References
- Baker, J. N., Rivera, C. J., Morgan, J. J., & Reese, N. (2015). Teaching algebraic equations to middle school students with intellectual disabilities. Journal of the American Academy of Special Education Professionals, 7(2), 29–43.
- Bouck, E. C., Chamberlain, C., & Park, J. (2017). Concrete and app-based manipulatives to support students with disabilities with subtraction. Education and Training in Autism and Developmental Disabilities, 52(3), 317–331. https://doi.org/10.2307/26420403
- Bouck, E. C., Mathews, L. A., & Peltier, C. (2019). Virtual manipulatives: A tool to support access and achievement with middle school students with disabilities. Journal of Special Education Technology, 35(1), 51–59. https://doi.org/10.1177/0162643419882422
- Bouck, E. C., & Park, J. (2018). A systematic review of the literature on mathematics manipulatives to support students with disabilities. Education and Treatment of Children, 41(1), 65–106. https://doi.org/10.1353/etc.2018.0003
- Bouck, E. C., Park, J., Levy, K., Cwiakala, K., & Whorley, A. (2020). App-based manipulatives and explicit instruction to support division with remainders. Exceptionality, 20(1), 44–59. https://doi.org/10.1080/09362835.2019.1586709
- Bouck, E. C., Park, J., Nickell, B. (2017). Using the concrete-representational-abstract approach to support students with intellectual disability to solve change-making problems. Research in Developmental Disabilities, 60(January 2017), 24–36. https://doi.org/10.1016/j.ridd.2016.11.006
- Bouck, E. C., Park, J., Satsangi, R., Cwiakala, K., & Levy, K. (2019). Using the virtual-abstract instructional sequence to support the acquisition of algebra. Journal of Special Education Technology, 34(4), 253–268. https://doi.org/10.1177/0162643419833022
- 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 Disabilities, 44(1), 180–193. https://doi.org/10.1007/s10803-013-1863-2
- Bouck, E. C., Satsangi, R., & Park, J. (2018). The concrete-representational-abstract approach for students with learning disabilities: An evidence-based practice synthesis. Remedial and Special Education, 39(4), 211–228. https://doi.org/10.1177/0741932517721712
- Bouck, E. C., Shurr, J., Bassette, L., Park, J., Kerr, J., & Whorley, A. (2018). Adding it up: Comparing concrete and app-based manipulatives to support students with disabilities with adding fractions. Journal of Special Education Technology, 33(3), 194–206. https://doi.org/10.1177/0162643418759341
- Bouck, E. C., Working, C., & Bone, E. (2018). Manipulative apps to support students with disabilities in mathematics. Intervention in School and Clinic, 53(3), 177–182. https://doi.org/10.1177/1053451217702115
- Brainingcamp, LLC. (2020). Algebra tiles [Mobile app]. App store. Brainingcamp. https://apps.apple.com/us/app/algebra-tiles/id568896224
- Carbonneau, K. J., Marley, S. C., & Selig, J. P. (2013). A meta-analysis of the efficacy of teaching mathematics with concrete manipulatives. Journal of Educational Psychology, 105(2), 380–400. https://doi.org/10.1037/a0031084
- CAST. (2018). Universal design for learning guidelines-Version 2.2. CAST. http://udlguidelines.cast.org
- Chapman, S. M., Ault, M. J., Spriggs, A. D., Bottge, B. A., & Shepley, S. B. (2019). Teaching algebra with a functional application to students with moderate intellectual disability. Education and Training in Autism and Developmental Disabilities, 54(2), 161–174.
- Connolly, A. J. (2007). KeyMath-3 diagnostic assessment. Pearson.
- Gast, D. L., & Spriggs, A. D. (2014). Visual analysis of graphic data. In D. L. Gast (Ed.), Single subject research methodology in behavioral sciences (pp. 176–210). Routledge.
- Hughes, E. M., Witzel, B. S., Riccomini, P. J., Fries, K. M., & Kanyongo, G. Y. (2014). A meta-analysis of algebra interventions for learners with disabilities and struggling learners. The Journal of the International Association of Special Education, 15(1), 36–47. https://www.learntechlib.org/p/159660/
- Ives, B. (2007). Graphic organizers applied to secondary algebra instruction for students with learning disorders. Learning Disabilities Research & Practice, 22(2), 110–118. https://doi.org/10.1111/j.1540-5826.2007.00235.x
- Ledford, J., & Gast, D. (2018). Single case research methodology. Routledge.
- National Center for, Education Statistics. (2019). National Assessment of Education Progress—Mathematics. Retrieved from, https://nces.ed.gov/nationsreportcard/mathematics/
- Maccini, P., & Hughes, C. A. (2000). Effects of a problem-solving strategy on the introductory algebra performance of secondary students with learning disabilities. Learning Disabilities Research & Practice, 15(1), 10–21. https://doi.org/10.1207/SLDRP1501_2
- Maccini, P., & Ruhl, K. L. (2000). Effects of a graduated instructional sequence on the algebraic subtraction of integers by secondary students with learning disabilities. Education and Treatment of Children, 23(4), 465–489. https://doi.org/42899634
- Marsh, L. G., & Cooke, N. L. (1996). The effects of using manipulatives in teaching math problem solving to students with learning disabilities. Learning Disabilities Research & Practice, 11(1), 58–65.
- McMahon, D. D., Smith, C. C., Cihak, D. F., Wright, R., & Gibbons, M. M. (2015). Effects of digital navigation aids on adults with intellectual disabilities: Comparison of paper map, google maps, and augmented reality. Journal of Special Education Technology, 30(3), 157–165. https://doi.org/10.1177/0162643415618927
- Moyer, P. S. (2001). Are we having fun yet? How teachers use manipulatives to teach mathematics. Educational Studies in Mathematics, 47(2), 175–197. https://doi.org/10.1023/A:1014596316942
- Moyer-Packenham, P. S., & Suh, J. M. (2012). Learning mathematics with technology: The influence of virtual manipulatives on different achievement groups. Journal of Computers in Mathematics and Science Teaching, 31(1), 39–59.
- Parker, R. I., Vannest, K. J., Davis, J. L., & Sauber, S. B. (2010). Combining non-overlap and trend for single case research: Tau-U. Behavior Therapy, 42(2), 284–299. https://doi.org/10.1016/j.beth.2010.08.006
- Peltier, C., Morin, K. L., Bouck, E. C., Lingo, M. E., Pulos, J., Scheffler, F. A., Suk, A., Mathews, L. A., Sinclair, T. E., & Deardorff, M. E. (2020). A meta-analysis of single-case research using mathematics manipulatives with students at risk or identified with a disability. Journal of Special Education, 54(1), 3–15. https://doi.org/10.1177/0022466919844516
- Root, J., Browder, D. M., & Jimenez, B. (2016). Access to algebra for students with moderate and severe developmental disabilities. In B. S. Witzel (Ed.), Bridging the gap between arithmetic and algebra (pp. 171–193). Council for Exceptional Children.
- Root, J. R., & Browder, D. M. (2017). Algebraic problem solving for middle school students with autism and intellectual disability. Exceptionality, 27(2), 118–132. https://doi.org/10.1080/09362835.2017.1394304
- Root, J. R., Browder, D. M., Saunders, A. F., & Lo, Y. (2017). Schema-based instruction with concrete and virtual manipulatives to teach problem solving to students with autism. Remedial and Special Education, 38(1), 42–52. https://doi.org/10.1177/0741932516643592
- Satsangi, R., & Bouck, E. C. (2015). Using virtual manipulatives instruction to teach the concepts of area and perimeter to secondary students with learning disabilities. Learning Disability Quarterly, 38(3), 174–186. https://doi.org/10.1177/0731948714550101
- Satsangi, R., Bouck, E. C., Doughty, T. T., Bofferding, L., & Roberts, C. A. (2016). Comparing the effectiveness of virtual and concrete manipulatives to teach algebra to secondary students with learning disabilities. Learning Disability Quarterly, 39(4), 240–253. https://doi.org/10.1177/0731948716649754
- Satsangi, R., Hammer, R., & Evmenova, A. S. (2018). Teaching multistep equations with virtual manipulatives secondary students with learning disabilities. Learning Disabilities Research & Practice, 33(2), 99–111. https://doi.org/10.1111/ldrp.12166
- Satsangi, R., & 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(4), 303–310. https://doi.org/10.1080/1045988X.2016.1275505
- Shepley, C., Lane, J. D., & Ault, M. J. (2019). A review and critical examination of the system of least prompts. Remedial and Special Education, 40(5), 313–327. https://doi.org/10.1177/0741932517751213
- Sindelar, P. T., Rosenberg, M. S., & Wilson, J. R. (1985). An adapted alternating treatments design for instructional research. Education and Treatment of Children, 8(1), 67–76.
- Stephens, A., Blanton, M., Knuth, E., Isler, I., & Gardiner, A. M. (2015). Just say yes to early algebra! Teaching Children Mathematics, 22(2), 92–101. https://doi.org/10.5951/teacchilmath.22.2.0092
- 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(2), 41–59.
- Van Garderen, D. (2007). Teaching students with LD to use diagrams to solve mathematical word problems. Journal of Learning Disabilities, 40(6), 540–553. https://doi.org/10.1177/00222194070400060501
- Vannest, K. J., Parker, R. I., Gonen, O., & Adiguzel, T. (2016). Single case research: Web-based calculator for SCR analysis. (Version 2.0) [Web-based application]. Texas A&M University. www.singlecaseresearch.org
- Wechsler, D. (2002). Wechsler preschool and primary scale of intelligence—third edition technical and interpretive manual. Psychological Corporation.
- Wechsler, D. (2014). Wechsler intelligence scale for children-fifth edition. Pearson.
- White, O. R., & Haring, N. G. (1980). Exceptional teaching (2nd ed.). Merrill.
- Witzel, B. S. (2005). Using CRA to teach algebra to students with math difficulties in inclusive settings. Learning Disabilities: A Contemporary Journal, 3(2), 49–60. https://doi.org/1937-6928
- Witzel, B. S. (Ed). (2016). Bridging the gap between arithmetic and algebra. Council for Exceptional Children.
- Witzel, B. S., Mercer, C. D., & Miller, M. D. (2003). Teaching algebra to students with learning difficulties: An investigation of an explicit instruction model. Learning Disabilities Research & Practice, 18(2), 121–131. https://doi.org/10.1111/1540-5826.00068
- 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(7), 2349–2362. https://doi.org/10.1007/s10803-016-2768-7