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

Published online by Cambridge University Press:  01 January 2025

Marian Hickendorff ,
Willem J. Heiser ,
Cornelis M. van Putten  and
Norman D. Verhelst
Marian Hickendorff*
Affiliation:
Leiden University
Willem J. Heiser
Affiliation:
Leiden University
Cornelis M. van Putten
Affiliation:
Leiden University
Norman D. Verhelst
Affiliation:
CITO, National Institute for Educational Measurement
*
Requests for reprints should be sent to Marian Hickendorff, Division of Methodology and Psychometrics, Institute for Psychological Research, Leiden University, P.O. Box 9555, 2300 RB, Leiden, The Netherlands. E-mail: hickendorff@fsw.leidenuniv.nl
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Abstract

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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.

Keywords

covariatepredictorexplanatory IRTlatent class analysisrepeated categorical observationsincomplete designmathematics education
Type
Application Reviews and Case Studies
Information
Psychometrika , Volume 74 , Issue 2 , June 2009 , pp. 331 - 350
Creative Commons
Creative Common License - CCCreative Common License - BYCreative Common License - NC
This article distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
Copyright
Copyright © 2008 The Author(s)

Footnotes

The research was supported by CITO, National Institute for Educational Measurement. For their efforts in coding the strategy use, we would like to thank Meindert Beishuizen, Gabriëlle Rademakers, and the Bachelor students from Educational and Child Studies who participated in the research project into strategy use.

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