Using the concrete representational abstract (CRA) instructional framework for mathematics with students with emotional and behavioral disorders

References

• Agrawal, J., & Morin, L. L. (2016). Evidence-based practices: Applications of concrete representational abstract framework across math concepts for students with mathematics disabilities. Learning Disabilities Research & Practice, 31(4), 34–44.
   Google Scholar
• Allsopp, D. H., Kyger, M., & Lovin, L. (2007). Teaching mathematics meaningfully: Solutions for reaching struggling learners. Baltimore, MD: Brookes.
   Google Scholar
• Archer, A. L., & Hughes, C. A. (2011). Explicit instruction: Effective and efficient teaching. New York, NY: The Guilford Press.
   Google Scholar
• Bandura, A. (2006). Adolescent development from an agentic perspective. In F. Pajares, & T. Urdan (Eds.), Self-efficacy beliefs of adolescents (Vol. 5, pp. 1–43). Greenwich, CT: Information Age Publishing.
   Google Scholar
• Belenky, D. M., & Nokes, T. J. (2009). Examining the role of manipulatives and metacognition on engagement, learning, and transfer. Journal of Problem Solving, 2(2), 102–129.
   Google Scholar
• Boreson, L. (2002). Educational evaluation of emotional behavioral disability (EBD)—2nd edition. Retrieved from Wisconsin Department of Public Instruction website: http://sped.dpi.wi.gov/sites/default/files/imce/sped/pdf/ebdguide.pdf.
   Google Scholar
• Bruner, J. S. (1966). Toward a theory of instruction. Cambridge, MA: Harvard University Press.
   Google Scholar
• Bryant, D. P., Bryant, B. R., Gersten, R., Scammacca, N., & Chavez, M. M. (2008). Mathematics intervention for first-and second-grade students with mathematics difficulties: The effects of tier 2 intervention delivered as booster lessons. Remedial and Special Education, 29(1), 20–32.
   Web of Science ®Google Scholar
• Butler, F. M., Miller, S. P., Crehan, K., Babbitt, B., & Pierce, T. (2003). Fraction instruction for students with mathematics disabilities: Comparing two teaching sequences. Learning Disabilities Research & Practice, 18(2), 99–111.
   Google Scholar
• Cain-Caston, M. (1996). Manipulative queen. Journal of Instructional Psychology, 23(4), 270–274.
   Google Scholar
• 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.
   Web of Science ®Google Scholar
• Chi, M. T. H. (2009). Active-constructive-interactive: A conceptual framework for differentiating learning activities. Topics in Cognitive Science, 1(1), 73–105.
   PubMed Web of Science ®Google Scholar
• 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.
   PubMed Web of Science ®Google Scholar
• Flores, M. M., Hinton, V. M., & Schweck, K. B. (2014). Teaching multiplication with regrouping to students with learning disabilities. Learning Disabilities Research & Practice, 29(4), 171–183.
   Web of Science ®Google Scholar
• Flores, M. M., Hinton, V., & Strozier, S. D. (2014). Teaching subtraction and multiplication with regrouping using the concrete-representational-abstract sequence and strategic instruction model. Learning Disabilities Research & Practice, 29(4), 75–88.
   Google Scholar
• 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), 547–554.
   Web of Science ®Google Scholar
• Geary, D. C., Hoard, M. K., Nugent, L., & Bailey, D. H. (2012). Mathematical cognition deficits in children with learning disabilities and persistent low achievement: A five-year prospective study. Journal of Educational Psychology, 104(1), 206–223.
   PubMed Web of Science ®Google Scholar
• Gresham, F. M., & Elliott, S. N. (2008). Social skills improvement system-rating scales. Minneapolis, MN: Pearson Assessments.
   Google Scholar
• Harris, C. A., Miller, S. P., & Mercer, C. D. (1995). Teaching initial multiplication skills to students with disabilities in general education classrooms. Learning Disabilities Research & Practice, 10(3), 180–195.
   Google Scholar
• Heddens, J. W. (1986). Bridging the gap between the concrete and the abstract. The Arithmetic Teacher, 33(6), 14–17.
   Google Scholar
• Heuser, D. (2000). Mathematics class becomes learner centered. Teaching Children Mathematics, 6(5), 288–295.
   Google Scholar
• Hinton, V., Strozier, S. D., & Flores, M. M. (2014). Building mathematical fluency for students with disabilities or students at-risk for mathematics failure. International Journal of Education in Mathematics, Science and Technology, 2(4), 257–265. Retrieved from http://www.ulakbim.gov.tr.
   Google Scholar
• Kame'enui, E. J., & Simmons, D. C. (2001). Introduction to this special issue: The DNA of reading fluency. Scientific Studies of Reading, 5(3), 203–210.
   Google Scholar
• Kaminski, J. A., Sloutsky, V. M., & Heckler, A. F. (2009). Concrete instantiations of mathematics: A double-edged sword. Journal for Research in Mathematics Education, 40(2), 90–93.
   Web of Science ®Google Scholar
• Lane, K. Y., Menzies, H. M., Oakes, W. P., Lambert, W., Cox, M., & Hankins, K. (2012). A validation of the student risk screening scale for internalizing and externalizing behaviors: Patterns in rural and urban elementary schools. Behavioral Disorders, 37(4), 244–270.
   Web of Science ®Google Scholar
• 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.
   Google Scholar
• Mancl, D. B., Miller, S. P., & Kennedy, M. (2012). Using the concrete-representational-abstract sequence with integrated strategy instruction to teach subtraction with regrouping to students with learning disabilities. Learning Disabilities Research & Practice, 27(4), 152–166.
   Web of Science ®Google Scholar
• Martin, T. (2009). A theory of physically distributed learning: How external environments and internal states interact in mathematics learning. Child Development Perspectives, 3(3), 140–144.
   Web of Science ®Google Scholar
• McNeil, N. M., Uttal, D. H., Jarvin, L., & Sternberg, R. J. (2009). Should you show me the money? Concrete objects both hurt and help performance on mathematics problems. Learning and Instruction, 19(2), 171–184.
   Web of Science ®Google Scholar
• Miller, S. P., & Kaffar, B. J. (2011). Developing addition and regrouping competence among second grade students. Investigations in Mathematics Learning, 4(1), 25–51.
   Google Scholar
• Miller, S. P., & Mercer, C. D. (1993). Using data to learn concrete-semiconcrete-abstract instruction for students with math disabilities. Learning Disabilities Research & Practice, 8(2), 89–96.
   Google Scholar
• Miller, S. P., Mercer, C. D., & Dillon, A. S. (1992). CSA: Acquiring and retaining math skills. Intervention in School and Clinic, 28(2), 105–110.
   Google Scholar
• Mowat, J. G. (2010). Towards the development of self-regulation in pupils experiencing social and emotional behavioural difficulties (SEBD). Emotional & Behavioural Difficulties, 15(3), 189–206.
   Google Scholar
• Moyer-Packenham, P. S., & Westenskow, A. (2013). Effects of virtual manipulatives on student achievement and mathematics learning. International Journal of Virtual and Personal Learning Environments, 4(3), 35–50.
   Google Scholar
• Mulcahy, C. A., & Krezmien, M. P. (2009). Effects of a contextualized instructional package on the mathematics performance of secondary students with EBD. Behavioral Disorders, 34(3), 136–150.
   Web of Science ®Google Scholar
• Mulcahy, C. A., Maccini, P., Wright, K., & Miller, J. (2014). An examination of intervention research with secondary students with EBD in light of Common Core State Standards for Mathematics. Behavioral Disorders, 39(3), 146–164.
   Web of Science ®Google Scholar
• National Council of Teachers of Mathematics (NCTM). (2000). Principles and standards for school mathematics. Reston, VA: Author.
   Google Scholar
• National Governors Association Center for Best Practices & Council of Chief State School Officers. (2010). Common Core State Standards for Mathematics. Washington, DC: Authors.
   Google Scholar
• National Mathematics Advisory Panel. (2008). Foundations for success: The final report of the National Mathematics Advisory Panel. Retrieved from http://www.ed.gov/about/bdscomm/list/mathpanel/report/final-report.pdf.
   Google Scholar
• Nelson, J. R., Benner, G. J., Lane, K., & Smith, B. W. (2004). Academic achievement of K–12 students with emotional and behavioral disorders. Exceptional Children, 71(1), 59–73.
   Web of Science ®Google Scholar
• Ness, B. M., & Middleton, M. J. (2012). A framework for implementing individualized self-regulated learning strategies in the classroom. Intervention in School and Clinic, 47(5), 267–275.
   Web of Science ®Google Scholar
• OECD. (2016). PISA 2015 results (Volume I): Excellent and equity in education, PISA. Paris, France: OECD Publishing.
   Google Scholar
• 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.
   Web of Science ®Google Scholar
• Ralston, N. C., Benner, G. J., Tsai, S. F., Riccomini, P. J., & Nelson, J. R. (2014). Mathematics instruction for students with emotional and behavioral disorders: A best-evidence synthesis. Preventing School Failure: Alternative Education for Children and Youth, 58(1), 1–16.
   Google Scholar
• Reid, R., Gonzalez, J. E., Nordness, P. D., Trout, A., & Epstein, M. H. (2004). A meta-analysis of the academic status of students with emotional/behavioral disturbance. Journal of Special Education, 38(3), 130–143.
   Web of Science ®Google Scholar
• Ross, R., & Kurtz, R. (1993). Making manipulatives work: A strategy for success. Arithmetic Teacher, 40(5), 254–258.
   Google Scholar
• Sanford, A. K., & Horner, R. H. (2012). Effects of matching instruction difficulty to reading level for students with escape-maintained problem behavior. Journal of Positive Behavior Interventions, 15(2), 79–89.
   Web of Science ®Google Scholar
• Satsangi, R., Bouch, E. C., Taber-Doughty, 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.
   Web of Science ®Google Scholar
• 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(1), 53–65.
   Google Scholar
• Strickland, T. K., & Maccini, P. (2013). The effects of the concrete-representational-abstract integration strategy on the ability of students with learning disabilities to multiply linear expressions within area problems. Remedial and Special Education, 34(3), 142–153.
   Web of Science ®Google Scholar
• 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), 223–236.
   Web of Science ®Google Scholar
• Templeton, T. N., Neel, R. S., & Blood, E. (2008). Meta-analysis of math interventions for students with emotional and behavioral disorders. Journal of Emotional and Behavioral Disorders, 16(4), 226–239.
   Web of Science ®Google Scholar
• Trout, A. L., Nordness, P. D., Pierce, C. D., & Epstein, M. H. (2003). Research on the academic status of children with emotional and behavioral disorders: A review of the literature from 1961 to 2000. Journal of Emotional and Behavioral Disorders, 11(4), 198–210.
   Web of Science ®Google Scholar
• U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress. (2015). 2015 Mathematics assessment. Retrieved from http://nces.ed.gov/nationsreportcard.
   Google Scholar
• U.S. Department of Education, Office of Special Education and Rehabilitative Services, Office of Special Education Programs. (2016). 38th Annual Report to Congress on the Implementation of the Individuals with Disabilities Education Act, 2016. Washington, DC.
   Google Scholar
• Uttal, D. H., O'Doherty, K., Newland, R., Hand, L. L., & DeLoache, J. (2009). Dual representation and the linking of concrete and symbolic representations. Child Development Perspectives, 3(3), 156–159.
   Web of Science ®Google Scholar
• Vannest, K. J., Temple-Harvey, K., & Mason, B. (2009). Adequate yearly progress for students with emotional and behavioral disorders through research-based practices. Preventing School Failure: Alternative Education for Children and Youth, 53(2), 73–84.
   Google Scholar
• Vaughn, S., Wanzek, J., Murray, C. S., & Roberts, G. (2012). Intensive interventions for students struggling in reading and mathematics: A practice guide. Portsmouth, NH: RMC Research Corporation, Center on Instruction.
   Google Scholar
• Watt, S. J., Watkins, J. R., & Abbitt, J. (2014). Teaching algebra to students with learning disabilities: Where have we come and where should we go? Journal of Learning Disabilities, 49(4), 437–447.
   PubMed Web of Science ®Google Scholar
• 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.
   Google Scholar
• Witzel, B. S., & Riccomini, P. J. (2009). Computation of fractions: Math intervention for elementary and middle grades students. Upper Saddle River, NJ: Merrill/Pearson.
   Google Scholar
• 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.
   Web of Science ®Google Scholar