Öğrenme Güçlüğü Olan Öğrenciler ile Düşük ve Ortalama Başarılı Öğrencilerin Matematik Problemi Çözerken Kullandıkları Bilişsel ve Üstbilişsel Stratejilerinin Belirlenmesi

Yıl 2021, Cilt: 22 Sayı: 3, 639 - 676, 01.09.2021

Ufuk Özkubat Emine Özmen

https://doi.org/10.21565/ozelegitimdergisi.736761

Cited By: 1

Öz

Giriş: Öğrencilerin matematik problemi çözmede kullandıkları bilişsel ve üstbilişsel stratejilerin belirlenmesi problem çözme öğretiminde yapılacak düzenlemeler açısından önemlidir. Bu araştırmanın amacı altıncı sınıfa devam eden öğrenme güçlüğü olan öğrenciler ile düşük ve ortalama başarılı öğrencilerin matematik problemi çözerken kullandıkları bilişsel ve üstbilişsel stratejileri karşılaştırma ve belirtilen stratejiler arasındaki farklılığın incelenmesidir.
Yöntem: Araştırmaya, kaynaştırma ortamında bulunan ve altıncı sınıfa devam eden 50 öğrenme güçlüğü, 50 düşük başarılı ve 50 ortalama başarılı olmak üzere toplam 150 öğrenci katılmıştır. Öğrenme güçlüğü olan öğrenciler ile düşük ve ortalama başarılı öğrencilerin kullandıkları bilişsel ve üstbilişsel stratejileri belirlemek amacıyla Sesli Düşünme Protokolleri kullanılmıştır. Araştırma sonucunda elde edilen veriler, ‘R Programlama Dili’ kullanılarak analiz edilmiştir.
Bulgular: Araştırma sonuçlarına göre öğrenme güçlüğü olan öğrenciler farklı zorluk düzeyinde matematik problemleri çözerken düşük ve ortalama başarılı olan akranlarından daha az bilişsel ve üstbilişsel strateji kullandıkları sonucuna ulaşılmıştır.
Tartışma: Araştırmanın sonuçları ilgili alanyazın ve teorik görüşler çerçevesinde tartışılmış, öğretmenlere uygulamaya ve alanda çalışan araştırmacılara da ileride yapılacak araştırmalara yönelik önerilerde bulunulmuştur.

Anahtar Kelimeler

Öğrenme güçlüğü, matematik problemi çözme, bilişsel stratejiler, üstbilişsel stratejiler, sesli düşünme protokolleri

Identifying the Cognitive and Metacognitive Strategies Used by Students with Learning Disabilities and Low -and Average- Achieving Students During Mathematical Problem Solving

Öz

Introduction: Identifying the cognitive and metacognitive strategies of students during mathematical problem solving is important in terms of the arrangements in the instruction. The aim of this study was to compare the cognitive and metacognitive strategy use of sixth-grade students with learning disabilities, low-achieving students, and average-achieving students and to investigate the difference between these strategies.
Method: The sample consisted of 150 sixth-grade students including 50 students with learning disabilities, 50 low-, and 50 average-achieving students. Think-aloud protocols were applied to identify the strategies. The data were analysed through R programming language.
Findings: The students with learning disabilities used less cognitive and metacognitive strategies than their low- and average-achieving peers when solving math problems with different difficulty levels.
Discussion: The results were discussed within the framework of the relevant literature and theoretical approaches. The suggestions were made for further research and implementation.

Anahtar Kelimeler

Learning disabilities, mathematical problem solving, cognitive strategies, metacognitive strategies, think aloud protocols

Kaynakça

• Ayyıldız, N. Y. (2014). İlkokul öğrencilerinin sayı doğrusunda tahmin becerilerinin çeşitli değişkenler açısından karşılaştırılması [Comparing number line estimations of elementary school students in terms of different variables] (Doktora tezi). Yükseköğretim Kurulu Ulusal Tez Merkezinden edinilmiştir. (Tez Numarası: 366565)
• Billingsley, F., White, O.R., & Munson, R. (1980). Procedural reliability: A rationale and an example. Behavioral Assessment. 2(2), 229-241.
• Booth, J. L., & Siegler, R. S. (2008). Numerical magnitude representations influence arithmetic learning. Child Development, 79(4), 1016-1031. https://doi.org/10.1111/j.1467-8624.2008.01173.x
• 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(2), 168-177. https://doi.org/10.1177/002221940003300205
• Butterworth, B. (2013). Understanding neurocognitive developmental disorders can improve education for all. Science, 340(300), 300-305. https://doi.org/10.1126/science.1231022
• 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. https://doi.org/10.2307/749152
• 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), 1–19. https://doi.org/10.1177/002246699202600101
• 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(2), 153–172. https://doi.org/10.1007/BF02110230
• Cawley, J., & Miller, J. (1986). Selected views on metacognition, arithmetic problem solving, and learning disabilities. Learning Disabilities Focus, 2(1), 36-48.
• Crowley, K., Shrager, J., & Siegler, R. S. (1997). Strategy discovery as a competitive negotiation between metacognitive and associative mechanisms. Developmental Review, 17(4), 462-489. https://doi.org/10.1006/drev.1997.0442
• Çelik, D., & Güler, M. (2013). İlköğretim 6. Sınıf öğrencilerinin gerçek yaşam problemlerini çözme becerilerinin incelenmesi [Examination of realistic problem solving skills of sixth grade students]. Dicle Üniversitesi Ziya Gökalp Eğitim Fakültesi Dergisi, 12(20), 180-195.
• Çetinkaya, G. (2010). Türkçe metinlerin okunabilirlik düzeylerinin tanımlanması ve sınıflandırılması [Identifying and classifying the readability levels of the turkish texts] (Doktora tezi). Yükseköğretim Kurulu Ulusal Tez Merkezinden edinilmiştir. (Tez Numarası: 265580)
• Çilingir, D., & Türnüklü, E. B. (2009). Estimation ability and strategies of the 6th-8th grades elementary school students. Ilkogretim Online, 8(3). 637-650.
• 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. https://doi.org/10.1037/0022-0663.96.4.635
• Geary, D. C. (2004). Mathematics and learning disabilities. Journal of Learning Disabilities, 37(1), 4-15. https://doi.org/10.1177/00222194040370010201
• Geary, D. C. (2011). Consequences, characteristics, and causes of mathematical learning disabilities and persistent low achievement in mathematics. Journal of Developmental and Behavioral Pediatrics: JDBP, 32(3), 250. https://doi.org/10.1097/DBP.0b013e318209edef
• 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/10.3102/0034654309334431
• 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.
• 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.
• Işık, A., & Konyalıoğlu, A. C. (2005). Matematik eğitiminde görselleştirme yaklaşımı. Atatürk Üniversitesi Kazım Karabekir Eğitim Fakültesi Dergisi, 0(11), 462-471. Retrieved from https://dergipark.org.tr/tr/pub/ataunikkefd/issue/2772/37097
• Ives, B. (2007). Graphic organizers applied to secondary algebra instruction for students with learning disorders. Learning Disabilities Research & Practice, 22(2), 110–118. https://doi.org/10.1111/j.1540-5826.2007.00235.x
• Johnstone, C. J., Bottsford-Miller, N. A., & Thompson, S. J. (2006). Using the think-aloud method (cognitive labs) to evaluate test design for students with disabilities and English language learners Minneapolis, MN: University of Minnesota, National Center on Educational Outcomes.
• Jordan, N. C., Glutting, J., & Ramineni, C. (2010). The importance of number sense to mathematics achievement in first and third grades. Learning and Individual Differences, 20(2), 82-88. https://doi.org/10.1016/j.lindif.2009.07.004
• Karabulut, A., & Özmen, E. R. (2018). Effect of “understand and solve!” strategy ınstruction on mathematical problem solving of students with mild ıntellectual disabilities. International Electronic Journal of Elementary Education, 11(2), 77-90. https://doi.org/10.26822/iejee.2018245314
• Karasar, N. (2009). Bilimsel araştırma yöntemleri [Research method]. Ankara: Nobel.
• Keeler, M. L., & Swanson, H. L. (2001). Does strategy knowledge ınfluence working memory in children with mathematical disabilities?. Journal of Learning Disabilities, 34(5), 418, 439. https://doi.org/10.1177/002221940103400504
• Konyalıoğlu, A. C. (2003). Üniversite düzeyinde vektör konusundaki kavramların anlaşılmasında görselleştirme yaklaşımının etkinliğinin incelenmesi [Investigation of effectiveness of visualization approach on understanding of concepts in vector spaces at the university level] (Doktora tezi). Yükseköğretim Kurulu Ulusal Tez Merkezinden edinilmiştir. (Tez Numarası: 131567)
• Landerl, K. (2013). Development of numerical processing in children with typical and dyscalculic arithmetic skills a longitudinal study. Frontiers in Psychology, 4, 459-471. https://doi.org/10.3389/fpsyg.2013.00459
• Lucangeli, D., & Cabrele, S. (2006). The relationship of metacognitive knowledge, skills and beliefs in children with and without mathematical learning disabilities. In A. Desoete & M. V. Veenman (Eds.), Metacognition in Mathematics Education (pp. 103-133) New York: Nova Science.
• MEB (2005). İlköğretim matematik programı 1-5.Sınıflar [Mathematics cirriculum for grades 1-5]. Ankara: MEB.
• Memnun, D. S. (2014). Beşinci ve altıncı sınıf öğrencilerinin sözel problemleri çözme konusundaki yetersizlikleri ve problem çözümlerindeki hataları. [Fifth and sixth grade students' deficiencies on word problem solving and failures in the problem solving process]. Turkish Journal of Computer and Mathematics Education, 5(2), 158-175.
• 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(4), 230-248. https://doi.org/10.1177/002221949202500404
• Montague, M. (1997). Cognitive strategy instruction in mathematics for students with learning disabilities. Journal of Learning Disabilities, 30(2), 164-177. https://doi.org/10.1177/002221949703000204
• Montague, M. (2007). Self‐regulation and mathematics instruction. Learning Disabilities Research & Practice, 22(1), 75-83. https://doi.org/10.1111/j.1540-5826.2007.00232.x
• Montague, M. (2008). Self-regulation strategies to improve mathematical problem solving for students with learning disabilities. Learning Disability Quarterly, 31(1), 37-44. https://doi.org/10.2307/30035524
• Montague, M., & Applegate, B. (1993). Middle school students mathematical problem solving: An analysis of think-aloud protocols. Learning Disabilities Quarterly, 16(1), 19-32. https://doi.org/10.2307/1511157
• Montague, M., & Dietz, S. (2009). Evaluating the evidence base for cognitive strategy instruction and mathematical problem solving. Exceptional Children, 75(3), 285-302. https://doi.org/10.1177/001440290907500302
• 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. https://doi.org/10.1177/0731948711421762
• 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(2), 469–481. https://doi.org/10.1037/a0035176
• 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(4), 223-232. https://doi.org/10.1177/002221949703000204
• Montague, M., Warger, C, & Morgan, H. (2000). Solve It!: Strategy instruction to improve mathematical problem solving. Learning Disabilities Research and Practice, 15(2), 110-116. https://doi.org/10.1207/SLDRP1502_7
• Olkun, S., Altun, A., Şahin, S. G., & Denizli, Z. A. (2015). Temel sayı yeterliklerindeki eksiklikler ilköğretim öğrencilerinde düşük matematik başarısına neden olabilir [Deficits in basic number competencies may cause low numeracy in primary school children]. Eğitim ve Bilim, 40(177), 141-159. https://doi.org/10.15390/EB.2015.3287
• Ostad, A., & Sorensen, P.M. (2007). Private speech and strategy-use patterns: Bidirectional comparisons of children with and without mathematical difficulties in a developmental perspective. Journal of Learning Disabilities, 40(1), 2-14. https://doi.org/10.1177/00222194070400010101
• Özdemir, E. İ. (2011). Self-regulated learning from a sociocultural perspective. Eğitim ve Bilim, 36(160), 298-317.
• Özdemir, İ. E., & Pape, S. J. (2012). Supporting students’ strategic competence: a case of a sixth-grade mathematics classroom. Mathematics Education Research Journal, 24(2), 153-168. https://doi.org/10.1007/s13394-012-0033-8
• Özkubat, U. (2019). Öğrenme güçlüğü olan öğrenciler ile düşük ve ortalama başarılı olan öğrencilerin matematik problemi çözerken kullandıkları bilişsel stratejiler ile üstbilişsel işlevler arasındaki ilişkilerin incelenmesi [An examination of the relationships between cognitive strategies and metacognitive functions used during mathematical problem solving by the students with learning disabilities, low achieving, and average achieving] (Doktora tezi). Yükseköğretim Kurulu Ulusal Tez Merkezinden edinilmiştir. (Tez Numarası: 602277)
• Özkubat, U., & Özmen, E. R. (2018). Öğrenme güçlüğü olan öğrencilerin matematik problemi çözme süreçlerinin incelenmesi: Sesli düşünme protokolü uygulaması. [Analysis of mathematical problem solving process of students with learning disability: Implementation of think aloud protocol]. Ankara Üniversitesi Eğitim Bilimleri Fakültesi Özel Eğitim Dergisi, 19(1), 155-180. https://doi.org/10.21565/ozelegitimdergisi.299494.
• Memnun, D. S. (2014). Beşinci ve altıncı sınıf öğrencilerinin sözel problemleri çözme konusundaki yetersizlikleri ve problem çözümlerindeki hataları. [Fifth and sixth grade students' deficiencies on word problem solving and failures in the problem solving process Turkish Journal of Computer and Mathematics Education, 5(2), 158-175.
• Özmen, E. R. (2017). Öğrenme Güçlüğü Hakkında Temel Bilgiler ve Uygulamalar. Ankara: Eğiten.
• Özsoy, G. (2005). Problem çözme becerisi ile matematik başarısı arasındaki ilişki. [The Relationship Between Problem Solving Skills and Mathematical Achievement]. Gazi Üniversitesi Gazi Eğitim Fakültesi Dergisi, 25(3), 179-190.
• Özsoy, G. (2017). The effect of metacognitive strategy training on mathematical problem solving achievement. International Electronic Journal of Elementary Education, 1(2), 67-82. Retrieved from https://www.iejee.com/index.php/IEJEE/article/view/278.
• Parmar, S., & Cawley, J. (1997). Preparing teachers to teach mathematics to students with learning disabilities. Journal of Learning Disabilities, 30(2), 188-197. https://doi.org/10.1177/002221949703000206
• 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(3), 731-753. https://doi.org/10.1207/s15326942dn2803_1
• Polya, G. (1957). How to solve it. Garden City, N.Y.: Doubleday-Anchor.
• Reid, R. & Lienemann, T. O. (2006). Self-regulated strategy development for students with learning disabilities, Teacher Education and Special Education,29(1), 3-11. https://doi.org/10.1177/088840640602900102
• Rivera, D. (1997). Mathematics education and students with learning disabilities: Introduction to special series. Journal of Learning Disabilities, 30(1), 19-68. https://doi.org/10.1177/002221949703000101
• 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. https://doi.org/10.1177/0022219410378445
• Rotzer, S., Loenneker, T., Kucian, K., Martin, E., Klaver, P., & Von Aster, M. (2009). Dysfunctional neural network of spatial working memory contributes to developmental dyscalculia. Neuropsychologia, 47(13), 2859-2865. https://doi.org/10.1016/j.neuropsychologia.2009.06.009
• Swanson, H. L. (1990). Influence of metacognitive knowledge and aptitude on problem solving. Journal of Educational Psychology, 82, 306-314. https://doi.org/10.1037/0022-0663.82.2.306
• Sweeney, C. M. (2010). The metacognitive functioning of middle school students with and without learning disabilities during mathematical problem solving (Doctoral dissertation). Retrieved from http://scholarlyrepository.miami.edu/cgi/viewcontent.cgi?article=1432&context=oa_dissertations.
• Van Garderen, D. (2006). Spatial visualization, visual ımagery, and mathematical problem solving of students with varying abilities. Journal of Learning Disabilities, 39(6), 496–506. https://doi.org/10.1177/00222194060390060201
• Van Garderen, D. (2007). Teaching students with LD to use diagrams to solve mathematical word problems. Journal of Learning Disabilities, 40, 540–553. https://doi.org/10.1177/00222194070400060501