In this study we investigated the structure of quantitative competence of kindergartners by testing a hypothesized four-factor model of quantitative competence consisting of the components counting, subitizing, additive reasoning and multiplicative reasoning. Data were collected from kindergartners in the Netherlands (n = 334) and in Cyprus (n =…

In learning, errors are ubiquitous and inevitable. As these errors may signal otherwise latent cognitive processes, tutors--and students alike--can greatly benefit from the information they provide. In this paper, we introduce and evaluate the Systematic Error Tracing (SET) model that identifies the possible causes of systematically observed…

Strategy flexibility, adaptivity, and the use of clever shortcut strategies are of major importance in current primary school mathematics education worldwide. However, empirical results show that primary school students use such shortcut strategies rather infrequently. The aims of the present study were to analyze the extent to which Dutch sixth…

This article offers a reflection on the findings of three PhD studies, in the domains of, respectively, subtraction under 100, fractions, and algebra, which independently of each other showed that Dutch students' proficiency fell short of what might be expected of reform in mathematics education aiming at conceptual understanding. In all three…

A first application of multilevel latent class analysis (MLCA) to educational large-scale assessment data is demonstrated. This statistical technique addresses several of the challenges that assessment data offers. Importantly, MLCA allows modeling of the often ignored teacher effects and of the joint influence of teacher and student variables.…

Developing fluency in arithmetic facts is instrumental to mathematics learning. This study compares the effects of two practice conditions on children's fluency in simple multiplication facts. Third and fourth graders in the Netherlands (N = 282) practised in either a conventional "recall" condition where they produced answers to…

Subtractions of the type M - S = ? can be solved by various strategies, including subtraction by addition. In this study, we investigated children's use of subtraction by addition by means of reaction time analyses. We presented 106 third to sixth graders with 32 large non-tie single-digit problems in both subtraction (12 - 9 = .) and addition…

This paper describes a dataset consisting of longitudinal data gathered in the BRXXX project. The aim of the project was to investigate the effectiveness of online mathematics mini-games in enhancing primary school students' multiplicative reasoning ability (multiplication and division). The dataset includes data of 719 students from 35 primary…

Predictions of the Identical Elements (IE) model of arithmetic fact representation (Rickard, 2005; Rickard & Bourne, 1996) about transfer between arithmetic facts were tested in primary school children. The aim of the study was to test whether the IE model, constructed to explain adult performance, also applies to children. The IE model…

This study investigated the development of children's knowledge of many-to-one counting. Four-year-olds ("n" = 51) either participated in a training or in a control group. The training taught children how to allot "Y" physically not present items to each of "X" objects and how to count these items in the process. It…

Described are two methods of calculating developed by the Dutch WISKOBAS Project: addition and subtraction with a loop abacus and multiplication using a grid model. (MP)

A mental multiplication test, containing items written in Dutch, Spanish, and Roman numerals was administered to 286 Dutch students. Further instruction was given in either Spanish or Roman, and a subtest combining languages was given. The iterative logit method was found to be useful in detecting biased test items. (GDC)

A method is proposed for the detection of item bias with respect to observed or unobserved subgroups. The method uses quasi-loglinear models for the incomplete subgroup x test score x item 1 x ... x item k contingency table. If the subgroup membership is unknown, the models are the incomplete-latent-class models of S. J. Haberman (1979). The…

The use of loglinear latent class models to detect item bias was studied. Purposes of the study were to: (1) develop procedures for use in assessing item bias when the grouping variable with respect to which bias occurs is not observed; (2) develop bias detection procedures that relate to a conceptually different assessed trait--a categorical…