Evelyn H. Kroesbergen

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.

The added value of eye-tracking in diagnosing dyscalculia: a case study

The present study compared eye movements and performance of a 9-year-old girl with Developmental Dyscalculia (DD) on a series of number line tasks to those of a group of typically developing (TD) children (n = 10), in order to answer the question whether eye-tracking data from number line estimation tasks can be a useful tool to discriminate between TD children and children with a number processing deficit. Quantitative results indicated that the child with dyscalculia performed worse on all symbolic number line tasks compared to the control group, indicated by a low linear fit (R2) and a low accuracy measured by mean percent absolute error. In contrast to the control group, her magnitude representations seemed to be better represented by a logarithmic than a linear fit. Furthermore, qualitative analyses on the data of the child with dyscalculia revealed more unidentifiable fixation patterns in the processing of multi-digit numbers and more dysfunctional estimation strategy use in one third of the estimation trials as opposed to ~10% in the control group. In line with her dyscalculia diagnosis, these results confirm the difficulties with spatially representing and manipulating numerosities on a number line, resulting in inflexible and inadequate estimation or processing strategies. It can be concluded from this case study that eye-tracking data can be used to discern different number processing and estimation strategies in TD children and children with a number processing deficit. Hence, eye-tracking data in combination with number line estimation tasks might be a valuable and promising addition to current diagnostic measures.

The Development of Executive Functions and Early Mathematics: A Dynamic Relationship.

BACKGROUND The relationship between executive functions and mathematical skills has been studied extensively, but results are inconclusive, and how this relationship evolves longitudinally is largely unknown. AIM The aim was to investigate the factor structure of executive functions in inhibition, shifting, and updating; the longitudinal development of executive functions and mathematics; and the relation between them. SAMPLE A total of 211 children in grade 2 (7-8 years old) from 10 schools in the Netherlands. METHOD Children were followed in grade 1 and 2 of primary education. Executive functions and mathematics were measured four times. The test battery contained multiple tasks for each executive function: Animal stroop, local global, and Simon task for inhibition; Animal Shifting, Trail Making Test in Colours, and Sorting Task for shifting; and Digit Span Backwards, Odd One Out, and Keep Track for updating. The factor structure of executive functions was assessed and relations with mathematics were investigated using growth modelling. RESULTS Confirmatory factor analysis (CFA) showed that inhibition and shifting could not be distinguished from each other. Updating was a separate factor, and its development was strongly related to mathematical development while inhibition and shifting did not predict mathematics in the presence of the updating factor. CONCLUSIONS The strong relationship between updating and mathematics suggest that updating skills play a key role in the maths learning process. This makes updating a promising target for future intervention studies.

Individual Differences in Early Numeracy: The Role of Executive Functions and Subitizing.

In this study, the question was raised how basic cognitive processes are related to math abilities and how it can be best determined which children are at risk for developing those disabilities. The role of four distinct basic processes in the development of early mathematics was investigated: executive functions, fluid intelligence, subitizing, and language. The counting skills of 115 five- and six-year-old children were also assessed. The results showed that both executive functions and number sense were important factors in childrens development of counting skills. Both executive functions and subitizing explained a significant part of variance in childrens counting skills. IQ scores could not add further explanation to the variance in early math. The implications of this study are that it seems promising to use the concept of executive functions for the early identification of children at risk for math learning difficulties.

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.

The Structure of Executive Functions in Children: A Closer Examination of Inhibition, Shifting, and Updating.

An increasing number of studies has investigated the latent factor structure of executive functions. Some studies found a three-factor structure of inhibition, shifting, and updating, but others could not replicate this finding. We assumed that the task choices and scoring methods might be responsible for these contradictory findings. Therefore, we selected tasks in which input modality was varied, controlled for baseline speed, and used both speed and accuracy scores, in order to investigate whether a three factor model with inhibition, shifting, and updating could still be replicated. In a group of 211 children, who were tested at the beginning of grade 1, at approximately 6 years of age, and again after 18 months, the best fitting model was not the three-factor model, but instead consisted of an updating factor and a combined inhibition and shifting factor, besides two baseline speed factors (verbal and motor). We argue that these results might indicate that the structural organization of executive functions might be different in children than in adults, but that there might also be an alternative explanation: the distinction in executive functions might not accurately represent cognitive structures but instead be a methodological artefact.

Training working memory in kindergarten children: effects on working memory and early numeracy.

This study investigated the relationship between working memory and early numeracy. It aimed to explore the possibility of training young children’s working memory and to investigate the effects of such training both on working memory and on the specific domain of early numerical skills. Measures of working memory and numeracy were used with low-performing children in kindergarten. A total of 51 five-year-old children received one of two different versions of working memory training or no training at all. The two versions differed in the type of information the children were given to practice: non-numerical or numerical. After a pretest, 4 weeks of intervention took place, followed by a posttest. Children who participated in one of the working memory interventions significantly improved their working memory skills. Furthermore, their early numeracy skills also improved. Differences between both experimental conditions were small.

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.

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.

Verbal and visual-spatial working memory and mathematical ability in different domains throughout primary school

The relative importance of visual-spatial and verbal working memory for mathematics performance and learning seems to vary with age, the novelty of the material, and the specific math domain that is investigated. In this study, the relations between verbal and visual-spatial working memory and performance in four math domains (i.e., addition, subtraction, multiplication, and division) at different ages during primary school are investigated. Children (N = 4337) from grades 2 through 6 participated. Visual-spatial and verbal working memory were assessed using online computerized tasks. Math performance was assessed at the start, middle, and end of the school year using a speeded arithmetic test. Multilevel Multigroup Latent Growth Modeling was used to model individual differences in level and growth in math performance, and examine the predictive value of working memory per grade, while controlling for effects of classroom membership. The results showed that as grade level progressed, the predictive value of visual-spatial working memory for individual differences in level of mathematics performance waned, while the predictive value of verbal working memory increased. Working memory did not predict individual differences between children in their rate of performance growth throughout the school year. These findings are discussed in relation to three, not mutually exclusive, explanations for such age-related findings.