Restricted accessResearch articleFirst published online 2013-5
The Effects of the Concrete–Representational–Abstract Integration Strategy on the Ability of Students With Learning Disabilities to Multiply Linear Expressions Within Area Problems
We examined the effects of the Concrete–Representational–Abstract Integration strategy on the ability of secondary students with learning disabilities to multiply linear algebraic expressions embedded within contextualized area problems. A multiple-probe design across three participants was used. Results indicated that the integration of the concrete manipulatives, sketches of manipulatives, and abstract notation with the support of a graphic organizer (i.e., expansion box) was an effective strategy to improve students’ conceptual understanding and procedural fluency of multiplying two linear expressions. Furthermore, participants generalized the algebraic material to novel problem tasks and maintained performance up to 6 weeks following intervention.
Brown-ChidseyR.SteegeM. W. (2005). Response to intervention: Principles and strategies for effective practice. New York, NY: Guilford.
2.
Common Core State Standards Initiative. (2010). Preparing American students for college and career. Retrieved from http://www.corestandards.org/
3.
FuchsD.FuchsL. S.SteckerP. M. (2010). The “blurring” of special education in a new continuum of general education placements and services. Exceptional Children, 76, 301–324.
4.
GerstenR.BeckmannS.ClarkeB.FoegenA.MarshL.StarJ. R.WitzelB. (2009). Assisting students struggling with mathematics: Response to Intervention (RtI) for elementary and middle schools (NCEE 2009-4060). Washington, DC: National Center for Education Evaluation and Regional Assistance, Institute of Education Sciences, U.S. Department of Education. Retrieved from http://ies.ed.gov/ncee/wwc/publications/practiceguides/
5.
GagnonJ. C.MacciniP. (2001). Preparing students with disabilities for algebra. Teaching Exceptional Children, 34, 8–15.
6.
GearyD. C. (2004). Mathematics and learning disabilities. Journal of Learning Disabilities, 37, 4–15.
7.
HuckS. W. (2008). Reading statistics and research. Boston, MA: Pearson Education.
8.
HudsonP.MillerS. P. (2006). Designing and implementing mathematics instruction for students with diverse learning needs. Boston, MA: Pearson Education.
9.
IvesB. (2007). Graphic organizers applied to secondary algebra instruction for students with learning disabilities. Learning Disabilities Research & Practice, 22, 110–118.
10.
KennedyC. H. (2005). Single-case designs for educational research. Boston, MA: Pearson Education.
11.
MacciniP.HughesC. A. (2000). Effects of a problem-solving strategy on the introductory algebra performance of secondary students with learning disabilities. Learning Disabilities Research & Practice, 15, 10–21.
12.
MacciniP.RuhlK. 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, 465–489.
13.
National Center for Education Statistics. (2009). The nation’s report card: Mathematics, 2009 (NCES 2010-451). Washington, DC: Institute of Education Sciences, U.S. Department of Education.
14.
National Center for Education Statistics. (2010). The Nation’s report card: Grade 12 reading and mathematics 2009 national and pilot state results (NCES 2011-455). Washington, DC: Institute of Education Sciences, U.S. Department of Education.
15.
National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: Author.
16.
National Mathematics Advisory Panel. (2008). Foundations for success: The final report of the national advisory panel. Washington, DC: U.S. Department of Education.
17.
PashlerH.BainP. M.BottgeB.GraesserA.KoedingerK.McDanielM.MetcalfeJ. (2007). Organizing instruction and study to improve student learning. Washington, DC: U.S. Department of Education.
18.
PicciottoH. (1990). The algebra lab. Sunnyvale, CA: Creative.
19.
ScruggsT. E.MastropieriM. A. (1998). Summarizing single-subject research: Issues and applications. Behavior Modification, 22, 221–242.
20.
ScruggsT. E.MastropieriM. A. (2001). How to summarize single-participant research: Ideas and applications. Exceptionality, 9, 227–244.
21.
StricklandT. K.MacciniP. (2010). Strategies for teaching algebra to students with learning disabilities: Making research to practice connections. Intervention for School and Clinic, 46, 38–45.
22.
TawnyJ. W.GastD. L. (1984). Single subject research in special education. Columbus: Charles E. Merrill.
23.
WitzelB. S.MercerC. D.MillerM. D. (2003). Teaching algebra to students with learning difficulties: An investigation of an explicit instruction model. Learning Disabilities Research & Practice, 18, 121–131.
