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…

Central elements of adaptive expertise in arithmetic problem solving are flexibility, using multiple strategies, and adaptivity, selecting the optimal strategy. Research shows that the strategies children actually use do not fully reflect the strategies they know: there is hidden potential. In the current study a sample of 147 third graders from…

Time perception has not been comprehensively examined in mathematics difficulties (MD). Therefore, verbal time estimation, production, and reproduction were tested in 13 individuals with MD and 16 healthy controls, matched for age, sex, and intellectual skills. Individuals with MD performed comparably to controls in time reproduction, but showed a…

Intellectual abilities are consistently found to be associated to child functioning. To date, however, it is unclear how varying intellectual profiles relate to differential aspects of child functioning. We screened 513 fifth-grade children on their intellectual abilities and selected three groups of gifted children, scoring in the top 10%:…

The present study investigated the role of both cognitive and linguistic predictors in basic arithmetic skills (i.e., addition and subtraction) in 69 first-language (L1) learners and 60 second-language (L2) learners from the second grade of primary schools in the Netherlands. All children were tested on non-verbal intelligence, working memory,…

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…

The aim of this study was to establish whether children with a physical disability resulting from central nervous system disorders (CNSd) show a level of arithmetic achievement lower than that of non-CNSd children and whether this is related to poor automaticity of number facts or reduced arithmetic instruction time. Twenty-two children with CNSd…

Students' strategies for solving long division problems under a realistic mathematics approach (RME) at Dutch primary schools were categorized in two ways: (a) according to the level of how students created multiples of the divisor (chunking) to be subtracted from the dividend; and (b) according to their use, or nonuse, of schematic notation.…

This study assesses the prevalence of combined reading and arithmetic disabilities in 799 Dutch schoolchildren using standardized school achievement tests. Scores of arithmetic, word recognition, reading comprehension, and spelling of children in fourth and fifth grade were used. The main interest involved the co-occurrence of word recognition and…

Hypothesized that arithmetic calculating procedures and types of problems that necessitate more subproblems will lead to longer solution times. Data from 36 third grade students who mentally computed problems with sums greater than 20 and less than 100, confirmed both hypotheses. (RH)

This paper presents a framework for understanding conditions of discovery learning in computer-based microworlds. It begins with a short discussion of problems related to a traditional type of microworld--i.e., learning tools for mathematics--using the Dienes Multibase Arithmetic blocks as an example. In this discussion, hypotheses are developed…