Book contents
- The Cambridge Handbook of Applied School Psychology
- The Cambridge Handbook of Applied School Psychology
- Copyright page
- Contents
- Contributors
- Contributor Biographies
- Acknowledgments
- 1 Broadening the Focus of School Psychology Practice
- Part I Individual-Level Academic Interventions
- 2 Enhancing Reading Motivation in Schools
- 3 Addressing “Won’t Do” Issues in Mathematics
- 4 Learning Disabilities in Mathematics
- 5 Executive Function and School Performance
- Part II Teacher- and System-Level Interventions
- Part III Interventions from Educational and Social/Personality Psychology
- Part IV Behavioral and Social-Emotional Interventions
- Part V Health and Pediatric Interventions
- Part VI Family Connections and Life Transitions
- Part VII Special Populations
- Part VIII Conclusion
- Index
- References
4 - Learning Disabilities in Mathematics
from Part I - Individual-Level Academic Interventions
Published online by Cambridge University Press: 18 September 2020
Book contents
- The Cambridge Handbook of Applied School Psychology
- The Cambridge Handbook of Applied School Psychology
- Copyright page
- Contents
- Contributors
- Contributor Biographies
- Acknowledgments
- 1 Broadening the Focus of School Psychology Practice
- Part I Individual-Level Academic Interventions
- 2 Enhancing Reading Motivation in Schools
- 3 Addressing “Won’t Do” Issues in Mathematics
- 4 Learning Disabilities in Mathematics
- 5 Executive Function and School Performance
- Part II Teacher- and System-Level Interventions
- Part III Interventions from Educational and Social/Personality Psychology
- Part IV Behavioral and Social-Emotional Interventions
- Part V Health and Pediatric Interventions
- Part VI Family Connections and Life Transitions
- Part VII Special Populations
- Part VIII Conclusion
- Index
- References
Summary
Research in the field of mathematical learning disability (MLD) is growing. Though a proportion of children in every school appear to struggle with mathematical achievement, MLD characterizes a subgroup of students with poor achievement and skill deficits that differentiate them from their low-achieving peers. This chapter explores some of the characteristics of children with MLD, including underachievement in mathematics, poor number sense, limited working memory, and additional processing deficits. Emerging evidence for universal screening, prevention, and early intervention are also presented. The chapter ends with guidelines for school psychologists to apply the extant literature to their own practice, along with a list of resources to gain further expertise on the typical and atypical development of numerical cognition.
Keywords
- Type
- Chapter
- Information
- The Cambridge Handbook of Applied School Psychology , pp. 48 - 63Publisher: Cambridge University PressPrint publication year: 2020
References
Berch, D. B. & Mazzocco., M. M. M. (Eds.). (2007). Why is math so hard for some children? The nature and origins of mathematical learning difficulties and disabilities. Baltimore, MD: Paul H. Brookes Publishing Co.Google Scholar
Dehaene, S. (2011). The number sense: How the mind creates mathematics. New York, NY: Oxford University Press.Google Scholar
Dowker, A. (2005). Individual differences in arithmetic: Implications for psychology, neuroscience and education. New York, NY: Psychology Press.Google Scholar
Dowker, A. (Ed.). (2008). Mathematical difficulties: Psychology and intervention. New York, NY: Academic Press.Google Scholar
Gersten, R. & Newman-Gonchar, R. (Eds.). (2011). Understanding RTI in mathematics: Proven methods and applications. Baltimore, MD: Paul H. Brookes Publishing Co.Google Scholar
Griffin, S. (2006, January 25). The Number Knowledge Test: Overview. Retrieved from https://www2.clarku.edu/faculty/sgriffin/nw_TestInfo.htmGoogle Scholar
Jordan, N. & Dyson, N. (2013). Number sense interventions. Baltimore, MD: Paul H. Brookes Publishing Co.Google Scholar
References
American Psychiatric Association. (2013). Diagnostic and statistical manual of mental disorders (5th ed.). Arlington, VA: American Psychiatric Publishing. https://doi.org/10.1176/appi.books.9780890425596Google Scholar
Anderson, P., Anderson, V., Northam, E., & Taylor, H. G. (2000). Standardization of the Contingency Naming Test (CNT) for school-aged children: A measure of reactive flexibility. Clinical Neuropsychological Assessment, 1, 247–273.Google Scholar
Baddeley, A. D., & Hitch, G. (1974). Working memory. Psychology of Learning and Motivation, 8, 47–89. https://doi.org/10.1016/s0079-7421(08)60452-1CrossRefGoogle Scholar
Baker, S., Gersten, R., Flojo, J., et al. (2002). Preventing mathematics difficulties in young children: Focus on effective screening of early number sense delays (Technical Report No. 0305). Eugene, OR: Pacific Institutes of Research.Google Scholar
Benson, D. F., & Weir, W. F. (1972). Acalculia: Acquired anarithmetia. Cortex, 8, 465–472. https://doi.org/10.1016/s0010-9452(72)80008-xGoogle Scholar
Berch, D. B. (2005). Making sense of number sense: Implications for children with mathematical disabilities. Journal of Learning Disabilities, 38, 333–339. https://doi.org/10.1177/00222194050380040901CrossRefGoogle ScholarPubMed
Booth, J. L., & Siegler, R. S. (2008). Numerical magnitude representations influence arithmetic learning. Child Development, 79, 1016–1031. https://doi.org/10.1111/j.1467-8624.2008.01173.xGoogle Scholar
Butterworth, B. & Reigosa, V. (2007). Information processing deficits in dyscalculia. In Mazzocco, M. & Berch, D. (Eds.) Why is math so hard for some children? The nature and origins of mathematical learning difficulties and disabilities (pp. 65–82). Baltimore, MD: Paul H. Brooks.Google Scholar
Butterworth, B., Sashank, V., & Laurillard, D. (2011). Dyscalculia: From brain to education. Science, 332, 1049–1053. https://doi.org/10.1126/science.1201536Google Scholar
Chiappe, P. (2005). How reading research informs mathematics difficulties: The search for the core deficit. Journal of Learning Disabilities, 38, 313–317. https://doi.org/10.1177/00222194050380040601Google Scholar
Clarke, B., Doabler, C. T., Baker, S. K., et al. (2011). Pursuing instructional coherence: Can strong Tier 1 systems better meet the needs of a range of students in general education settings? The emerging research base. In Gersten, R. and Newman-Gonchar, R. (Eds.) Understanding RTI in mathematics: Proven methods and applications (pp. 49–64). Baltimore: MD: Paul H. Brooks Publishing Co.Google Scholar
Dehaene, S. (2011). The number sense: How the mind creates mathematics. New York, NY: Oxford University Press.Google Scholar
Dehaene, S., Piazza, M., Pinel, P., & Cohen, L. (2003). Three parietal circuits for number processing. Cognitive Neuropsychology, 20, 487–506. https://doi.org/10.1080/02643290244000239Google Scholar
Desoete, A., Ceulemans, A., De Weerdt, F., & Pieters, S. (2012). Can we predict mathematical learning disabilities from symbolic and non‐symbolic comparison tasks in kindergarten? Findings from a longitudinal study. British Journal of Educational Psychology, 82, 64–81. https://doi.org/10.1348/2044-8279.002002Google Scholar
Floyd, R. G., Evans, J. J., & McGrew, K. S. (2003). Relations between measures of Cattell‐Horn‐Carroll (CHC) cognitive abilities and mathematics achievement across the school‐age years. Psychology in the Schools, 40, 155–171. https://doi.org/10.1002/pits.10083Google Scholar
Geary, D. C. (1993). Mathematical disabilities: cognitive, neuropsychological, and genetic components. Psychological Bulletin, 114, 345–362. https://doi.org/10.1037//0033-2909.114.2.345Google Scholar
Geary, D. C. (2010). Mathematical disabilities: Reflections on cognitive, neuropsychological, and genetic components. Learning and Individual Differences, 20, 130–133. https://doi.org/10.1016/j.lindif.2009.10.008Google Scholar
Geary, D. C., & Hoard, M. K. (2005). Learning disabilities in arithmetic and mathematics. In Campbell, J. I. D. (Ed.), Handbook of mathematical cognition (pp. 253–267). New York, NY: Psychology Press.Google Scholar
Geary, D. C., Hoard, M. K., & Bailey, D. H. (2012). Fact retrieval deficits in low achieving children and children with mathematical learning disability. Journal of Learning Disabilities, 45, 291–307. https://doi.org/10.1177/0022219410392046.Google Scholar
Geary, D. C., Hoard, M. K., Byrd‐Craven, J., Nugent, L., & Numtee, C. (2007). Cognitive mechanisms underlying achievement deficits in children with mathematical learning disability. Child Development, 78, 1343–1359. https://doi.org/10.1111/j.1467-8624.2007.01069.xCrossRefGoogle ScholarPubMed
Geary, D. C., Hoard, M. K., Nugent, L., & Bailey, D. H. (2012). Mathematical cognition deficits in children with learning disabilities and persistent low achievement: A five-year prospective study. Journal of Educational Psychology, 104, 206–223. https://dx.doi.org/10.1037%2Fa0025398Google Scholar
Geary, D. C., Hoard, M. K., Nugent, L., & Byrd-Craven, J. (2008). Development of number line representations in children with mathematical learning disability. Developmental Neuropsychology, 33, 277–299. https://doi.org/10.1080/87565640801982361Google Scholar
Gelman, R., & Gallistel, C. R. (1978). The child’s understanding of number. Cambridge, MA: Harvard University Press.Google Scholar
Gersten, R., & Chard, D. (1999). Number sense: Rethinking arithmetic instruction for students with mathematical disabilities. Journal of Special Education, 33, 18–28. https://doi.org/10.1177/002246699903300102Google Scholar
Gersten, R., Dimino, J. A., & Haymond, K. (2011). Universal screening for students in mathematics for the primary grades: The emerging research base. In Gersten, R. and Newman-Gonchar, R. (Eds.) Understanding RTI in mathematics: Proven methods and applications (pp. 17–34). Baltimore, MD: Paul H. Brooks Publishing Co.Google Scholar
Gersten, R., Jordan, N. C., & Flojo, J. R. (2005). Early identification and interventions for students with mathematics difficulties. Journal of Learning Disabilities, 38, 293–304. https://doi.org/10.1177/00222194050380040301Google Scholar
Gersten, R. & Newman-Gonchar, R. (Eds.). (2011). Understanding RTI in mathematics: Proven methods and applications. Baltimore, MD: Paul H. Brookes Publishing Co.Google Scholar
Jordan, N. C. & Dyson, N. (2013). Number sense interventions. Baltimore, MD: Paul H. Brookes Publishing Co.Google Scholar
Jordan, N. C., Glutting, J., & Dyson, N. (2012). Number Sense Screener (NSS) user’s guide, K-1. Baltimore, MD: Paul H. Brookes.Google Scholar
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, 36–46. https://doi.org/10.1111/j.1540-5826.2007.00229.xGoogle Scholar
Jordan, N. C., Kaplan, D., Ramineni, C., & Locuniak, M. N. (2009). Early math matters: Kindergarten number competence and later mathematics outcomes. Developmental Psychology, 45, 850–867. https://doi.org/10.1037/a0014939Google Scholar
Kalchman, M., Moss, J., & Case, R. (2001). Psychological models for the development of mathematical understanding: Rational numbers and functions. In Carver, S. and Klahr, D (Eds.), Cognition and Instruction: Twenty-five years of progress (pp. 1–38). Mahwah, NJ: Lawrence Erlbaum.Google Scholar
Kaufmann, L., Vogel, S. E., Starke, M., Kremser, C., & Schocke, M. (2009). Numerical and non-numerical ordinality processing in children with and without developmental dyscalculia: Evidence from fMRI. Cognitive Development, 24, 486–494. https://doi.org/10.1016/j.cogdev.2009.09.001Google Scholar
Kucian, K., Loenneker, T., Martin, E., & von Aster, M. (2011). Non-symbolic numerical distance effect in children with and without developmental dyscalculia: A parametric fMRI study. Developmental Neuropsychology, 36, 741–762. https://doi.org/10.1080/87565641.2010.549867Google Scholar
Mazzocco, M. M. (2007). Defining and differentiating mathematical learning disabilities and difficulties. In Mazzocco, M. & Berch, D. (Eds.) Why is math so hard for some children? The nature and origins of mathematical learning difficulties and disabilities (pp. 29–48). Baltimore, MD: Paul H. Brooks.Google Scholar
Mazzocco, M. M., & Kover, S. T. (2007). A longitudinal assessment of executive function skills and their association with math performance. Child Neuropsychology, 13, 18–45. https://doi.org/10.1080/09297040600611346CrossRefGoogle ScholarPubMed
Mazzocco, M. M. M., & Räsänen, P. (2013). Contributions of longitudinal studies to evolving definitions and knowledge of developmental dyscalculia. Trends in Neuroscience and Education, 2, 65–73. https://doi.org/10.1016/j.tine.2013.05.001Google Scholar
Murphy, M. M., Mazzocco, M. M., Hanich, L. B., & Early, M. C. (2007). Cognitive characteristics of children with mathematics learning disability (MLD) vary as a function of the cutoff criterion used to define MLD. Journal of Learning Disabilities, 40, 458–478. https://doi.org/10.1177/00222194070400050901Google Scholar
Okamoto, Y., & Case, R. (1996). Exploring the microstructure of children’s central conceptual structures in the domain of number. Monographs of the Society for Research in Child Development, 61, 27–59. https://doi.org/10.1111/j.1540-5834.1996.tb00536.xGoogle Scholar
Pickering, S., & Gathercole, S. E. (2001). Working memory test battery for children (WMTB-C). San Antonio, TX: Psychological Corporation.Google Scholar
Price, G. R., Holloway, I., Räsänen, P., Vesterinen, M., & Ansari, D. (2007). Impaired parietal magnitude processing in developmental dyscalculia. Current Biology, 17, R1042–R1043. https://doi.org/10.1016/j.cub.2007.10.013Google Scholar
Schmidt, W., Houang, R., & Cogan, L. (2002). A coherent curriculum. American Education (Summer), 1–18.Google Scholar
Shaywitz, S. (2005). Overcoming dyslexia: A new and complete science-based program for reading problems at any level. New York, NY: Vintage.Google Scholar
Siegler, R. S., & Opfer, J. E. (2003). The development of numerical estimation evidence for multiple representations of numerical quantity. Psychological Science, 14, 237–250. https://doi.org/10.1111/1467-9280.02438Google Scholar
Siegler, R. S., & Ramani, G. B. (2009). Playing linear number board games – but not circular ones – improves low-income preschoolers’ numerical understanding. Journal of Educational Psychology, 101, 545–560. https://doi.org/10.1037/a0014239CrossRefGoogle Scholar
Siegler, R. S., & Shrager, J. (1984). Strategy choices in addition and subtraction: How do children know what to do? In Sophian, C. (Ed.), The origins of cognitive skills (pp. 229–293). Hillsdale, NJ: ErlbaumGoogle Scholar
Swanson, H. L., Harris, K. R., & Graham, S. (Eds.). (2014). Handbook of learning disabilities. New York, NY: Guilford Press.Google Scholar
Temple, C. M. (1991). Procedural dyscalculia and number fact dyscalculia: Double dissociation in developmental dyscalculia. Cognitive neuropsychology, 8, 155–176. https://doi.org/10.1080/02643299108253370Google Scholar
Vygotsky, L. S. (1978). Mind in society: The development of higher psychological processes. Cambridge, MA: Harvard University Press.Google Scholar
Whalen, J., McCloskey, M., Lester, R. P., & Gordon, B. (1997). Localizing arithmetic processing in the brain: Evidence from a transient deficit during cortical stimulation. Journal of Cognitive Neuroscience, 9, 409–417. https://doi.org/10.1162/jocn.1997.9.3.409Google Scholar
Wright, R. J. (2008). Mathematics recovery: An early number program focusing on intensive intervention. In Dowker, A. (Ed.), Mathematical difficulties: Psychology and intervention. (pp. 203–222). San Diego, CA: Academic Press.Google Scholar