Organisation und Leitung: Roland H. Grabner | Pädagogische Neurowissenschaften , Institut für Psychologie, Universität Graz, Österreich
Diskutant: Andreas Obersteiner | Institut für Mathematische Bildung, Pädagogische Hochschule Freiburg, Deutschland
There is increasing awareness and empirical evidence that mathematical competencies are key cognitive abilities in modern technological societies. They have been found to be equally important for life success as reading and writing abilities, and deficits in these competencies place a heavy burden on the individual and major costs on nations. In light of their paramount importance, the last decade has witnessed a tremendous increase of educational neuroscience research on the development of mathematical competencies. The research field of educational neuroscience is characterized by a multi-methodological and inter-disciplinary approach that aims to advance our understanding of school-related learning by integrating different levels of analyses. This symposium consists of four papers in which the added value of this research approach for a more comprehensive understanding of individual differences in mathematics learning are illustrated. First, Stephan E. Vogel presents behavioral and neuroimaging studies that underline the importance of individual differences in numerical order processing for arithmetic skills and that provide novel insights into the underlying neuro-cognitive mechanisms. In the second paper, Bert De Smedt demonstrates how brain imaging data can contribute not only to a more comprehensive understanding of arithmetic development in children but also to the prediction ofindividual differences in arithmetic skills. The third paper by Dietsje Jolles reveals how an intensive math tutoring program in school reorganizes large-scale brain circuits and that individual differences in performance gains were associated with functional and structural connectivity changes in these circuits. In the fourth contribution, Michael A. Skeide adds the genetic level of analysis and provides first insights into associations between candidate genes for mathematical performance, brain structure in children before schooling, and their mathematical competencies in elementary school. The four papers of the symposium will finally be discussed by Andreas Obersteiner with specific attention to implications for mathematics education research and practice.
On the representation of order and how it relates to individual differences in arithmetic abilities.
Stephan E. Vogel | Education al Neuroscience, Institute of Psychology, University of Graz, Austria
A growing body of studies has provided compelling evidence that individual variations in symbolic number processing are associated with arithmetic abilities in children and adults. Although our knowledge about how the human mind and brain mediates this relationship has significantly increased over the past years, a number of important questions about the involved cognitive mechanisms and their cortical specialization remain to be answered. In this talk, I will discuss a set of behavioural and neuroimaging studies that focus on one central feature of symbolic number representation: that of numerical order—defined as the knowledge that a number symbol contains information about its relative rank or position within a particular sequence (e.g., the number 203 comes right before 204 and after 202).
The first of these studies examines the unique contribution of symbolic ordinal processing to arithmetic abilities in adults. Findings from this work demonstrate that symbolic ordinal processing engages different cognitive mechanisms compared to non-symbolic ordinal processing and that symbolic relationships constitute a reliable predictor of arithmetic fluency. The second work investigates whether symbolic relationships are processed without conscious monitoring (i.e., automatically) and whether intentional or automatic processing are differentially related to arithmetic performance. The results of this work suggest that ascending symbolic relationships (i.e., 5 6 7) are processed without conscious monitoring and that only variations in intentional ordinal processing are associated with arithmetic fluency. Finally, I will present novel neuroimaging data from functional resonance imaging (fMRI) studies in which we investigate the neural correlates of ordinal relationships and how these brain responses mediate the relationship with arithmetic abilities in primary school children. Findings from this work highlight the engagement of a brain network that is associated with the acquisition of object associations, and that individual variations in brain activation constitute a significant predictor of arithmetic abilities over and above the processing of symbolic numerical magnitudes (i.e., knowledge of the quantity to which a number symbols refers). I will conclude this talk by integrating these different findings and by discussing how numerical order contributes to our understanding of the development of arithmetic abilities.
Arithmetic in the developing brain
Bert De Smedt | Faculty of Psychology and Educational Sciences, University of Leuven, Belgium
What has educational neuroscience contributed to our understanding of the development of arithmetic in children? I will provide three examples that speak to this question and for each of them, I will illustrate the value added of brain imaging data. Decades of behavioral data have shown that the development of arithmetic is characterized by strategy shifts between procedural strategy use and arithmetic fact retrieval. In a first study in fourth graders, which focused on subtraction and multiplication, we observed that brain activity during arithmetic in children was modulated by these different strategies. Specifically, procedural strategy use was correlated with increases in brain activity in a wide fronto-parietal network, whereas retrieval strategy use was associated with increases in the angular gyri and middle temporal lobe. In a second, more recent, study in fourth grade children, we manipulated the transition from procedural strategy use to fact retrieval via an fMRI training study in which children had to learn new sets of multi-digit multiplications. This allowed us to experimentally investigate how brain networks change when children’s strategies change as a function of learning. This data revealed a significant reduction of fronto-parietal activity in newly learned multi-digit multiplications after training, making them similar in terms of their brain activity patterns compared to previously learned (easier) single-digit multiplications. In a final study, we investigated the extent to which structural brain imaging data can be used to predict individual differences in arithmetic fluency. In this study, fourth grade children completed a wide range of measures that are known to be critical cognitive predictors of arithmetic fluency. Diffusion weighted imaging data and structural MRI data were further collected to investigate white and grey matter, respectively. Symbolic number processing and rapid automatized naming were critical behavioral predictors of arithmetic. The right Inferior Longitudinal Fasciculus and complexity of the left postcentral gyrus were critical neuroanatomical predictors of arithmetic. A regression model with all collected measures indicated that the neuro-anatomical predictors provided the best prediction of individual differences in arithmetic fluency.
Reconfiguration of large-scale brain circuits with math tutoring in elementary school children
Dietsje Jolles | Institute of Education and Child Studies, Leiden University, The Netherlands
Most current theories of neurocognitive development emphasize the role of experience in shaping brain function and structure. Little is known, however, about brain plasticity associated with learning in domains of academic relevance such as mathematics. Here, we will present a series of analyses investigating the reorganization of brain circuits in response to an intensive math tutoring program in third-grade children. The program emphasized both procedural and conceptual knowledge, as well as fluent math fact retrieval. In line with prior classroom-based studies, math performance improved after tutoring, and there was a shift from counting to memory-based retrieval. To examine changes in functional network organization, we performed resting-state fMRI analyses focusing on connectivity of the intraparietal sulcus (IPS) and the angular gyrus (AG), two cytoarchitectonicallydistinct subdivisions of the parietal cortex with different roles in math cognition. Results showed increased connectivity of the IPS with lateral prefrontal cortex and ventral temporal-occipital cortex, regions typically co-activated with IPS during math performance. In contrast, AG showed increased connectivity with pre/postcentral gyrus. These findings are in line with an interactive specialization account of functional brain development, which postulates that experience drives differentiation between functional brain networks. Nevertheless, there was also one area of convergence; IPS and AG showed similar levels of tutoring-related connectivity changes with the medial temporal lobe (MTL). Importantly, there were large individual differences in performance gains, which were correlated with connectivity changes of the IPS (but not AG). Furthermore, diffusion tensor imaging (DTI) data revealed that individual differences in performance gains were also associated with plasticity in the underlying white matter, particularly the fronto-temporal section of the left superior longitudinal fasciculus (SLF). Finally, in a task-based connectivity study, we found that increases in connectivity between IPS and MTL were associated with training-induced increases in retrieval use, recapitulating previously reported longitudinal changes in IPS-MTL connectivity. Taken together, our findings provide important insights into experience-dependent brain network changes, showing differentiation of parietal networks, as well as integration between parietal cortex and MTL in relation to math skill acquisition.
A gene-brain-behavior pathway to individual differences in mathematical ability
Michael A. Skeide | Department of Neuropsychology, Max Planck Institute for Human Cognitive and Brain Sciences, Leipzig, Germany
Mathematical ability is shaped by a complex interplay between genetic and environmental factors, in which genetic variance explains about 60% of the behavioral variance. Building on this evidence, several DNA variants have been found to be associated with mathematical performance. Many of these variants are located on genes that express proteins in the brain. It is unknown, however, which intermediate neuralphenotypes could explain how DNA variation relates to mathematical ability.
The aim of the present study was to explore associations between known math candidate genes and brain structure in children that did not yet receive math instruction. In addition, we investigated longitudinally whether these associations would predict mathematical ability in school. We selected 18 single nucleotide polymorphisms on 10 genes previously found to be associated with mathematical ability. Associations between these SNPs and grey matter volume were calculated at the whole-brain level in a sample of 101 children aged 3-6 years. Individual volume clusters obtained from the genetic association model were then related to individual math test scores in second grade (8-9 years of age).
ROBO1, a gene known to regulate prenatal growth of cerebral cortical layers, was found to be specifically associated with the volume of the right parietal cortex, a key region for numerosity representation (d = 1.86, P < 0.05, family-wise-error-corrected). Individual volume differences in this region predicted more than a fifth of variance in mathematical ability (R² = 0.21, P < 0.05). This prediction effect was not explained by parental education levels which served as a proxy for the quality of the home learning environment.
Our findings suggest that a fundamental genetic component of the numerosity processing system may be rooted in the early development of the parietal cortex.