Johannes E. H. Van Luit

Mathematics Interventions for Children with Special Educational Needs A Meta-Analysis

This article presents the results of a meta-analysis of 58 studies of mathematics interventions for elementary students with special needs. Interventions in three different domains were selected: preparatory mathematics, basic skills, and problem-solving strategies. The majority of the included studies described interventions in the domain of basic skills. In general, these interventions were also the most effective. Furthermore, a few specific characteristics were found to influence the outcomes of the studies. In addition to the duration of the intervention, the particular method of intervention proved important: Direct instruction and self-instruction were found to be more effective than mediated instruction. Interventions involving the use of computer-assisted instruction and peer tutoring showed smaller effects than interventions not including these supports.

Executive Functions as Predictors of Math Learning Disabilities

In the past years, an increasing number of studies have investigated executive functions as predictors of individual differences in mathematical abilities. The present longitudinal study was designed to investigate whether the executive functions shifting, inhibition, and working memory differ between low achieving and typically achieving children and whether these executive functions can be seen as precursors to math learning disabilities in children. Furthermore, the predictive value of working memory ability compared to preparatory mathematical abilities was examined. Two classifications were made based on (persistent) mathematical ability in first and second grade. Repeated measures analyses and discriminant analyses were used to investigate which functions predicted group membership best. Group differences in performance were found on one inhibition and three working memory tasks. The working memory tasks predicted math learning disabilities, even over and above the predictive value of preparatory mathematical abilities.

Improving Early Numeracy of Young Children with Special Educational Needs

Difficulties with early numeracy can interfere with the acquisition of mathematics skills in later childhood. Early math intervention is therefore an important issue. Sixty-two 5- to 7-year-old pupils from kindergartens for children with special educational needs were given early mathematics intervention. The early numeracy program was specifically developed for young children with special educational needs and early numeracy difficulties by basing the instruction on perceptual gestalt theory. The results showed that the 62 children in the experimental group performed better at posttest than the 62 children in the comparison group. The children failed, however, to transfer their knowledge to novel math problems.

Mathematical Thinking Intervention Programmes for Preschool Children with Normal and Low Number Sense.

This study investigated the possibility of enhancing the level of preschoolers’ number sense by introducing two intervention programmes, Let’s think! and Young children with special educational needs count, too! .Forty‐five preschoolers, mean age 66.4 months, were randomly assigned to the experimental and control groups. The experimental group received instruction twice a week, for half an hour, and for a period of nine months. Pretest–postest comparison revealed that the experimental group showed enhanced number‐sense performance immediately after the instruction ended, but the between‐group difference faded after six months. There were no statistically significant differences between the groups in general mathematical thinking abilities (transfer tasks) after the intervention.

Effectiveness of the Additional Early Mathematics program for teaching children early mathematics

This paper presents the results of a study of the development of early mathematical competence among young poor arithmetic achievers in the 4–7 year age group. Research has shown that arithmetic difficulties later in life can be explained by an insufficient development of early mathematical competence: i.e. different aspects of early mathematical competence. The different aspects of early mathematical competence are derived from cognitive psychology and from a didactical point of view with an emphasis on (the various phases of) counting. The Piagetian operations (seriation, correspondence and classification) are used, however, as much as possible embedded in a counting context.After selection by way of an early mathematical competence test, children with a score below a criterium are presented with an additional program. This program consists of activities, embedded in real (daily) life themes, in which attention is paid to the different aspects of early mathematical competence. The program is given to the children with a guiding or a structuring instruction form. The results of the study show that it is possible to stimulate the development of early mathematical competence among young poor arithmetic achievers. The way in which instruction is offered has no influence on achievement.This paper presents the results of a study of the development of early mathematical competence among young poor arithmetic achievers in the 4–7 year age group. Research has shown that arithmetic difficulties later in life can be explained by an insufficient development of early mathematical competence: i.e. different aspects of early mathematical competence. The different aspects of early mathematical competence are derived from cognitive psychology and from a didactical point of view with an emphasis on (the various phases of) counting. The Piagetian operations (seriation, correspondence and classification) are used, however, as much as possible embedded in a counting context.

Effectiveness of the MASTER Program for Teaching Special Children Multiplication and Division

In this study, the utility of a MAthematics Strategy Training for Educational Remediation (MASTER) program, (Van Luit, Kaskens, & Van der Krol, 1993) was examined. The effectiveness of the program, designed to encourage strategy utilization with multiplication and division problems, was investigated for 84 students with poor mathematics skills, some of whom had learning disabilities (n = 42) and others with mild levels of mental retardation (n = 42). The results showed that the use of the self-instruction program resulted in significant improvement over the general instruction program. Furthermore, far transfer was found for the children with learning disabilities in the experimental group when they used effective problem-solving strategies on nontrained tasks. The results are consistent with previous findings suggesting the importance of self-instruction in mathematics training programs.

Mathematical Learning Difficulties and PASS Cognitive Processes

This study examined the relationships between mathematical learning difficulties (MLD) and the planning, attention, simultaneous, successive (PASS) theory of cognitive processing. The Cognitive Assessment System (CAS) was used to measure the PASS processes for a group of 267 Dutch students with MLD who attended either general or special education. The results showed that students with MLD performed lower than their peers on all CAS scales and that the MLD group contained many students with cognitive weaknesses in planning or successive processing. Moreover, students who had specific difficulties with the acquisition of basic math facts, the automatization of such facts, or word-problem solving were found to have distinct PASS cognitive profiles. In order to investigate the relationships between cognitive abilities and improvement in the mastery of basic math facts and problem solving, 165 of the students with MLD were given a special multiplication intervention. It appeared that the effectiveness of this particular intervention did not differ across the groups of students with specific cognitive weaknesses.

Young children's number sense in Finland, Hong Kong and Singapore

This study examines young childrens number sense in subjects from Finland (n=254), Hong Kong (n=246), and Singapore (n=130). Chinese, English and Finnish versions of the Early Numeracy Test (ENT; Van Luit et al., 1994) were used. Two highly correlated aspects of number sense were measured, one reflecting childrens abilities to organize and compare quantities (i.e. relational skills), and the other pertaining to their ability to operate with number-word sequence (i.e. counting skills). The results showed significant age-related gain on the relational and counting scales. No gender or language differences were found. The children in Hong Kong and Singapore outperformed those in Finland in relational and counting tasks starting at the age of four years. The children in Singapore also had better relational and counting skills than those in Hong Kong. Differences in teaching were assumed to explain the findings.

The Development of Early Numeracy in Europe

This article describes a limited longitudinal European study of young children’s early numeracy development within three testing cycles, onaverage, at the mid-point and towards the end of their fifth to sixth year and again at the mid-point of their sixth to seventh year. Assessment was carried out using the Utrecht Early Numeracy Test (ENT) (Van Luit, Van de Rijt and Pennings, 1994). The multilevel modelling method of analysis used for the study provided an extension of multiple regression to incorporate the hierarchical structure of the data collected, with boys and girls of different social-economic status, nested within different institutions within different countries. The results showed that the ENT was a useful tool for international comparison. The finding that differences between countrieswere negligible was surprising bearing in mind that the English pupils werein formal schooling throughout the testing cycle, the Belgian, German, Greek and Dutch children from the mid-point, and the Slovene children, not at all.

Utility of the PASS Theory and Cognitive Assessment System for Dutch Children With and Without ADHD

This study examined the utility of the Planning, Attention, Simultaneous, Successive (PASS) theory of intelligence as measured by the Cognitive Assessment System (CAS) for evaluation of children with attention-deficit/hyperactivity disorder (ADHD). The CAS scores of 51 Dutch children without ADHD were compared to the scores of a group of 20 Dutch children with ADHD. The scores of the Dutch children were also compared to American standardization samples of children with and without ADHD. The findings showed that children with ADHD in both countries demonstrated relatively low scores on the Planning and Attention scales of the CAS, but average scores on the Simultaneous and Successive scales. These findings are similar to previously published research suggesting that the PASS theory, as operationalized by the CAS, has sensitivity to the cognitive processing difficulties found in some children with ADHD.