Weaker number sense accounts for impaired numerosity perception in dyscalculia: Behavioral and computational evidence.
approximate number system
continuous visual magnitudes
deep neural networks
developmental dyscalculia
numerical cognition
Journal
Developmental science
ISSN: 1467-7687
Titre abrégé: Dev Sci
Pays: England
ID NLM: 9814574
Informations de publication
Date de publication:
01 Jul 2024
01 Jul 2024
Historique:
revised:
29
04
2024
received:
23
05
2023
accepted:
27
05
2024
medline:
1
7
2024
pubmed:
1
7
2024
entrez:
1
7
2024
Statut:
aheadofprint
Résumé
Impaired numerosity perception in developmental dyscalculia (low "number acuity") has been interpreted as evidence of reduced representational precision in the neurocognitive system supporting non-symbolic number sense. However, recent studies suggest that poor numerosity judgments might stem from stronger interference from non-numerical visual information, in line with alternative accounts that highlight impairments in executive functions and visuospatial abilities in the etiology of dyscalculia. To resolve this debate, we used a psychophysical method designed to disentangle the contribution of numerical and non-numerical features to explicit numerosity judgments in a dot comparison task and we assessed the relative saliency of numerosity in a spontaneous categorization task. Children with dyscalculia were compared to control children with average mathematical skills matched for age, IQ, and visuospatial memory. In the comparison task, the lower accuracy of dyscalculics compared to controls was linked to weaker encoding of numerosity, but not to the strength of non-numerical biases. Similarly, in the spontaneous categorization task, children with dyscalculia showed a weaker number-based categorization compared to the control group, with no evidence of a stronger influence of non-numerical information on category choice. Simulations with a neurocomputational model of numerosity perception showed that the reduction of representational resources affected the progressive refinement of number acuity, with little effect on non-numerical bias in numerosity judgments. Together, these results suggest that impaired numerosity perception in dyscalculia cannot be explained by increased interference from non-numerical visual cues, thereby supporting the hypothesis of a core number sense deficit. RESEARCH HIGHLIGHTS: A strongly debated issue is whether impaired numerosity perception in dyscalculia stems from a deficit in number sense or from poor executive and visuospatial functions. Dyscalculic children show reduced precision in visual numerosity judgments and weaker number-based spontaneous categorization, but no increasing reliance on continuous visual properties. Simulations with deep neural networks demonstrate that reduced neural/computational resources affect the developmental trajectory of number acuity and account for impaired numerosity judgments. Our findings show that weaker number acuity in developmental dyscalculia is not necessarily related to increased interference from non-numerical visual cues.
Types de publication
Journal Article
Langues
eng
Sous-ensembles de citation
IM
Pagination
e13538Subventions
Organisme : Cariparo Foundation (Italy)
ID : NUMSENSE
Organisme : Italian Ministry of Education and Research
ID : 2022EBC78W
Informations de copyright
© 2024 The Author(s). Developmental Science published by John Wiley & Sons Ltd.
Références
American Psychiatric Association. (2013). Diagnostic and statistical manual of mental disorders (5th ed.). American Psychiatric Association.
Abalo‐Rodríguez, I., De Marco, D., & Cutini, S. (2022). An undeniable interplay: Both numerosity and visual features affect estimation of non‐symbolic stimuli. Cognition, 222, 104944. https://doi.org/10.1016/j.cognition.2021.104944
Ashkenazi, S., Rosenberg‐Lee, M., Metcalfe, A. W. S., Swigart, A. G., & Menon, V. (2013). Visuo‐spatial working memory is an important source of domain‐general vulnerability in the development of arithmetic cognition. Neuropsychologia, 51(11), 2305–2317. https://doi.org/10.1016/j.neuropsychologia.2013.06.031
Bartelet, D., Ansari, D., Vaessen, A., & Blomert, L. (2014). Cognitive subtypes of mathematics learning difficulties in primary education. Research in Developmental Disabilities, 35(3), 657–670. https://doi.org/10.1016/j.ridd.2013.12.010
Biancardi, A., Nicoletti, C., & Bachmann, C. (2016). BDE 2‐Batteria discalculia evolutiva: Test per la diagnosi dei disturbi dell'elaborazione numerica e del calcolo in età evolutiva–8‐13 anni. Edizioni Centro Studi Erickson.
Bugden, S., & Ansari, D. (2016). Probing the nature of deficits in the “Approximate Number System” in children with persistent Developmental Dyscalculia. Developmental Science, 19(5), 817–833. https://doi.org/10.1111/desc.12324
Bulthé, J., Prinsen, J., Vanderauwera, J., Duyck, S., Daniels, N., Gillebert, C. R., Mantini, D., Op de Beeck, H. P., & De Smedt, B. (2019). Multi‐method brain imaging reveals impaired representations of number as well as altered connectivity in adults with dyscalculia. NeuroImage, 190, 289–302. https://doi.org/10.1016/j.neuroimage.2018.06.012
Butterworth, B., Varma, S., & Laurillard, D. (2011). Dyscalculia: From brain to education. Science, 332, 1049–1053. https://doi.org/10.1126/science.1201536
Cantrell, L., Boyer, T. W., Cordes, S., & Smith, L. B. (2015). Signal clarity: An account of the variability in infant quantity discrimination tasks. Developmental Science, 18(6), 877–893. https://doi.org/10.1111/desc.12283
Cappelletti, M., Didino, D., Stoianov, I., & Zorzi, M. (2014). Number skills are maintained in healthy ageing. Cognitive Psychology, 69, 25–45. https://doi.org/10.1016/j.cogpsych.2013.11.004
Castaldi, E., Mirassou, A., Dehaene, S., Piazza, M., & Eger, E. (2018). Asymmetrical interference between number and item size perception provide evidence for a domain specific impairment in dyscalculia. PloS ONE, 13(12), e0209256. https://doi.org/10.1101/332155
Chen, Q., & Li, J. (2014). Association between individual differences in non‐symbolic number acuity and math performance: A meta‐analysis. Acta Psychologica, 148, 163–172. https://doi.org/10.1016/j.actpsy.2014.01.016
Cirino, P. T., Fuchs, L. S., Elias, J. T., Powell, S. R., & Schumacher, R. F. (2015). Cognitive and mathematical profiles for different forms of learning difficulties. Journal of Learning Disabilities, 48(2), 156–175. https://doi.org/10.1177/0022219413494239
Clayton, S., & Gilmore, C. (2015). Inhibition in dot comparison tasks. ZDM, 47(5), 759–770. https://doi.org/10.1007/s11858‐014‐0655‐2
Clayton, S., Gilmore, C., & Inglis, M. (2015). Dot comparison stimuli are not all alike: The effect of different visual controls on ANS measurement. Acta Psychologica, 161, 177–184. https://doi.org/10.1016/j.actpsy.2015.09.007
Cragg, L., & Gilmore, C. (2014). Skills underlying mathematics: The role of executive function in the development of mathematics proficiency. Trends in Neuroscience and Education, 3(2), 63–68. https://doi.org/10.1016/j.tine.2013.12.001
Dakin, S. C., Tibber, M. S., Greenwood, J. A., Kingdom, F. A. A., & Morgan, M. J. (2011). A common visual metric for approximate number and density. Proceedings of the National Academy of Sciences of the United States of America, 108(49), 19552–19557. https://doi.org/10.1073/pnas.1113195108
Decarli, G., Paris, E., Tencati, C., Nardelli, C., Vescovi, M., Surian, L., & Piazza, M. (2020). Impaired large numerosity estimation and intact subitizing in developmental dyscalculia. PLoS ONE, 15(12), e0244578. https://doi.org/10.1371/journal.pone.0244578
Decarli, G., Sella, F., Lanfranchi, S., Gerotto, G., Gerola, S., Cossu, G., & Zorzi, M. (2023). Severe developmental dyscalculia is characterized by core deficits in both symbolic and nonsymbolic number sense. Psychological Science, 34(1), 8–21. https://doi.org/10.1177/09567976221097947
Decarli, G., Zingaro, D., Surian, L., & Piazza, M. (2023). Number sense at 12 months predicts 4‐year‐olds’ maths skills. Developmental Science, 26(6), e13386. https://doi.org/10.1111/desc.13386
Dehaene, S. (2011). The number sense: How the mind creates mathematics. Oxford University Press.
Dehaene, S., Dehaene‐Lambertz, G., & Cohen, L. (1998). Abstract representations of numbers in the animal and human brain. Trends in Neurosciences, 21(8), 355–361. https://doi.org/10.1016/S0166‐2236(98)01263‐6
DeWind, N. K., Adams, G. K., Platt, M. L., & Brannon, E. M. (2015). Modeling the approximate number system to quantify the contribution of visual stimulus features. Cognition, 142, 247–265. https://doi.org/10.1016/j.cognition.2015.05.016
DeWind, N. K., & Brannon, E. M. (2016). Significant inter‐test reliability across approximate number system assessments. Frontiers in Psychology, 7, 310. https://doi.org/10.3389/fpsyg.2016.00310
Dziak, J. J., Dierker, L. C., & Abar, B. (2020). The interpretation of statistical power after the data have been gathered. Current Psychology, 39, 870–877.
Ferrigno, S., Jara‐Ettinger, J., Piantadosi, S. T., & Cantlon, J. F. (2017). Universal and uniquely human factors in spontaneous number perception. Nature Communications, 8, 13968. https://doi.org/10.1038/ncomms13968
Fias, W., Menon, V., & Szucs, D. (2013). Multiple components of developmental dyscalculia. Trends in Neuroscience and Education, 2(2), 43–47. https://doi.org/10.1016/j.tine.2013.06.006
Gebuis, T., & Reynvoet, B. (2012a). The interplay between nonsymbolic number and its continuous visual properties. Journal of Experimental Psychology: General, 141(4), 642–648. https://doi.org/10.1037/a0026218
Gebuis, T., & Reynvoet, B. (2012b). The role of visual information in numerosity estimation. PLoS ONE, 7(5), e37426. https://doi.org/10.1371/journal.pone.0037426
Gilmore, C., Attridge, N., Clayton, S., Cragg, L., Johnson, S., Marlow, N., Simms, V., & Inglis, M. (2013). Individual differences in inhibitory control, not non‐verbal number acuity, correlate with mathematics achievement. PloS ONE, 8(6), e67374. https://doi.org/10.1371/journal.pone.0067374
Halberda, J., & Feigenson, L. (2008). Developmental change in the acuity of the “Number Sense”: The approximate number system in 3‐, 4‐, 5‐, and 6‐year‐olds and adults. Developmental Psychology, 44(5), 1457–1465. https://doi.org/10.1037/a0012682
Halberda, J., Mazzocco, M. M. M., & Feigenson, L. (2008). Individual differences in non‐verbal number acuity correlate with maths achievement. Nature, 455(7213), 665–668. https://doi.org/10.1038/nature07246
Hannula, M. M., Lepola, J., & Lehtinen, E. (2010). Spontaneous focusing on numerosity as a domain‐specific predictor of arithmetical skills. Journal of Experimental Child Psychology, 107(4), 394–406. https://doi.org/10.1016/j.jecp.2010.06.004
Hinton, G. E., & Salakhutdinov, R. R. (2006). Reducing the dimensionality of data with neural networks. Science, 313(5786), 504–507. https://doi.org/10.1126/science.1127647
Iuculano, T., Rosenberg‐Lee, M., Richardson, J., Tenison, C., Fuchs, L., Supekar, K., & Menon, V. (2015). Cognitive tutoring induces widespread neuroplasticity and remediates brain function in children with mathematical learning disabilities. Nature Communications, 6, 8453. https://doi.org/10.1038/ncomms9453
Izard, V., Sann, C., Spelke, E. S., & Streri, A. (2009). Newborn infants perceive abstract numbers. Proceedings of the National Academy of Sciences, 106(25), 10382–10385. https://doi.org/10.1073/pnas.0812142106
Kass, R. E., & Raftery, A. E. (1995). Bayes factors. Journal of the American Statistical Association, 90(430), 773–795.
Kaufmann, L., Mazzocco, M. M., Dowker, A., von Aster, M., Göbel, S. M., Grabner, R. H., Henik, A., Jordan, N. C., Karmiloff‐Smith, A. D., Kucian, K., Rubinsten, O., Szucs, D., Shalev, R., & Nuerk, H. C. (2013). Dyscalculia from a developmental and differential perspective. Frontiers in Psychology, 4, 516. https://doi.org/10.3389/fpsyg.2013.00516
Kuhl, U., Friederici, A. D., Legascreen Consortium, & Skeide, M. A. (2020). Early cortical surface plasticity relates to basic mathematical learning. NeuroImage, 204, 116235. https://doi.org/10.1016/j.neuroimage.2019.116235
Kuhl, U., Sobotta, S., Legascreen Consortium, & Skeide, M. A. (2021). Mathematical learning deficits originate in early childhood from atypical development of a frontoparietal brain network. PLoS Biology, 19(9), e3001407. https://doi.org/10.1371/journal.pbio.3001407
Korkman, M., Kirk, U., & Kemp, S. (2007). NEPSY‐II: A developmental neuropsychological assessment. The Psychological Corporation.
Kucian, K., Ashkenazi, S. S., Hänggi, J., Rotzer, S., Jäncke, L., Martin, E., & Aster, M. V. (2014). Developmental dyscalculia: A dysconnection syndrome? Brain Structure & Function, 219, 1721–1733. https://doi.org/10.1007/s00429‐013‐0597‐4
Landerl, K., Bevan, A., & Butterworth, B. (2004). Developmental dyscalculia and basic numerical capacities: A study of 8–9‐year‐old students. Cognition, 93(2), 99–125.
Landerl, K., Fussenegger, B., Moll, K., & Willburger, E. (2009). Dyslexia and dyscalculia: Two learning disorders with different cognitive profiles. Journal of Experimental Child Psychology, 103(3), 309–324. https://doi.org/10.1016/j.jecp.2009.03.006
Leibovich, T., & Henik, A. (2014). Comparing performance in discrete and continuous comparison tasks. Quarterly Journal of Experimental Psychology, 67(5), 899–917. https://doi.org/10.1080/17470218.2013.837940
Libertus, M. E., & Brannon, E. M. (2010). Stable individual differences in number discrimination in infancy. Developmental Science, 13(6), 900–906. https://doi.org/10.1111/j.1467‐7687.2009.00948.x
Mammarella, I. C., Caviola, S., Giofrè, D., & Szűcs, D. (2018). The underlying structure of visuospatial working memory in children with mathematical learning disability. British Journal of Developmental Psychology, 36(2), 220–235. https://doi.org/10.1111/bjdp.12202
Mazzocco, M. M. M., Feigenson, L., & Halberda, J. (2011). Impaired acuity of the approximate number system underlies mathematical learning disability (dyscalculia). Child Development, 82(4), 1224–1237. https://doi.org/10.1111/j.1467‐8624.2011.01608.x
McCaskey, U., Von Aster, M., Maurer, U., Martin, E., O'Gorman Tuura, R., & Kucian, K. (2018). Longitudinal brain development of numerical skills in typically developing children and children with developmental dyscalculia. Frontiers in Human Neuroscience, 11, 629. https://doi.org/10.3389/fnhum.2017.00629
Mejias, S., Grégoire, J., & Noël, M. P. (2012). Numerical estimation in adults with and without developmental dyscalculia. Learning and Individual Differences, 22(1), 164–170. https://doi.org/10.1016/j.lindif.2011.09.013
Mejias, S., Mussolin, C., Rousselle, L., Grégoire, J., & Noël, M. P. (2012). Numerical and nonnumerical estimation in children with and without mathematical learning disabilities. Child Neuropsychology, 18(6), 550–575. https://doi.org/10.1080/09297049.2011.625355
Molko, N., Cachia, A., Rivière, D., Mangin, J. F., Bruandet, M., Le Bihan, D., Cohen, L., & Dehaene, S. (2003). Functional and structural alterations of the intraparietal sulcus in a developmental dyscalculia of genetic origin. Neuron, 40(4), 847–858. https://doi.org/10.1016/S0896‐6273(03)00670‐6
Mussolin, C., De Volder, A., Grandin, C., Schlögel, X., Nassogne, M. C., & Noël, M. P. (2010). Neural correlates of symbolic number comparison in developmental dyscalculia. Journal of Cognitive Neuroscience, 22(5), 860–874. https://doi.org/10.1162/jocn.2009.21237
Mussolin, C., Mejias, S., & Noël, M. P. (2010). Symbolic and nonsymbolic number comparison in children with and without dyscalculia. Cognition, 115(1), 10–25. https://doi.org/10.1016/j.cognition.2009.10.006
Noël, M. P., & Rousselle, L. (2011). Developmental changes in the profiles of dyscalculia: An explanation based on a double exact‐and‐approximate number representation model. Frontiers in Human Neuroscience, 5, 1–4. https://doi.org/10.3389/fnhum.2011.00165
Nys, J., & Content, A. (2012). Judgement of discrete and continuous quantity in adults: Number counts! Quarterly Journal of Experimental Psychology, 65(4), 675–690. https://doi.org/10.1080/17470218.2011.619661
Passolunghi, M. C., & Siegel, L. S. (2004). Working memory and access to numerical information in children with disability in mathematics. Journal of Experimental Child Psychology, 88(4), 348–367. https://doi.org/10.1016/j.jecp.2004.04.002
Peng, P., Wang, C., & Namkung, J. (2018). Understanding the cognition related to mathematics difficulties: A meta‐analysis on the cognitive deficit profiles and the bottleneck theory. Review of Educational Research, 88(3), 434–476. https://doi.org/10.3102/0034654317753350
Peters, L., & Ansari, D. (2019). Are specific learning disorders truly specific, and are they disorders? Trends in Neuroscience and Education, 17, 100115. https://doi.org/10.1016/j.tine.2019.100115
Piazza, M., De Feo, V., Panzeri, S., & Dehaene, S. (2018). Learning to focus on number. Cognition, 181, 35–45. https://doi.org/10.1016/j.cognition.2018.07.011
Piazza, M., Facoetti, A., Trussardi, A. N., Berteletti, I., Conte, S., Lucangeli, D., Dehaene, S., & Zorzi, M. (2010). Developmental trajectory of number acuity reveals a severe impairment in developmental dyscalculia. Cognition, 116(1), 33–41. https://doi.org/10.1016/j.cognition.2010.03.012
Price, G. R., Holloway, I., Räsänen, P., Vesterinen, M., & Ansari, D. (2007). Impaired parietal magnitude processing in developmental dyscalculia. Current Biology, 17(24), 1042–1043. https://doi.org/10.1016/j.cub.2007.10.013
Price, G. R., Palmer, D., Battista, C., & Ansari, D. (2012). Nonsymbolic numerical magnitude comparison: Reliability and validity of different task variants and outcome measures, and their relationship to arithmetic achievement in adults. Acta psychologica, 140(1), 50–57.
Reynvoet, B., Ribner, A. D., Elliott, L., Van Steenkiste, M., Sasanguie, D., & Libertus, M. E. (2021). Making sense of the relation between number sense and math. Journal of Numerical Cognition, 7(3), 308–327. https://doi.org/10.5964/jnc.6059
Rotzer, S., Kucian, K., Martin, E., Aster, M. V., Klaver, P., & Loenneker, T. (2008). Optimized voxel‐based morphometry in children with developmental dyscalculia. NeuroImage, 39(1), 417–422. https://doi.org/10.1016/j.neuroimage.2007.08.045
Rousselle, L., & Noël, M. P. (2007). Basic numerical skills in children with mathematics learning disabilities: A comparison of symbolic vs non‐symbolic number magnitude processing. Cognition, 102(3), 361–395. https://doi.org/10.1016/j.cognition.2006.01.005
Rykhlevskaia, E., Uddin, L. Q., Kondos, L., & Menon, V. (2009). Neuroanatomical correlates of developmental dyscalculia: Combined evidence from morphometry and tractography. Frontiers in Human Neuroscience, 3, 1014. https://doi.org/10.3389/neuro.09.051.2009
Salti, M., Katzin, N., Katzin, D., Leibovich, T., & Henik, A. (2017). One tamed at a time: A new approach for controlling continuous magnitudes in numerical comparison tasks. Behavior Research Methods, 49, 1120–1127. https://doi.org/10.3758/s13428‐016‐0772‐7
Schneider, M., Beeres, K., Coban, L., Merz, S., Schmidt, S. S., Stricker, J., & De Smedt, B. (2017). Associations of non‐symbolic and symbolic numerical magnitude processing with mathematical competence: A meta‐analysis. Developmental Science, 20(3), e12372. https://doi.org/10.1111/desc.12372
Sella, F., Berteletti, I., Lucangeli, D., & Zorzi, M. (2016). Spontaneous non‐verbal counting in toddlers. Developmental science, 19(2), 329–337.
Skagerlund, K., & Träff, U. (2016). Number processing and heterogeneity of developmental dyscalculia: Subtypes with different cognitive profiles and deficits. Journal of Learning Disabilities, 49(1), 36–50. https://doi.org/10.1177/0022219414522707
Smets, K., Sasanguie, D., Szücs, D., & Reynvoet, B. (2015). The effect of different methods to construct non‐symbolic stimuli in numerosity estimation and comparison. Journal of Cognitive Psychology, 27(3), 310–325. https://doi.org/10.1080/20445911.2014.996568
Starr, A., DeWind, N. K., & Brannon, E. M. (2017). The contributions of numerical acuity and non‐numerical stimulus features to the development of the number sense and symbolic math achievement. Cognition, 168, 222–233. https://doi.org/10.1016/j.cognition.2017.07.004
Starr, A., Libertus, M. E., & Brannon, E. M. (2013). Number sense in infancy predicts mathematical abilities in childhood. Proceedings of the National Academy of Sciences of the United States of America, 110(45), 18116–18120. https://doi.org/10.1073/pnas.1302751110
Stoianov, I., & Zorzi, M. (2012). Emergence of a “visual number sense” in hierarchical generative models. Nature Neuroscience, 15(2), 194–196. https://doi.org/10.1038/nn.2996
Stoianov, I., & Zorzi, M. (2017). Computational foundations of the visual number sense. Behavioral and Brain Sciences, 40, e191. https://doi.org/10.1017/S0140525X16002326
Szucs, D., Devine, A., Soltesz, F., Nobes, A., & Gabriel, F. (2013). Developmental dyscalculia is related to visuo‐spatial memory and inhibition impairment. Cortex, 49(10), 2674–2688. https://doi.org/10.1016/j.cortex.2013.06.007
Testolin, A., Dolfi, S., Rochus, M., & Zorzi, M. (2020a). Visual sense of number vs. sense of magnitude in humans and machines. Scientific Reports, 10(1), 10045. https://doi.org/10.1038/s41598‐020‐66838‐5
Testolin, A., Zou, W. Y., & McClelland, J. L. (2020b). Numerosity discrimination in deep neural networks: Initial competence, developmental refinement and experience statistics. Developmental science, 23(5), e12940.
Tomlinson, R. C., DeWind, N. K., & Brannon, E. M. (2020). Number sense biases children's area judgments. Cognition, 204, 104352. https://doi.org/10.1016/j.cognition.2020.104352
Wang, J., & Feigenson, L. (2021). Dynamic changes in numerical acuity in 4‐month‐old infants. Infancy, 26(1), 47–62. https://doi.org/10.1111/infa.12373
Wechsler, D. (2003). Wechsler intelligence scale for children (4th ed.). The Psychological Corporation.
Wilkey, E. D. (2023). The domain‐specificity of domain‐generality: Attention, executive function, and academic skills. Mind, Brain, and Education, 17(4), 349–361.
Wilkey, E. D., Pollack, C., & Price, G. R. (2020). Dyscalculia and typical math achievement are associated with individual differences in number‐specific executive function. Child Development, 91(2), 596–619. https://doi.org/10.1111/cdev.13194
Xu, F., & Spelke, E. (2000). Large number discrimination in 6‐month‐old infants. Cognition, 74(1), B1–B11.
Zambra, M., Testolin, A., & Zorzi, M. (2022). A developmental approach for training deep belief networks. Cognitive Computation, 15(1), 103–120. https://doi.org/10.1007/s12559‐022‐10085‐5
Zorzi, M., & Testolin, A. (2018). An emergentist perspective on the origin of number sense. Philosphical Transactions of the Royal Society B: Biological Sciences, 373(1740), 20170043. https://doi.org/10.1098/rstb.2017.0043
Zorzi, M., & Testolin, A. (2022). Computational models of reading and mathematical difficulties. In M. Skeide (Ed.), The Cambridge handbook of dyslexia and dyscalculia (Cambridge Handbooks in Psychology, pp. 45–60). Cambridge University Press. https://doi.org/10.1017/9781108973595.004