Skip to main content Accessibility help

Mathematical Outcomes and Working Memory in Children With TBI and Orthopedic Injury

  • Kimberly P. Raghubar (a1), Marcia A. Barnes (a2), Mary Prasad (a2), Chad P. Johnson (a2) and Linda Ewing-Cobbs (a2)...


This study compared mathematical outcomes in children with predominantly moderate to severe traumatic brain injury (TBI; n = 50) or orthopedic injury (OI; n=47) at 2 and 24 months post-injury. Working memory and its contribution to math outcomes at 24 months post-injury was also examined. Participants were administered an experimental cognitive addition task and standardized measures of calculation, math fluency, and applied problems; as well as experimental measures of verbal and visual-spatial working memory. Although children with TBI did not have deficits in foundational math fact retrieval, they performed more poorly than OIs on standardized measures of math. In the TBI group, performance on standardized measures was predicted by age at injury, socioeconomic status, and the duration of impaired consciousness. Children with TBI showed impairments on verbal, but not visual working memory relative to children with OI. Verbal working memory mediated group differences on math calculations and applied problems at 24 months post-injury. Children with TBI have difficulties in mathematics, but do not have deficits in math fact retrieval, a signature deficit of math disabilities. Results are discussed with reference to models of mathematical cognition and disability and the role of working memory in math learning and performance for children with TBI. (JINS, 2013, 19, 1–10)


Corresponding author

Correspondence and reprint requests to: Linda Ewing-Cobbs, Children's Learning Institute, Department of Pediatrics, University of Texas-Houston Health Science Center, 7000 Fannin – UCT 2401, Houston, TX 77030. E-mail:


Hide All
Anderson, V., Catroppa, C., Morse, S., Haritou, F., Rosenfeld, J. (2005). Functional plasticity or vulnerability after early brain injury? Pediatrics, 116(6), 13741382.
Ashcraft, M. (1992). Cognitive arithmetic: A review of data and theory. Cognition, 44, 75106.
Association for the Advancement of Automotive Medicine. (1990). The Abbreviated Injury Scale (1990 revision) Des Plaines, IL: Association for the Advancement of Automotive Medicine.
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.
Baddeley, A.D., Logie, R.H. (1999). Working memory: The multiple-component model. In A. Miyake & P. Shah (Eds.), Models of working memory: Mechanisms of active maintenance and executive control (pp. 2861). Cambridge: Cambridge University Press.
Barnes, M.A., Dennis, M., Wilkinson, M. (1999). Reading after closed brain injury in childhood: Effects on accuracy, fluency, and comprehension. Developmental Neuropsychology, 15, 124.
Barnes, M.A., Fletcher, J.M., Ewing-Cobbs, L. (2007). Mathematical disabilities in congenital and acquired neurodevelopmental disorders. In D.B. Berch & M.M. Mazzocco (Eds.), Why is math so hard for some children? The nature and origins of mathematical learning difficulties and disabilities (pp. 195217). Baltimore, MD: Paul H. Brookes Publishing Co.
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.
Bijur, P.E., Haslum, M., Golding, J. (1990). Cognitive and behavioral sequelae of mild head injury in children. Pediatrics, 86, 337344.
Bisanz, J., Sherman, J.L., Rasmussen, C., Ho, E. (2005). Development of arithmetic skills and knowledge in preschool children. In J.I.D. Campbell (Ed.), Handbook of mathematical cognition (pp. 143162). New York: Psychology Press.
Catroppa, C., Anderson, V.A., Morse, S.A., Haritou, F., Rosenfeld, J.V. (2008). Outcome and predictors of functional recovery 5 years following pediatric traumatic brain injury (TBI). Journal of Pediatric Psychology, 33, 707718.
Catroppa, C., Anderson, V.A., Muscara, F., Morse, S.A., Haritou, F., Rosenfeld, J.V., Heinrich, L.M. (2009). Educational skills: Long-term outcome predictors following paediatric traumatic brain injury. Neuropsychological Rehabilitation, 19, 716732.
Chadwick, O., Rutter, M., Shaffer, D., Shrout, P.E. (1981). A prospective study of children with head injuries: Specific cognitive difficulties. Journal of Clinical Neuropsychology, 3, 101120.
Chein, J.M., Morrison, A.B. (2010). Expanding the mind's workspace: Training and transfer effects with a complex working memory span task. Psychonomic Bulletin & Review, 17, 193199.
Conklin, H.M., Salorio, C.F., Slomine, B.S. (2008). Working memory performance following paediatric traumatic brain injury. Brain Injury, 22, 847857.
Cornoldi, C., Marzocchi, G.M., Belotti, M., Caroli, M.G., De Meo, T., Braga, C. (2001). Working memory interference control deficit in children referred by teachers for ADHD symptoms. Child Neuropsychology, 7, 230240.
Dehaene, S., Piazza, M., Pinel, P., Cohen, L. (2005). Three parietal circuits for number processing. In J.I.D. Campbell (Ed.), Handbook of mathematical cognition (pp. 433453). New York: Psychology Press.
Donders, J., Janke, K. (2008). Criterion validity of the Wechsler Intelligence Scale for Children – Fourth Edition after pediatric traumatic brain injury. Journal of the International Neuropsychological Society, 14, 651655.
Espy, K.A., McDiarmid, M.M., Cwik, M.F., Stalets, M.M., Hamby, A., Senn, T.E. (2004). The contribution of executive functions to emergent mathematical skills in preschool children. Developmental Neuropsychology, 26, 465486.
Ewing-Cobbs, L., Barnes, M.A., Fletcher, J.M., Levin, H.S., Swank, P.R., Song, J. (2004). Modeling of longitudinal academic achievement scores after pediatric traumatic brain injury. Developmental Neuropsychology, 25, 107134.
Ewing-Cobbs, L., Levin, H.S., Fletcher, J.M., Iovino, I., Miner, M.E. (1998). Academic achievement and academic placement following traumatic brain injury in children and adolescents: A two-year longitudinal study. Journal of Clinical and Experimental Neuropsychology, 20, 769781.
Ewing-Cobbs, L., Prasad, M., Fletcher, J.M., Levin, H.S., Miner, M.E., Eisenberg, H.M. (1998). Attention after pediatric traumatic brain injury: A multidimensional assessment. Child Neuropsychology, 4, 3548.
Ewing-Cobbs, L., Prasad, M., Kramer, L., Cox, C., Baumgartner, J., Fletcher, S., Swank, P. (2006). Late intellectual and academic outcomes following traumatic brain injury sustained during early childhood. Journal of Neurosurgery, 105(Suppl 4), 287296.
Fay, G.C., Jaffe, K.M., Polissar, N.L., Liao, S., Rivara, J.B., Martin, K.M. (1994). Outcome of pediatric traumatic brain injury at three years: A cohort study. Archives of Physical Medicine and Rehabilitation, 75, 733741.
Fletcher, J.M., Ewing-Cobbs, L., Francis, D.J., Levin, H.S. (1995). Variability in outcomes after traumatic brain injury in children: A developmental perspective. In S.H. Broman & M.E. Michel (Eds.), Traumatic head injury in children (pp. 321). New York: Oxford University Press.
Fuchs, L.S., Fuchs, D., Compton, D.L., Powell, S.R., Seethaler, P.M., Capizzi, A.M., Fletcher, J.M. (2006). The cognitive correlates of third-grade skill in arithmetic, algorithmic computation, and arithmetic word problems. Journal of Educational Psychology, 98, 2943.
Fuchs, L.S., Fuchs, D., Stuebing, K., Fletcher, J.M., Hamlett, C.L., Lambert, W. (2008). Problem solving and computational skill: Are they shared or distinct aspects of mathematical cognition? Journal of Educational Psychology, 100, 3047.
Geary, D.C. (1990). A componential analysis of an early learning deficit in mathematics. Journal of Experimental Child Psychology, 49, 363383.
Geary, D.C., Fan, L., Bow-Thomas, C.C. (1992). Numerical cognition: Loci of ability differences comparing children from China and the United States. Psychological Science, 3, 180185.
Gorman, S., Barnes, M.A., Swank, P., Prasad, M., Ewing-Cobbs, L. (2011). The effects of pediatric traumatic brain injury on verbal and visual-spatial working memory. Journal of the International Neuropsychological Society, 17, 110.
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.
Hayes, A.F. (2009). Beyond Baron and Kenny: Statistical mediation analysis in the new millennium. Communication Monographs, 76, 408420.
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.
Hollingshead, A. (1975). Four factor index of social status. Unpublished manuscript. Yale University.
Holmes, J., Adams, J.W. (2006). Working memory and children's mathematical skills: Implications for mathematical development and mathematical curricula. Educational Psychology, 26, 339366.
Holmes, J., Adams, J.W., Hamilton, C.J. (2008). The relationship between visuospatial sketchpad capacity and children's mathematical skills. European Journal of Cognitive Psychology, 20, 272289.
Holmes, J., Gathercole, S.E., Dunning, D.L. (2009). Adaptive training leads to sustained enhancement of poor working memory in children. Developmental Science, 12, F9F15.
Huttenlocher, J., Jordan, N.C., Levine, S.C. (1994). A mental model for early arithmetic. Journal of Experimental Psychology: General, 123, 284296.
Jaffe, K.M., Fay, G.C., Polissar, N.L., Martin, K.M., Shurtleff, H., Rivara, J.B., Winn, H.R. (1992). Severity of pediatric traumatic brain injury and early neurobehavioral outcome: A cohort study. Archives of Physical Medicine and Rehabilitation, 73, 540547.
Kinsella, G., Prior, M., Sawyer, M., Murtagh, D., Eisenmajer, R., Anderson, V., Klug, G. (1995). Neuropsychological deficit and academic performance in children and adolescents following traumatic brain injury. Journal of Pediatric Psychology, 20, 753767.
Klingberg, T., Fernell, E., Olesen, P.J., Johnson, M., Gustafsson, P., Dahlstrom, K., Westerberg, H. (2005). Computerized training of working memory in children with ADHD – A randomized, controlled trial. Journal of the American Academy of Child and Adolescent Psychiatry, 44, 177186.
Langlois, J.A., Rutland-Brown, W., Thomas, K.E. (2004). Traumatic brain injury in the United States: Emergency department visits, hospitalizations, and deaths. Atlanta, GA: Centers for Disease Control and Prevention, National Center for Injury Prevention and Control.
Levin, H.S., Hanten, G., Chang, C., Zhang, L., Schachar, R., Ewing-Cobbs, L., Max, J.E. (2002). Working memory after traumatic brain injury in children. Annals of Neurology, 52, 8288.
Levin, H.S., Hanten, G., Roberson, G., Li, X., Ewing-Cobbs, L., Dennis, M., Swank, P. (2008). Predictors of cognitive sequelae based on abnormal computed tomography findings in children following mild traumatic brain injury. Journal of Neurosurgery, 1, 461470.
Levin, H.S., Hanten, G., Zhang, L., Dennis, M., Barnes, M.A., Schachar, R., Hunter, J.V. (2004). Changes in working memory after traumatic brain injury in children. Neuropsychology, 18, 240247.
Mabbot, D.J., Bisanz, J. (2008). Computational skills, working memory, and conceptual knowledge in older children with mathematics learning disabilities. Journal of Learning Disabilities, 41, 1528.
Mazzocco, M.M.M., Murphy, M.M., McCloskey, M. (2007). The contribution of syndrome research to understanding mathematical learning disability. In D. Berch & M.M.M. Mazzocco (Eds.), Why is math so hard for some children? The nature and origins of mathematical learning difficulties and disabilities (pp. 173193). Baltimore, MD: Paul H. Brookes Publishing.
Melby-Lervåg, M., Hulme, C. (2012). Is working memory training effective? A meta-analytic review. Developmental Psychology. [Epub ahead of print]. doi:10.1037/a0028228
Menon, V., Mackenzie, K., Rivera, S.M., Reiss, A.L. (2002). Prefrontal cortex involvement in processing incorrect arithmetic equations: Evidence from event-related fMRI. Human Brain Mapping, 16, 119130.
Murray, R., Shum, D., McFarland, K. (1992). Attentional deficits in head-injured children: An information processing analysis. Brain and Cognition, 18, 99115.
Preacher, K.J., Hayes, A.F. (2008). Asymptotic and resampling strategies for assessing and comparing indirect effects in multiple mediator models. Behavior Research Methods, 40, 879891.
Raghubar, K.P., Barnes, M.A., Hecht, S.A. (2010). Working memory and mathematics: A review of developmental, individual difference, and cognitive approaches. Journal of Individual Differences, 20, 110122.
Rivera-Batiz, F.L. (1992). Quantitative literacy and the likelihood of employment among young adults in the United States. The Journal of Human Resources, 27, 313328.
Roncadin, C., Guger, S., Archibald, J., Barnes, M., Dennis, M. (2004). Working memory after mild, moderate, or severe childhood closed head injury. Developmental Neuropsychology, 25, 2136.
Swanson, H.L., Jerman, O. (2006). Math disabilities: A selective meta-analysis of the literature. Review of Educational Research, 76, 249274.
Taylor, H.G., Swartwout, M.D., Yeates, K.O., Walz, N.C., Stancin, T., Wade, S.L. (2008). Traumatic brain injury in young children: Post-acute effects on cognitive and school readiness skills. Journal of the International Neuropsychological Society, 14, 734745.
Taylor, H.G., Yeates, K.O., Wade, S.L., Drotar, D., Klein, S. (1999). Influences on first-year recovery from traumatic brain injury in children. Neuropsychology, 13, 7689.
Taylor, H.G., Yeates, K.O., Wade, S.L., Drotar, D., Stancin, T., Minich, N. (2002). A prospective study of short- and long-term outcomes after traumatic brain injury in children: Behavior and achievement. Neuropsychology, 16, 1527.
Teasdale, G., Jennett, B. (1974). Assessment of coma and impaired consciousness: A practical scale. Lancet, 2, 8184.
Thompson, N.M., Francis, D.J., Stuebing, K.K., Fletcher, J.M., Ewing-Cobbs, L., Miner, M.E., Eisenberg, H.M. (1994). Motor, visual-spatial, and somatosensory skills after closed head injury in children and adolescents: A study of change. Neuropsychology, 8, 333342.
Woodcock, R.W., McGrew, K.S., Mather, N. (2001). Woodcock-Johnson Psychoeducational Battery – Third Edition. Itasca, IL: Riverside Publishing.



Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed