Numbers may be manipulated and represented mentally over a compressible number line oriented from left to right. According to numerous studies, one of the primary reasons for dyscalculia is related to improper understanding of the mental number line. Children with dyscalculia usually show difficulty when they have to place Arabic numbers on a physical number line. However, it remains unclear whether they have a deficit with the mental number line per se or a deficit with accessing it from nonsymbolic and/or symbolic numbers. Quebec French-speaking 8- to 9-year-old children with (24) and without (37) dyscalculia were assessed with transcoding tasks (number-to-position and position-to-number) designed to assess the acuity of the mental number line with Arabic and spoken numbers as well as with analogic numerosities. Results showed that children with dyscalculia produced a larger percentage absolute error than children without mathematics difficulties in every task except the number-to-position transcoding task with analogic numerosities. Hence, these results suggested that children with dyscalculia do not have a general deficit of the mental number line but rather a deficit with accessing it from symbolic numbers.
American Psychiatric Association. (2013). Manuel diagnostique et statistique des troubles mentaux. Paris, France: Elsevier Masson.
2.
AnderssonU.ÖstergrenR. (2012). Number magnitude processing and basic cognitive functions in children with mathematical learning disabilities. Learning and Individual Differences, 22(6), 701–714. Retrieved from http://doi.org/10.1016/j.lindif.2012.05.004
3.
AntellS. E.KeatingD. P. (1980). Perception of numerical invariance in neonates. Child Development, 54, 695–701.
4.
AshcraftM. H.MooreA. M. (2012). Cognitive processes of numerical estimation in children. Journal of Experimental Child Psychology, 111(2), 246–267. Retrieved from http://doi.org/10.1016/j.jecp.2011.08.005
5.
BadianN. (1999). Persistent arithmetic, reading, or arithmetic and reading disability. Annals of Dyslexia, 49, 45–70.
6.
BarbaresiW. J.KatusicS. K.ColliganR. C.WeaverA. L.JacobsenS. J. (2005). Math learning disorder: Incidence in a population-based birth cohort, 1976–82, Rochester, Minn. Ambulatory Pediatrics, 5(5), 281–289. Retrieved from http://doi.org/10.1367/A04-209R.1
7.
BarthH. C.PaladinoA. M. (2011). The development of numerical estimation: Evidence against a representational shift. Developmental Science, 14(1), 125–135. Retrieved from http://doi.org/10.1111/j.1467-7687.2010.00962.x
8.
BertelettiI.LucangeliD.PiazzaM.DehaeneS.ZorziM. (2010). Numerical estimation in preschoolers. Developmental Psychology, 46(2), 545–551. Retrieved from http://doi.org/10.1037/a0017887
9.
BoothJ. L.SieglerR. S. (2006). Developmental and individual differences in pure numerical estimation. Developmental Psychology, 42(1), 189–201. Retrieved from http://doi.org/10.1037/0012-1649.41.6.189
10.
BoothJ. L.SieglerR. S. (2008). Numerical magnitude representations influence arithmetic learning. Child Development, 79(4), 1016–1031. Retrieved from http://doi.org/10.1111/j.1467-8624.2008.01173.x
11.
BrannonE. M. (2005). What animals know about numbers. In CampbellJ. I. D. (Ed.), Handbook of mathematical cognition (pp. 85–107). New York, NY: Hove Psychology Press.
12.
ButterworthB.ReeveR.ReynoldsF.LloydD. (2008). Numerical thought with and without words: Evidence from indigenous Australian children. Proceedings of the National Academy of Sciences of the United States of America, 105(35), 13179–13184. Retrieved from http://doi.org/10.1073/pnas.0806045105
13.
CirinoP. T.FuchsL. S.EliasJ. T.PowellS. R.SchumacherR. F. (2015). Cognitive and mathematical profiles for different forms of learning difficulties. Journal of Learning Disabilities, 48(2), 156–175. Retrieved from http://doi.org/10.1177/0022219413494239
CorsiP. M. (1972). Human memory and the medial temporal region of the brain. Montreal, Canada: McGill University.
16.
CowanR.PowellD. (2014). The contributions of domain-general and numerical factors to third-grade arithmetic skills and mathematical learning disability. Journal of Educational Psychology, 106(1), 214–229. Retrieved from http://doi.org/10.1037/a0034097
17.
DehaeneS. (1992). Varieties of numerical abilities. Cognition, 44, 1–42.
18.
DehaeneS. (2010). La bosse des maths, 15 ans après. Paris, France: Odile Jacob.
19.
DellatolasG.Von AsterV. (2006). Zareki-R, Batterie pour l’évaluation du traitement des nombres et du calcul chez l’enfant. Paris, France: ECPA.
20.
DevineA.SoltészF.NobesA.GoswamiU.SzűcsD. (2013). Gender differences in developmental dyscalculia depend on diagnostic criteria. Learning and Instruction, 27, 31–39. Retrieved from http://doi.org/10.1016/j.learninstruc.2013.02.004
21.
DirksE.SpyerG.van LieshoutE. C. D. M.de SonnevilleL. (2008). Prevalence of combined reading and arithmetic disabilities. Journal of Learning Disabilities, 41(5), 460–473. Retrieved from http://doi.org/10.1177/0022219408321128
22.
EverettC. (2013). Independent cross-cultural data reveal linguistic effects on basic numerical cognition. Language and Cognition, 5(1), 99–104. Retrieved from http://doi.org/10.1515/langcog-2013-0005
23.
ForsterK. I.ForsterJ. C. (2003). DMDX: A windows display program with millisecond accuracy. Behavior Research Methods, Instruments, & Computers: A Journal of the Psychonomic Society, Inc, 35(1), 116–124. Retrieved from http://www.ncbi.nlm.nih.gov/pubmed/12723786
24.
FrankM. C.EverettD. L.FedorenkoE.GibsonE. (2008). Number as a cognitive technology: Evidence from Pirahã language and cognition. Cognition, 108(3), 819–824. Retrieved from http://doi.org/10.1016/j.cognition.2008.04.007
25.
Friso-van den BosI.KroesbergenE. H.Van Luit, JE. H.Xenidou-DervouI.JonkmanL. M.Van der SchootM.Van LieshoutE. C. D. M. (2015). Longitudinal development of number line estimation and mathematics performance in primary school children. Journal of Experimental Child Psychology, 134, 12–29. Retrieved from http://doi.org/10.1016/j.jecp.2015.02.002
26.
GearyD. C. (1993). Mathematical disabilities: Cognitive, neuropsychological, and genetic components. Psychological Bulletin, 114(2), 345–362. Retrieved from http://doi.org/10.1037/0033-2909.114.2.345
27.
GearyD. C. (2010). Mathematical disabilities: Reflections on cognitive, neuropsychological, and genetic components. Learning and Individual Differences, 20(2), 130–133. Retrieved from http://doi.org/10.1016/j.lindif.2009.10.008
28.
GearyD. C.HoardM. K.NugentL.Byrd-cravenJ. (2008). Developmental neuropsychology development of number line representations in children with mathematical learning disability. Developmental Neuropsychology, 33(3), 277–299.
29.
GordonP. (2004). Numerical cognition without words: Evidence from Amazonia. Science, 306(5695), 496–499. Retrieved from http://doi.org/10.1126/science.1094492
30.
Gross-TsurV.ManorO.ShalevR. S. (1996). Developmental dyscalculia: Prevalence and demographic features. Developmental Medicine and Child Neurology, 38(1), 25–33. Retrieved from http://www.ncbi.nlm.nih.gov/pubmed/8606013
31.
HornungC.SchiltzC.BrunnerM.MartinR. (2014). Predicting first-grade mathematics achievement: The contributions of domain-general cognitive abilities, nonverbal number sense, and early number competence. Frontiers in Psychology, 5, 1–18. Retrieved from http://doi.org/10.3389/fpsyg.2014.00272
32.
IsaacsE. B.Vargha KhademF. (1989). Differential course of development of spatial and verbal memory span: A study normative. British Journal of Developmental Psychology, 7, 377–380.
33.
IuculanoT.ButterworthB. (2011). Understanding the real value of fractions and decimals. Quarterly Journal of Experimental Psychology, 64(11), 2088–2098. Retrieved from http://doi.org/10.1080/17470218.2011.604785
34.
KhomsiA. (2001). Evaluation du Langage Oral. Paris, France: ECPA.
35.
LafayA.St-PierreM.-C.MacoirJ. (2014). Revue narrative de littérature relative aux troubles cognitifs numériques impliqués dans la dyscalculie développementale: Déficit du sens du nombre ou déficit de l’accès aux représentations numériques mentales. Canadian Psychology/Psychologie Canadienne, 55(3), 161–176.
36.
LafayA.St-PierreM.-C.MacoirJ. (in press). Performances moyennes des enfants franco-québécois de 8-9 ans au test mathématique Zareki-R. Glossa.
37.
LanderlK.FusseneggerB.MollK.WillburgerE. (2009). Dyslexia and dyscalculia: Two learning disorders with different cognitive profiles. Journal of Experimental Child Psychology, 103(3), 309–324. Retrieved from http://doi.org/10.1016/j.jecp.2009.03.006
38.
LaskiE. VSieglerR. S. (2007). Is 27 a big number? Correlational and causal connections among numerical categorization, number line estimation, and numerical magnitude comparison. Child Development, 78(6), 1723–1743. Retrieved from http://doi.org/10.1111/j.1467-8624.2007.01087.x
39.
LewisC.HitchG. J.WalkerP. (1994). The prevalence of specific arithmetic difficulties and specific reading difficulties in 9- to 10-year-old boys and girls. Journal of Child Psychology and Psychiatry, and Allied Disciplines, 35(2), 283–292. Retrieved from http://www.ncbi.nlm.nih.gov/pubmed/8188799
40.
Ministère de l’Éducation du Loisir et du Sport. (2014). Indices de défavorisation. Montreal, Canada: Author.
41.
NoëlM.-P.RousselleL. (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, 165. Retrieved from http://doi.org/10.3389/fnhum.2011.00165
42.
NoëlM.-P.RousselleL.De VisscherA. (2013). La dyscalculie développementale: À la croisée de facteurs numériques spécifiques et de facteurs cognitifs généraux. Développements, 15, 24–31.
43.
OpferJ. E.SieglerR. S. (2007). Representational change and children’s numerical estimation. Cognitive Psychology, 55(3), 169–195. Retrieved from http://doi.org/10.1016/j.cogpsych.2006.09.002
44.
PraetM.DesoeteA. (2014). Number line estimation from kindergarten to grade 2: A longitudinal study. Learning and Instruction, 33, 19–28. Retrieved from http://doi.org/10.1016/j.learninstruc.2014.02.003
45.
PriceG. R.PalmerD.BattistaC.AnsariD. (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. Retrieved from http://doi.org/10.1016/j.actpsy.2012.02.008
46.
PurpuraD. J.BaroodyA. J.LoniganC. J. (2013). The transition from informal to formal mathematical knowledge: Mediation by numeral knowledge. Journal of Educational Psychology, 105(2), 453–464. Retrieved from http://doi.org/10.1037/a0031753
47.
RavenJ. C. (1977). Standard Progressive Matrices. Manuel PM47. Issy-les-Moulineaux, France: Editions Scientifiques et Psychologiques.
48.
ReeveR. A.PaulJ. M.ButterworthB. (2015). Longitudinal changes in young children’s 0–100 to 0–1000 number-line error signatures. Frontiers in Psychology, 6, 1–9. Retrieved from http://doi.org/10.3389/fpsyg.2015.00647
49.
ReinertR. M.HuberS.NuerkH.-C.MoellerK. (2015). Strategies in unbounded number line estimation? Evidence from eye-tracking. Cognitive Processing. Retrieved from http://doi.org/10.1007/s10339-015-0675-z
50.
ShareD. L.MoffittT. E.SilvaP. A. (1988). Factors associated with arithmetic-and-reading disability and specific arithmetic disability. Journal of Learning Disabilities, 21(5), 313–320. Retrieved from http://doi.org/10.1177/002221948802100515
SieglerR. S.OpferJ. E. (2003). The development of numerical estimation: Evidence for multiple representations of numerical quantity. Psychological Science, 14(3), 237–250. Retrieved from http://doi.org/10.1111/1467-9280.02438
53.
StarkeyP.CooperR. G. (1980). Perception of numbers by human infants. Science, 210, 1033–1035.
54.
van ViersenS.SlotE. M.KroesbergenE. H.van’t NoordendeJ.E.LesemanP. P. M. (2013). The added value of eye-tracking in diagnosing dyscalculia: A case study. Frontiers in Psychology, 4, 679. Retrieved from http://doi.org/10.3389/fpsyg.2013.00679
55.
Von AsterM.ShalevR. S. (2007). Number development and developmental dyscalculia. Developemental Medicine & Child Neurology, 49, 868–873.
56.
WynnK. (1992). Addition and subtraction by human infants. Nature, 358, 749–750.
57.
Xenidou-DervouI.van der SchootM.van LieshoutE. C. D. M. (2014). Working memory and number line representations in single-digit addition: Approximate versus exact, nonsymbolic versus symbolic. Quarterly Journal of Experimental Psychology, 68(6), 1–20. Retrieved from http://doi.org/10.1080/17470218.2014.977303
