Solution Strategies and Achievement in Dutch Complex Arithmetic: Latent Variable Modeling of Change

• Published in: Psychometrika 2009-06, Vol.74 (2), p.331-350
• Main Authors: Hickendorff, Marian, Heiser, Willem J., van Putten, Cornelis M., Verhelst, Norman D.
• Format: Article
• Language: English
• Subjects: Addition & subtraction; Algorithms; Application Reviews and Case Studies; Arithmetic; Assessment; Behavioral Science and Psychology; Biological and medical sciences; Division; Educational evaluation; Educational Objectives; Educational psychology; Educational tests & measurements; Elementary School Students; Foreign Countries; Fundamental and applied biological sciences. Psychology; Gender Differences; Grade 6; Humanities; Investigations; Item Response Theory; Law; Learning; Learning Strategies; Mathematics Achievement; Mathematics education; Mental Computation; Multiplication & division; National Competency Tests; Netherlands; Primary Education; Problem Solving; Psychology; Psychology. Psychoanalysis. Psychiatry; Psychology. Psychophysiology; Psychometrics; Psychometrics. Statistics. Methodology; Pupil and student. Academic achievement and failure; Scores; Statistical Analysis; Statistical Theory and Methods; Statistics for Social Sciences; Statistics. Mathematics; Students; Testing and Evaluation; Trends
• ISSN: 0033-3123; 1860-0980
• DOI: 10.1007/s11336-008-9074-z

In the Netherlands, national assessments at the end of primary school (Grade 6) show a decline of achievement on problems of complex or written arithmetic over the last two decades. The present study aims at contributing to an explanation of the large achievement decrease on complex division, by investigating the strategies students used in solving the division problems in the two most recent assessments carried out in 1997 and in 2004. The students’ strategies were classified into four categories. A data set resulted with two types of repeated observations within students: the nominal strategies and the dichotomous achievement scores (correct/incorrect) on the items administered. It is argued that latent variable modeling methodology is appropriate to analyze these data. First, latent class analyses with year of assessment as a covariate were carried out on the multivariate nominal strategy variables. Results showed a shift from application of the traditional long division algorithm in 1997, to the less accurate strategy of stating an answer without writing down any notes or calculations in 2004, especially for boys. Second, explanatory IRT analyses showed that the three main strategies were significantly less accurate in 2004 than they were in 1997.