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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.

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.

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).