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Abstract

This study investigated the effects of the concrete—representational—abstract (CRA) instructional sequence on the subtraction performance of students identified as at-risk for mathematics failure. Although the CRA sequence has been demonstrated as effective for teaching a variety of mathematical skills and processes its effects when used to teach subtraction with regrouping have not been studied. This study examined the effects of CRA instruction on elementary students’ fluency in computing subtraction problems with regrouping in the tens place as well as regrouping in both the tens and hundreds places. The study also investigated the effects of CRA instruction on students’ maintenance of regrouping skills. A multiple probe across students with embedded changing behaviors design was employed. A functional relation between CRA instruction and subtraction with regrouping was demonstrated across all students. The results and their implications are discussed further.

Keywords

instruction mathematics general education classroom strategy instruction elementary school(s)single-subject research methodology mathematics

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References

Beck, R. , Conrad, D. , & Anderson, P. ( 1999). Basic Skill Builders. Longmont, CO : Sopris West Educational Services.

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 and Practice, 18(2), 99-111.

Deshler, D.D. , Schumaker, J. , Harris, K. , & Graham, S. ( 1999). Teaching every adolescent every day: Learning in diverse high school classrooms. Cambridge, MA: Brookline Books.

Fuchs, L.S. , & Fuchs, D. ( 2005). Using curriculum-based measurement for progress monitoring in math. Washington, DC: U.S. Office of Special Education Programs.

Fuchs, L.S. , Fuchs, D. , & Hollenbeck, K.N. (2007). Extending responsiveness to intervention to mathematics at first and third grades. Learning Disabilities Research and Practice, 22(1), 13-24.

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 and Practice, 10, 180-196.

Individuals With Disabilities Education Improvement Acts of 2004, Pub. L. No. 108-446, 118 Stat. 2647 (2004) (amending 20 U.S.C. §§ 1440 et seq.).

Kazdin, A.E. ( 1982). Single-case research designs: Methods for clinical and applied settings. New York: Oxford University Press.

Maccini, P. , & Ruhl, K.L. ( 2000). Effects of graduated instructional sequence on the algebraic subtraction of integers by secondary students with learning disabilities. Education and Treatment of Children, 23, 465-489.

10.

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.

11.

Miller, S.P. , & Mercer, C.D. ( 1992). Strategic math series: Place value. Lawrence, KS: Edge Enterprises.

12.

Miller, S.P. , & Mercer, C.D. ( 1993). Using data to learn about concrete-semiconcrete-abstract instruction for students with math disabilities. Journal of Learning Disabilities Research and Practice, 8, 89-96.

13.

Morin, V.A. , & Miller, S.P. ( 1998). Teaching multiplication to middle school students with mental retardation. Education and Treatment of Children, 21, 22-36.

14.

National Council of Teachers of Mathematics. ( 2000). Principles and standards for school mathematics. Reston, VA: Author.

15.

National Research Council. (2002). Helping children learn mathematics. Washington, DC: National Academy Press.

16.

Peterson, S.K. , Mercer, C.D. , & O’ Shea, L. (1988). Teaching learning disabled students place value using the concrete to abstract sequence. Learning Disabilities Research, 4, 52-56.

17.

Poling, A. , Methot, L.L. , & LeSage, M.G. (1995). Fundamentals of behavior analytic research. New York: Plenum .

18.

Schmidt, J.L. , Deshler, D.D. , Schumaker, J.B. , & Alley, G.R. ( 1989). Effects of generalization instruction on the written language performance of adolescents with learning disabilities in the mainstream classroom. Journal of Reading and Writing and Learning Disabilities , 4, 291-309.

19.

Tawney, J.W. , & Gast, D.L. ( 1984). Single subject research in special education. Columbus, OH: Merrill.

20.

VanDerHeyden, A.M. , & Witt, J.C. ( 2005). Quantifying the context of assessment: Capturing the effect of base rates of teacher referral and a problem solving model of identification . School Psychology Review, 34, 161-183.

21.

Witzel, B. ( 2005). Using CRA to teach algebra to students with mathematics difficulties in inclusive settings. Learning Disabilities: A Contemporary Journal, 3(2), 49-60.

22.

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.

Using the Concrete-Representational-Abstract Sequence to Teach Subtraction With Regrouping to Students at Risk for Failure

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