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PLOS ONE  2011 

Processing Ordinality and Quantity: The Case of Developmental Dyscalculia

DOI: 10.1371/journal.pone.0024079

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Abstract:

In contrast to quantity processing, up to date, the nature of ordinality has received little attention from researchers despite the fact that both quantity and ordinality are embodied in numerical information. Here we ask if there are two separate core systems that lie at the foundations of numerical cognition: (1) the traditionally and well accepted numerical magnitude system but also (2) core system for representing ordinal information. We report two novel experiments of ordinal processing that explored the relation between ordinal and numerical information processing in typically developing adults and adults with developmental dyscalculia (DD). Participants made “ordered” or “non-ordered” judgments about 3 groups of dots (non-symbolic numerical stimuli; in Experiment 1) and 3 numbers (symbolic task: Experiment 2). In contrast to previous findings and arguments about quantity deficit in DD participants, when quantity and ordinality are dissociated (as in the current tasks), DD participants exhibited a normal ratio effect in the non-symbolic ordinal task. They did not show, however, the ordinality effect. Ordinality effect in DD appeared only when area and density were randomized, but only in the descending direction. In the symbolic task, the ordinality effect was modulated by ratio and direction in both groups. These findings suggest that there might be two separate cognitive representations of ordinal and quantity information and that linguistic knowledge may facilitate estimation of ordinal information.

 References

[1]  Cantlon JF, Platt ML, Brannon EM (2009) Beyond the number domain. Trends in Cognitive Sciences 13: 83–91.
[2]  Dehaene S (1992) Varieties of numerical abilities. Cognition 44:
[3]  Feigenson L, Dehaene S, Spelke ES (2004) Core systems of number. Trend in Cognitive Science 8: 307–314.
[4]  Jacob NS, Neider A (2008) The ABC of cardinal and ordinal number representations. Trends in cognitive sciences 12: 41–43.
[5]  Nieder A (2005) Counting on neurons: The neurobiology of numerical competence. Nature Reviews Neuroscience 6: 177–190.
[6]  Dehaene S (2009) Origins of mathematical intuitions: the case of arithmetic. Annals of the New York Academy 1156: 232–259.
[7]  Shepard NR (2001) Perceptual-cognitive universals as reflections of the world. Behavioral and Brain Science 24: 581–601.
[8]  Feigenson L (2007) The equality of quantity. Trends in Cognitive Sciences 11: 185–187.
[9]  Walsh VN (2003) A theory of magnitude: common cortical metrics of time, space and quantity. Trends in Cognitive Sciences 7: 483–488.
[10]  Spelke E (2003) What makes us Smart? Core knowledge and natural language. In: Gentner D, Goldin-Meadow S, editors. Language in mind: Advances in the investigation of language and thought. Cambridge, MA: MIT Press. pp. 277–311.
[11]  Platt ML, Spelke ES (2009) What can developmental and comparative cognitive neuroscience tell us about the adult human brain? Current Opinion in Neurobiology 19: 1–5.
[12]  Carey S, editor. (2009) (2009) The origin of concepts: Oxford University Press.
[13]  Hermer-Vazquez L, Moffet A, Munkholm P (2001) Language, space, and the development of cognitive flexibility in humans: The case of two spatial memory tasks. Cognition 79: 263–299.
[14]  Sury D, Rubinsten O (submitted) Ordinal processing in numerical and non-numerical information. In: Molfese D, Breznit Z, Berninger V, Rubinsten O, editors. Reading, writing, mathematics and the developing brain: Listening to many voices (Tentative). Texas A & M University: Springer.
[15]  Ansari D (2008) Effects of development and enculturation on number representation in the brain. Nature Reviews Neuroscience 9: 278–291.
[16]  Suanda SH, Tompson W, Brannon EM (2008) Changes in the Ability to Detect Ordinal Numerical Relationships Between 9 and 11 Months of Age. Infancy 13: 308–337.
[17]  Brannon EM, Terrace HS (1998) Ordering of the numerosities 1 to 9 by monkeys. Science 282: 746–749.
[18]  Rugani R, Regolin L, Vallortigara G (2007) Rudimental numerical competence in 5-day-old domestic chicks (Gallus gallus): identification of ordinal position. Journal of Experimental Psychology: Animal Behavior Processes 33: 21–31.
[19]  Kaufmann L, Vogel SE, Starke M, Schocke M (2009) Numerical and non-numerical ordinality processing in children with and without developmental dyscalculia: Evidence from fMRI. Cognitive Development 24: 486–494.
[20]  Fulbright RK, Manson SC, Skurdlasky P, Ladadie CM, Gore JC (2003) Quantity determination and the distance effect with letters, numbers, and shapes: a functional MR imaging study of number processing. American Journal of Neuroradiology 24: 193–200.
[21]  Fias W, Lammertyn J, Caessens B, Orban GA (2007) Processing of abstract ordinal knowledge in the horizontal segment of the intraparietal sulcus. Journal of Neuroscience 27: 8952–8956.
[22]  Ischebeck A, Heim S, Siedentopf C, Zamarian L, Schocke M, et al. (2008) Are numbers special? Comparing the generation of verbal materials from ordered categories (months) to numbers and other categories (animals) in an fMRI study. Human Brain Mapping 29: 894–909.
[23]  Zorzi M, Di Bono MG, Fias W (in press) Distinct representations of numerical and non-numerical order in the human intraparietal sulcus revealed by multivariate pattern recognition. NeuroImage.
[24]  Delazer M, Butterworth B (1997) A dissociation of number meanings. Cognitive Neuropsychology 14: 613–636.
[25]  Turconi E, Seron X (2002) Dissociation between order and quantity meaning in a patient with Gerstmann syndrome. Cortex 38: 911–914.
[26]  Turconi E, Campbell JID, Seron X (2006) Numerical order and quantity processing in number comparison. Cognition 98: 273–285.
[27]  Brannon EM, Van de Walle GA (2001) The Development of Ordinal numerical competence in young children. Cognitive Psychology 43: 53–81.
[28]  Pavese A, Umiltà C (1998) Symbolic distance between numerosity and identity modulates Stroop interference. Journal of experimental psychology Human perception and performance 24: 1535–1545.
[29]  Dehaene S (1997) The Number Sense: How the Mind Creates Mathematics. Oxford, UK: Oxford University Press.
[30]  Barth H, La Mont K, Lipton JS, Spelke ES (2005) Abstract number and arithmetic in preschool children. Proceedings of the National Academy of Science, USA 102: 14116–14121.
[31]  Barth H, La Mont K, Lipton JS, Dehaene S, Kanwisher N, et al. (2006) Non-symbolic arithmetic in adults and young children. Cognition 98: 199–222.
[32]  van Oeffelen MP, Vos PG (1982) A probabilistic model for the discrimination of visual number. Perception and Psychophysis 32: 163–170.
[33]  Cantlon JF, Brannon EM (2006) Shared system for ordering small and large numbers in monkeys and humans. Psychological Science 17: 401–406.
[34]  Wood G, Nuerk HC, Willmes K, Fischer MH (2008) On the cognitive link between space and number: A meta-analysis of the SNARC effect. Psychology Science Quarterly 50: 489–525.
[35]  Dehaene S, Bossini S, Giraux P (1993) The mental representation of parity and number magnitude. Journal of Experimental Psychology: General 122: 371–396.
[36]  Shaki S, Fischer MH, Petrusic WM (2009) Reading habits for both words and numbers contribute to the SNARC effect. Psychonomic Bulletin & Review 16: 328–331.
[37]  Rugani R, Kelly DM, Szelest I, Regolin L, Vallortigara G (2010) Is it only humans that count from left to right? Biology Letters 6: 290–292.
[38]  Bachot J, Gevers W, Fias W, Roeyers H (2005) Number sense in children with visuospatial disabilities: Orientation of the mental number line. Psychology Science 47: 172–183.
[39]  Butterworth B (2005) Developmental dyscalculia. In: Campbell D, editor. Handbook of Mathematical Cognition. New York: Psychology Press.
[40]  Isaacs EB, Edmonds CJ, Lucas A, Gadian DG (2001) Calculation difficulties in children of very low birthweight: A neural correlate. Brain 124: 1701–1707.
[41]  Rotzer S, Kucian K, Martin E, von Aster M, Klaver P, et al. (2008) Optimized voxel-based morphometry in children with developmental dyscalculia. NeuroImage 39: 417–422.
[42]  Kaufmann L, Vogel S, Starke M, Kremser C, Schocke M, et al. (in press) Neural correlates of number processing in developmental dyscalculia: Evidence from fMRI. Cognitive Development.
[43]  Kucian K, Leoenneker T, Dietrich T, Dosch M, Martin E, et al. (2006) Impaired neural networks for approximate calculation in dyscalculic children: A functional MRI study. Behavior and Brain Functions 5: 31.
[44]  Kucian K, Grond U, Rotzer S, Henzi B, Schonmann C, et al. (in press) Mental number line training in children with developmental dyscalculia. Neuroimage.
[45]  Mussolin C, De Volder A, Grandin C, Schl？gel X, Nassogne MC, et al. (2010) Neural Correlates of Symbolic Number Comparison in Developmental Dyscalculia. Journal of Cognitive Neuroscience 22: 147–152.
[46]  Price GR, Holloway I, Vesterinen M, Rasanen P, Ansari D (2007) Impaired parietal magnitude processing in Developmental Dyscalculia. Current Biology 17: R1024–1023.
[47]  Cohen Kadosh R, Cohen Kadosh K, Schuhmann T, Kaas A, Goebel R, et al. (2007) Virtual dyscalculia after TMS to the right parietal lobe: A combined fMRI and neuronavigated TMS study. Current Biology 17: 689–693.
[48]  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: 309–324.
[49]  Mussolin C, Mejias S, No？l M (2010) Symbolic and nonsymbolic number comparison in children with and without dyscalculia. Cognition 115: 10–25.
[50]  Wilson AJ, Dehaene S (2007) Number sense and developmental dyscalculia. In: Coch D, Dawson G, Fischer K, editors. Human Behavior, Learning and the Developing Brain: Atypical Development. New York: Guilford Press.
[51]  Rousselle L, Noel MP (2007) Basic numerical skills in children with mathematical learning disabilities: A comparison of symbolic vs non-symbolic number magnitude processing. Cognition 102: 361–395.
[52]  Kaufmann L, Vogel SE, Starke M, Kremser C, Schocke M, et al. (2009) Developmental dyscalculia: compensatory mechanisms in left intraparietal regions in response to nonsymbolic magnitudes. Behavioral and Brain Functions 5: 5–35.
[53]  Kaufmann L, Nuerk HC (2005) Numerical development: current issues and future perspectives. Psychology Science 47(1): 142–170.
[54]  Rubinsten O (2009) Co-occurrence of developmental disorders: The case of Developmental Dyscalculia. Cognitive Development 24: 362–370.
[55]  Rubinsten O, Henik A (2009) Developmental Dyscalculia: Heterogeneity May Not Mean Different Mechanisms. Trends in Cognitive Sciences 13: 92–99.
[56]  Kucian K, Grond U, Rotzer S, Henzi B, Sch？nmann C, et al. (in press) Mental number line training in children with developmental dyscalculia. NeuroImage.
[57]  Kennet-Cohen T, Bronner S, B-S A, Intrator N (2008) Different Approaches for Combining Scores on the Test Battery for the Diagnosis of Learning Disabilities. National Institute for Testing & Evaluation (NITE). . ISBN: 965-502-144-960.
[58]  Rubinsten O, Henik A (2005) Automatic activation of internal magnitude: A study of developmental dyscalculia. Neuropsychology 19: 641–648.
[59]  Landerl K, K？lle C (2009) Typical and atypical development of basic numerical skills in elementary school. Journal of Experimental Child Psychology 103: 546–565.
[60]  Landerl K, Bevan A, Butterworth B (2004) Developmental dyscalculia and basic numerical capacities: A study of 8–9 year old students. Cognition 93: 99–125.
[61]  Brannon EM (2002) The development of ordinal knowledge in infancy. Cognition 836: 223–240.
[62]  Suanda SH, Tompson W, Brannon EM (2008) Changes in the ability to detect ordinal numerical relationships between 9 and 11 months of age. Infancy 13: 308–337.

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