# Mathematical Problem-Solving Processes of Students with Special Needs: A Cognitive Strategy Instruction Model 'Solve It!'

## Main Article Content

## Abstract

A Cognitive Strategy Instruction Model namely 'Solve It!' which involves cognitive and metacognitive elements, was developed by Montague (1992) and it is one of the process based teaching strategies. Solve It! is a strategy which aims to teach seven cognitive strategy steps (i.e., read, paraphrase, visualize, hypothesize, predict, calculate, and check) and in each of the cognitive strategy step it contains three metacognitive steps (ask, say, and check). This strategy was used to teach solving word problems to students with special needs. This study aims to evaluate the studies using Solve It!. The reviewed studies are located by conducting searching in the electronic databases, journal indexes and references of studies. A total of 48 studies were found. The researchers reviewed them in terms of inclusion and exclusion criteria and retained 12 of them for descriptive analysis. Analyses showed that Solve It! was found to be effective in teaching mathematical problem solving skills to *students with special needs. *Findings are discussed, suggestions for researchers and practitioners are made.

### Downloads

## Article Details

**International Electronic Journal of Elementary Education**, [S.l.], v. 12, n. 5, p. 405-416, july 2020. ISSN 1307-9298. Available at: <https://iejee.com/index.php/IEJEE/article/view/1083>. Date accessed: 19 sep. 2020.

## References

Bryant, D. P., Bryant, B. R., & Hammill, D. D. (2000). Characteristic behaviors of students with LD who have teacher-identified math weaknesses. Journal of Learning Disabilities, 33, 168-177.

Carpenter, T. P., Ansell, E., Franke, M. L., Fennema, E., & Weisbeck, L. (1993) Models of Problem Solving: A Study of Kindergarten Children's Problem-Solving Processes. Journal for Research in Mathematics Education, 24 (5), 428-441.

Case, L., & Harris, K. R. (1988). Self-Instructional Strategy Training: Improving the Mathematical Problem Solving Skills of Learning Disabled Students. Speeches/Conference Papers.

Cawley, J. & Miller, J. (1986). Selected views on metacognition, arithmetic problem solving, and learning disabilities. Learning Disabilities Focus, 2(1), 36–48.

Cawley, J. F., Parmar, R., Yan, W., & Miller, J. H. (1998). Arithmetic computation performance of students with learning disabilities: Implications for curriculum. Learning Disabilities Research and Practice 13(2):68-74

*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.

*Coughlin, J., & Montague, M. (2010). The effects of cognitive strategy instruction on the mathematical problem solving ability of adolescents with spina bifida. Journal of Special Education, 45, 171–183.

*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.

DeCorte, E., Greer, B., & Verschaffel, L. (1996). Mathematics teaching and learning. In D. Berliner & R. Calfee (Eds.), Handbook of educational psychology. New York: Macmillan.

Fuchs, L. S., Fuchs, D., Prentice, K., Hamlett, C. L., Finelli, R., & Courey, S. J. (2004). Enhancing mathematical problem solving among third-grade students with schema-based instruction. Journal of Educational Psychology, 96(4), 635-647.

Geary, D. C. (2004). Mathematics and learning disabilities. Journal of Learning Disabilities, 37, 4-15.

Güzel-Özmen, R. (2008). Öğrenme güçlüğü olan öğrenciler. İ. H. Diken (Ed.), Özel eğitime gereksinimi olan öğrenciler ve özel eğitim (sf.333-367). Ankara: Pegem Yayınevi.

Happe, F., Booth, R., Charlton, R., & Hughes, C. (2006). Executive function deficits in autism spectrum disorders and attention- deficit/hyperactivity disorder: Examining profiles across domains and ages. Brain and Cognition, 61, 25–39.

Hughes, C. A., Maccini, P., & Gagnon, J. C. (2003). Interventions that positively impact the performance of students with learning disabilities in secondary general education classes. Learning Disabilities: A Multidisciplinary Journal, 12, 101–111.

Hunt, J. H., & Vasquez, E. (2014). Effects of ratio strategies intervention on knowledge of ratio equivalence for students with learning disability. The Journal of Special Education, 48, 180–190.

Ives, B. (2007). Graphic organizers applied to secondary algebra instruction for students with learning disorders. Learning Disabilities Research & Practice, 22, 110–118.

Jitendra, A. K., Star, J. R., Starosta, K., Leh, J. M., Sood, S., Caskie, G., Mack, T. R. (2009). Improving seventh grade students' learning of ratio and proportion: The role of schema-based instruction. Contemporary Educational Psychology, 34(3), 250-264.

Jonassen, D. H. (2003). Using Cognitive Tools to Represent Problems. Journal of Research on Technology in Education 35(3), 142-163.

*Karabulut, A. (2015). Effectiveness Of “Understand And Solve!” Strategy Instruction On Mathematical Problem Solving Of Students With Mild Intellectual Disabilities. Doctoral Dissertation, Gazi University.

*Karabulut, A., & Özmen, E. R. (2018). Effect of “Understand and Solve!” Strategy Instruction on Mathematical Problem Solving of Students with Mild Intellectual Disabilities. International Electronic Journal of Elementary Education, 11(2), 77-90.

Keeler, M. L. & Swanson, H. L. (2001). Does Strategy Knowledge Influence Working Memory in Children with Mathematical Disabilities? Journal of Learning Disabilities, 34(5), 418, 439.

Krawec, J. L. (2010). Problem representation and mathematical problem solving of students with varying abilities, Doctoral Dissertation, University of Miami.

*Krawec, J,. Huang, J. Montague M., Kressler B.& Alba A. M., (2013). 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

Mayer, R. E. (1985). Mathematical ability. In R. J. Sternberg (Ed.), Human abilities: An information processing approach (pp. 127–150). San Francisco, CA: Freeman.

Miller, S., & Mercer, C. (1997). Education aspects of mathematics disabilities. Journal of Learning Disabilities, 30(1), 47-56.

Miller, S., Butler, F., & Lee, K. (1998). Validated practices for teaching mathematics to students with learning disabilities: A review of the literature. Focus on Exceptional Children, 31(1), 1-24.

*Montague, M. (1984). The effect of cognıtıve strategy traınıng on verbal math problem solvıng performance of learnıng dısabled adolescents. Php Thesis, The University of Arizona, Arizona.

Montague, M. (1991). Gifted and learning-disabled gifted students knowledge and use of mathematical problem-solving strategies. Journal for Education of the Gifted, 14, 393–411.

*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. (1998). Cognitive Strategy Instruction in Mathematics for Students with Learning Disabilities. In Rivera, D. P. (Ed.), Mathematics Education for Students with Learning Disabilities (p. 177-200). Pro-ed, Inc.

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

*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. & 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., & Marquard, K. (1993). Cognitive strategy instruction and mathematical problem-solving performance of students with learning disabilities. Learning Disabilities Research and Practice, 8, 223-232.

*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., Krawec, J., Enders, C., & Dietz, S. (2014). The effects of cognitive strategy instruction on math problem solving of middle-school students of varying ability. Journal of Educational Psychology, 106, 469–481.

Montague, M., Warger, C, & Morgan, H. (2000). Solve It!: Strategy instruction to improve mathematical problem solving. Learning Disabilities Research and Practice, 15, 110-116.

Özkubat, U., & Özmen, E. R. (2018). Öğrenme güçlüğü olan öğrencilerin matematik problemi çözme süreçlerinin incelenmesi: Sesli düşünme protokolü uygulaması. Ankara Üniversitesi Eğitim Bilimleri Fakültesi Özel Eğitim Dergisi, 19(1), 155-180.

Parmar, S., & Cawley, J. (1997). Preparing teachers to teach mathematics to students with learning disabilities. Journal of Learning Disabilities, 30(2), 188-197.

Passolunghi, M. C., Marzocchi, G. M., & Fiorillo, F. (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.

Polya, G. (1957). How to solve it. Garden City, N.Y.: Doubleday-Anchor.

Powell, S. (2011). Solving word problems using schemas: A review of the literature. Learning Disabilities Research & Practice, 26(2), 94-108.

Powell, S. R., Fuchs, L. S., Fuchs, D., Cirino, P. T., & Fletcher, J. M. (2008). Do word-problem features differentially affect problem difficulty.

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. (1997). Mathematics education and students with learning disabilities: Introduction to special series. Journal of Learning Disabilities, 30(1), 19-68.

Schurter, W. A. (2002). Comprehension monitoring: An aid to mathematical problem solving. Journal of Developmental Education, 26 (2), 22- 33.

Swanson, H.L. & Jerman, O. (2006) Math Disabilities: A Selective Meta-Analysis of the Literature. Review of Educational Research, 76, 249-274.

Sweeney, C. M. (2010). The metacognitive functioning of middle school students with and without learning disabilities during mathematical problem solving. Doctor of Philosophy Dissertations, University of Miami, Florida.

Van Garderen, D. (2006). Spatial visualization, visual ımagery, and mathematical problem solving of students with varying abilities. Journal Of Learnıng Dısabılıtıes, 39(6), 496–506

Van Garderen, D. (2007). Teaching students with LD to use diagrams to solve mathematical word problems. Journal of Learning Disabilities, 40, 540–553.

*Whitby, P. J. S. (2012). The Effects of Solve It! on the Mathematical Word Problem Solving Ability of Adolescents With Autism Spectrum Disorders. Focus on Autism and Other Developmental Disabilities 28(2) 78-88.

Xin, Y. P., & Jitendra, A. (1999). The effects of instruction in solving mathematical word problems for students with learning problems: A meta-analysis. Journal of Special Education, 32, 207–225.