Patterns Across the Years—Singapore Learners’ Epistemology

Abstract

Pattern has a prominent position in the Singapore mathematics curriculum. This chapter reports how learners across the grades thought about patterns, how they recognised patterns, and how they constructed rules to describe the structure underpinning specific patterns. The corpus of data came from four studies. Primary children participated in the first three studies: Age and Individual Differences, Forward and Backward Rule, Colour Contrast whilst Secondary 2 students participated in the fourth, Strategies and Justifications in Mathematical Generalization. All these studies used the mathematics curriculum to design grade-specific mathematical tasks. In general, two types of pattern tasks were used, number patterns presented in tandem with figures and figural patterns. Data with primary children were collected using paper-and-pencil task and clinical interviews were used to collaborate their responses. The fourth study analysed the written responses of the secondary students to paper-and-pencil task. These studies found that learners focused on the surface features to arrive at a rule to describe these number patterns. In the colour-contrast study, compared with monochromatic presentation, those using two colours encouraged learners to present possible general rules. The more able academic stream secondary students were able to arrive at general rules for linear figural patterns. However, all students across the academic spectrum were challenged by quadratic patterns. Findings from the four suggest that it important for teachers to know how to move learners to look for the structure underpinning patterns, numerical and figural, and to construct the all-important general rule.