Cebir Problemlerinin Çözümüne Yeni Yaklaşım: Singapur Şerit Model Yöntemi

Yıl 2020, Cilt: 21 Sayı: 2, 942 - 962, 31.08.2020

Esra Baysal Şerife Sevinç

https://doi.org/10.17679/inuefd.709349

Cited By: 1

Öz

Bu çalışmada, yedinci sınıf öğrencilerinin cebir problemlerini çözmede tercih ettikleri yöntemleri ve öğrencilerin Singapur çubuk model yöntemi hakkındaki görüşleri incelenmiştir. Tek durum çalışması olarak tasarlanan çalışmada, yedinci sınıf öğrencilerinden cebir problemlerinin sorulduğu ön değerlendirme testinin cevaplarına göre seçilen 10 öğrenci ile klinik görüşmeler yapılmıştır. Öğrenciler ders saatlerinde yedinci sınıf matematik öğretim programına uygun olarak cebirsel denklem kurma yöntemi ile problem çözmeyi öğrenmiştir. Buna ek olarak, öğrencilere okul sonrasında üç saatlik Singapur bar/çubuk model eğitimi verilmiştir. Eğitimden sonra yapılan bire bir klinik görüşmelerde öğrencilerin tercih ettikleri çözüm yöntemleri, nitel veri kodlaması yoluyla analiz edilmiştir. Çalışmanın bulguları, öğrencilerin ilk tercihlerinin çubuk model yöntemi olduğunu göstermiştir. Öğrencilerin, çubuk modeli özellikle problemde verilen bilinmeyen nicelikleri anlamlandırmak amacıyla kullandıkları görülmüştür. Öğrencilerin büyük çoğunluğu probleme uygun doğru çubuk modeli çizerek doğru cevaba ulaşabilmiş ve sonrasında da çubuk modelden yararlanarak cebirsel denklem oluşturabilmiştir. Dolayısıyla, çubuk model öğrencilerin problemi anlamasına yardımcı olurken cebirsel denklem kurmaları için de bir ara basamak görevi görmüştür. Öğrenciler, çubuk modeli “daha anlaşılır” bulduklarını, problem çözme sürecini zevkli hale getirdiğini ve diğer matematik problemlerini de bu yöntemle çözmek istediklerini belirtmiştir. Bu bulgu da, çubuk modelin öğrencilerin problem çözmeye karşı motivasyonlarına katkı sağladığını göstermektedir. Bu çalışma, öğrencilerin zorlandıkları cebir problemlerinde ve denklem kurma sürecinde görsel bir araç olan çubuk modelin etkisini ortaya koymuştur. Bu anlamda, matematik öğretmenlerine, öğretmen eğitimcilerine ve matematik eğitimi alanındaki araştırmacılara katkı sağlaması beklenmektedir.

Anahtar Kelimeler

Singapur Çubuk Model Yöntemi, Cebir Problemleri, Denklem Kurma

An Alternative Approach to Solving Algebra Word Problems: Singapore Bar Model Method

Öz

This study investigated seventh grade students’ solution preferences while solving algebraic word problems and their thoughts about the Singapore bar model method. The study was designed as a single case study for which 10 seventh grade students were selected for the clinical interviews based on their performances on an initial assessment involving algebra problems. During the regular class hours, students learned how to solve algebra problems by writing linear equations. In addition, students were provided with an after school instruction for three hours and taught Singapore bar model method. Following the instruction, students’ solution preferences on algebra problems were analyzed qualitatively through coding students’ solutions and explanations in the clinical interviews. The study showed that, in most of the problems, students’ first preference was the bar model method. Students used the bar model particularly to conceptualize the unknown quantities given in the problems. The majority of the students could draw the correct bar model and reach the correct solution for the problems with this method, and those students could also write correct algebraic equation based on their models. Therefore, the bar model method not only helped students making sense with the problem but also served as a step towards writing algebraic equation. Furthermore, students stated that bar model method made the problem solving process more enjoyable, and they wanted to learn other math topics using the bar model. This result indicated that the bar model method as a visual tool also increased students’ motivation and played an important role in the algebra problems.

Anahtar Kelimeler

Singapore Bar Model Method, Algebra Word Problems, Writing Algebraic Equations.

Kaynakça

• Adu, E., Assuah, C., & Asiedu-Addo, S. (2015), Students’ Errors in Solving Linear Equation Word Problems: Case Study of a Ghanaian Senior High School, African Journal of Educational Studies in Mathematics and Sciences, 11, 17-30.
• Bal, A. P., & Karacaoğlu, A. (2017), Cebirsel Sözel Problemlerde Uygulanan Çözüm Stratejilerinin ve Yapilan Hatalarin Analizi: Ortaokul Örneklemi, Ç. Ü. Sosyal Bilimler Enstitüsü Dergisi, 26(3), 313-327
• Bednarz, N., & Janvier, B. (1996), Emergence and development of algebra as a problem-solving tool: Continuities and discontinuities with arithmetic, In N. Bednarz., C. Kieran., & L. Lee (Eds.), Approaches to algebra: Perspectives for research and teaching (pp. 115–136), Dordrecht, The Netherlands: Kluwer.
• Bütüner, S. Ö, & Güler, M. (2017). Gerçeklerle yüzleşme: Türkiye’nin TIMSS matematik başarısı üzerine bir çalışma [Facing the truth: An investigation on the mathematics achievement of Turkey in TIMSS]. Bayburt Eğitim Fakültesi Dergisi, 12(23), 353-376.
• Cai, J., Ng, S. F., & Moyer, J. (2011). Developing students’ algebraic thinking in earlier grades: Lessons from China and Singapore. In J. Cai & E. Knuth (Eds.), Early algebraization (pp. 25–42). New York: Springer.
• Clarke, L. (2017), Singapore Bar Models Appear To Be the Answer, But What Then Was the Question? Proceedings of the British Society for Research into Learning Mathematics, 37(2), 1-6.
• Clements, M. A. (1980). Analyzing children's errors on written mathematical tasks, Educational Studies in Mathematics, 11(1), 1-21.
• Creswell, J. W. (2009), Research Design: Qualitative, Quantitative, and Mixed Methods Approaches (3rd ed.), Thousand Oaks, CA: Sage Publications.
• Didiş, M. G., & Erbaş, K. (2012), Lise Öğrencilerinin Cebirsel Problemleri Çözmedeki Başarısı. Ulusal Fen Bilimleri ve Matematik Eğitimi Kongresi: http://kongre.nigde.edu.tr/xufbmek/dosyalar/tam_metin/pdf/2488-30_05_2012-23_05_03.pdf.
• Egodawatte, G. (2011). Secondary school students’ misconceptions in algebra, Unpublished Ph.D. Thesis, University of Toronto, Canada, http://hd1.handle.net/1807/29712.
• Ginsburg, A., Leinwand, S., Anstrom, T., & Pollock, E. (2005), What the United States can Learn from Singapore's World-class Mathematics System, Washington, DC: American Institutes for Research.
• Hong, K. T., Mei, Y. S., & Lim, J. (2009), The Singapore Model Method for Learning Mathematics, Singapore: EPB Pan Pacific.
• Hoven, J., & Garelick, B. (2007). Singapore math: Simple or complex? Educational Leadership, 65(3), 28-31.
• Jupri, A., & Drijvers, P. (2016), Student Difficulties in Mathematizing Word Problems in Algebra, Eurasia Journal of Mathematics, Science & Technology Education, 12(9), 2481-2502. doi: 10.12973/eurasia.2016.1299a
• Kabael, T., & Akin, A. (2016), Yedinci Sınıf Öğrencilerinin Cebirsel Sözel Problemlerini Çözerken Kullandıkları Stratejiler ve Niceliksel Muhakeme Becerileri, Kastamonu Eğitim Dergisi, 24(2), 875-894.
• Kaur, B. (2019), The Why, What and How of the ‘Model’ Method: A Tool for Representing and Visualising Relationships When Solving Whole Number Arithmetic Word Problems. ZDM Mathematics Education, 51, 151-168. doi:https://doi.org/10.1007/s11858-018-1000-y
• Kayani, M., & Ilyas, S. Z. (2014). Is algebra an issue for learning mathematics at pre-college level? Journal of Educational Research, 17(2), 100-106.
• Kieran, C., & Chalouh, L. (1993), Prealgebra: The Transition from Arithmetic to Algebra, In P. S. WILSON (Ed.), Research İdeas for the Classroom: Middle Grades Mathematics, (pp. 119-139). New York: Macmillan.
• Kieran, C. (2004). Algebraic thinking in the early grades: What is it? The Mathematics Educator, 8(1), 131–138.
• Koleza, E. (2015), The Bar Model As a Visual Aid For Developing Complementary/variation Problems, K. KONRAD ve N. VONDROVA içinde, Proceedings of CERME 9 (The ninth congress of the European Society for research in mathematics education), February 2015, Prague, Czech Republic.
• Lacampagne, C. B. (1995), The Algebra Initiative Colloquium, Vol. 2. Working group papers, Washington, DC: U.S. Department of Education, OERI.
• Ladele, O. A. (2013), The teaching and learning of word problems in beginning algebra: a Nigerian (Lagos State) study. Retrieved from https://ro.ecu.edu.au/theses/693
• Lawrance, A. (2007), Teaching and Learning Algebra Word Problems, (Unpublished Master Thesis), Massey University, New Zealand.
• Mahoney, K. (2012). Effects of Singapore’s model method on elementary student problem-solving performance: Single-case research. Northeastern University (School of Education) Education Doctoral Theses. Paper 70. http://hdl.handle.net/2047/d20002962.
• MEB, TTKB. (2018), Ortaokul Matematik Dersi 5-8. Sınıflar Öğretim Programı, Ankara: Devlet Kitapları Müdürlüğü Basım Evi.
• Ng, S. F., & Lee, K. (2009). The model method: Singapore children's tool for representing and solving algebra word problems. Journal for Research in Mathematics Education, 40(3), 282-313.
• Thiyagu, K. (2013). Effectiveness of Singapore math strategies in learning mathematics among fourth standard students. Vetric Education, 1, 1-14.
• Waight, M. M. (2006). The implementation of Singapore Math in a regional school district in Massachusetts 2000-2006. Remarks to national mathematics advisory panel, Cambridge, MA. Retrieved from http://www2.ed.gov/about/ bdscomm/list/mathpanel/3rd-meeting/presentations/waight.mary.pdf.