Özel Öğrenme Güçlüğü Olan Öğrencilerin Problem Çözme Performanslarını Geliştirmede Diyagram Kullanımının Etkililiği

Year 2024, Volume: 25 Issue: 3, 1265 - 1291, 31.12.2024

Sıla Doğmaz Tunalı , Burak Karabey

https://doi.org/10.17679/inuefd.1435610

Abstract

Sözel matematik problemlerinin çözümü, ilgili ve ilgisiz bilgilerin belirlenmesini, problemin zihinsel bir temsilinin oluşturulmasını, uygun bir çözüm stratejisinin seçimini ve uygulanmasını içeren bilişsel bir süreçtir. Özel öğrenme güçlüğü olan öğrenciler matematik becerilerini edinmede eksiklikler yaşayabilirler, ayrıca sözel matematik problemleriyle başa çıkmak bu öğrenciler için özellikle zorlayıcıdır. Bu çalışmada, özel öğrenme güçlüğü olan öğrencilerin iki aşamalı matematiksel rutin problem çözme performanslarını geliştirmede diyagram stratejisi kullanımın etkililiği araştırılmıştır. Araştırma yarı deneysel desenlerden ön-test son-test kontrol gruplu desen üzerinden planlanmıştır. Çalışmada veri toplama aracı olarak, 15 açık uçlu sayı probleminden oluşan bir başarı testi kullanılmıştır. Genelleme için farklı türde problemleri içeren 5 açık uçlu sorudan oluşan ikinci bir başarı testi kullanılmıştır. Ayrıca, bu testlerdeki problem çözme süreçlerini değerlendirmek için analitik dereceli bir puanlama anahtarı hazırlanmıştır. Çalışma grubu 10 tanesi deney grubu ve 10 tanesi kontrol grubu olmak üzere toplam 20 özel öğrenme güçlüğü tanısı olan öğrenciden oluşmaktadır. Deney grubunda yer alan 10 öğrenciyle 8 hafta boyunca bireysel oturumlar ile problem çözümünde diyagram kullanımı programı yürütülmüştür. Deney ve kontrol gruplarında yer alan öğrencilerin başarı testinden elde edilen ön test ve son test verilerinin analizinde parametrik olmayan Mann Whitney-U ve Wilcoxon işaretli sıralar testi testleri kullanılmıştır. Verilerin analizi neticesinde deney ve kontrol gruplarında yer alan öğrencilerin başarı testinden aldıkları puanlar arasında anlamlı bir farklılık bulunmuştur. Bu anlamlı farklılığın deney grubu lehine olduğu görülmüştür. Bulgular, diyagram stratejisi kullanımın iki aşamalı sözel matematik problemlerinin çözümünde etkili olduğunu göstermektedir. Sonuç olarak, diyagram stratejisi matematik problemlerini anlamada ve çözmede etkili bir araç olarak değerlendirilebilir.

Keywords

Problem çözme, Diyagram, Öğrenme güçlüğü

The Effectiveness of Using Diagrams in Improving the Problem-Solving Performance of Students with Learning Disabilities

Abstract

The solution of verbal mathematical problems is a cognitive process that includes identifying and distinguishing relevant from irrelevant information, constructing a mental representation of the problem, and selecting and implementing an appropriate solution strategy. Students with learning disabilities may have deficiencies in acquiring mathematical skills, and coping with verbal mathematics problems can be particularly challenging for them. This study investigated the effectiveness of the diagram strategy in improving the two-step word problem-solving performance of students with learning disabilities. The research was designed using a quasi-experimental pretest-posttest control group design. The study utilized two types of achievement tests as data collection instruments: one comprised 15 open-ended numerical problems, while the other contained 5 open-ended problems of varied types. Additionally, an analytical grading rubric was prepared to assess the solution processes of the problems in these tests. The study group consisted of 20 students with learning disabilities, divided evenly into an experimental group of 10 students and a control group of 10 students. The process of using diagrams in problem-solving was carried out in individual sessions with the 10 students in the experimental group for 8 weeks. Non-parametric tests, namely the Mann-Whitney U test and the Wilcoxon test, were used to analyze the pre-test and post-test data obtained from the achievement tests of the experimental and control groups. As a result of the data analysis, a significant difference was found between the scores of the students in the experimental and control groups on the achievement test, with the experimental group showing better results. These findings indicate that the use of diagrams has a positive effect on solving two-step word problems. The diagram strategy can be an effective tool for understanding and solving mathematical problems.

Keywords

Problem solving, Diagram, Learning disability

References

• Altay, M. K., Yalvaç, B., & Yeltekin, E. (2017). 8th grade student's skill of connecting mathematics to real life. Journal of Education and Training Studies, 5(10), 158-166. https://doi.org/10.11114/jets.v5i10.2614
• Butterworth, B. (2018). Dyscalculia: From science to education. Routledge.
• Cortiella, C., & Horowitz, S. H. (2014). The state of learning disabilities: Facts, trends, and emerging issues (3rd ed). New York: National center for learning disabilities.Retrieved from http://www.ncld.org/wpcontent/uploads/2014/11/2014-State-of-LD.pdf.
• Daroczy, G., Wolska, M., Meurers, W. D., & Nuerk, H. C. (2015). Word problems: A review of linguistic and numerical factors contributing to their difficulty. Frontiers in Psychology, 6, 348, 1-13. https://doi.org/10.3389/fpsyg.2015.00348
• Diezmann, C. (2002). Enhancing Students' Problem-solving through Diagram Use. Australian Primary Mathematics Classroom, 7(3), 4-8. https://search.informit.org/doi/10.3316/informit.403099421222930
• Diezmann, C. M., & English, L. D. (2001). Promoting the use of diagrams as tools for thinking. In A. A. Cuoco & F. R.
• Curcio (Eds.), The roles of representation in school mathematics: 2001 yearbook (pp. 77– 89). Reston, VA: National Council of Teachers of Mathematics. Available at SSRN: https://www.researchgate.net/publication/27464063_Promoting_the_use_of_diagrams_as_tools_for_thinking
• Freeman‐Green, S. M., O'Brien, C., Wood, C. L., & Hitt, S. B. (2015). Effects of the SOLVE strategy on the mathematical problem solving skills of secondary students with learning disabilities. Learning Disabilities Research & Practice, 30(2), 76-90. https://doi.org/10.1111/ldrp.12054
• Gallagher Landi, M. A. (2001). Helping students with learning disabilities make sense of word problems. Intervention in School and Clinic, 37(1), 13-18. https://doi.org/10.1177/105345120103700103 Geary, D. C. (1996). Children’s mathematical development: Research and practical applications. Washington, DC: American Psychological Association.
• Geary, D. C. (2004). Mathematics and learning disabilities. Journal of Learning Disabilities, 37(1), 4-15. https://doi.org/10.1177/002221940403700102
• Geary, D. C., Hoard, M. K., Nugent, L., & Bailey, D. H. (2012). Mathematical cognition deficits in children with learning disabilities and persistent low achievement: A five-year prospective study. Journal of Educational Psychology, 104(1), 206-223. https://doi.org/10.1037/a0025398
• Gersten, R., Chard, D. J., Jayanthi, M., Baker, S. K., Morphy, P., & Flojo, J. (2009). Mathematics instruction for students with learning disabilities: A meta-analysis of instructional components. Review of Educational Research, 79(3), 1202- 1242. https://doi.org/10.3102/00346543093344
• Gobadze, T., & Düzkantar, A. (2019). Özel eğitimde matematik ile ilgili yapılan çalışmaların incelenmesi. Journal of Gifted Education and Creativity, 6(2), 147-165. https://dergipark.org.tr/en/download/article-file/801706
• Graham, S., & Harris, K. R. (2003). Students with learning disabilities and the process of writing: A meta-analysis of SRSD studies. In H. L. Swanson, K. R. Harris, & S. Graham (Eds.), Handbook of Learning Disabilities (pp. 323–344). The Guilford Press. Available at SSRN: https://psycnet.apa.org/record/2003-02238-019
• Grimshaw, J., Campbell, M., Eccles, M., & Steen, N. (2000). Experimental and quasi-experimental designs for evaluating guideline implementation strategies. Family Practice, 17(suppl_1), S11-S16. https://doi.org/10.1093/fampra/17.suppl_1.S11
• Hegarty, M., & Kozhevnikov, M. (1999). Types of visual–spatial representations and mathematical problem solving. Journal of Educational Psychology, 91, 684–689. https://doi.org/10.1037/0022-0663.91.4.684
• Hutchinson, N. L. (1993). Effects of cognitive strategy instruction on algebra problem solving with adolescents. Learning Disability Quarterly, 16, 34–63. https://doi.org/10.2307/1511158
• Im, S. H., & Jitendra, A. K. (2020). Analysis of proportional reasoning and misconceptions among students with mathematical learning disabilities. The Journal of Mathematical Behavior, 57, 100753. https://doi.org/10.1016/j.jmathb.2019.100753
• 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. https://doi.org/10.1177/0022219410391190
• Jitendra, A. K., & Hoff, K. (1996). The effects of schema-based instruction on the mathematical word-problem–solving performance of students with learning disabilities. Journal of Learning Disabilities, 29, 422–431. https://doi.org/10.1177/002221949602900410
• Jitendra, A. K., & Star, J. R. (2011). Meeting the needs of students with learning disabilities in inclusive mathematics classrooms: The role of schema-based instruction on mathematical problem-solving. Theory into Practice, 50(1), 12-19. https://doi.org/10.1080/00405841.2011.534912
• Jitendra, A. K., Griffin, C. C., McGoey, K., Gardill, M. C., Bhat, P., & Riley, T. (1998). Effects of mathematical word problem solving by students at risk or with mild disabilities. The Journal of Educational Research, 91, 345–355. https://doi.org/10.1080/00220679809597564
• Jitendra, A. K., Hoff, K., & Beck, M. M. (1999). Teaching middle school students with learning disabilities to solve word problems using a schema-based approach. Remedial and Special Education, 20(1), 50-64. https://doi.org/10.1177/07419325990200010
• Jitendra, A., DiPipi, C. M., & Perron-Jones, N. (2002). An exploratory study of schema-based word-problem—Solving instruction for middle school students with learning disabilities: An emphasis on conceptual and procedural understanding. The Journal of Special Education, 36(1), 23-38. https://doi.org/10.1177/0022466902036001030
• Jonassen, D. H. (2000). Toward a design theory of problem solving. Educational Technology Research and Development, 48(4), 63-85. https://doi.org/10.1007/BF02300500
• Kırmızıgül, H. G. (2021). Zihin yetersizliği olan bireylerin matematik eğitimleri ile ilgili yapılan çalışmaların incelenmesi. E-International Journal of Educational Research, 12(1), 233-251. https://doi.org/10.19160/ijer.875469
• Kozhevnikov, M., Hegarty, M., & Mayer, R. E. (2002). Revising the visualizer– verbalizer dimension: Evidence for two types of visualizers. Cognition and Instruction, 20, 47–77. https://doi.org/10.1207/S1532690XCI2001_3
• Larkin, J. H., & Simon, H. A. (1987). Why a diagram is (sometimes) worth ten thousand words. Cognitive Science, 11(1), 65-100. https://doi.org/10.1016/S0364-0213(87)80026-5
• Lein, A. E., Jitendra, A. K., & Harwell, M. R. (2020). Effectiveness of mathematical word problem solving interventions for students with learning disabilities and/or mathematics difficulties: A meta-analysis. Journal of Educational Psychology, 112(7), 1388–1408. https://doi.org/10.1037/edu0000453
• Mayer, R. E. & Hegarty, M. (1996). The process of understanding mathematical problem solving. In R. J. Sternberg & T. Ben-Zeev (Eds.), The nature of mathematical thinking (pp. 29–54). Hillsdale, NJ, England: Lawrence Erlbaum 138 Associates, Inc. https://doi.org/10.4324/9780203053270
• MEB (2019). PISA 2022 Türkiye raporu. Ankara. MEB yayınları. Available at SSRN: https://pisa.meb.gov.tr/meb_iys_dosyalar/2024_03/21120745_26152640_pisa2022_rapor.pdf
• Milli Eğitim Bakanlığı. (2018). Matematik dersi öğretim programı. Ankara: Devlet Kitapları Basım Evi.
• Montague, M. (1997). Cognitive strategy instruction in mathematics for students with learning disabilities. Journal of Learning Disabilities, 30, 164–177. https://doi.org/10.1177/0022219497030002
• Montague, M. (2003). Solve it! A practical approach to teaching mathematical problem solving skills. Reston, VA: Exceptional Innovations.
• Montague, M. (2006). Self-regulation strategies for better math performance in middle school. In M. Montague & A. K. Jitendra (Eds.), Teaching mathematics to middle school students with learning difficulties (pp. 72–88). New York: Guilford Press
• 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, 262-272. https://doi.org/10.1177/0731948711421762
• National Center for Education Statistics (2013). The Nation’s Report Card: A First Look: 2013 Mathematics and Reading (NCES 2014-451). Institute of Education Sciences, U.S. Department of Education, Washington, D.C.
• National Mathematics Advisory Panel. (2008). Foundation for success: The final report of the National Mathematics Advisory Panel. Washington, DC: U.S. Department of Education. Available at SSRN: https://files.eric.ed.gov/fulltext/ED500486.pdf
• Ngu, B. H., & Phan, H. P. (2022). Developing Problem-Solving Expertise for Word Problems. Frontiers in Psychology, 13, 725280. https://doi.org/10.3389/fpsyg.2022.725280
• Novick, L. R., & Francis, M. (1993, November). Assessing students’ knowledge and use of symbolic representations in problem solving. Paper presented at the 34th annual meeting of the Psychonomic Society, Washington.
• Novick, L. R., & Hmelo, C. E. (1994). Transferring symbolic representations across nonisomorphic problems. Journal of Experimental Psychology: Learning, Memory, and Cognition, 20(6), 1296–1321. https://doi.org/10.1037/0278-7393.20.6.1296
• Novick, L. R., Hurley, S. M., & Francis, M. (1999). Evidence for abstract, schematic knowledge of three spatial diagram representations. Memory & Cognition, 27(2), 288–308. https://doi.org/10.3758/BF03211413
• Nunokawa, K. (2005). Mathematical problem solving and learning mathematics: What we expect students to obtain. The Journal of Mathematical Behavior, 24(3-4), 325-340. https://doi.org/10.1016/j.jmathb.2005.09.002
• Özkubat, U., Karabulut, A., & Akçayır, İ. (2020). Şemalarla matematik problemi çözme: Öğrenme güçlüğü olan öğrencilerle yürütülen şema temelli öğretim araştırmaların incelenmesi. Ondokuz Mayis University Journal of Education Faculty, 39(2), 327-342. DOI: 10.7822/omuefd.774137
• Özkubat, U., Karabulut, A., & Sert, C. (2022). Öğrenme güçlüğü olan ortaokul öğrencilerine uygulanan matematik problemi çözme müdahaleleri: Kapsamlı alanyazın incelenmesi. Ankara Üniversitesi Eğitim Bilimleri Fakültesi Özel Eğitim Dergisi, 23(1), 191-218. https://doi.org/10.21565/ozelegitimdergisi.774650
• Parmar, R. S. (1992). Protocol analysis of strategies used by students with mild disabilities when solving arithmetic word problems. Diagnostique, 17(4), 227–243. https://doi.org/10.1177/153450849201700401
• Poch, A. L., van Garderen, D., & Scheuermann, A. M. (2015). Students’ Understanding of Diagrams for Solving Word Problems: A Framework for Assessing Diagram Proficiency. TEACHING Exceptional Children, 47(3), 153-162. https://doi.org/10.1177/0040059914558947
• Polya, G. (1997). Nasıl çözmeli. Çev: F. Halatçı. İstanbul: Sistem Yayıncılık.
• Polya, G. (2004). How to solve it: A new aspect of mathematical method (Vol. 85). Princeton University Press.
• Powell, S. R. (2011). Solving word problems using schemas: A review of the literature. Learning Disabilities Research & Practice, 26(2), 94-108. https://doi.org/10.1111/j.1540-5826.2011.00329.x
• Price, G. R., & Ansari, D. (2013). Dyscalculia: Characteristics, causes, and treatments. Numeracy, 6(1), 1-16. http://dx.doi.org/10.5038/1936-4660.6.1.2
• Ruswanto, R., Dwijanto, D., & Widowati, W. (2018). A realistic mathematics education model ıncludes characteristic to ımprove the skill of communication mathematic. Unnes Journal of Mathematics Education Research, 7(1), 94-101. Available at SSRN: http://journal.unnes.ac.id/sju/index.php/ujme
• Shalev, R. S. (2004). Developmental dyscalculia. Journal of Child Neurology, 19(10), 765-771. https://doi.org/10.1177/08830738040190100601
• Strickland, T. K., & Maccini, P. (2010). Strategies for teaching algebra to students with learning disabilities: Making research to practice connections. Intervention in School and Clinic, 46(1), 38-45. https://doi.org/10.1177/1053451210369519
• Şimşek, N., & Arslan, K. (2022). Matematik öğrenme güçlüğü ile ilgili çalışmaların betimsel analizi. Batı Anadolu Eğitim Bilimleri Dergisi, 13(1), 433-449. https://doi.org/10.51460/baebd.983453
• Uesaka, Y., & Manalo, E. (2007). Peer instruction as a way of promoting spontaneous use of diagrams when solving math word problems. In Proceedings of the annual meeting of the Cognitive Science Society, 29(29), 677-682. Available at SSRN: https://escholarship.org/content/qt1xf9q095/qt1xf9q095.pdf
• Van de Walle, J. A. (2004). Elementary and middle school mathematics: Teaching developmentally (5th ed.). New York: Longman.
• van Garderen, D. (2007). Teaching students with LD to use diagrams to solve mathematical word problems. Journal of Learning Disabilities, 40(6), 540-553. https://doi.org/10.1177/00222194070400060
• van Garderen, D., & Montague, M. (2003). Visual-spatial representation, mathematical problem solving, and students of varying abilities. Learning Disabilities Research and Practice, 18, 246-254. doi:10.1111/1540-5826.00079. https://doi.org/10.1111/1540-5826.00079
• van Garderen, D., & Scheuermann, A. M. (2015). Diagramming word problems: A strategic approach for instruction. Intervention in School and Clinic, 50(5), 282-290. https://doi.org/10.1177/1053451214560889
• van Garderen, D., Scheuermann, A., & Jackson, C. (2012). Examining how students with diverse abilities use diagrams to solve mathematics word problem. Learning Disability Quarterly, https://doi.org/10.1177/0731948712438558.
• van Garderen, D., Scheuermann, A., & Jackson, C. (2013). Examining how students with diverse abilities use diagrams to solve mathematics word problems. Learning Disability Quarterly, 36(3), 145-160. https://doi.org/10.1177/07319487124385
• Von Aster, M. G., & Shalev, R. S. (2007). Number development and developmental dyscalculia. Developmental Medicine & Child Neurology, 49(11), 868-873. https://doi.org/10.1111/j.1469-8749.2007.00868.x
• Xin, Y. P., Jitendra, A. K., & Deatline-Buchman, A. (2005). Effects of mathematical word Problem—Solving instruction on middle school students with learning problems. The Journal of Special Education, 39(3), 181-192. https://doi.org/10.1177/00224669050390030501
• Yıkmış, A., Kot, M., Terzioğlu, N. K., & Aktaş, B. (2018). Türkiye’de özel eğitim alanında yapılan matematik araştırmalarının betimsel analizi. Abant İzzet Baysal Üniversitesi Eğitim Fakültesi Dergisi, 18(4), 2475-2501. https://doi.org/10.17240/aibuefd.2018.18.41844-445908