References
- Agrawal, J., and Morin, L. L. 2016. Evidence-based practices: Applications of concrete representational abstract framework across math concepts for students with disabilities. Learning Disabilities Research & Practice, 31, 34–44.
- Alberto, P., and Troutman, A. 2009. Applied behavior analysis for teachers. 8th ed. Upper Saddle River, NJ: Pearson.
- Allen, R. J., Baddeley, A. D., and Hitch, G. J. 2006. Is the binding of visual features in working memory resource-demanding? Journal of Experimental Psychology, 135, 298–313.
- Baddeley, A. D. 2003. Working memory and language: An overview. Journal of Communication Disorders, 36, 189–208.
- Bouck, E. C., Bassette, L., Taber-Doughty, T., Flanagan, S. M., and Szwed, K. 2009. Pentop computers as tools for teaching multiplication to students with MID. Education and Training in Developmental Disabilities, 44, 367–380.
- Bouck, E. C., Chamberlain, C., and Park, J. 2017. Concrete and app-based manipulatives to support students with disabilities with subtraction. Education and Training in Autism and Developmental Disabilities, 52, 317–331.
- Bouck, E. C., and Park, J. 2018. Mathematics manipulatives to support students with disabilities: A systematic review of the literature. Education and Treatment of Children, 41, 65–106.
- Bouck, E. C., Park, J., Satsangi, R., Cwiasksi, K., and Levy, K. 2019. Using the virtual-abstract instructional sequence to support acquisition of algebra. Journal of Special Education Technology. Advanced Online Publication.
- Bouck, E. C., Park, J., Shurr, J., Bassette, L., and Whorley, A. 2018. Using the virtual-representational-abstract approach to support students with intellectual disability in mathematics. Focus on Autism and Other Developmental Disabilities, 33, 237–248.
- Bouck, E. C., Park, J., Sprick, J., Shurr, J., Bassette, L., and Whorley, A. 2017. Using the virtual-abstract instructional sequence to teach addition of fractions. Research in Developmental Disabilities, 70, 163–174.
- Bouck, E. C., Satsangi, R., Doughty, T. T., and 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 Disabilities, 44, 180–193
- Bouck, E. C., Satsangi, R., and Park, J. 2018. The concrete-representational-abstract approach for students with disabilities: An evidence-based practice synthesis. Remedial and Special Education, 39, 211–228.
- Brainingcamp, 2018. Color tiles manipulative. Available at: https://itunes.apple.com/us/app/color-tiles-manipulative/id656246736
- Carr, M., and Alexeev, N. 2011. Fluency, accuracy, and gender predict developmental trajectories of arithmetic strategies. Journal of Educational Psychology, 103, 617–631.
- Cass, M., Cates, D., Smith, M., and Jackson, C. 2003. Effects of manipulative instruction on solving area and perimeter problems by students with learning disabilities. Learning Disabilities Research & Practice, 18, 112–120.
- Collins, B. C. 2012. Systematic instruction for students with moderate and severe disabilities. Baltimore, MD: Paul H Brookes Publishing.
- Common Core State Standards Initiative, 2019. Standards for mathematical practice. Available at: http://www.corestandards.org/Math/Practice/
- Connolly, A. J. 2007. KeyMath-3 diagnostic assessment. Boston, MA: Pearson.
- Doyle, P. M., Wolery, M., Ault, M. J., and Gast, D. L. 1988. System of least prompts: A literature review of procedural parameters. Journal of the Association for Persons with Severe Handicaps, 13, 28–40.
- Dube, A. K., and Robinson, K. M. 2018. Children’s understanding of multiplication and division: Insights from a pooled analysis of seven studies conducted across 7 years. British Journal of Developmental Psychology, 36, 206–219.
- Flores, M. M., Hinton, V. M., and Schweck, K. B. 2014. Teaching multiplication with regrouping to students with learning disabilities. Learning Disabilities Research & Practice, 29, 171–183.
- Fyfe, E. R., McNeil, N. M., Son, J. Y., and Goldstone, R. L. 2014. Concreteness fading in mathematics and science instruction: A systematic review. Educational Psychology Review, 26, 9–25.
- Gast, D. L., and Ledford, J. R. 2014. Single case research methodology. New York, NY: Routledge.
- Geary, D. C., Hoard, M. K., and Bailey, D. H. 2012. Fact retrieval deficits in low achieving children and children with mathematical learning disability. Journal of Learning Disabilities, 45, 291–307.
- Grossman, H. J. 1983. Classification in mental retardation. Washington, DC: American Association on Mental Deficiency.
- Haring, N. G., and Eaton, M. D. 1978. Systematic instructional technology: An instructional hierarchy. In: N. G. Haring, T. C. Lovitt, M. D. Eaton, and C. L. Hansen, eds. The fourth R: Research in the classroom. Columbus, OH: Merrill, pp. 23–40.
- Harris, C. A., Miller, S. P., and Mercer, C. D. 1995. Teaching initial multiplication skills to students with disabilities in general education classroom. Learning Disabilities Research & Practice, 10, 180–195.
- Hayter, S., Scott, E., McLaughlin, T. F., and Weber, K. P. 2007. The use of a modified direct instruction flashcard system with two high school students with developmental disabilities. Journal of Developmental & Physical Disabilities, 19, 409–415.
- Hord, C., and Bouck, E. C. 2012. A review of academic mathematics instruction for students with mild intellectual disabilities. Education and Training in Autism and Developmental Disabilities, 47, 389–400.
- Jitendra, A., DiPipi, C. M., and Perron-Jones, N. 2002. An exploratory student 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, 23–38.
- Jitendra, A. K., Nelson, G., Pulles, S. M., Kiss, A. J., and Houseworth, J. 2016. Is mathematical representation of problems an evidence-based strategy for students with mathematical difficulties? Exceptional Children, 83, 8–25.
- Ketterlin-Geller, L. R., Chard, D. J., and Fien, H. 2008. Making connections in mathematics: Conceptual mathematics intervention for low performing students. Remedial and Special Education, 29, 33–45.
- Lafay, A., Osana, H. P., and Valat, M. 2019. Effects of interventions with manipulatives on immediate learning, maintenance, and transfer in children with mathematics learning disabilities: A systematic review. Education Research International, 2019, 1–21.
- Marita, S., and Hord, C. 2017. Reviews of mathematics interventions for secondary students with learning disabilities. Learning Disability Quarterly, 40, 29–40.
- Milton, J. H., Flores, M. M., Moore, A. J., Taylor, J. J., and Burton, M. E. 2019. Using the concrete-representational-abstract sequence to teach conceptual understanding of basic multiplication and division. Learning Disability Quarterly, 42, 32–45.
- National Council of Teachers of Mathematics, 2000. Principles and standards for school mathematics. Reston, VA: Author.
- National Mathematics Advisory Panel, 2008. Foundations for success: Final report of the national math advisory panel. Washington, DC: U.S. Department of Education.
- Ng, S. F., and Lee, K. 2009. The model method: Singapore children’s tools for representing and solving algebraic word problems. Journal for Research in Mathematics Education, 40, 282–313.
- Park, J.-H., and Nunes, T. 2001. The development of the concept of multiplication. Cognitive Development, 16, 763–773.
- Powell, S. R., Fuchs, L. S., and Fuchs, D. 2013. Reaching the mountaintop: Addressing the common core standards in mathematics for students with mathematics difficulties. Learning Disabilities Research & Practice, 28, 38–48.
- Rao, S., and Mallow, L. 2009. Using simultaneous prompting procedure to promote recall of multiplication facts by middle school students with cognitive impairment. Education and Training in Developmental Disabilities, 44, 80–90.
- Richards, A. 2014. Working towards a child friendly’ written progression for division. Mathematics Teaching, 240, 15–18.
- Rohrer, D. 2015. Student instruction should be distributed over long time periods. Educational Psychology Review, 27, 635–643.
- Sante, A. D., McLaughlin, T. F., and Weber, K. P. 2001. The use and evaluation of a direct instruction flash card strategy on multiplication math facts mastery with two students with developmental disabilities and attention deficit hyperactivity disorder. Journal of Precision Teaching and Celeration, 17, 68–75.
- Satsangi, R., and Bouck, E. C. 2015. Using virtual manipulative instruction to teach the concepts of area and perimeter to secondary students with learning disabilities. Learning Disability Quarterly, 38, 174–186.
- Satsangi, R., and Miller, B. 2017. The case for adopting virtual manipulatives in mathematics education for students with disabilities. Preventing School Failure: Alternative Education for Children and Youth, 61, 303–310.
- Schalock, R., Borthwick-Duffy, S., Bradley, V., Buntinx, W., Coulter, D., Craig, E., and Yeager, M. 2010. Intellectual disability: Definition, classification, and systems of supports. 11th ed. Washington, DC: American Association on Intellectual and Developmental Disabilities.
- Schuchardt, K., Gebhardt, M., and Maehler, C. 2010. Working memory functions in children with different degrees of intellectual disability. Journal of Intellectual Disability Research, 54, 346–353.
- Shurr, J., Jimenez, B., and Bouck, E. C. 2019. Maintenance. In: J. Shurr, B. Jimenez, and E. C. Bouck, eds. Research-based practices and instructional information for students with autism and intellectual disability (pp. 35–46). Arlington, VA: Council for Exceptional Children.
- Spooner, Fred., Knight, Victoria F., Browder, Diane M., Smith, Bethany R.. 2012. Evidence-based practice for teaching academics to students with severe developmental disabilities. Remedial and Special Education, 33(6) 374–387. doi:10.1177/0741932511421634.
- Stroizer, S., Hinton, V., Flores, M., and 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, 223–236.
- Vannest, K. J., Parker, R. I., Gonen, O., and Adiguzel, T. 2016. Single case research: Web-based calculator for SCR analysis. (Version 2.0) [Web-based application]. College Station, TX: Texas A&M University.
- Wechsler, D. 2002. Wechsler Preschool and Primary Scale of Intelligence-III. Boston, MA: Pearson.
- Wechsler, D. 2004. Wechsler Intelligence Scale for Children. London: Pearson Assessments.
- Wechsler, D. 2014. Wechsler Intelligence Scale for Children-Fourth Edition (WISC-IV). Boston, MA: Pearson.
- White, O. R., and Haring, N. G. 1980. Exceptional teaching. 2nd ed. Columbus, OH: Merrill.
- Woodward, J., and Montague, M. 2002. Meeting the challenge of mathematics reform for students with LD. The Journal of Special Education, 36, 89–101.
- Yell, M. 2019. The law and special education. 5th ed. Boston, MA: Pearson Education.