Investigating Individual Differences in and Measurement of Adaptive (Rational) Number Knowledge in a Sample of High School Students

Abstract

This thesis examines the performance of a sample of 447 Grade 9-12 students on three different measures of adaptive number knowledge (ANK) with both whole numbers and rational numbers. The aims were to establish whether adaptive whole number knowledge and adaptive rational number knowledge (ARNK) were distinct constructs, to investigate individual differences in A(R)NK in this age group, and to evaluate a new measurement instrument for A(R)NK. The research produced three major findings. First, an exploratory factor analysis of the results on the arithmetic sentence production (ASP) task revealed that adaptive whole number knowledge and adaptive rational number knowledge were not distinct. Second, participant performance on the ASP task was examined using TwoStep cluster analysis and several statistical tests. It was found that the sample performance could be described by a five-cluster model, and membership of high-achieving clusters was strongly associated with mathematics module enrolment and gender, but not with age or school grade. Third, another exploratory factor analysis found that the test comprising of the ASP task and two new tasks was unidimensional, which suggested that all three tasks may measure adaptive number knowledge. The three-task test is therefore a strong candidate for further evaluation and refinement in the quest for a more comprehensive measure of adaptive number knowledge. Each of the three tasks was also examined closely and suggestions for improvements in future iterations of the test were given.