# Effect of “Understand and Solve!” Strategy Instruction on Mathematical Problem Solving of Students with Mild Intellectual Disabilities

## Main Article Content

## Abstract

The purpose of this study was to examine the effects of “Understand and Solve!” Strategy on change problems including change of a one-step addition and subtraction of children with mild intellectual disabilities and whether they maintained their achievements 3, 5, and 8 weeks after the intervention. Moreover, the effects of the Understand and Solve! Strategy on generalization to different types of problems and multiple step problems as well as on the perception, attitudes, knowledge, use, and control of problem solving strategy were investigated. Three students with intellectual disabilities who were 11 to 12 years old and attended 5th grade participated in the study. “A Multiple Probe Design Across Subjects,” which is one of the single subject research designs, was used in the study. The findings of this study showed that Understand and Solve! Strategy was effective in teaching students with mild intellectual disabilities solving change problems including one-step addition and subtraction, they maintained their skills and generalized their skills to different problem types, two-step change problems. As a result of the intervention, students’ perception and attitudes towards mathematics as well as knowledge, use and control of strategies to solve mathematical problems positively changed.

### Downloads

## Article Details

**International Electronic Journal of Elementary Education**, [S.l.], v. 11, n. 2, p. 77-90, nov. 2018. ISSN 1307-9298. Available at: <https://iejee.com/index.php/IEJEE/article/view/644>. Date accessed: 23 aug. 2019.

## References

Case, L. P., Harris, K. R. & Graham, s.(1992). Improving the mathematical problem-solving skills of students with learning disabilities: Self-regulated strategy development. The Journal of Special Education, 26, 1–19.

Cassel, J. & Reid, R. (1996). Use of a self-regulated strategy intervention to improve word problem solving skills of students with mild disabilities. Journal of Behavioral Education,6,153–172.

Chung K. H. & Tam, Y. H. (2005) Effects of cognitive-based instruction on mathematical problem solving by learners with mild intellectual disabilities. Journal of intellectual and developmental Disability, 30(4) 207-216.

Cote, D., Pierce T., Higgins K., Miller S., Tandy R.& Sparks S. (2010). Increasing skill performances of problem solving in students with intellectual disabilities. Education and Training in Autism and Developmental Disabilities, 45(4), 512-524

Daniel, G. E. (2003). Effects of cognitive strategy instruction on the mathematical problem solving of middle school students with learning disabilities. Php Thesis, Ohio State University, Columbus.

Das, J. P., Naglieri, J. A. & Kirby, J. R. (1994). Assessment of cognitive processes: The PASS theory of intelligence. Boston: Allyn & Bacon.

Doğanay-Bilgi A., (2009). Zihinsel yetersizliği olan öğrencilerin bilgi veren metinleri anlamalarında uyarlanmış çok ögeli bilişsel strateji öğretiminin etkililiği [he effectiveness of modified multi-component cognitive strategy instruction in comprehension of expository texts students with mental retardation], Gazi Unviersity, Institute of Educational Sciences, Ankara, Turkey.

Efklides, A. (2001). Metacognitive experiences in problem solving: Metacognition, motivation and self-regulation. In A. Efklides, J. Kuhl, & R. M. Sorrentino (Eds.), Trends and prospects in motivation research (pp. 297–323). Dordrecht, The Netherlands: Kluwer

Efklides, A. (2006). Metacognition and affect: What can metacognitive experiences tell us about the learning process?. Educational Research Review, 1, 3–14.

Efklides, A. & Petkaki, C. (2005). Effects of mood on students’ metacognitive experiences. Learning and Instruction, 15,415–431.

Efklides, A.,(2009). The role of metacognitive experiences in the learning process. Psicothema. Vol. 21(1) 76-82

Efklides, A.,(2011). Interactions of Metacognition with motivation and affect in self-regulated learning: The masrl model. Educational Psychologist,46(1), 6–25

Englert, C. S., Raphael, T. E. & Anderson, L. M. (1992). Socially mediated instruction: Improving students’ knowledge and talk about writing. The Elementary School Journal, 92, 411-449.

Geary, D. C. (1994). Children’s mathematical development. Research and practical applications. Washington, DC: American Psychological Association.

Geary, D. C., Brown, s.C. & Samaranayake, V. A. (1991). Cognitive addition: A short longitudinal study of strategy choice and speed of processing differences in normal and mathematically disabled children. Developmental Psychology, 27, 787-797.

Goldman, S.R. (1989). Strategy instruction in mathematics. Learning Disabilities Quarterly, 12, ss.43-55.

Graham, s.& Harris, K. R. (2003). Students with learning disabilities and the process of writing: A mecaanalysis of SRSD studies. In L. H. Swanson. K. Harris, & S. Graham (Eds.), Handbook of learning disabilities (pp. 323-344). New York: Guilford.

Güler-Bülbül, Ö. (2016). Zihinsel yetersizlikten etkilenmiş öğrencilerin ve yazmada düşük performans gösteren akranlarının öykü yazma becerilerinde 'seç + düzenle + yaz ve oku - düzelt + paylaş - düzelt' stratejisinin etkililiği [Effectiveness of 'pick + organize + write and read - edit + share - edit' strategy on story writing of children with intellectual disability and their peers underperforming in writing]. Doctoral Dissertation, Gazi Institute of Education, Ankara, Turkey.

Güzel-Özmen, R. (2006). The effectiveness of modified cognitive strategy instruction in writing on mildly mentally retarded Turkish students. Exceptional Children, 72(3), 281-297.

Güzel-Özmen, R. (2011). Evaluating the effectiveness of combined reading interventions on improving oral reading fluency of students with reading difficulties. Electronic Journal of Research in Educational Psychology, 93, 1063-1086.

Harris, K. R. & Graham, s.(1996). Making the writing process work: Strategies for composition and self-regulation. Cambridge, MA: Brookline.

Horner, R. H., Carr, E. G„ Halle, J., McGee, G., Odom, s.& Wolery, M. (2005). The use of single-subject research to identify evidence-based practice in special education. Exceptional Children, 71, 165-179.

House, A. W., House, B. G.& Campbell, M. B. (1981). Measures of interobserver agreement: Calculation formula and distribution effect. Journal of Behavioral Assessment, 3, 37-57.

Huffman, L. F., Fletcher, K. L., Grupe, L. A. & Bray, N. W. (2004). Similarities and differences in early addition strategies in children with and without mental retardation. Education and Training in Developmental Disabilities, 39, 317-325.

Iseman J. S.& Naglieri J. A. (2011) A cognitive strategy instruction to improve math calculation for children with ADHD and LD: A randomized controlled study. Journal of Learning Disabilities 44(2), 184–195

Jitendra A., George M.P., Sood S. & Price K. (2010). Schema-based instruction: Facilitating mathematical word problem solving for students with emotional and behavioral disorders. Preventing School Failure, 54(3), 145-151.

Jitendra, A. K. (2002). Teaching students math problem-solving through graphic representations. Teaching Exceptional Children, 34(4), 34-38.

Jitendra, A. K. & Hoff, K. (1996). The effects of schema-based instructionon the mathematical word problem solving performance of students with learning disabilities. Journal of Learning Disabilities, 29, 422– 431.

Jitendra, A. K., Star, J.R., Rodriguez, M., Lindell, M. & Someki, F. (2011). Improving students' proportional thinking using schema-based instruction. Learning and Instruction, 21, 731-745.

Karabulut, A., Yıkmış, A., Özak, H. ve Karabulut, H. (2015). Şemaya dayalı problem çözme stratejisinin zihinsel yetersizliği olan öğrencilerin problem çözme performanslarına etkisi [The effect of schema based problem solving strategy on problem solving performance of students with intellectual disabilities]. Abant İzzet Baysal Üniversitesi Eğitim Fakültesi Dergisi, 15, 243-258.

Keogh, D. A., Whitman, T. L. & Maxwell, s.E. (1988). Self-instruction versus external instruction: Individual differences and training effectiveness. Cognitive Therapy and Research, 12,591– 610.

Krawec, J,. Huang, J. Montague M., Kressler B.& Alba A. M., (2012) The effects of cognitive strategy instruction on knowledge of math problem-solving processes of middle school students with learning disabilities. Learning Disability Quarterly 36(2) 80 –92

Krawec, J,.(2014). Problem representation and mathematical problem Solving of students of varying math ability. Journal of Learning Disability 47(2) 103–115.

Lundberg, I. & Reichenberg, M. (2013). Developing reading comprehension among students with mild intellectual disabilities: An intervention study. Scandinavian Journal of Educational Research, 57(1), 89-100.

Maccini, P. & Gagnon, J. (2001). Preparing students with disabilities for algebra. Teaching Exceptional Children, 34(1) , 8-15.

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, 15,10–21.

Mancl, Dustin B. (2011). Investigating the effects of a combined problem-solving strategy for students with learning difficulties in mathematics. Php Thesis, University of Nevada, Las Vegas.

Marshall, s.P. (1995). Schemas in problem solving. New York: Cambridge University Press.

Mesler, J. (2004). The effects of cognitive strategy instruction on the mathematical problem solving of students with spina bifida. Php Thesis, University of Miami, Coral Gables, Florida.

Milford, T.& Harrison, G. L. (2010). Using the PLEASE Strategy with a Struggling Middle School Writer with a Disability, Intervention in School and Clinic, 45, (5), 326-332.

Montague M., Enders C. & Dietz, S. (2011) Effects of cognitive strategy instruction on math problem solving of middle school students with learning disabilities. Learning Disability Quarterly 34(4) 262 –272.

Montague, M. (1992). The effects of cognitive and metacognitive strategy instruction on mathematical problem solving of middle school students with learning disabilities. Journal of Learning Disabilities, 25, 230-248.

Montague, M. (1997). Cognitive strategy instruction in mathematics for students with learning disabilities. Journal of Learning Disabilities, 30, 164-177.

Montague, M. (2000). Solve It! Strategy instruction to improve mathematical problem solving. learning disabilities. Research and Practice, 15(2), 110-116.

Montague, M. (2007). Self-regulation and mathematics instruction. Learning Disabilities Research and Practice 22, 75–83.

Montague, M. (2008). Self-regulation strategies to improve mathematical problem solving for students with learning disabilities. Learning Disability Quarterly, 31, 37–44.

Montague, M. & Applegate, B. (1993). Mathematical problem solving characteristics of middle school students with learning disabilities. Journal of Special Education, 27, 175–201.

Montague, M. & Applegate, B. (2000). Middle school students perceptions, persistence, and performance in mathematical problem solving. Learning Disability Quarterly, 23, 215-227.

Montague, M. & Bos, C. (1986). The effect of cognitive strategy training on verbal math problem solving performance of learning disabled adolescents. Journal of Learning Disabilities, 19, 26-33.

Montague, M. & Dietz, s.(2009). Evaluating the evidence base for cognitive strategy instruction and mathematical problem solving. Exceptional Children, 75(3), 285-302.

Naglieri, J. A. & Gottling, s.H. (1995). A study of planning and mathematics instruction for students with learning disabilities. Psychological Reports,76, 1343–1354.

Naglieri, J. A. & Johnson, D. (2000). Effectiveness of a cognitive strategy intervention in improving arithmetic computation based on the PASS theory. Journal of Learning Disabilities, 33, 591–597.

National Council of Teachers of Mathematics. (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: Author.

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

Reid, R. & Lienemann, T.O. (2006).Self-regulated strategy development for students with learning disabilities, Teacher Education and Special Education,29(1), 3-11.

Rivera, D. P. (1997). Mathematics education and students with learning disabilities: introduction to the special series. Journal of Learning Disabilities, 30, 2–19.

Rosenzweig C., Krawec, J.& Montague, M. (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(6), 508-520

Schraw, G. (1998). Promoting General Metacognitive Awareness. Instructional Science, 26, 113-125.

Swanson H. L., Lussier C. & Orosco M. (2013) Effects of Cognitive Strategy Interventions and Cognitive Moderators on Word Problem Solving in Children at Risk for Problem Solving Difficulties Learning Disabilities. Research & Practice, 28(4), 170–183

Swanson, H. L. Orosco M. J.and Lussier C. M. (2014). The effects of mathematics strategy instruction for children with serious problem-solving difficulties. Exceptional Children 80 (2) 149-168.

Sweeney, C. M. (2010). The Metacoqnitive Functioning of Middle school students with and without learning disabilities during mathematical problem solving. Php Thesis University of Miami, Coral Gables, Florida.

Van Luit, J. E. H. & Van der Aalsvoort, G. M. (1985). Learning subtraction in a special school: A self-instructional training strategy for educable mentally retarded children with arithmetic deficits. Instructional Science, 14,179–189

Whitby P. J. S. (2009) The effects of a modified learning strategy on the multiple step mathematical word problem solving ability of middle school students with high-functioning autism or asperger’s syndrome Php Thesis. University of Central Florida Orlando, Florida.