Der Einfluss des Zahlensinns und räumlicher Informationsverarbeitung auf das Kopfrechnen
Final Report Abstract
This project investigated the functional properties and the contribution of the spatial system and the approximate number system (ANS), i.e. the innate capacity to approximately perceive and process the number of items in a set, to mental arithmetic. To further characterize the ANS, we tested the abstractness of its neural implementation, that is, whether it encodes information regardless of modality or notation. We did not observe a modality-abstract response in the intraparietal sulcus (IPS). In contrast, the human IPS response to sets of spatially distributed dots resembles previous findings at the neuronal level in macaques. To elucidate the question how the ANS contributes to arithmetic competencies, we participated in a developmental cross-sectional study that involved the examination of first- to sixth-graders with mathematical learning difficulties (MLD) and without (control). In line with the idea that mathematical competencies build on the ANS, the MLD group showed significant ANS impairments. ANS performance improved with age for the control group but remained constant for the MLD group. This suggests that the ANS represents a stepping stone for the numerical development. Mental arithmetic requires the combination of information from long-term memory and current information. We provide evidence that both multiplication and subtraction make use of phonological and visuo-spatial working memory resources, contradicting the assumptions of the Triple-Code model, one of the most prominent neuro-cognitive models of number processing. To investigate the contribution of the spatial system we used the operational momentum (OM) effect as a test bed, which arises from attentional biases. The OM effect describes the fact that participants systematically overestimate the results of addition problems while underestimating subtraction results. We found that the OM does not have its origin in the ANS, occurs in non-symbolic (but not symbolic) multiplication and division, develops during the first years in school, and correlates with behavioral attention parameters. Together, these results suggest that visual attention exerts a measurable effect on approximate calculation which is mitigated during arithmetic fact retrieval. Subitizing describes the capacity to effortlessly and flawlessly determine small numerosities from one to three items. Using, fMRI, we found that subitizing involves the individuation of objects in visual space, which, in turn, relies on the flexible allocation of resources in a spatiotopic priority map. In sum, our results show that mental arithmetic crucially hinges on the contribution of the spatial system. The ANS has proven as a stepping stone for the development of numerical competencies.
Publications
- (2013). Examining the presence and determinants of operational momentum in childhood. Frontiers in Psychology, 4:325
Knops, A., Zitzmann, S. & McCrink, K.
(See online at https://doi.org/10.3389/fpsyg.2013.00325) - (2014). A shared, flexible neural map architecture reflects capacity limits in both visual short term memory and enumeration. The Journal of Neuroscience, 34(30); 9857-9866
Knops, A., Piazza, M., Sengupta, R., Eger, E., & Melcher, D.
(See online at https://doi.org/10.1523/JNEUROSCI.2758-13.2014) - (2014). Can Approximate Mental Calculation Account for Operational Momentum in Addition and Subtraction? The Quarterly Journal of Experimental Psychology, 67(8): 1541-1556
Knops, A., Dehaene, S., Bertelletti, I., Zorzi, M.
(See online at https://doi.org/10.1080/17470218.2014.890234) - (2014). In how many ways is the approximate number system associated with exact calculation? PLoS One. 9(11): e111155
Pinheiro-Chargas, P., Wood, G., Knops, A., Krinzinger, H., Lonnemann, J., Startling-Alves, I., Willmes, K., & Haase, V.
(See online at https://doi.org/10.1371/journal.pone.0111155) - (2014). Operational momentum in approximate multiplication and division? PLoS One; 9(8):e104777
Katz, C. & Knops, A.
(See online at https://doi.org/10.1371/journal.pone.0104777) - (2015). Asymmetric activation spreading in the multiplication associative network due to asymmetric overlap between numerosities semantic representations? Cognition, 141, 1-8
Didino, D., Knops, A., Vespignani, F., & Kornpetpanee, S.
(See online at https://doi.org/10.1016/j.cognition.2015.04.002) - (2015). Dissociating estimation from comparison and response eliminates parietal involvement in sequential numerosity perception, Neuroimage, 116: 135-148
Cavdaroglu, S., Katz, C. & Knops, A.
(See online at https://doi.org/10.1016/j.neuroimage.2015.04.019) - (2016). Considering structural connectivity in the triple code model of numerical cognition – Differential connectivity for magnitude processing and arithmetic facts. Brain Structure & Function, 221(2): 979-95
Klein, E., Suchan, J., Moeller, K., Karnath, H.-O., Knops, A., Wood, G., Nuerk, H.-C., & Willmes, K.
(See online at https://doi.org/10.1007/s00429-014-0951-1) - (2016). Decreased cerebellar-cerebral connectivity contributes to complex task performance. Journal of Neurophysiology, 116, 1434–1448
Katz, C. & Knops, A.
(See online at https://doi.org/10.1152/jn.00684.2015) - (2016). Mental subtraction and multiplication recruit both phonological and visuospatial resources: evidence from a symmetric dual-task design. Psychological Research, 80(4): 608-624
Cavdaroglu, S. & Knops, A.
(See online at https://doi.org/10.1007/s00426-015-0667-8)
