The role of spatial reasoning in growing and spatial-repeating patterns in first and second graders' structural development of mathematics

A cross-sectional qualitative study examined how different pattern types accounted for wide variation in children’s Awareness of Mathematical Pattern and Structure (AMPS), illustrating how spatial and patterning skills are interrelated. An interpretive descriptive analysis of responses was conducted for two interview-based Growing Square Array (GA) and Spatial-Repeating Pattern (SP) tasks with 405 children from Grade 1 (n = 189) and Grade 2 (n = 216). Analysis of developmental levels of AMPS indicated that advanced multiplicative spatial structures were employed in GA patterns for 20% of Grade 1 and 35% of Grade 2 children, respectively. Responses to SP tasks extended beyond the ‘unit of repeat’ to the use of dynamic visualization, and orientation and transformation skills for 60% of children. Responses showing advanced structural features moderately increased at Grade 2 for both tasks. Micro-level analyses of illustrations of interview responses and from a Pattern Construction task, drawn from five case studies, revealed how multiplicative and transformation skills were utilized in forming repetitions and growing patterns in complex and novel ways. While the ‘unit of repeat’ is fundamental, the integration of more complex multi-dimensional patterning with spatial concepts can re-focus learning and pedagogy on establishing interrelationships between patterning and spatial concepts, and broader mathematical knowledge.