The construction of general terms for shape patterns: strategies adopted by children attending Fourth class in two Irish primary schools

Generalisation is considered by many to be a highly significant component of algebraic thinking (Carpenter & Levi, 2000; Kaput et al., 2008). In particular, constructing general terms for shape patterns supports children in reasoning algebraically about covariance and rates of change (Rivera & Becker, 2011). Generalisation is not mentioned within the current Irish Primary School Mathematics Curriculum, and shape patterns are not presented as learning activities, beyond simple repeating patterns explored with very young children (Government of Ireland, 1999). This thesis reports on a research study that explored the strategies Irish children adopted in seeking to construct general terms for shape patterns. Within the context of task-based group interviews, patterning tasks were presented to groups of three or four children (aged nine or ten years old), where the children were asked to describe and extend the patterns, and to consider near and far generalisations. Following the interviews I analysed the strategies that children used to generalise from the patterns, drawing from the work of Lannin (2005) and Rivera and Becker (2011). Taking a hermeneutic phenomenological approach, I included identification and analysis of factors that contributed to children’s strategy choices, which included explicit, recursive, numerical and figural approaches. Findings evidence the potential of children to respond in complex and sophisticated ways to novel tasks, when rich engagement with the mathematics was facilitated through the context of a task-based group interview. The research study demonstrates the necessity for conceptualising children’s thinking as multi-faceted whereby observations of relationships within patterns interact with attention to numerical and figural aspects. In addition, evidence is presented to support the contention that observations of structure exist along a continuum from numerical to figural. The study highlights the potential of task-based group interviewing coupled with hermeneutic phenomenological analysis in facilitating in-depth research into children’s emerging mathematical thinking