# Mathematical Problem Solving Instruction for Students with Autism Spectrum Disorder

Chapter
Part of the Autism and Child Psychopathology Series book series (ACPS)

## Abstract

Mathematical problem solving is a central theme of K-12 mathematics and an essential skill for college and career readiness. However, problem solving is a challenging task for many young students, especially for students with cognitive difficulties because it requires not only mathematics skills but also reading comprehension, reasoning, and ability to transform words and numbers into the appropriate operations. This chapter is designed to provide helpful suggestions for teaching students with autism spectrum disorder (ASD) who have math problem solving difficulties. The emphasis is made on the visual supports that aid students with ASD to develop abstract and conceptual understanding and apply the learned concepts in real-life problem solving. The following are topics included in this chapter: (1) the general guidelines for math instruction targeting students with ASD; (2) teaching problem solving based on the concrete-representational-abstract (CRA) approach; (3) teaching students in concrete level using manipulative; and (4) teaching students at semiabstract level: schema-based instruction (SBI) for students with ASD. Several lesson ideas are also included in the chapter to illustrate the visual strategies and SBI for problem solving skills.

## References

1. Bae, Y. S., Chiang, H. M., & Hickson, L. (2015). Mathematical word problem solving ability of children with autism spectrum disorder and their typically developing peers. Journal of Autism and Developmental Disorders, 45(7), 2200–2208.Google Scholar
2. Baio, J. (2012). Prevalence of autism spectrum disorders: Autism and Developmental Disabilities Monitoring Network, 14 sites, United States, 2008. MMWR Surveill Summ, 61(3), 1–19.Google Scholar
3. Bouck, E. C., Satsangi, R., Doughty, T. T., & Courtney, W. T. (2014). Virtual and concrete manipulatives: A comparison of approaches for solving mathematics problems for students with autism spectrum disorder. Journal of Autism and Developmental Disorders, 44(1), 180–193.Google Scholar
4. Boutot, E. A., & Myles, B. S. (2011). Autism spectrum disorder: Foundations, characteristics, and effective strategies. Upper Saddle River, NJ: Pearson Education.Google Scholar
5. Clements, D. H., & Sarama, J. (2014). Learning and teaching early math: The learning trajectories approach. New York: Routledge.Google Scholar
6. Cochran-Smith, M., & Lytle, S. L. (1999). The teacher research movement: A decade later. Educational Researcher, 28(7), 15–25.Google Scholar
7. Dingfelder, H. E., & Mandell, D. S. (2011). Bridging the research-to-practice gap in autism intervention: An application of diffusion of innovation theory. Journal of Autism and Developmental Disorders, 41(5), 597. Retrieved from http://go.galegroup.com.eduproxy.tc-library.org:8080/ps/i.do?p=HRCA&sw=w&u=new30429&v=2.1&it=r&id=GALE%7CA342570893&asid=f6362a82b5aa7c584591a268196841d7
8. Donaldson, J. B., & Zager, D. (2010). Mathematics interventions for students with high functioning autism/Asperger’s syndrome. Teaching Exceptional Children, 42(6), 40–46.Google Scholar
9. Fede, J. L., Pierce, M. E., Matthews, W. J., & Wells, C. S. (2013). The effects of a computer-assisted, schema-based instruction intervention on word problem-solving skills of low-performing fifth grade students. Journal of Special Education Technology, 28(1), 9–21.Google Scholar
10. Flores, M. M., Hinton, V. M., Strozier, S. D., & Terry, S. L. (2014). Using the concrete-representational-abstract sequence and the strategic instruction model to teach computation to students with autism spectrum disorders and developmental disabilities. Education and Training in Autism and Developmental Disabilities, 49(4), 547.Google Scholar
11. Fosnot, C. T., & Dolk, M. (2001). Young mathematicians at work: Constructing number sense, addition, and subtraction. Portsmouth, NH: Heinemann.Google Scholar
12. Griswold, D. E., Barnhill, G. P., Myles, B. S., Hagiwara, T., & Simpson, R. L. (2002). Asperger syndrome and academic achievement. Focus on Autism & Other Developmental Disabilities, 17(2), 94.Google Scholar
13. Hegarty, M., Mayer, R. E., & Monk, C. A. (1995). Comprehension of arithmetic word problems: A comparison of successful and unsuccessful problem solvers. Journal of Educational Psychology, 87(1), 18.Google Scholar
14. 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.Google Scholar
15. Jitendra, A. K., Star, J. R., Starosta, K., Leh, J. M., Sood, S., Caskie, G., et al. (2009). Improving seventh grade students’ learning of ratio and proportion: The role of schema-based instruction. Contemporary Educational Psychology, 34(3), 250–264.Google Scholar
16. Jones, C. R. G., Happe, F., Golden, H., Marsden, A. J. S., Tregay, J., Simonoff, E., et al. (2009). Reading and arithmetic in adolescents with autism spectrum disorders: Peaks and dips in attainment. Neuropsychology, 23(6), 718–728.Google Scholar
17. Just, M. A., Cherkassky, V. L., Keller, T. A., & Minshew, N. J. (2004). Cortical activation and synchronization during sentence comprehension in high-functioning autism: Evidence of underconnectivity. Brain, 127, 1811–1821.Google Scholar
18. Maccini, P., & Gagnon, J. C. (2000). Best practices for teaching mathematics to secondary students with special needs: Implications from teacher perceptions and a review of the literature. Focus on Exceptional Children, 32, 1–22.Google Scholar
19. Marshall, S. P. (1995). Schemas in problem solving. New York: Cambridge University Press.Google Scholar
20. Mayer, R. E. (1999). The promise of educational psychology: Learning in the content areas (p. 280). Upper Saddle River, NJ: Prentice-Hall.Google Scholar
21. Mayes, S. D., & Calhoun, S. L. (2008). WISC-IV and WIAT-II profiles in children with high-functioning autism. Journal of Autism and Developmental Disorders, 38(3), 428–439.Google Scholar
22. Mercer, C. D., & Miller, S. P. (1992). Teaching students with learning problems in math to acquire, understand, and apply basic math facts. Remedial and Special Education, 13(3), 19–35.Google Scholar
23. Montague, M., & van Garderen, D. (2003). A cross-sectional study of mathematics achievement, estimation skills, and academic self-perception in students of varying ability. Journal of Learning Disabilities, 36(5), 437–448.Google Scholar
24. Mayer, R. E. (1985). Implications of cognitive psychology for instruction in mathematical problem solving. In Teaching and learning mathematical problem solving: Multiple research perspectives (pp. 123–138).Google Scholar
25. National Autism Center. (2009). Evidence-based practice and autism in the schools: A guide to providing appropriate interventions to students with autism spectrum disorder. Randolph, MA: National Autism Center.Google Scholar
26. National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics. Retrieved from http://www.nctm.org/standards/content.aspx?id=16909
27. Neef, N. A., Nelles, D. E., Iwata, B. A., & Page, T. J. (2003). Analysis of precurrent skills in solving mathematical story problems. Journal of Applied Behavior Analysis, 36(1), 21.Google Scholar
28. Piaget, J. (1977). The development of thought: Equilibration of cognitive structures (A. Rosin, Trans.). New York: Viking Press.Google Scholar
29. 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 autism. Focus on Autism and Other Developmental Disabilities, 26(2), 87–95.Google Scholar
30. Root, J. R., Browder, D. M., Saunders, A. F., & Lo, Y. Y. (2016). Schema-based instruction with concrete and virtual manipulatives to teach problem solving to students with autism. Remedial and Special Education, 38, 42–52.Google Scholar
31. Satsangi, R., & Bouck, E. C. (2014). Using virtual manipulative instruction to teach the concepts of area and perimeter to secondary students with disabilities. Learning Disability Quarterly, 38(3), 174–186. https://doi.org/10.1177/0731948714550101
32. Sealander, K. A., Johnson, G. R., Lockwood, A. B., & Medina, C. M. (2012). Concrete–semiconcrete–abstract (CSA) instruction: A decision rule for improving instructional efficacy. Assessment for Effective Intervention, 38, 53–65.Google Scholar
33. Stroizer, S., Hinton, V., Flores, M., & Terry, L. (2015). An investigation of the effects of CRA instruction and students with autism spectrum disorder. Education and Training in Autism and Developmental Disabilities, 50(2), 223.Google Scholar
34. Tournaki, N., Bae, Y. S., & Kerekes, J. (2008). Rekenrek: A manipulative used to teach addition and subtraction to students with learning disabilities. Learning Disabilities: A Contemporary Journal, 6, 41–59.Google Scholar
35. Wei, X., Christiano, E. R., Jennifer, W. Y., Wagner, M., & Spiker, D. (2015). Reading and math achievement profiles and longitudinal growth trajectories of children with an autism spectrum disorder. Autism, 19, 200–210.Google Scholar
36. Witzel, B. S., Riccomini, P. J., & Schneider, E. (2008). Implementing CRA with secondary students with learning disabilities in mathematics. Intervention in School and Clinic, 43(5), 270–276.Google Scholar
37. Yakubova, G., Hughes, E. M., & Shinaberry, M. (2016). Learning with technology: Video modeling with concrete-representational-abstract sequencing for students with autism spectrum disorder. Journal of Autism and Developmental Disorders, 46, 2349–2362.Google Scholar