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Mathematical Skills in 3- and 5-Year-Olds with Spina Bifida and Their Typically Developing Peers: A Longitudinal Approach

  • Marcia A. Barnes (a1), Allison Stubbs (a2), Kimberly P. Raghubar (a3), Alba Agostino (a2), Heather Taylor (a1), Susan Landry (a1), Jack M. Fletcher (a3) and Brenda Smith-Chant (a4)...


Preschoolers with spina bifida (SB) were compared to typically developing (TD) children on tasks tapping mathematical knowledge at 36 months (n = 102) and 60 months of age (n = 98). The group with SB had difficulty compared to TD peers on all mathematical tasks except for transformation on quantities in the subitizable range. At 36 months, vocabulary knowledge, visual–spatial, and fine motor abilities predicted achievement on a measure of informal math knowledge in both groups. At 60 months of age, phonological awareness, visual–spatial ability, and fine motor skill were uniquely and differentially related to counting knowledge, oral counting, object-based arithmetic skills, and quantitative concepts. Importantly, the patterns of association between these predictors and mathematical performance were similar across the groups. A novel finding is that fine motor skill uniquely predicted object-based arithmetic abilities in both groups, suggesting developmental continuity in the neurocognitive correlates of early object-based and later symbolic arithmetic problem solving. Models combining 36-month mathematical ability and these language-based, visual–spatial, and fine motor abilities at 60 months accounted for considerable variance on 60-month informal mathematical outcomes. Results are discussed with reference to models of mathematical development and early identification of risk in preschoolers with neurodevelopmental disorder. (JINS, 2011, 17, 431–444)


Corresponding author

Correspondence and reprint requests to: Marcia A. Barnes, University of Texas Health Science Center-Houston, 7000 Fannin Street, Suite 2400, Houston, Texas 77030. E-mail:


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Alibali, M.W., DiRusso, A.A. (1999). The function of gesture in learning to count: More than keeping track. Cognitive Development, 14, 3756.
Ansari, D., Dhital, B. (2006). Age-related changes in the activation of the intraparietal sulcus during nonsymbolic magnitude processing: An event-related functional magnetic resonance imaging study. Journal of Cognitive Neuroscience, 18, 18201828.
Ansari, D., Donlan, C., Thomas, M.S.C., Ewing, S.A., Peen, T., Karmiloff-Smith, A. (2003). What makes counting count? Verbal and visuo-spatial contributions to typical and atypical number development. Journal of Experimental Child Psychology, 85, 5062.
Assel, M.A., Landry, S.H., Swank, P., Smith, K.E., Steelman, L.M. (2003). Precursors to mathematical skills: Examining the roles of visual-spatial skills, executive processes, and parenting factors. Applied Developmental Science, 7, 2738.
Ayr, L.K., Yeates, K.O., Enrile, B.G. (2005). Arithmetic skills and their cognitive correlates in children with acquired and congenital brain disorder. Journal of the International Neuropsychological Society, 11, 249262.
Barnes, M.A., Dennis, M. (1992). Reading in children and adolescents after early onset hydrocephalus and in their normally developing age-peers: Phonological analysis, word recognition, word comprehension, and passage comprehension skill. Journal of Pediatric Psychology, 17, 445456.
Barnes, M.A., Pengelly, S., Dennis, M., Wilkinson, M., Rogers, T., Faulkner, H. (2002). Mathematics skills in good readers with hydrocephalus. Journal of the International Neuropsychological Society, 8, 7282.
Barnes, M.A., Smith-Chant, B., Landry, S. (2005). Number processing in neurodevelopmental disorders: Spina bifida myelomeningocele. In Campbell, J. (Ed.), Handbook of mathematical cognition (pp. 299314). New York: Psychology Press.
Barnes, M.A., Wilkinson, M., Khemani, E., Boudesquie, A., Dennis, M., Fletcher, J.M. (2006). Arithmetic processing in children with spina bifida: Calculation accuracy, strategy use, and fact retrieval fluency. Journal of Learning Disabilities, 39, 174187.
Berch, D.B. (2005). Making sense of number sense: Implications for children with mathematical disabilities. Journal of Learning Disabilities, 38, 333339.
Bisanz, J., Sherman, J.L., Rasmussen, C., Ho, E. (2005). Development of arithmetic skills and knowledge in preschool children. In Campbell, J.I.D. (Ed.), Handbook of mathematical cognition (pp. 143162). New York: Psychology Press.
Blair, C., Razza, R.P. (2007). Relating effortful control, executive function, and false belief understanding to emerging math and literacy ability in kindergarten. Child Development, 78, 647663.
Briars, D., Siegler, R.S. (1984). A featural analysis of preschoolers’ counting knowledge. Developmental Psychology, 20, 607618.
Bull, R. (2007). Commentary Part II, Section III: Neuropsychological factors. In Berch, D.B.Mazzocco, M.M.M. (Eds.), Why is math so hard for some children? The nature and origins of mathematical learning difficulties and disabilities (pp. 265278). Baltimore: Paul H. Brookes Publishing Co.
Bull, R., Espy, K.A., Wiebe, S.A. (2008). Short-term memory, working memory, and executive functioning in preschoolers: Longitudinal predictors of mathematical achievement at 7 years. Developmental Neuropsychology, 33, 205228.
Butterworth, B. (1999). The mathematical brain. London: Macmillan.
Coughlin, J., Montague, M. (2010). The effects of cognitive strategy instruction on the mathematical problem solving of adolescents with spina bifida. Journal of Special Education, doi:10.1177/0022466910363913.
de Jong, P.F., van der Leij, A. (2002). Effects of phonological abilities and linguistic comprehension on the development of reading. Scientific Studies of Reading, 6, 5177.
De Smedt, B., Taylor, J., Archibald, L., Ansari, D. (2009). How is phonological processing related to individual differences in children's arithmetic skills? Developmental Science, 13, 508520.
Dehaene, S., Izard, V., Spelke, E., Pica, P. (2008). Log or linear? Distinct intuitions of the number scale in western and Amazonian indigene cultures. Science, 30, 12171220.
Dehaene, S., Piazza, M., Pinel, P., Cohen, L. (2005). Three parietal circuits for number processing. In Campbell, J.I.D. (Ed.), Handbook of mathematical cognition (pp. 433453). New York: Psychology Press.
Dennis, M., Barnes, M. (2002). Math and numeracy in young adults with spina bifida and hydrocephalus. Developmental Neuropsychology, 21, 141155.
Dennis, M., Barnes, M.A. (2010). The cognitive phenotype of spina bifida meningomyelocele. Developmental Disabilities Research Reviews, 16, 3139.
Dennis, M., Fletcher, J.M., Rogers, S., Hetherington, R., Francis, D. (2002). Object-based and action-based visual perception in children with spina bifida and hydrocephalus. Journal of the International Neuropsychological Society, 8, 95106.
Dennis, M., Landry, S.H., Barnes, M., Fletcher, J.M. (2006). A model of neurocognitive function in spina bifida over the life span. Journal of the International Neuropsychological Society, 12, 285296.
Durand, M., Hulme, C., Larkin, R., Snowling, M. (2005). The cognitive foundations of reading and arithmetic skills in 7- to 10-year olds. Journal of Experimental Child Psychology, 91, 113136.
English, L.H., Barnes, M.A., Taylor, H.B., Landry, S.H. (2009). Mathematical development in spina bifida. Developmental Disabilities Research Reviews, 15, 2834.
Fischer, M.H. (2008). Finger counting habits modulate spatial-numerical associations. Cortex, 44, 386392.
Fletcher, J.M., Copeland, K., Frederick, J., Blaser, S.E., Kramer, L.A., Northrup, H., Dennis, M. (2005). Spinal lesion level in spina bifida meningomyelocele: A source of neural and cognitive heterogeneity. Journal of Neurosurgery, 102(Suppl. 3), 268279.
Fletcher, J.M., Dennis, M., Northrup, H., Barnes, M.A., Hannay, H.J., Landry, S., Francis, D.J. (2004). Spina bifida: Genes, brain, and development. In Glidden, L. (Ed.), International review of research in mental retardation (pp. 63117). San Diego, CA: Elsevier.
Friedrich, W.N., Lovejoy, M.C., Shaffer, J., Shurtleff, D.B., Beilke, R.L. (1991). Cognitive abilities and achievement status of children with myelomeningocele: A contemporary sample. Journal of Pediatric Psychology, 16, 423428.
Fuchs, L.S., Geary, D.C., Compton, D.L., Fuchs, D., Hamlett, C.L., Bryant, J.D. (2010). The contributions of numerosity and domain-general abilities to school readiness. Child Development, 81(5), 15201533.
Geary, D.C., Bailey, D.H., Littlefield, A., Wood, P., Hoard, M.K., Nugent, L. (2009). First-grade predictors of mathematical learning disability: A latent class trajectory analysis. Cognitive Development, 24, 411429.
Geary, D.C., Hoard, M.K., Hamson, C.O. (1999). Numerical and arithmetical cognition: Patterns of functions and deficits in children at risk for a mathematical disability. Journal of Experimental Child Psychology, 74, 213239.
Gelman, R., Galistell, C.R. (1978). The child's understanding of number. Cambridge, MA: Harvard University Press.
Ginsburg, H.P., Baroody, A.J. (1990). Test of early mathematics ability (2nd ed.). Austin, TX: Pro-Ed.
Ginsburg, H.P., Klein, A., Starkey, P. (1998). The development of children's mathematical thinking: Connecting research with practice. In Damon, W., Sigel, I.E.Renninger, A.K. (Eds.), Handbook of child psychology: Child psychology in practice (5th ed., Vol 4, pp. 401476). NJ: John Wiley & Sons Inc.
Hanich, L.B., Jordan, N.C., Kaplan, D., Dick, J. (2001). Performance across different areas of mathematical cognition in children learning difficulties. Journal of Educational Psychology, 93, 615626.
Hecht, S.A., Torgesen, J.K., Wagner, R.K., Rashotte, C.A. (2001). The relations between phonological processing abilities and emerging individual differences in mathematical computation skills: A longitudinal study from second to fifth grades. Journal of Experimental Child Psychology, 79, 192227.
Hetherington, R., Dennis, M., Barnes, M., Drake, J., Gentili, F. (2006). Functional outcome in young adults with spina bifida and hydrocephalus. Child Nervous System, 22, 117124.
Hodent, C., Bryant, P., Houde, O. (2005). Language-specific effects on number computation in toddlers. Developmental Science, 8, 420423.
Hollingshead, J. (1975). A four-factor index of social position. New Haven, CT: Author.
Jordan, N.C., Huttenlocher, J., Levine, S.C. (1992). Differential calculation abilities in young children from middle- and lower-income families. Developmental Psychology, 28, 644653.
Jordan, N.C., Huttenlocher, J., Levine, S.C. (1994). Assessing early arithmetic abilities: Effects of verbal and nonverbal response types on the calculation performance of middle- and low-income children. Learning and Individual Differences, 6, 413432.
Jordan, N.C., Kaplan, D., Locuniak, M.N., Ramineni, C. (2007). Predicting first-grade math achievement from developmental number sense trajectories. Learning Disabilities Research & Practice, 22, 3646.
Jordan, N.C., Kaplan, D., Olah, L.N., Locuniak, M.N. (2006). Number sense growth in kindergarten: A longitudinal investigation of children at risk for mathematics difficulties. Child Development, 77, 153175.
Kamawar, D., LeFevre, J.-A., Bisanz, J., Fast, L., Skwarchuk, S.-L., Smith-Chant, B., Penner-Wilger, M. (2010). Knowledge of counting principles: How relevant is order irrelevance? Journal of Experimental Child Psychology, 105, 138145.
Krajewski, K., Schneider, W. (2009). Exploring the impact of phonological awareness, visual-spatial working memory, and preschool quantity-number competencies on mathematics achievement in elementary school: Findings from a 3-year longitudinal study. Journal of Experimental Child Psychology, 103, 516531.
LeFevre, J.-A. (2000). Research on the development of academic skills: Introduction to the special issue on early literacy and early numeracy. Canadian Journal of Experimental Psychology, 54, 5760.
LeFevre, J.-A., Fast, L., Skwarchuk, S.-L., Smith-Chant, B.L., Bisanz, J., Kamawar, D., Penner-Wilger, M. (2010). Pathways to mathematics: Longitudinal predictors of performance. Child Development, 81(6), 17531767.
LeFevre, J.-A., Smith-Chant, B.L., Fast, L., Skwarchuk, S.-L., Sargla, E., Arnup, J.S., Kamawar, D. (2006). What counts as knowing? The development of conceptual and procedural knowledge of counting from kindergarten through grade 2. Journal of Experimental Child Psychology, 93, 285303.
Lomax-Bream, L.E., Barnes, M., Copeland, K., Taylor, H.B., Landry, S.H. (2007). The impact of spina bifida on development across the first three years. Developmental Neuropsychology, 31, 120.
Miller, K.F., Smith, C.M., Zhu, J., Zhang, H. (1995). Preschool origins of cross-national differences in mathematical competence: The role of number-naming systems. Psychological Science, 6, 5660.
Mix, K.S., Huttenlocher, J., Levine, S.C. (2002). Quantitative development in infancy and early childhood. New York: Oxford University Press.
Miyake, A., Friedman, N.P., Rettinger, D.A., Shah, P., Hegarty, M. (2001). How are visuospatial working memory, executive functioning, and spatial abilities related? A latent-variable analysis. Journal of Experimental Psychology: General, 130, 621640.
Noel, M. (2005). Finger gnosia: A predictor of numerical abilities in children? Child Neuropsychology, 11, 413430.
Noles, N.S., Scholl, B.J., Mitroff, S.R. (2005). The persistence of object file representations. Perception & Psychophysics, 67, 324334.
Penner-Wilger, M., Anderson, M.L. (2008). An alternative view of the relation between finger gnosis and math ability: Redeployment of finger representations for the representation of number. In Love, B.C., McRae, K.Sloutsky, V.M. (Eds.), Proceedings of the 30th Annual Cognitive Science Society (pp. 16471652). Austin, TX: Cognitive Science Society.
Penner-Wilger, M., Fast, L., LeFevre, J., Smith-Chant, B.L., Skwarchuk, S., Kamawar, D., Bisanz, J. (2007). The foundations of numeracy: Subitizing, finger gnosia, and fine-motor ability. In McNamara, D.S.Trafton, J.G. (Eds.), Proceedings of the 29th Annual Cognitive Science Society (pp. 13851390). Austin, TX: Cognitive Science Society.
Piazza, M., Mechelli, A., Butterworth, B., Price, C.J. (2002). Are subitizing and counting implemented as separate or functionally overlapping processes? Neuroimage, 15, 435446.
Piazza, M., Mechelli, A., Price, C.J., Butterworth, B. (2006). Exact and approximate judgments of visual and auditory numerosity: An fMRI study. Brain Research, 1106, 177188.
Raghubar, K.P., Barnes, M.A., Hecht, S.A. (2010). Working memory and mathematics: A review of developmental, individual difference, and cognitive approaches. Learning and Individual Differences, 20, 110122.
Raghubar, K., Cirino, P., Barnes, M., Ewing-Cobbs, L., Fletcher, J., Fuchs, L. (2009). Errors in multi-digit arithmetic and behavioral inattention in children with math difficulties. Journal of Learning Disabilities, 42, 356371.
Rasmussen, C., Bisanz, J. (2005). Representation and working memory in early arithmetic. Journal of Experimental Child Psychology, 91, 137157.
Rasmussen, C., Ho, E., Bisanz, J. (2003). Use of the mathematical principle of inversion in young children. Journal of Experimental Child Psychology, 85, 89102.
Simmons, F.R., Singleton, C. (2008). Do weak phonological representations impact on arithmetic development? A review of research into arithmetic and dyslexia. Dyslexia, 14, 7794.
Swanson, H.L., Jerman, O. (2006). Math disabilities: A selective meta-analysis of the literature. Review of Educational Research, 76, 249274.
Thorndike, R.L., Hagen, E.P., Sattler, J.M. (1989). Stanford-Binet Intelligence Scale (4th ed.). Chicago: Riverside.
Trick, L.M., Plyshyn, Z.W. (1994). Why are small and large numbers enumerated differently? A limited-capacity preattentive stage in vision. Psychological Review, 10, 80102.
Wagner, R., Torgesen, J.K., Rashotte, C.A. (1999). Comprehensive test of phonological processing. Austin, TX: Pro-Ed.
Wills, K.E. (1993). Neuropsychological functioning in children with spina bifida and/or hydrocephalus. Journal of Clinical Child Psychology, 22, 247265.
Woodcock, R.M., Johnson, M.B. (1989). Woodcock-Johnson Psychoeducational Battery – Revised. Allen, TX: DLM Teaching Resources.



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