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The development of numerical abilities

The development of numerical abilities is crucial in our modern societies and constitute a critical foundation in order to acquire arithmetic and mathematical knowledge. One important stepping stone for the acquisition of numerical abilities is the construction of symbolic numerical knowledge: Children have to learn to represent numerical information via symbols, which can be number words or Arabic digits. In our research, we focus on how the brain constructs symbolic representations of numerical magnitude (i.e., knowledge about the number of objects) and numerical order (i.e., knowledge about the relative rank or position within a sequence) in children and adults.

Findings from our research has shown that the left intraparietal sulcus (IPS) of the parietal cortex is sensitive to the processing of numerical magnitudes and that this region shows a developmental specialization to represent symbolic information about numerical magnitudes. This brain specialization is characterized by an age-related increase in brain activity, which suggests an automatization of the left IPS to process symbolic numerical information as children get more experienced. Results from our work on numerical order has demonstrated that the understanding of numerical order (a) explains unique variance in children’s arithmetic abilities, (b) mediates the well-established association between numerical magnitude processing and arithmetic, and (c) shows specific neurocognitive developmental trajectories within the first years of formal education. More specifically, our recent neuroimaging work has demonstrated that the left IPS also shows an age-dependent increase in brain activation in response to numerical order processing. Furthermore, we found a significant association between the neural responses of ordinal processing and arithmetic performance in regions of the semantic control network, especially in the right posterior middle temporal gyrus (pMTG) and at the right inferior frontal gyrus (IFG). Together, these findings indicate that multiple resources work in concert to support the construction of symbolic representations in the brain.

Selected publications (*shared authorships)

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

Goffin, C., Vogel, S. E., Slipenkyj, M., & Ansari, D. (2020). A comes before B, like 1 comes before 2. Is the parietal cortex sensitive to ordinal relationships in both numbers and letters? An fMRI-adaptation study. Human Brain Mapping, 41(6), 1591–1610. https://doi.org/10.1002/hbm.24897

Vogel, S. E., Koren, N., Falb, S., Haselwander, M., Spradley, A., Schadenbauer, P., Tanzmeister, S., & Grabner, R. H. (2019). Automatic and intentional processing of numerical order and its relationship to arithmetic performance. Acta Psychologica, 193, 30–41. https://doi.org/10.1016/j.actpsy.2018.12.001

Vogel, S. E., Goffin, C., Bohnenberger, J., Koschutnig, K., Reishofer, G., Grabner, R. H., & Ansari, D. (2017). The left intraparietal sulcus adapts to symbolic number in both the visual and auditory modalities: Evidence from fMRI. NeuroImage, 153, 16–27. https://doi.org/10.1016/j.neuroimage.2017.03.048

Wilkey, E. D., Barone, J. C., Mazzocco, M. M. M., Vogel, S. E., & Price, G. R. (2017). The effect of visual parameters on neural activation during nonsymbolic number comparison and its relation to math competency. NeuroImage, 159, 430–442. https://doi.org/10.1016/j.neuroimage.2017.08.023

Vogel, S. E., Haigh, T., Sommerauer, G., Spindler, M., Brunner, C., Lyons, I. M., & Grabner, R. H. (2017). Processing the order of symbolic numbers: A reliable and unique predictor of arithmetic fluency. Journal of Numerical Cognition, 3(2), 288–308. https://doi.org/10.5964/jnc.v3i2.55

Lyons, I. M., Vogel, S. E., & Ansari, D. (2016). On the ordinality of numbers: A review of neural and behavioural studies. Progress in Brain Research, 227, 187–221. https://doi.org/10.1016/S1099-4831(10)06803-3

Leibovich, T., Vogel, S. E., Henik, A., & Ansari, D. (2015). Asymmetric Processing of Numerical and Nonnumerical Magnitudes in the Brain: An fMRI Study. Journal of Cognitive Neuroscience, 28(1), 166–176. doi.org/10.1162/jocn_a_00887

Vogel, S. E., Goffin, C., & Ansari, D. (2015). Developmental specialization of the left parietal cortex for the semantic representation of Arabic numerals: An fMR-Adaptaton study. Developmental Cognitive Neuroscience, 12, 61–73. https://doi.org/10.1016/j.dcn.2014.12.001

Vogel, S. E., Remark, A., & Ansari, D. (2015). Differential processing of symbolic numerical magnitude and order in first-grade children. Journal of Experimental Child Psychology, 129, 26–39. https://doi.org/10.1016/j.jecp.2014.07.010

Vogel, S. E., Grabner, R. H., Schneider, M., Siegler, R. S., & Ansari, D. (2013). Overlapping and distinct brain regions involved in estimating the spatial position of numerical and non-numerical magnitudes: An fMRI study. Neuropsychologia, 51(5), 979–989. doi.org/10.1016/j.neuropsychologia.2013.02.001


Priv.-Doz. Mag.rer.nat. PhD

Stephan Vogel

Institut für Psychologie

Phone:+43 316 380 - 8478

nach Vereinbarung

Head of section

Univ.-Prof. Mag. Dr.rer.nat.

Roland Grabner

Institut für Psychologie



Silvia Haberhofer

Institut für Psychologie

Phone:+43 316 380 - 8536

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