Explanatory latent variable modeling of mathematical ability in primary school : crossing the border between psychometrics and psychology

Abstract

This thesis focuses on primary school students’ mathematical ability in the Netherlands. Starting with a systematic research synthesis of performance outcomes of different mathematics programs in Chapter 1, the remaining Chapters 2 to 7 report the results of six empirical studies. These studies address the determinants of students’ ability in the domain of arithmetic (addition, subtraction, multiplication, and division). Moreover, they can be said to cross the border between the academic fields of substantive (educational and cognitive) psychology on the one hand, and psychometrics on the other. Chapters 2 and 3 report on the results of secondary analyses on data collected for CITO’s national mathematics assessment in grade six (12-year-olds) focusing on the strategies students used to solve the problems. Chapters 4 and 5 aimed to more systematically investigate the distinction between mental and written solution strategies for solving division problems. Finally, Chapters 6 and 7 address the role of realistic contexts in mathematics problems, both for students in early grades as well as in grade six. The data analyzed in the empirical studies are complex, requiring advanced psychometric modeling. It is argued that latent variable models incorporating explanatory variables are appropriate to analyze data on solution strategies and performance.