Solving word problems is a common area of struggle for students with learning disabilities (LD). In order for instruction to be effective, we first need to have a clear understanding of the specific errors exhibited by students with LD during problem solving. Error analysis has proven to be an effective tool in other areas of math but has had little application to errors in word problems. Using an error analysis approach, this study aimed to investigate in depth the various types and frequency of errors made by students with LD and their AA peers during math problem solving. The resulting similarities and differences between the two groups of students are discussed with insight into underlying cognitive processes, and implications for future research.
Get full access to this article
View all access options for this article.
References
1.
AshlockR. B. (1990). Error patterns in computation: A semi–programmed approach (5th ed.). Columbus, OH: Charles E. Merrill.
2.
BryantD. P., BryantB. R., & HammillD. D. (2000). Characteristic behaviors of students with LD who have teacher–identifed math weaknesses. Journal of Learning Disabilities, 33, 168–177, 199.
3.
ButlerF. M., MillerS. P., CrehanK., BabbittB., & PierceT. (2003). Fraction instruction for students with mathematics disabilities: Comparing two teaching sequences. Learning Disabilities Research & Practice, 18, 99–111. doi: 10.1111/1540–5826.00066.
CalhoonM. B., EmersonR. W., FloresM., & HouchinsD. E. (2007). Computational fluency performance profile of high school students with mathematics disabilities. Remedial and Special Education, 28, 292–303. doi: 10.1177/07419325070280050401.
6.
CarpenterT. P., AnsellE., FrankeM. L., FennemaE., & WeisbeckL. (1993). Models of problem solving: A study of kindergarten children's problem–solving processes. Journal for Research in Mathematics Education, 24, 428–441.
7.
CawleyJ. F., & MillerJ. H. (1986). Selected views on metacognition, arithmetic problem solving, and learning disabilities. Learning Disabilities Focus, 2(1), 36–48.
8.
CirinoP. T., & BerchD. B. (2010). Introduction: Perspectives on math difficulty and disability in children. Learning and Individual Differences, 20(2), 61–62.
9.
CohenJ. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Hillsdale, NJ: Lawrence Erlbaum.
FleishchnerJ. E., & ManheimerM. A. (1997). Math interventions for students with learning disabilities myths and realities. School Psychology Review, 26(3), 397–413.
12.
FuchsL. S., FuchsD., & PrenticeK. (2004). Responsiveness to mathematical problem–solving instruction: Comparing students at risk of mathematics disability with and without risk of reading disability. Journal of Learning Disabilities, 37, 293–306.
13.
GearyD. C. (2004). Mathematics and learning disabilities. Journal of Learning Disabilities, 37(1), 4–15.
14.
HudsonP., & MillerS. P. (2006). Designing and implementing mathematics instruction for students with diverse learning needs. New York, NY: Pearson Education, Inc.
15.
LaiK., GriffinP., MakA., WuM., & DulhuntyM. (2001). Modeling strategies in problem solving. In Proceedings of the 2001 Annual Conference of the Australian Association for Reserach in Education. Perth.
16.
LunetaK., & MakonyeP. J. (2010). Learner errors and misconceptions in elementary analysis: A case study of a grade 12 class in South Africa. Acta Didactica Napocensia, 3(3), 35–46.
17.
MayerR. E. (1985). Implications of cognitive psychology for instruction in mathematical problem solving. In SilverE. A. (Ed.), Teaching and learning mathematical problem solving: Multiple research perspectives (pp. 123–138). Hillsdale, NJ: Lawrence Erlbaum Associates.
18.
MontagueM., & ApplegateB. (2000). Middle school students’ perceptions, persistence, and performance in mathematical problem solving. Learning Disability Quarterly, 23, 215–227. doi: 10.2307/1511165.
19.
MontagueM., EnderC., & DietzS. (2011). Effects of cognitive strategy instruction on math problem solving of middle school students with disabilities. Learning Disability Quarterly, 34(4), 262–272.
20.
MontagueM., PenfieldR., EndersC., & HuangJ. (2010). Curriculum–based measurement of math problem solving: A methodology and rationale for establishing equivalence of scores. Journal of School Psychology, 48, 39–52. http://dx.doi.org/10.1016/j.jsp.2009.08.002.
21.
PassolunghiM. C., MarzocchiG. M., & FiorilloF. (2005). Selective effect of inhibition of literal or numerical irrelevant information in children with attention deficit hyperactivity disorder (ADHD) or arithmetic learning disorder (ALD). Developmental Neuropsychology, 28, 731–753.
22.
PowellS. (2011). Solving word problems using schemas: A review of the literature. Learning Disabilities Research & Practic, 26(2), 94–108.
23.
PowellS. R., FuchsL. S., FuchsD., CirinoP. T., & FletcherJ. M. (2008). Do word–problem features differentially affect problem difficulty as a function of students’ mathematics difficulty with and without reading difficulty?Journal of Learning Disabilities, 42(2), 99–110.
24.
RaghubarK., CirinoP., BarnesM., Ewing–CobbsL., FletcherJ., & FuchsL. (2009). Errors in multi–digit arithmetic and behavioral inattention in children with math difficulties. Journal of Learning Disabilities, 42(4), 356–371. doi: 10.1177/0022219409335211.
25.
RiccominiP. J. (2005). Identification and remediation of systematic error patterns in subtraction. Learning Disability Quaterly, 28, 233–242.
26.
RosenzweigC., KrawecJ., & MontagueM. (2011). Metacognitive strategy use of eighth–grade students with and without learning disabilities during mathematical problem solving: A think–aloud analysis. Journal of Learning Disabilities, 44, 508–520. doi: 10.1177/0022219410378455.
27.
RussellR. L., & GinsburgH. P. (1984). Cognitive analysis of children's mathematical difficulties. Cognition and Instruction, 1, 217–244.
28.
SengL. K. (2010). An error analysis of Form 2 (grade 7) students in simplifying algebraic expressions: A descriptive study. Electronic Journal of Research in Educational Psychology, 8(1), 139–162.
29.
SmithJ. P., diSessaA. A., & RoschelleJ. (1993). Misconceptions reconceived: A constructivist analysis of knowledge in transition. The Journal of the Learning Sciences, 3(2). 115–163.
VukovicR. K., & SiegelL. S. (2010). Academic and cognitive characteristics of persistent mathematics difficulty from first through fourth grade. Learning Disabilities Research & Practice, 25, 25–38. doi: 10.1111/j.1540–5826.2009.00298.x
32.
WoodwardJ., & MontagueM. (2002). Meeting the challenges of mathematics reform for students with LD. The Journal of Special Education, 36, 89–101. doi: 10.1177/00224669020360020401.
