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Dyscalculie is een stoornis die niet in een enkelvoudig theoretisch kader is te vatten. Het is een dynamisch ontwikkelingsprobleem dat vanuit verschillende en elkaar aanvullende theorieën is te benaderen. Dit vraagt van de professional in de praktijk om gedegen achtergrondkennis, niet in de vorm van dogma’s, maar van betrouwbare gegevens uit empirisch onderzoek die in de eigen beslissingen op bruikbaarheid en toepasbaarheid zijn mee te wegen.Sinds de eerste druk van Rekenproblemen en Dyscalculie (Ruijssenaars, van Luit & van Lieshout, 2004) is er heel veel veranderd in het vakgebied. Er is een grote stroom aan wetenschappelijk onderzoek tot stand gekomen met nieuwe oriëntaties. Om het overzicht van alle ontwikkelingen en resultaten te behouden is de samenwerkende auteursgroep verder uitgebreid en deze samenwerking heeft geleid tot een volledig herschreven handboek over dyscalculie en rekenproblemen.Een standaardwerk voor iedereen die met dit aspect van het onderwijs te maken heeft.

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.

Contains fulltext : 189803.pdf (Publisher’s version ) (Closed access) This large-scale study examined the effects of a teacher professional development (PD) programme about differentiated instruction on students’ mathematics achievement. Thirty primary schools (N = 5658 students of grade 1-6) divided over three cohorts participated: Cohort 1 received the PD programme in Year 1, Cohort 2 in Year 2, and Cohort 3 was control. During the PD, teachers learned how to adapt mathematics education to diverse educational needs using within-class ability groups. In Year 1, the PD had a significant small positive effect on student achievement growth. The effect size was similar for low-achieving, average-achieving and high-achieving students. In Year 2, no significant effects were demonstrated. In sum, teacher PD about differentiation has the potential to promote the achievement of all students. However, implementing differentiation is not straightforward and future research is necessary to unravel which factors make PD about differentiation succeed. 13 p.

Rede ter gelegenheid van het afscheid als hoogleraar Orthopedagogiek met als leeropdracht ‘Diagnostiek en behandeling van kinderen met dyscalculie’ aan de Universiteit Utrecht

De rekenmethode geeft vaak suggesties voor verwerking op meerdere niveaus, maar wat kun je als leerkracht zelf doen om je onderwijs beter af te stemmen op de onderwijsbehoefte van de kinderen? Hoe pak je differentiatie aan?

Item does not contain fulltext 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. 14 p.

Contains fulltext : 192025.pdf (Publisher’s version ) (Open Access) 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 programme. Effects of both programmes were compared through a quasi-experimental design, and moderation effects of age and 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 programmes and the consequences of variation in these parameters. 11 p.

Item does not contain fulltext Motivation and achievement are known to be related, but the nature of this relation is complex. This study investigated the relations between achievement and several core aspects of motivation for mathematics in primary school: self-efficacy, self-concept, task value, and mathematics anxiety (N = 4306 students of grade 2 - 6). Moreover, it was investigated whether these relations were similar or different for low-achieving, average-achieving, and high-achieving students. Students completed a standardised mathematics achievement test at T1 and T3 and a mathematics motivation questionnaire at T2. Working memory was measured as a covariate. Self-efficacy and self-concept were combined into a single perceived competence variable due to their high intercorrelation. T1 achievement positively predicted perceived competence and task value and negatively predicted mathematics anxiety. Only perceived competence had a significant effect on T3 achievement after controlling for T1 achievement and working memory, and significantly mediated between previous and subsequent achievement. This pattern of effects was largely similar across achievement groups, although the effects of previous achievement on task value and perceived competence were stronger for high-achieving students. In each achievement group, perceived competence was the only motivational variable with a significant effect on subsequent achievement over and above the effects of previous achievement. 13 p.

In this study, we investigated how early numeracy skills develop in kindergarten-age children. The participants were 235 Finnish children (111 girls and 124 boys). At the time of the first measurement, the average age of the children was 6 years. The measurements were conducted three times during 1 year of kindergarten. We used a between-group repeated-measures analysis of variance and post hoc group comparisons for three measurement times on two related mathematical scales. The results showed that differences in mathematics skills among children are already visible in kindergarten before formal primary education in mathematics starts. The early numeracy skills measured, namely, relational skills in a numerical context and counting skills, were weaker over the kindergarten year in low-performing children, and, although their skills improved, they did not catch up to their average peers.

This study examines the relation between math self-concept, test and math anxiety, achievement motivation, and math achievement in typically developing 12 to 14-year-old adolescents (N = 108) from a school for secondary education in the Netherlands. Data was obtained using a math speed test, achievement motivation test, and the math experience questionnaire. A significant positive correlation was found between math self-concept and math achievement in all four math domains (measurement, relations, numbers, and scale), as well as automatized math skills. Furthermore, there was a significant negative correlation between math anxiety and math achievement in the math domain “scale”. Math anxiety was not a mediator in the correlation between math self-concept and math achievement. There was no correlation between achievement motivation, test anxiety, and math achievement. Regression analyses indicated that math self-concept was the only variable that accounted for a significant unique proportion of variance in math scores. Together, these results suggest that stimulating positive feelings and beliefs of students in their own competence in math may lead to better math achievement.

Digital Learning Material (DLM) are fast becoming a key instrument in teaching. The focus on E-learning systems with Digital Learning Material (DLM) is mostly on the medium and resources, instead of on the role of teachers. But like students, teachers also need to professionalize their digital competencies. And rather than describing how the teacher should take up his/her online role, teachers can also be trained by using online materials and experiencing DLM themselves. Therefore the first objective of this study is to design an e-learning system with DLM to train seven vocational math teachers. The second objective is to investigate the aspects of the learning activities in terms of “learning engagement,” “teachers’ self learning process” and “professional learning to enhance teachers’ knowledge.” In this research, teachers participating in this project had a 6 week online training in an e-learning system with DLM. After this, teachers completed the questionnaires on these aspects. Teachers were satisfied with the components “learning engagement” and “teachers’ self learning process.” They specifically appreciated the domain-specific literature and the online moderation of the expert teacher. With regard to the component “professional learning,” teachers did not collaborate and only three teachers abstract and detach information from its original context and applied to it in new contexts by their questions and contributions in the forum discussions. For other teachers the “space to act and arrange” seemed too broadly. Future study should pay more attention to the development of assignments that require specific tasks in collaboration between the teachers.

The diversity of students’ achievement levels within classrooms has made it essential for teachers to adapt their lessons to the varying educational needs of their students (‘differentiation’). However, the term differentiation has been interpreted in diverse ways and there is a need to specify what effective differentiation entails. Previous reports of low to moderate application of differentiation underscore the importance of practical guidelines for implementing differentiation. In two studies, we investigated how teachers should differentiate according to experts, as well as the degree to which teachers already apply the recommended strategies. Study 1 employed the Delphi technique and focus group discussions to achieve consensus among eleven mathematics experts regarding a feasible model for differentiation in primary mathematics. The experts agreed on a five-step cycle of differentiation: (1) identification of educational needs, (2) differentiated goals, (3) differentiated instruction, (4) differentiated practice, and (5) evaluation of progress and process. For each step, strategies were specified. In Study 2, the Differentiation Self-Assessment Questionnaire (DSAQ) was developed to investigate how teachers self-assess their use of the strategies recommended by the experts. While teachers (N = 268) were moderately positive about their application of the strategies overall, we also identified areas of relatively low usage (including differentiation for high-achieving students) which require attention in teacher professional development. Together, these two studies provide a model and strategies for differentiation in primary mathematics based on expert consensus, the DSAQ which can be employed in future studies, and insights into teachers’ self-assessed application of specific aspects of differentiation.

Working memory is an important predictor of academic performance, and of math performance in particular. Most working memory tasks depend on one-to-one administration by a testing assistant, which makes the use of such tasks in large-scale studies time-consuming and costly. Therefore, an online, self-reliant visual–spatial working memory task (the Lion game) was developed for primary school children (6–12 years of age). In two studies, the validity and reliability of the Lion game were investigated. The results from Study 1 (n = 442) indicated satisfactory six-week test–retest reliability, excellent internal consistency, and good concurrent and predictive validity. The results from Study 2 (n = 5,059) confirmed the results on the internal consistency and predictive validity of the Lion game. In addition, multilevel analysis revealed that classroom membership influenced Lion game scores.We concluded that the Lion game is a valid and reliable instrument for the online computerized and self-reliant measurement of visual– spatial working memory (i.e., updating).

In this study, we investigated how early numeracy skills develop in kindergarten-age children. The participants were 235 Finnish children (111 girls and 124 boys). At the time of the first measurement, the average age of the children was 6 years. The measurements were conducted three times during 1 year of kindergarten. We used a between-group repeated-measures analysis of variance and post hoc group comparisons for three measurement times on two related mathematical scales. The results showed that differences in mathematics skills among children are already visible in kindergarten before formal primary education in mathematics starts. The early numeracy skills measured, namely, relational skills in a numerical context and counting skills, were weaker over the kindergarten year in low-performing children, and, although their skills improved, they did not catch up to their average peers.

Background: The goal of this study is to evaluate the effectiveness of a computerised working memory (WM) training on memory, response inhibition, fluid intelligence, scholastic abilities and the recall of stories in adolescents with mild to borderline intellectual disabilities attending special education. Method: A total of 95 adolescents with mild to borderline intellectual disabilities were randomly assigned to either a training adaptive to each child's progress in WM, a non-adaptive WM training, or to a control group. Results: Verbal short-term memory (STM) improved significantly from pre- to post-testing in the group who received the adaptive training compared with the control group. The beneficial effect on verbal STM was maintained at follow-up and other effects became clear at that time as well. Both the adaptive and non-adaptive WM training led to higher scores at follow-up than at post-intervention on visual STM, arithmetic and story recall compared with the control condition. In addition, the non-adaptive training group showed a significant increase in visuo-spatial WM capacity. Conclusion: The current study provides the first demonstration that WM can be effectively trained in adolescents with mild to borderline intellectual disabilities.

Dyscalculie is een synoniem voor een ernstige rekenstoornis. In dit artikel wordt kort aangegeven wat de problemen globaal zijn en wat de stoornis kenmerkt. Deze kenmerken hebben vooral betrekking op problemen met het uitvoeren van denkhandelingen, de informatieverwerking en het probleemoplossingsproces. Daarna wordt een casus beschreven. Het gaat om een diagnostisch onderzoek van Dorine, een pabostudent, die de rekentoets niet haalde en dreigde van de pabo gestuurd te worden. Inhoudelijk wordt ingegaan op haar problemen met het rekenen en de dyscalculieverklaring die ze heeft gehad. Afsluitend wordt beschreven hoe het verder met Dorine is gegaan.