of pattern reveals wide variation in individual’s understanding of pattern beyond composite unit structure. A general construct, Awareness of Mathematical Pattern and Structure (AMPS) has described the role of patterning, structural relationships and emergent generalization in early mathematics (Mulligan & Mitchelmore, 2009). Our broad aim is to develop learning and instructional strategies that promote AMPS from an early age. This study analyses AMPS levels of response from interview-based patterning tasks: Repeating, Border, Triangular, Rotational and Growing across a sample of 173 Kindergarten and 196 Grade 1 Australian students, aged from 5y 9mo to 6y 11mo. Analysis of five increasing levels of structure in responses demonstrated links between patterning and spatial, and multiplicative structure, and between Repeating and Rotational patterns. Our findings confirm that the unit of repeat is fundamental and supports multiplicative thinking, and there are some developmental features including engagement in growing patterns identified in recent studies. We found complex conceptual connections depended on pattern type and depth of analysis. Pattern types that required visualization, prediction, or dynamic processes such as ‘growing’ or ‘moving’ were identified, and accounted for differences in response levels in novel ways. These findings contribute to more extensive application and evaluation of learning and instruction based on patterns, and the impact of the Pattern and Structure Mathematics Awareness Program (PASMAP) at scale and in more diverse contexts.