Abstract
Children who have learning difficulties or intellectual disabilities have similar challenges when solving mathematical word problems, including creating an internal representation of the problem structure and organizing the information to generate a solution strategy. Students with learning difficulties in mathematics and those with intellectual disabilities benefit from mathematics instruction that incorporates visual aids and repetition, and promotes strategy flexibility to help develop conceptual understanding. With regard to mathematical word problem solving, one approach has shown promise for individuals with learning difficulties and typically developing youth. Schema-based instruction (SBI) uses visual representations to teach students the mathematical structure of word problems. In this paper, we draw on existing literature to outline some of the cognitive deficits that have been observed in children with learning difficulties in mathematics and in those with intellectual disabilities and describe the ways in which those deficits can manifest themselves in the context of mathematical problem solving. We then describe the data we collected from our own delivery of SBI to a group of students with intellectual disabilities and compared their performance to students with and without learning difficulties. We focus on instances of meaningful problem solving after the intervention, with a focus on how the students may have circumvented or compensated for specific cognitive deficiencies. We conclude the chapter with a discussion about the elements of the instruction that may account for the students’ performance after the intervention.
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Notes
- 1.
For the remainder of the chapter, we use the term “schema” to refer to the schematic drawing that represents the structure of the word problem.
References
Andersson, U. (2007). The contribution of working memory to children’s mathematical word problem solving. Applied Cognitive Psychology, 21(9), 1201–1216. https://doi.org/10.1002/acp.1317.
Baroody, A. J. (1996). Self-invented addition strategies by children with mental retardation. American Journal on Mental Retardation, 101, 72–89.
Baroody, A. J. (1999). The development of basic counting, number, and arithmetic knowledge among children classified as mentally handicapped. International Review of Research in Mental Retardation, 22, 51–103. https://doi.org/10.1016/s0074-7750(08)60131-7.
Baxter, J. A., Woodward, J., & Olson, D. (2001). Effects of reform-based mathematics instruction on low achievers in five third-grade classrooms. The Elementary School Journal, 101(5), 529–547. https://doi.org/10.1086/2F499686.
Bird, G., & Buckley, S. (2001). Number skills for individuals with down syndrome—An overview. In Down Syndrome Issues and Information. https://doi.org/10.3104/9781903806135.
Bissonnette, S., Richard, M., Gauthier, C., & Bouchard, C. (2010). Quelles sont les stratégies d’enseignement efficaces favorisant les apprentissages fondamentaux auprès des élèves en difficulté de niveau élémentaire? Résultats d’une méga-analyse. Revue de Recherche Appliquée sur l’Apprentissage, 3, art. 1.
Boonen, A. J., de Koning, B. B., Jolles, J., & van der Schoot, M. (2016). Word problem solving in contemporary math education: A plea for reading comprehension skills training. Frontiers in Psychology, 7, 191. https://doi.org/10.3389/fpsyg.2016.00191.
Bransford, J. D., & Johnson, M. K. (1972). Contextual prerequisites for understanding: Some investigations of comprehension and recall. Journal of Verbal Learning and Verbal Behavior, 11(6), 717–726. https://doi.org/10.1016/s0022-5371(72)80006-9.
Browder, D. M., Spooner, F., Ahlgrim-Delzell, L., Harris, A. A., & Wakemanxya, S. (2008). A meta-analysis on teaching mathematics to students with significant cognitive disabilities. Exceptional Children, 74(4), 407–432. https://doi.org/10.1177/001440290807400401.
Butler, F. M., Miller, S. P., Lee, K. H., & Pierce, T. (2001). Teaching mathematics to students with mild-to-moderate mental retardation: A review of the literature. Mental Retardation, 39(1), 20–31. https://doi.org/10.1352/0047-6765(2001)039%3c0020:tmtswm%3e2.0.co;2.
Carpenter, T. P., Fennema, E., Franke, M. L., Levi, L., & Empson, S. B. (2014). Children’s mathematics: Cognitively guided instruction (2nd ed.). Portsmouth, NH: Heinemann.
Cawley, J. F., Parmar, R. S., Yan, W., & Miller, J. H. (1998). Arithmetic computation performance of students with learning disabilities: Implications for curriculum. Learning Disabilities Research & Practice, 13(2), 68–74.
Chen, Z. (1999). Schema induction on children’s analogical problem solving. Journal of Educational Psychology, 91(4), 703–715. https://doi.org/10.1037/0022-0663.91.4.703.
Clements, D. H., & Sarama, J. (2009). Learning and teaching early math: The learning trajectories approach. New York: NY: Routledge. https://doi.org/10.4324/9780203883389.
Cummins, D. D. (1991). Children’s interpretations of arithmetic word problems. Cognition and Instruction, 8(3), 261–289. https://doi.org/10.1207/s1532690xci0803_2.
Daroczy, G., Wolska, M., Meurers, W. D., & Nuerk, H. C. (2015). Word problems: A review of linguistic and numerical factors contributing to their difficulty. Frontiers in Psychology, 6, 348. https://doi.org/10.3389/fpsyg.2015.00348.
De Corte, E., Verschaffel, L., & De Win, L. (1985). Influence of rewording verbal problems on children’s problem representations and solutions. Journal of Educational Psychology, 77(4), 460–470. https://doi.org/10.1037/0022-0663.77.4.460.
Duncker, K. (1945). On problem solving. Psychological Monographs, 58(5), 270.
Fletcher, J. M., Lyon, G. R., Fuchs, L. S., & Barnes, M. A. (2006). Learning disabilities: From identification to intervention. Guilford Press. 10.1080%2F09297040701455171.
Fuchs, L. S., Fuchs, D., Finelli, R., Courey, S. J., & Hamlett, C. L. (2004a). Expanding schema-based transfer instruction to help third graders solve real-life mathematical problems. The American Educational Research Journal, 41(2), 419–445. https://doi.org/10.3102/00028312041002419.
Fuchs, L. S., Fuchs, D., Prentice, K., Hamlett, C. L., Finelli, R., & Courey, S. J. (2004b). Enhancing mathematical problem solving among third-grade students with schema-based instruction. Journal of Educational Psychology, 96(4), 635–647. https://doi.org/10.1037/0022-0663.96.4.635.
Geary, D. C. (2004). Mathematics and learning disabilities. Journal of Learning Disabilities, 37(4), 4–15. https://doi.org/10.1177/00222194040370010201.
Geary, D. C., Hoard, M. K., Byrd-Craven, J., & DeSoto, M. C. (2004). Strategy choices in simple and complex addition: Contributions of working memory and counting knowledge for children with mathematical disability. Journal of Experimental Child Psychology, 88(2), 121–151. https://doi.org/10.1016/2Fj.jecp.2004.03.002.
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(4), 1343–1359. https://doi.org/10.1111/j.1467-8624.2007.01069.x.
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(3), 277–299. https://doi.org/10.1080/87565640801982361.
Ginsburg, H. P. (1997). Mathematics learning disabilities: A view from developmental psychology. Journal of Learning Disabilities, 30(1), 20–33. https://doi.org/10.1177/002221949703000102.
Griffin, C. G., & Jitendra, A. K. (2009). Word problem-solving instruction in inclusive third-grade mathematics classrooms. The Journal of Educational Research, 12(3), 187–201. https://doi.org/10.3200/joer.102.3.187-202.
Henry, L. A., Messer, D. J., & Poloczek, S. (2018). Working memory and intellectual disabilities. In T. P. Alloway (Ed.), Working memory and clinical developmental disorders: Theories, debates and interventions (pp. 9–21). Abingdon-on-Thames, UK: Routledge. https://doi.org/10.4324/9781315302072.
Human Resources and Skills Developmental Canada. (2011). Disability in Canada: A 2006 profile (Cat. No. HS64/2010). Retrieved from http://www.hrsdc.gc.ca/eng/disability_issues/reports/disability_profile/2011/index.shtml.
Hutchinson, N. L. (1993). Effects of cognitive strategy instruction on algebra problem solving of adolescents with learning disabilities. Learning Disability Quarterly, 16(1), 34–63. https://doi.org/10.2307/1511158.
Individuals with Disabilities Education Improvement Act. (2004). 20 U.S.C. § 1400.
Jitendra, A. K., & Star, J. R. (2011). Meeting the needs of students with learning disabilities in inclusive mathematics classrooms: The role of schema-based instruction on mathematical problem-solving. Theory into Practice, 50(1), 12–19. https://doi.org/10.1080/00405841.2011.534912.
Jitendra, A. K., DePipi, C. M., & Perron-Jones, N. (2002). An exploratory study of schema-based-word-problem-solving instruction for middle school students with learning disabilities: An emphasis on conceptual and procedural understanding. The Journal of Special Education, 36(1), 23–38. https://doi.org/10.1177/00224669020360010301.
Jitendra, A. K., Nelson, G., Pulles, S. M., Kiss, A. J., & Houseworth, J. (2016). Is mathematical representation of problems an evidence-based strategy for students with mathematics difficulties? Exceptional Children, 83(1), 8–25. https://doi.org/10.1177/0014402915625062.
Judd, T. P., & Bilsky, L. H. (1989). Comprehension and memory in the solution of verbal arithmetic problems by mentally retarded and nonretarded individuals. Journal of Educational Psychology, 81(4), 541–546. https://doi.org/10.1037/0022-0663.81.4.541.
Lee, K., Ng, E. L., & Ng, S. F. (2009). The contributions of working memory and executive functioning to problem representation and solution generation in algebraic word problems. Journal of Educational Psychology, 101(2), 373–387. https://doi.org/10.1037/a0013843.
Lucangeli, D., Tressoldi, P. E., & Cendron, M. (1998). Cognitive and metacognitive abilities involved in the solution of mathematical word problems: Validation of a comprehensive model. Contemporary Educational Psychology, 23(3), 257–275. https://doi.org/10.1006/ceps.1997.0962.
Mastropieri, M. A., Bakken, J. P., & Scruggs, T. E. (1991). Mathematics instruction for individuals with mental retardation: A perspective and research synthesis. Education and Training in Mental Retardation, 26, 115–129.
Ministère de l’éducation et de l’enseignement supérieur (1999). Policy on special education: Adapting our schools to the needs of all students. Retrieved from: http://www.education.gouv.qc.ca/fileadmin/site_web/documents/dpse/adaptation_serv_compl/polite00A.pdf.
Montague, M., & Applegate, B. (1993). Mathematical problem-solving characteristics of middle school students with learning disabilities. Journal of Special Education, 27, 175–201. https://doi.org/10.1177/002246699302700203.
National Mathematics Advisory Panel. (2008). Foundations for success: The final report of the National Mathematics Advisory Panel. Washington, D.C..: U.S. Department of Education.
No Child Left Behind Act of 2001. (2002). P.L. 107–110, 20 U.S.C. § 6319.
Ontario Ministry of Education. (1990). The Education Act, Bill 82, § 7 et seq.
Ostad, S. A. (1997). Developmental differences in addition strategies: A comparison of mathematically disabled and mathematically normal children. British Journal of Educational Psychology, 67(3), 345–357. https://doi.org/10.1111/j.2044-8279.1997.tb01249.x.
Ozonoff, S., & Schetter, P. L. (2007). Executive dysfunction in Autism spectrum disorders: From research to practice. In L. Meltzer (Ed.), Executive function in education: From theory to practice (pp. 287–308). New York, NY: Guilford. https://doi.org/10.5860/choice.45-1588.
Powell, S. R., Fuchs, L. S., & Fuchs, D. (2013). Reaching the mountaintop: Addressing the common core standards in mathematics for students with mathematics difficulties. Learning Disabilities Research & Practice, 28(1), 38–48. https://doi.org/10.1111/ldrp.12001.
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(2), 110–122. https://doi.org/10.1016/j.lindif.2009.10.005.
Rockwell, S. B., Griffin, C. C., & Jones, H. A. (2011). Schema-based strategy instruction in mathematics and the word problem-solving performance of a student with. Focus on Autism and Other Developmental Disabilities, 26(2), 87–95. https://doi.org/10.1177/1088357611405039.
Rose, D., & Rose, K. (2007). Deficits in executive function processes. In L. Meltzer (Ed.), Executive function in education: From theory to practice (pp. 287–308). New York, NY: Guilford. https://doi.org/10.5860/choice.45-1588.
Stein, J. A., & Krishnan, K. (2007). Nonverbal learning disabilities: The challenges of effective assessment and teaching. In L. Meltzer (Ed.), Executive function in education: From theory to practice (pp. 287–308). New York, NY: Guilford. https://doi.org/10.5860/choice.45-1588.
Swanson, H. L., & Beebe-Frankenberger, M. (2004). The relationship between working memory and mathematical problem solving in children at risk and not at risk for serious math difficulties. Journal of Educational Psychology, 96(3), 471–491. https://doi.org/10.1037/0022-0663.96.3.471.
Swanson, H. L., & Sachse-Lee, C. (2001). Mathematical problem solving and working memory in children with learning disabilities: Both executive and phonological processes are important. Journal of Experimental Child Psychology, 79(3), 294–321. https://doi.org/10.1006/jecp.2000.2587.
Verschaffel, L., Torbeyns, J., De Smedt, B., Luwel, K., & Van Dooren, W. (2007). Strategy flexibility in children with low achievement in mathematics. Educational and Child Psychology, 24(2), 16–27.
Xin, Y. P., & Jitendra, A. K. (1999). The effects of instruction in solving mathematical word problems for students with learning problems: A meta-analysis. The Journal of Special Education, 32(4), 207–225. https://doi.org/10.1177/002246699903200402.
Xin, Y. P., Jitendra, A. K., & Deatline-Buchman, A. (2005). Effects of mathematical word problem-solving instruction on middle school students with learning problems. The Journal of Special Education, 39(2), 181–192. https://doi.org/10.1177/00224669050390030501.
Zheng, X., Swanson, H. L., & Marcoulides, G. A. (2011). Working memory components as predictors of children’s mathematical word problem solving. Journal of Experimental Child Psychology, 110(4), 481–498. https://doi.org/10.1016/j.jecp.2011.06.001.
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Desmarais, K., Osana, H.P., Lafay, A. (2019). Schema-Based Instruction: Supporting Children with Learning Difficulties and Intellectual Disabilities. In: Robinson, K., Osana, H., Kotsopoulos, D. (eds) Mathematical Learning and Cognition in Early Childhood. Springer, Cham. https://doi.org/10.1007/978-3-030-12895-1_12
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