Screening for Characteristics of Dyscalculia: Identifying Unconventional Fraction Understandings

References

1. Armstrong, B. E., & Larson, C. N. (1995). Students’ use of part-whole and direct comparison strategies for comparing partitioned rectangles. Journal for Research in Mathematics Education, 26, 2–19. doi:10.2307/749225
2. American Psychiatric Association. (2013). Diagnostic and statistical manual of mental disorders (5th ed.). Arlington, VA: American Psychiatric Publishing.
3. Berch, D. B. (2005). Making sense of number sense: implications for children with mathematical disabilities. Journal of Learning Disabilities, 38(4), 333–345. doi:10.1177/00222194050380040901
4. Bossé, M. J., Bayaga, A., Fountain, C., Lynch-Davis, K., Preston, R., & Adu-Gyamfi, K. (2019). Fraction learners: Assessing understanding through language acquisition. International Electronic Journal of Elementary Education, 11(2), 113–124. Retrieved from https://www.iejee.com/index.php/IEJEE/article/view/649
5. Butterworth, B. (2003). Dyscalculia screener: Highlighting children with specific learning difficulties in mathematics. London: NFER Nelson.
6. Butterworth, B. (2005). The development of arithmetical abilities. Journal of Child Psychology and Psychiatry, 46(1), 3–18. doi:10.1111/j.1469-7610.2004.00374.x
7. Compton, D. L., Fuchs, L. S., Fuchs, D., Lambert, W., & Hamlett, C. (2012). The Cognitive and academic profiles of reading and mathematics learning disabilities. Journal of Learning Disabilities, 45(1), 79–95. doi:10.1177/0022219410393012
8. Davis, L. R. (2006). Constructing normalcy the bell curve, the novel, and the invention of the disabled body in the nineteenth century. In L. R. Davis (Ed.), The Disability Studies Reader (pp. 3–16). New York, NY: Routledge.
9. Dehaene, S. (2011). The number sense: How the mind creates mathematics. New York: Oxford University Press.
10. Desoete, A., & Roeyers, H. (2005). Cognitive skills in mathematical problem solving in Grade 3. British Journal of Educational Psychology, 75(1), 119–138. doi:10.1348/000709904X22287
11. Dowker, A. (2015). Individual differences in arithmetical abilities: The componential nature of arithmetic. In R. Kadosh, & A. Dowker (Eds.). Oxford Handbook of Numerical Cognition. Oxford University Press.
12. Duane, D. D. (1979). Toward a definition of dyslexia: A summary of views. Bulletin of the Orton Society, 29, 56–64. doi:10.1007/BF02653733
13. Empson, S. B. (1999). Equal sharing and shared meaning: The development of fraction concepts in a first-grade classroom. Cognition and Instruction, 17(3), 283–342.
14. Fletcher, J. M., Lyon, G. R., Fuchs, L. S., & Barnes, M. A. (2007). Learning disabilities: From identification to intervention. New York: Guilford Press.
15. Geary, D. C. (2004). Mathematics and learning disabilities. Journal of Learning Disabilities, 37(1), 4–15. doi:10.1177/00222194040370010201
16. Geary, D. C., Hamson, C. O., & Hoard, M. K. (2000). Numerical and arithmetical cognition: A longitudinal study of process and concept deficits in children with learning disability. Journal of Experimental Child Psychology, 77(3), 236–263. doi:10.1006/jecp.2000.2561
17. Geary, D. C., & Hoard, M. K. (2005). Learning disabilities in arithmetic and mathematics: Theoretical and empirical perspectives. In J. I. D. Campbell (Ed.), Handbook of mathematical cognition. (pp. 253–267). New York, NY US: Psychology Press.
18. Gifford, S., & Rockliffe, F. (2012). Mathematics difficulties: Does one approach fit all? Research in Mathematics Education, 14(1), 1–15. doi:10.1080/14794802.2012.657436
19. Gonzalez, J. E. J., & Espinel, A. I. G. (2002). Strategy choice in solving arithmetic word problems: Are there differences between students with learning disabilities, G-V poor performance, and typical achievement students? Learning Disability Quarterly, 25(2), 113–122.
20. Gross-Tsur, V., Manor, O., & Shalev, R. S. (1996). Developmental dyscalculia: Prevalence and demographic features. Developmental Medicine & Child Neurology, 38(1), 25–33. doi:10.1111/j.1469-8749.1996.tb15029.x
21. Hanich, L. B., Jordan, N. C., Kaplan, D., & Dick, J. (2001). Performance across different areas of mathematical cognition in children with learning difficulties. Journal of Educational Psychology, 93(3), 615–626. doi:10.1037/0022-0663.93.3.615
22. Hunting, R. P., & Davis, G. E. (1991). Dimensions of young children’s knowledge of the fraction of one half. In Early Fraction Learning. New York, NY: Springer Verlag.
23. Keeler, M. L., & Swanson, H. L. (2001). Does strategy knowledge influence working memory in children with mathematical disabilities? Journal of Learning Disabilities, 34(5), 418–434. doi:10.1177/002221940103400504
24. Knopik, V. S., Alarcón, M., & DeFries, J. C. (1997). Comorbidity of mathematics and reading deficits: Evidence for a genetic etiology. Behavior Genetics, 27(5), 447–453.
25. Lange, K. W., Reichl, S., Lange, K. M., Tucha, L., & Tucha, O. (2010). The history of attention deficit hyperactivity disorder. ADHD Attention Deficit and Hyperactivity Disorders, 2(4), 241–255. doi:10.1007/s12402-010-0045-8
26. Lewis, K. E. (2014). Difference not deficit: Reconceptualizing mathematical learning disabilities. Journal for Research in Mathematics Education, 45(3), pp. 351-396.
27. Lewis, K. E. (2016). Beyond error patterns: A sociocultural view of fraction comparison error patterns in students with mathematical learning disabilities. Learning Disability Quarterly 39(4), 199-212. doi:10.1177/0731948716658063
28. Lewis, K. E. (2017). Designing a bridging discourse: Re-mediation of a mathematical learning disability. Journal of the Learning Sciences, 26(2). 320-365. doi: 10.1080/10508406.2016.1256810
29. Lewis, K. E. & Fisher, M. B. (2016). Taking stock of 40 years of research on mathematical learning disability: Methodological issues and future directions. Journal for Research in Mathematics Education, 47(4), 338-371. doi:10.5951/jresematheduc.47.4.0338
30. Lewis, K. E. & Lynn, D. L. (2018). Access through compensation: Emancipatory view of a mathematics learning disability. Cognition & Instruction.
31. Lewis, K. E., Sweeney, G., Thompson, G. M., & Adler, R. (2020). Integer number sense and notation: A case study of a student with a mathematics learning disability. Journal of Mathematical Behavior. doi: 10.1016/j.jmathb.2020.100797
32. Lewis, K. E., Sweeney, G., Thompson, G. M., Adler, R. M., & Alhamad, K. (2022). Dyscalculia in Algebra: A Case Study. Manuscript accepted with minor revisions.
33. Lyon, G. R. (1995). Toward a definition of dyslexia. Annals of Dyslexia, 45, 3–27. doi:10.1007/BF02648210
34. Lyon, G. R., Shaywitz, S. E., & Shaywitz, B. A. (2003). A definition of dyslexia. Annals of Dyslexia, 53, 1–14.
35. Mabbott, D. J., & Bisanz, J. (2008). Computational skills, working memory, and conceptual knowledge in older children with mathematics learning disabilities. Journal of Learning Disabilities, 41(1), 15–28. doi:10.1177/0022219407311003
36. Mazzocco, M. M. M. (2007). Defining and differentiating mathematical learning disabilities and difficulties. In D. B. 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. 29–47). Baltimore, MD, US: Paul H Brookes Publishing.
37. Mazzocco, M. M. M. (2009). Mathematical learning disability in girls with Turner syndrome: A challenge to defining MLD and its subtypes. Developmental Disabilities Research Reviews, 15(1), 35–44. doi:10.1002/ddrr.50
38. Mazzocco, M. M. M., & Devlin, K. T. (2008). Parts and “holes”: Gaps in rational number sense among children with vs. without mathematical learning disabilities. Developmental Science, 11(5), 681–691. doi:10.1111/j.1467-7687.2008.00717.x
39. Mazzocco, M. M. M., Devlin, K. T., & McKenney, S. J. (2008). Is it a fact? Timed arithmetic performance of children with mathematical learning disabilities (MLD) varies as a function of how MLD is defined. Developmental Neuropsychology, 33(3), 318–344. doi:10.1080/87565640801982403
40. Mazzocco, M. M. M., & Myers, G. F. (2003). Complexities in identifying and defining mathematics learning disability in the primary school-age years. Annals of Dyslexia, 53, 218–253. doi:10.1007/s11881-003-0011-7
41. Mazzocco, M. M. M., Myers, G. F., Lewis, K. E., Hanich, L. B., & Murphy, M. M. (2013). Limited knowledge of fraction representations differentiates middle school students with mathematics learning disability (dyscalculia) versus low mathematics achievement. Journal of Experimental Child Psychology, 115(2), 371–387. doi:10.1016/j.jecp.2013.01.005
42. Meert, G., Grégoire, J., & Noël, M.-P. (2009). Rational numbers: Componential versus holistic representation of fractions in a magnitude comparison task. The Quarterly Journal of Experimental Psychology, 62(8), 1598–1616. https://doi.org/10.1080/17470210802511162
43. Mejias, S., Grégoire, J., & Noël, M.-P. (2012). Numerical estimation in adults with and without developmental dyscalculia. Learning and Individual Differences, 22(1), 164–170. https://doi.org/10.1016/j.lindif.2011.09.013
44. Messenger, C., Emerson, J., & Bird, R. (2007). Dyscalculia in Harrow. Mathematics Teaching Incorporating Micromath, (204), 37–39.
45. Mundia, L. (2017). The assessment of math learning difficulties in a primary grade-4 child with high support needs: Mixed methods approach. International Electronic Journal of Elementary Education, 4(2), 347–366. Retrieved from https://www.iejee.com/index.php/IEJEE/article/view/203
46. Mussolin, C., Mejias, S., & Noël, M.-P. (2010). Symbolic and nonsymbolic number comparison in children with and without dyscalculia. Cognition, 115(1), 10–25. https://doi.org/10.1016/j.cognition.2009.10.006
47. National Governors Association Center for Best Practices & Council of Chief State School Officers. (2010). Common Core State Standards for Mathematics. Washington, DC: Author. Retrieved from http://www.corestandards.org/assets/CCSSI_Math%20Standards.pdf
48. Ni, Y. (2001). Semantic domains of rational numbers and the acquisition of fraction equivalence. Contemporary Educational Psychology, 26(3), 400–417. doi:10.1006/ceps.2000.1072
49. Price, G. R., & Ansari, D. (2013). Dyscalculia: Characteristics, causes, and treatments. Numeracy: Advancing Education in Quantitative Literacy, 6(1), 1–16. doi:10.5038/1936-4660.6.1.2
50. Schneider, M., & Siegler, R. S. (2010). Representations of the magnitudes of fractions. Journal of Experimental Psychology: Human Perception and Performance, 36(5), 1227-1238. doi:10.1037/a0018170
51. Schrank, F. A., Mather, N., & McGrew, K. S. (2014). Woodcock-Johnson IV Tests of Achievement. Rolling Meadows, IL: Riverside.
52. Sfard, A. (1991). On the dual nature of mathematical conceptions: reflections on processes and objects as different sides of the same coin. Educational Studies in Mathematics, 22, 1–36. doi:10.1007/BF00s302715
53. Shalev, R. S. (2007). Prevalence of developmental dyscalculia. In D. B. 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. 49–60). Baltimore, MD: Paul H. Brookes.
54. Steffe, L. P. (2010). The partitioning and fraction schemes. In L. P. Steffe & J. Olive (Eds.), Children’s Fractional Knowledge (pp. 315-340). New York, NY: Springer
55. Verhoeff, B. (2013). Autism in flux: A history of the concept from Leo Kanner to DSM-5. History of Psychiatry, 24(4), 442–458. doi:10.1177/0957154X13500584
56. Viseu, F., Pires, A. L., Menezes, L., & Costa, A. M. (2021). Semiotic representations in the learning of rational numbers by 2nd grade Portuguese students. International Electronic Journal of Elementary Education, 13(5), 611–624. Retrieved from https://www.iejee.com/index.php/IEJEE/article/view/1453
57. Vygotsky, L. S. (1981). The genesis of higher mental functions. In J. V. Wertsch (Ed.), The Concept of Activity in Soviet Psychology (pp. 144–188). Armonk, NY: M. E. Sharpe, Inc.,.
58. Vygotsky, L. S. (1929/1993). Introduction: Fundamentals problems of defectology. In R. W. Rieber & A. S. Carton (Eds.), The collected works of L. S. Vygotsky, Volume 2: The fundamentals of defectology. London, NY: Plenum Press.
59. Wilkins, J. L. M., & Norton, A. (2011). The splitting loope. Journal for Research in Mathematics Education, 42(4), 386–416.
60. Wilson, A. J., Andrewes, S. G., Struthers, H., Rowe, V. M., Bogdanovic, R., & Waldie, K. E. (2015). Dyscalculia and dyslexia in adults: Cognitive bases of comorbidity. Learning & Individual Differences, 37, 118–132. doi:10.1016/j.lindif.2014.11.017
61. Wolff, S. (2004). The history of autism. European Child & Adolescent Psychiatry, 13(4), 201–208. doi:10.1007/s00787-004-0363-5

Keywords

math, learning disability, rational numbers, assessment

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