Characterizing Creative Thinking and Creative Achievements in Relation to Symptoms of Attention-Deficit/Hyperactivity Disorder and Autism Spectrum Disorder

Previous research on ADHD and ASD has mainly focused on the deficits associated with these conditions, but there is also evidence for strengths. Unfortunately, our understanding of potential strengths in neurodevelopmental conditions is limited. One particular strength, creativity, has been associated with both ADHD and ASD. However, the distinct presentations of both conditions beg the question whether ADHD and ASD associate with the same or different aspects of creativity. Therefore, the current study investigated the links between ADHD and ASD symptoms, creative thinking abilities, and creative achievements. To investigate the spectrum of ADHD and ASD symptoms, self-reported ADHD and ASD symptoms, convergent (Remote Associations Test) and divergent thinking (Alternative Uses Task) and creative achievements (Creative Achievement Questionnaire) were assessed in a self-reportedly healthy sample of adults (n = 470). We performed correlation analysis to investigate the relation between ADHD/ASD symptoms and creativity measures. In a second phase of analysis, data from an adult ADHD case-control study (n = 151) were added to investigate the association between ADHD symptoms and divergent thinking in individuals with and without a diagnosis of ADHD. Our analysis revealed that having more ADHD symptoms in the general population was associated with higher scores on all the outcome measures for divergent thinking (fluency, flexibility, and originality), but not for convergent thinking. Individuals with an ADHD diagnosis in the case-control sample also scored higher on measures of divergent thinking. Combining data of the population based and case-control studies showed that ADHD symptoms predict divergent thinking up to a certain level of symptoms. No significant associations were found between the total number of ASD symptoms and any of the creativity measures. However, explorative analyses showed interesting links between the ASD subdomains of problems with imagination and symptoms that relate to social difficulties. Our findings showed a link between ADHD symptoms and divergent thinking abilities that plateaus in the clinical spectrum of symptoms. For ASD symptoms, no relation was found with creativity measures. Increasing the knowledge about positive phenotypes associated with neurodevelopmental conditions and their symptom dimensions might aid psychoeducation, decrease stigmatization and improve quality of life of individuals living with such conditions.

Prepulse Inhibition and P50 Suppression in Relation to Creativity and Attention: Dispersed Attention Beneficial to Quantitative but Not Qualitative Measures of Divergent Thinking

The current study investigated whether lower sensory and sensorimotor gating were related to higher levels of creativity and/or attentional difficulties in a natural population of primary school children (9- to 13-year-old). Gating abilities were measured with P50 suppression and prepulse inhibition of the startle reflex (PPI). The final sample included 65 participants in the P50 analyses and 37 participants in the PPI analyses. Our results showed that children with a high P50 amplitude to testing stimuli scored significantly higher on the divergent outcome measures of fluency and flexibility but not originality compared to children with a lower amplitude. No significant differences were found on any of the creativity measures when the sample was split on average PPI parameters. No significant differences in attention, as measured with a parent questionnaire, were found between children with low or high levels of sensory or sensorimotor gating. The data suggest that quantitative, but not qualitative measures of divergent thinking benefit from lower psychophysiological gating and that attentional difficulties stem from specific instead of general gating deficits. Future studies should take the effect of controlled attention into consideration.

Creativity in mathematics performance: The role of divergent and convergent thinking

BACKGROUND

Creativity requires both divergent and convergent thinking. Previous research established that divergent thinking relates to mathematics performance, but generally ignored the role of convergent thinking and, hence, leaves it unclear how both might interact when children work on mathematical tasks. This study addressed this paucity in the research literature, with the goal of improving our understanding of the role of creative thinking in primary school mathematics.

AIMS

This study examined how divergent and convergent thinking contribute to mathematics performance, both directly and jointly, on single- and multiple-solution tasks.

SAMPLE

The study was conducted with 229 Dutch fifth graders of 12 primary schools.

METHOD

Divergent and convergent thinking were measured with a visual and verbal task. Path analysis was used including verbal and visual divergent and convergent thinking tasks in relation to single- and multiple-solution mathematics task performance. Working memory was included as a covariate.

RESULTS

Verbal convergent thinking positively predicted single- and multiple-solution task performance. Verbal divergent and convergent thinking interacted in relation to single-solution task performance, while visual divergent and convergent thinking interacted in relation to multiple-solution task performance.

CONCLUSIONS

Children's mathematics performance mainly relies on convergent thinking. The role of divergent thinking is twofold: it complements convergent thinking on multiple-solution tasks and compensates convergent thinking on single-solution tasks.

Personalized brain stimulation for effective neurointervention across participants

Accumulating evidence from human-based research has highlighted that the prevalent one-size-fits-all approach for neural and behavioral interventions is inefficient. This approach can benefit one individual, but be ineffective or even detrimental for another. Studying the efficacy of the large range of different parameters for different individuals is costly, time-consuming and requires a large sample size that makes such research impractical and hinders effective interventions. Here an active machine learning technique is presented across participants-personalized Bayesian optimization (pBO)-that searches available parameter combinations to optimize an intervention as a function of an individual's ability. This novel technique was utilized to identify transcranial alternating current stimulation (tACS) frequency and current strength combinations most likely to improve arithmetic performance, based on a subject's baseline arithmetic abilities. The pBO was performed across all subjects tested, building a model of subject performance, capable of recommending parameters for future subjects based on their baseline arithmetic ability. pBO successfully searches, learns, and recommends parameters for an effective neurointervention as supported by behavioral, simulation, and neural data. The application of pBO in human-based research opens up new avenues for personalized and more effective interventions, as well as discoveries of protocols for treatment and translation to other clinical and non-clinical domains.

Serial Order Effect in Divergent Thinking in Five- to Six-Year-Olds: Individual Differences as Related to Executive Functions

This study examined the unfolding in real time of original ideas during divergent thinking (DT) in five- to six-year-olds and related individual differences in DT to executive functions (EFs). The Alternative Uses Task was administered with verbal prompts that encouraged children to report on their thinking processes while generating uses for daily objects. In addition to coding the originality of each use, the domain-specific DT processes memory retrieval and mental operations were coded from children’s explanations. Six EF tasks were administered and combined into composites to measure working memory, shifting, inhibition, and selective attention. The results replicated findings of a previous study with the same children but at age four years: (1) there was a serial order effect of the originality of uses; and (2) the process mental operations predicted the originality of uses. Next, the results revealed that both domain-general EFs and domain-specific executive processes played a role in the real-time unfolding of original ideas during DT. Particularly, the DT process mental operations was positively related to the early generation of original ideas, while selective attention was negatively related to the later generation of original ideas. These findings deepen our understanding of how controlled executive processes operate during DT.

How Cognitive Strengths Compensate Weaknesses Related to Specific Learning Difficulties in Fourth-Grade Children

The goal of the present study was to investigate whether children's cognitive strengths can compensate the accompanied weaknesses related to their specific learning difficulties. A Bayesian multigroup mediation SEM analysis in 281 fourth-grade children identified a cognitive compensatory mechanism in children with mathematical learning difficulties (n = 36): Children with weak number sense, but strong rapid naming performed slightly better on mathematics compared to peers with weak rapid naming. In contrast, a compensatory mechanism was not identified for children with a comorbid mathematical and reading difficulty (n = 16). One explanation for the latter finding could relate to the lack of ability to compensate, because of the difficulties these children experience in both academic domains. These findings lead to a new direction in research on learning difficulties in mathematics and/or reading by suggesting that children with a learning disability each have a unique profile of interrelated cognitive strengths and weaknesses. Children might compensate with these strengths for their weaknesses, which could lead to (small) learning gains in the affected domain.

The Influence of Situational Cues on Children's Creativity in an Alternative Uses Task and the Moderating Effect of Selective Attention

Taking a perception-action perspective, we investigated how the presence of different real objects in children's immediate situation affected their creativity and whether this effect was moderated by their selective attention. Seventy children between ages 9 and 12 years old participated. Verbal responses on a visual Alternative Uses Task with a low stimulus and high stimulus condition were coded on fluency, flexibility, and originality. Selective attention was measured with a visual search task. Results showed that fluency was not affected by stimulus condition and was unrelated to selective attention. Flexibility was positively associated with selective attention. Originality, net of fluency and flexibility, showed a main effect of stimulus condition in an unexpected direction, as children gave more original responses in the low stimulus condition compared to the high stimulus condition. A significant moderation effect revealed that children with better selective attention skills benefitted from a low stimulus environment, whereas children with weaker selective attention performed better in a high stimulus environment. The findings demonstrate differential effects of the immediate situation and selective attention, and support the hypothesis that creativity is impacted by immediate situation and selective attention, yet in unexpected ways.

The relevance of subtyping children with mathematical learning disabilities

BACKGROUND

Profiles of mathematical learning disability (MLD) have been conceptualized in the literature, but empirical evidence to support them based on academic and cognitive characteristics is lacking.

AIMS

We examined whether profiles of mathematics performance can empirically be identified and whether the identified profiles also differ in underlying cognitive skills.

METHODS AND PROCEDURES

Latent profile analysis in 281 fourth-graders. Basic arithmetic and advanced mathematics were used to identify profiles. Cognitive skills were then described for each profile of mathematics performance.

OUTCOMES AND RESULTS

Four profiles of mathematics performance were retrieved from the data, including one general low-achieving profile. Additional profiles of MLD were not found, possibly because individual variation was substantial.

CONCLUSIONS AND IMPLICATIONS

It is highly important to understand children's mathematics performance from an individual perspective, rather than by averaging these children over subgroups. These new insights can be used to better tend to the specific needs of children with mathematical difficulties.

The Contribution of Executive Functions in Predicting Mathematical Creativity in Typical Elementary School Classes: A Twofold Role for Updating

The goal of the current study was to investigate the role of executive functions in mathematical creativity. The sample included 278 primary school children (ages 8–13). Two models were compared: the starting model tested whether executive functions (shifting, updating, and inhibition), domain-general creativity, and mathematical ability directly predicted mathematical creativity. The second model, which fitted the data best, included the additional assumption that updating influences mathematical creativity indirectly through mathematical ability and domain-general creativity. Updating was positively related to mathematical creativity. Additionally, updating was positively related to mathematical ability and domain-general creativity. Inhibition, shifting, domain-general creativity and mathematical ability did not have a significant contribution to either model but did positively correlate with mathematical creativity. This study reports the first empirical evidence that updating is a predictor of mathematical creativity in primary school children and demonstrates that creativity is a higher order cognitive process, activating a variety of cognitive abilities.

The Use of Local and Global Ordering Strategies in Number Line Estimation in Early Childhood

A lot of research has been devoted to number line estimation in primary school. However, less is known about the early onset of number line estimation before children enter formal education. We propose that ordering strategies are building blocks of number line estimation in early childhood. In a longitudinal study, children completed a non-symbolic number line estimation task at age 3.5 and 5 years. Two ordering strategies were identified based on the children's estimation patterns: local and global ordering. Local ordering refers to the correct ordering of successive quantities, whereas global ordering refers to the correct ordering of all quantities across the number line. Results indicated a developmental trend for both strategies. The percentage of children applying local and global ordering strategies increased steeply from 3.5 to 5 years of age. Moreover, children used more advanced local and global ordering strategies at 5 years of age. Importantly, level of strategy use was related to more traditional number line estimation outcome measures, such as estimation accuracy and regression fit scores. These results provide evidence that children use dynamic ordering strategies when solving the number line estimation task in early stages of numerical development.

On the Difference Between Numerosity Processing and Number Processing

The ANS theory on the processing of non-symbolic numerosities and the ANS mapping account on the processing of symbolic numbers have been the most popular theories on numerosity and number processing, respectively, in the last 20 years. Recently, both the ANS theory and the ANS mapping account have been questioned. In the current study, we examined two main assumptions of both the ANS theory and the ANS mapping account. ERPs were measured in 21 participants during four same-different match-to-sample tasks, involving non-symbolic stimuli, symbolic stimuli, or a combination of symbolic and non-symbolic stimuli (i.e., mapping tasks). We strictly controlled the visual features in the non-symbolic stimuli. Based on the ANS theory, one would expect an early distance effect for numerosity in the non-symbolic task. However, the results show no distance effect for numerosity. When analyzing the stimuli based on visual properties, an early distance effect for area subtended by the convex hull was found. This finding is in line with recent claims that the processing of non-symbolic stimuli may be dependent on the processing of visual properties instead of on numerosity (only). With regards to the processing of symbolic numbers, the ANS mapping account states that symbolic numbers are first mapped onto their non-symbolic representations before further processing, since the non-symbolic representation is at the basis of processing the symbolic number. If the non-symbolic format is the basic format of processing, one would expect that the processing of non-symbolic numerosities would not differ between purely non-symbolic tasks and mapping tasks, resulting in similar ERP waveforms for both tasks. Our results show that the processing of non-symbolic numerosities does differ between the tasks, indicating that processing of non-symbolic number is dependent on task format. This provides evidence against the ANS mapping account. Alternative theories for both the processing of non-symbolic numerosities and symbolic numbers are discussed.

Counting and Number Line Trainings in Kindergarten: Effects on Arithmetic Performance and Number Sense

Children’s early numerical capacities form the building blocks for later arithmetic proficiency. Linear number placements and counting skills are indicative of mapping, as an important precursor to arithmetic skills, and have been suggested to be of vital importance to arithmetic development. The current study investigated whether fostering mapping skills is more efficient through a counting or a number line training program. Effects of both programs were compared through a quasi-experimental design, and moderation effects of age and socio-economic status (SES) were investigated. Ninety kindergartners were divided into three conditions: a counting, a number line, and a control condition. Pretests and posttests included an arithmetic (addition) task and a battery of number sense tasks (comparison, number lines, and counting). Results showed significantly greater gains in arithmetic, counting, and symbolic number lines in the counting training group than in the control group. The number line training group did not make significantly greater gains than the control group. Training gains were moderated by age, but not SES. We concluded that counting training improved numerical capacities effectively, whereas no such improvements could be found for the number line training. This suggests that only a counting approach is effective for fostering number sense and early arithmetic skills in kindergarten. Future research should elaborate on the parameters of training programs and the consequences of variation in these parameters.

Cognitive predictors of children's development in mathematics achievement: A latent growth modeling approach

Research has identified various domain-general and domain-specific cognitive abilities as predictors of children's individual differences in mathematics achievement. However, research into the predictors of children's individual growth rates, namely between-person differences in within-person change in mathematics achievement is scarce. We assessed 334 children's domain-general and mathematics-specific early cognitive abilities and their general mathematics achievement longitudinally across four time-points within the first and second grades of primary school. As expected, a constellation of multiple cognitive abilities contributed to the children's starting level of mathematical success. Specifically, latent growth modeling revealed that WM abilities, IQ, counting skills, nonsymbolic and symbolic approximate arithmetic and comparison skills explained individual differences in the children's initial status on a curriculum-based general mathematics achievement test. Surprisingly, however, only one out of all the assessed cognitive abilities was a unique predictor of the children's individual growth rates in mathematics achievement: their performance in the symbolic approximate addition task. In this task, children were asked to estimate the sum of two large numbers and decide if this estimated sum was smaller or larger compared to a third number. Our findings demonstrate the importance of multiple domain-general and mathematics-specific cognitive skills for identifying children at risk of struggling with mathematics and highlight the significance of early approximate arithmetic skills for the development of one's mathematical success. We argue the need for more research focus on explaining children's individual growth rates in mathematics achievement.

An Embodiment Perspective on Number-Space Mapping in 3.5-Year-Old Dutch Children

Previous research suggests that block adding, subtracting and counting direction are early forms of number–space mapping. In this study, an embodiment perspective on these skills was taken. Embodiment theory assumes that cognition emerges through sensory–motor interaction with the environment. In line with this assumption, it was investigated if counting and adding/subtracting direction in young children is related to the hand they use during task performance. Forty‐eight 3.5‐year‐old children completed a block adding, subtracting and counting task. They had to add and remove a block from a row of three blocks and count a row of five blocks. Adding, subtracting and counting direction were related to the hand the children used for task performance. Most children who used their right hand added, removed and started counting the blocks at the right side of the row. Most children who used their left hand added, removed and started counting the blocks at the left side of the row. It can be concluded that number–space mapping, as measured by direction of adding, subtracting and counting blocks, in young children is embodied: It is not fixed, but is related to the situation. © 2016 The Authors Infant and Child Development Published by John Wiley & Sons, Ltd.

Self-concept mediates the relation between achievement and emotions in mathematics

BACKGROUND

Mathematics achievement is related to positive and negative emotions. Pekrun's control-value theory of achievement emotions suggests that students' self-concept (i.e., self-appraisal of ability) may be an important mediator of the relation between mathematics achievement and emotions.

AIMS

The aims were (1) to investigate the mediating role of mathematical self-concept in the relation between mathematics achievement and the achievement emotions of enjoyment and anxiety in a comprehensive model, and (2) to test possible differences in this mediating role between low-, average-, and high-achieving students.

SAMPLE

Participants were ninth-grade students (n = 1,014) from eight secondary schools in the Netherlands.

METHODS

Through an online survey including mathematical problems, students were asked to indicate their levels of mathematics enjoyment, anxiety, and self-concept. Structural equation modelling was used to test the mediating role of self-concept in the relation between mathematics achievement and emotions. Multigroup analyses were performed to compare these relations across the three achievement groups.

RESULTS

Results confirmed full mediation of the relation between mathematics achievement and emotions by mathematical self-concept. Furthermore, we found higher self-concepts, more enjoyment and less math anxiety in high-achieving students compared to their average and low-achieving peers. No differences across these achievement groups were found in the relations in the mediational model.

CONCLUSIONS

Mathematical self-concept plays a pivotal role in students' appraisal of mathematics. Mathematics achievement is only one factor explaining students' self-concept. Likely also classroom instruction and teachers' feedback strategies help to shape students' self-concept.

Foreign language reading and spelling in gifted students with dyslexia in secondary education

A few studies suggest that gifted children with dyslexia have better literacy skills than averagely intelligent children with dyslexia. This finding aligns with the hypothesis that giftedness-related factors provide compensation for poor reading. The present study investigated whether, as in the native language (NL), the level of foreign language (FL) literacy of gifted students with dyslexia is higher than the literacy level of averagely intelligent students with dyslexia and whether this difference can be accounted for by the difference in their NL literacy level. The sample consisted of 148 Dutch native speaking secondary school students divided in four groups: dyslexia, gifted/dyslexia, typically developing (TD), and gifted. All students were assessed on word reading and orthographic knowledge in Dutch and English when they were in 7th or 8th grade. A subsample (n = 71) was (re)assessed on Dutch, English, French, and German literacy one year later. Results showed that Dutch gifted students with dyslexia have higher NL literacy levels than averagely intelligent students with dyslexia. As in the NL, a stepwise pattern of group differences was found for English word reading and spelling, i.e., dyslexia < gifted/dyslexia < TD < gifted. However, it was not found for French and German literacy performance. These results point towards compensation: the higher English literacy levels of gifted/dyslexic students compared to their averagely intelligent dyslexic peers result from mechanisms that are unique to English as a FL. Differences in results between FLs are discussed in terms of variation in orthographic transparency and exposure.

Limited Near and Far Transfer Effects of Jungle Memory Working Memory Training on Learning Mathematics in Children with Attentional and Mathematical Difficulties

The goal of this randomized controlled trial was to investigate whether Jungle Memory working memory training (JM) affects performance on working memory tasks, performance in mathematics and gains made on a mathematics training (MT) in school aged children between 9-12 years old (N = 64) with both difficulties in mathematics, as well as attention and working memory. Children were randomly assigned to three groups and were trained in two periods: (1) JM first, followed by MT, (2) MT first, followed by JM, and (3) a control group that received MT only. Bayesian analyses showed possible short term effects of JM on near transfer measures of verbal working memory, but none on visual working memory. Furthermore, support was found for the hypothesis that children that received JM first, performed better after MT than children who did not follow JM first or did not train with JM at all. However, these effects could be explained at least partly by frequency of training effects, possibly due to motivational issues, and training-specific factors. Furthermore, it remains unclear whether the effects found on improving mathematics were actually mediated by gains in working memory. It is argued that JM might not train the components of working memory involved in mathematics sufficiently. Another possible explanation can be found in the training's lack of adaptivity, therefore failing to provide the children with tailored instruction and feedback. Finally, it was hypothesized that, since effect sizes are generally small, training effects are bound to a critical period in development.

Shared and Unique Risk Factors Underlying Mathematical Disability and Reading and Spelling Disability

High comorbidity rates have been reported between mathematical learning disabilities (MD) and reading and spelling disabilities (RSD). Research has identified skills related to math, such as number sense (NS) and visuospatial working memory (visuospatial WM), as well as to literacy, such as phonological awareness (PA), rapid automatized naming (RAN) and verbal short-term memory (Verbal STM). In order to explain the high comorbidity rates between MD and RSD, 7–11-year-old children were assessed on a range of cognitive abilities related to literacy (PA, RAN, Verbal STM) and mathematical ability (visuospatial WM, NS). The group of children consisted of typically developing (TD) children (n = 32), children with MD (n = 26), children with RSD (n = 29), and combined MD and RSD (n = 43). It was hypothesized that, in line with the multiple deficit view on learning disorders, at least one unique predictor for both MD and RSD and a possible shared cognitive risk factor would be found to account for the comorbidity between the symptom dimensions literacy and math. Secondly, our hypotheses were that (a) a probabilistic multi-factorial risk factor model would provide a better fit to the data than a deterministic single risk factor model and (b) that a shared risk factor model would provide a better fit than the specific multi-factorial model. All our hypotheses were confirmed. NS and visuospatial WM were identified as unique cognitive predictors for MD, whereas PA and RAN were both associated with RSD. Also, a shared risk factor model with PA as a cognitive predictor for both RSD and MD fitted the data best, indicating that MD and RSD might co-occur due to a shared underlying deficit in phonological processing. Possible explanations are discussed in the context of sample selection and composition. This study shows that different cognitive factors play a role in mathematics and literacy, and that a phonological processing deficit might play a role in the occurrence of MD and RSD.

The Monkey game: A computerized verbal working memory task for self-reliant administration in primary school children

In two studies, the psychometric properties of an online self-reliant verbal working memory task (the Monkey game) for primary school children (6-12 years of age) were examined. In Study 1, children (n = 5,203) from 31 primary schools participated. The participants completed computerized verbal and visual-spatial working memory tasks (i.e., the Monkey game and the Lion game) and a paper-and-pencil version of Raven's Standard Progressive Matrices. Reading comprehension and math achievement test scores were obtained from the schools. First, the internal consistency of the Monkey game was examined. Second, multilevel modeling was used to examine the effects of classroom membership. Multilevel multivariate regression analysis was used to examine the Monkey game's concurrent relationship with the Lion game and its predictive relationships with reading comprehension and math achievement. Also, age-related differences in performance were examined. In Study 2, the concurrent relationships between the Monkey game and two tester-led computerized working memory tasks were further examined (n = 140). Also, the 1- and 2-year stability of the Monkey game was investigated. The Monkey game showed excellent internal consistency, good concurrent relationships with the other working memory measures, and significant age differences in performance. Performance on the Monkey game was also predictive of subsequent reading comprehension and mathematics performance, even after controlling for individual differences in intelligence. Performance on the Monkey game was influenced by classroom membership. The Monkey game is a reliable and suitable instrument for the online computerized and self-reliant assessment of verbal working memory in primary school children.

High Reading Skills Mask Dyslexia in Gifted Children

This study investigated how gifted children with dyslexia might be able to mask literacy problems and the role of possible compensatory mechanisms. The sample consisted of 121 Dutch primary school children that were divided over four groups (typically developing [TD] children, children with dyslexia, gifted children, gifted children with dyslexia). The test battery included measures of literacy (reading/spelling) and cognitive abilities related to literacy and language (phonological awareness [PA], rapid automatized naming [RAN], verbal short-term memory [VSTM], working memory [WM], grammar, and vocabulary). It was hypothesized that gifted children with dyslexia would outperform children with dyslexia on literacy tests. In addition, a core-deficit model including dyslexia-related weaknesses and a compensational model involving giftedness-related strengths were tested using Bayesian statistics to explain their reading/spelling performance. Gifted children with dyslexia performed on all literacy tests in between children with dyslexia and TD children. Their cognitive profile showed signs of weaknesses in PA and RAN and strengths in VSTM, WM, and language skills. Findings indicate that phonology is a risk factor for gifted children with dyslexia, but this is moderated by other skills such as WM, grammar, and vocabulary, providing opportunities for compensation of a cognitive deficit and masking of literacy difficulties.

Number line estimation strategies in children with mathematical learning difficulties measured by eye tracking

Introduction

Number line estimation is one of the skills related to mathematical performance. Previous research has shown that eye tracking can be used to identify differences in the estimation strategies children with dyscalculia and children with typical mathematical development use on number line estimation tasks. The current study extends these findings to a larger group of children with mathematical learning disabilities (MLD).

Method

A group of 9–11-year-old children with MLD (N = 14) was compared to a control group of children without math difficulties (N = 14). Number line estimation was measured using a 0–100 and a 0–1000 number-to-position task. A Tobii T60 eye tracker was used to measure the children’s eye movements during task performance.

Results

The behavioral data showed that the children with MLD had higher error scores on both number lines than the children in the control group. The eye tracking data showed that the groups also differed in their estimation strategies. The children with MLD showed less adaptation of their estimation strategies to the number to be estimated.

Conclusion

This study shows that children with MLD attend to different features of the number line than children without math difficulties. Children with math difficulties are less capable of adapting their estimation strategies to the numbers to be estimated and of effectively using reference points on the number line.

Electronic supplementary material

The online version of this article (doi:10.1007/s00426-015-0736-z) contains supplementary material, which is available to authorized users.

Risk and protective factors in gifted children with dyslexia

This study investigated risk and protective factors associated with dyslexia and literacy development, both at the group and individual level, to gain more insight in underlying cognitive profiles and possibilities for compensation in high-IQ children. A sample of 73 Dutch primary school children included a dyslexic group, a gifted-dyslexic group, and a borderline-dyslexic group (i.e., gifted children with relative literacy problems). Children were assessed on literacy, phonology, language, and working memory. Competing hypotheses were formulated, comparing the core-deficit view to the twice-exceptionality view on compensation with giftedness-related strengths. The results showed no indication of compensation of dyslexia-related deficits by giftedness-related strengths in gifted children with dyslexia. The higher literacy levels of borderline children compared to gifted children with dyslexia seemed the result of both fewer combinations of risk factors and less severe phonological deficits in this group. There was no evidence for compensation by specific strengths more relevant to literacy development in the borderline group. Accordingly, the findings largely supported the core-deficit view, whereas no evidence for the twice-exceptionality view was found. Besides practical implications, the findings also add to knowledge about the different manifestations of dyslexia and associated underlying cognitive factors at the higher end of the intelligence spectrum.

Pathways of Number Line Development in Children

Dyscalculia, or mathematics learning disability, has received growing attention in recent years. Working memory and number sense are hypothesized to form important determinants of dyscalculia, but longitudinal assessments of number sense in children with or at-risk for dyscalculia are scarce. The current study investigated number line development in first and second grade, in addition to kindergarten predictors and mathematical proficiency as an outcome. Children (n = 396) could be divided into three latent growth classes: at-risk, catch-up, and typical, based on their number line development. Growth was predicted by kindergarten number sense and verbal working memory. According to the class to which they were assigned, children differed in mathematical proficiency at the end of grade 2. The current study makes an important contribution to the understanding of risk for dyscalculia, showing that children at-risk can be distinguished based on their number line development, and that kindergarten variables are predictive of subsequent development.

Working Memory and Number Sense as Predictors of Mathematical (Dis-)Ability

Recent research has pointed to two possible causes of mathematical (dis-)ability: working memory and number sense, although only few studies have compared the relations between working memory and mathematics and between number sense and mathematics. In this study, both constructs were studied in relation to mathematics in general, and to mathematical learning disabilities (MLD) in particular. The sample consisted of 154 children aged between 6 and 10 years, including 26 children with MLD. Children performing low on either number sense or visual-spatial working memory scored lower on math tests than children without such a weakness. Children with a double weakness scored the lowest. These results confirm the important role of both visual-spatial working memory and number sense in mathematical development.

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 (R (2)) 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.

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.

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.

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.

PASS Processes and Early Mathematics Skills in Dutch and Italian Kindergarteners

The purpose of this study was to investigate the relation between early mathematical skills and cognitive processing abilities for two samples of children in Italy ( N = 40) and the Netherlands ( N = 59) who completed both a cognitive test that measures Planning, Attention, Simultaneous, and Successive (PASS) processing and an early mathematical skills test. Correlations between the PASS processes as measured by the Cognitive Assessment System and math tasks showed that Planning and Simultaneous processing were most related to early math skills. Simultaneous processing was most related to the Piagetian tasks and Planning to the counting tasks. Although some differences were found between the Italian and Dutch group on their scores on both tests, the relations between PASS processes and early math skills were comparable for both groups. The results may have implications for early identification of math learning difficulties.

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.

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.