Leiden University Scholarly Publications

Hickendorff, M. (2011)

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

Doctoral Thesis

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...Show moreThis 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.Show less

Arithmetic

Explanatory variables

Item response theory

Latent class analysis

Mathematics education

Strategy adaptivity

Strategy choice

Word problems

All authors

Hickendorff, M.

Supervisor

Heiser, W.J.

Co-supervisor

Putten, C.M. van; Verhelst, N.D.

Committee

-

Qualification

Doctor (dr.)

Awarding Institution

Department of Psychology, Faculty of Social and Behavioural Sciences, Leiden University

Date

2011-10-25

ISBN (print)

9789088913266

Juridical information

Court

LEI Universiteit Leiden

Funding

Sponsorship

Cito, National Institute for Educational Measurement