Numerical cognition and mathematics learning

Mathematical learning difficulties (i.e. dyscalculia) occur when children do not understand the meaning of numbers. To help these children, we need to know how our minds and brains learn and represent the meaning of numbers. Our research uses various behavioral and neuroimaging methods to investigate the basic principles of this process. This knowledge can provide crucial insights into why some children have difficulty grasping the meaning of numbers. Ultimately, they can lead to interventions that effectively promote the development of mathematical skills in children with learning difficulties.

1. Vogel, S. E. & B. De Smedt. (2021). Developmental brain dynamics of numerical and arithmetic abilities. Npj Science of Learning, 6(1), Article 1. https://doi.org/10.1038/s41539-021-00099-3
2. Sommerauer, G., Graß, K.-H., Grabner, R. H., & Vogel, S. E. (2020). The semantic control network mediates the relationship between symbolic numerical order processing and arithmetic performance in children. Neuropsychologia, 141, 107405. https://doi.org/10.1016/j.neuropsychologia.2020.107405
3. Heidekum, A. E., Grabner, R. H., De Smedt, B., De Visscher, A., & Vogel, S. E. (2019). Interference during the retrieval of arithmetic and lexico-semantic knowledge modulates similar brain regions: Evidence from functional magnetic resonance imaging (fMRI). Cortex, 120, 375-393. https://doi.org/10.1016/j.cortex.2019.06.007

Many children and adults find it difficult to learn and apply efficient calculation strategies. The consequences of inefficient strategies and the resulting miscalculations can be severe and also very costly. We are using imaging techniques to better understand how the brain supports the acquisition of computational strategies and how we switch from ineffective computational strategies (e.g. counting) to more efficient ones (e.g. recalling arithmetic facts). The findings from this research can be directly applied to the classroom and form the knowledge base for research into brain stimulation techniques to promote and improve the development of arithmetic strategies.

1. Brunner, C., Koren, N. A., Scheucher, J., Mosbacher, J. A., De Smedt, B., Grabner, R. H., & Vogel, S. E. (2021). Oscillatory electroencephalographic patterns of arithmetic problem solving in fourth graders. Scientific Reports, 11(1), Article 1. https://doi.org/10.1038/s41598-021-02789-9
2. Grabner, R. H., Brunner, C., Lorenz, V., Vogel, S. E., & De Smedt, B. (2021). Fact retrieval or compacted counting in arithmetic-A neurophysiological investigation of two hypotheses. Journal of Experimental Psychology. Learning, Memory, and Cognition. https://doi.org/10.1037/xlm0000982

Have you ever wondered why some people seem to be better at math, such as how much money they spent on their lunch or at the market? To answer this question, we need to examine the factors that influence this ability and understand how the brain works when doing calculations. One of these central factors is metacognition: the ability to monitor mental operations (e.g. knowing that I have made a mistake) and adjust them accordingly (e.g. changing strategies). In this project, we will use a combination of cross-sectional and longitudinal experiments and imaging techniques (EEG) to investigate the mental and brain processes associated with metacognitive regulation and computation in children and adults. The findings from this work will help us improve teaching materials and learning methods to help all people perform better in math.

1. Vogel, S. E., & De Smedt, B. (2021). Developmental brain dynamics of numerical and arithmetic abilities. Npj Science of Learning, 6(1), Article 1. https://doi.org/10.1038/s41539-021-00099-3
2. Bellon, E., Fias, W., & De Smedt, B. (2019). More than number sense: The additional role of executive functions and metacognition in arithmetic. Journal of Experimental Child Psychology, 182, 38-60. https://doi.org/10.1016/j.jecp.2019.01.012
3. Bellon, E., Fias, W., Ansari, D., & De Smedt, B. (2020). The neural basis of metacognitive monitoring during arithmetic in the developing brain. Human Brain Mapping, 41(16), 4562-4573. https://doi.org/10.1002/hbm.25142

Is the equation 1/3 + 1/4 = 2/7 correct? Or is it not? Sometimes our first impression contradicts scientific findings: the above equation feels right, but it is not (1/3 + 1/4 = 7/12). We often give in to this intuition and make hasty decisions, which can also lead us to make critical mistakes. In this research area, we investigate how the human brain represents mathematical (mis)concepts and how we can suppress and overcome intuitive mistakes in the context of mathematics. The findings from this research help us to develop new learning and teaching methods to counteract conceptual misconceptions and reduce interference.

1. Stricker, J., Vogel, S. E., Schöneburg-Lehnert, S., Krohn, T., Dögnitz, S., Jud, N., Spirk, M., Windhaber, M.-C., Schneider, M., & Grabner, R. H. (2021). Interference between naïve and scientific theories occurs in mathematics and is related to mathematical achievement. Cognition, 214, 104789. https://doi.org/10.1016/j.cognition.2021.104789
2. Meier, M. A., Wambacher, D., Vogel, S. E., & Grabner, R. H. (2022). Interference between naïve and scientific theories in mathematics and science: An fMRI study comparing mathematicians and non-mathematicians. Trends in Neuroscience and Education, 29, 100194. https://doi.org/10.1016/j.tine.2022.100194

Learning environments in which learning content is presented in languages other than the learners' mother tongue have become increasingly popular in recent years. However, this type of learning is always associated with costs, which arise as soon as the acquired knowledge is needed in another language. These costs can affect both the accuracy and the speed of reproduction of this content in another language. In the course of the BilMath project, we are trying to understand the mechanisms behind these costs in more detail. The knowledge gained can thus contribute to the efficient design of multilingual learning environments.

1. Wußing, M., Grabner, R. H., Sommer, H., & Saalbach, H. (2023) Language-switching and retrieval-based learning: an unfavorable combination Frontiers in Psychology, 14, https://doi.org/10.3389%2Ffpsyg.2023.1198117
2. Saalbach, H., Eckstein, D., Andri, N., Hobi, R., & Grabner, R. H. (2013). When language of instruction and language of application differ: Cognitive costs of bilingual mathematics learning. Learning and Instruction, 26, 36-44. doi. org/10.1016/j.learninstruc.2013.01.002