Children's patterning skills and their roles in mathematics learning

Abstract

Patterning skills, the ability to detect the regularities from a sequence of elements arranged in a predictable manner, are referred as fundamental to early mathematic learning. Yet, it remains elusive about the association between different aspects of patterning ability and specific mathematics abilities, the cognitive mechanisms of how patterning skills support mathematics learning, and the role of home factors in the development of early patterning skills. Hence, this thesis aimed to provide a broader picture of patterning development and its contribution to mathematics learning. Study 1 aimed to investigate the longitudinal links between different patterning skills and different mathematics abilities, and the role of spatial skills in these links. Study 2 aimed to examine the contribution of home factors on children’s patterning skills. Study 3 was a cross-cultural study which aimed to evaluate the association between patterning skills, spatial skills, number line estimation ability, and various mathematics abilities among elementary school students in Hong Kong and Montreal.

Study 1, which collected longitudinal data at three time points (T1, T2, and T3) across the second and third year of kindergarten, tested children with multiple types of patterns, namely repeating patterns, spatial structure patterns, and growing patterns. The factor structure of patterning skills was best fit when using task natures, i.e., duplication, extension, generalization, and unit recognition. Children’s performance of pattern duplication at T1 and pattern extension at T2 predicted multiple mathematics abilities at T3. Also, patterning skills were found to be a mediator relating spatial abilities and mathematics performance.

Study 2 focused on the influence of home factors at T1 on children’s patterning skills at later time points. Parents’ attitudes towards spatial and patterning activities explained individual differences in the frequency of categorization activities at home, which predicted children’s performance in pattern unit recognition at T2. Surprisingly, the frequency of patterning activities at home negatively predicted children’s performance in pattern extension at T3. It was likely that the quality of patterning input at home matters more than the quantity. Furthermore, spatial ability remained as a unique predictor of patterning skills when considering the effect of home factors.

Study 3, a cross-cultural study in Hong Kong and Montreal, focused on the patterning skills of elementary school students aged 6 to 11 and their relationships with spatial abilities, number line estimation performance, and mathematics abilities. Across the two cultures, patterning skills significantly predicted performance in numeration, geometry, addition and subtraction, and applied problem solving. Also, number line estimation ability played a mediator role relating patterning and numeration. Similar to the finding in Study 1, patterning skills mediated the link between spatial ability and geometry. Cultural difference existed in the mediator role of number line estimation ability in the relation between patterning and addition and subtraction, and applied problem solving.

Collectively, this thesis showed that patterning skills contribute uniquely to both kindergarteners’ and elementary children’s mathematics achievement via different cognitive mechanisms. The present findings provide implications for considering patterning skills as a key construct in learning and teaching mathematics before and during formal schooling.