Ortaokul Matematik Öğretmen Adaylarının Oran Kavramına Yönelik Öğrenci Düşünme Modelleri Oluşturma Süreçleri

Year 2024, Volume: 44 Issue: 1, 273 - 309, 30.04.2024

Sultan Yıldırım İffet Yetkin Özdemir

https://doi.org/10.17152/gefad.1375772

Abstract

Bu çalışmanın amacı, araştırma temelli bir hizmet öncesi eğitim programına katılan öğretmen adaylarının oran kavramıyla ilgili öğrenci düşünme modelleri geliştirme sürecini araştırmaktır. Nitel araştırma yöntemlerinin kullanıldığı çalışmada katılımcılar bir devlet üniversitesinde son sınıfta okuyan dört ortaokul matematik öğretmeni adayıdır. Eğitim programının tasarımı, Bilişsel Yönlendirmeli Öğretim (CGI) ilkelerine dayanmakta olup, öğretmen adaylarının öğrencilerin oran kavramı gelişimine dair araştırma temelli bilgiyle etkili bir şekilde etkileşimde bulunmalarını sağlayan görevleri içermektedir. Çalışmanın verileri, beş oturumdan elde edilen görüşmelerin kayıtlarından ve öğretmen adaylarının görevlere verdiği yazılı cevaplardan oluşmaktadır. Verilerin analizinde öğrenci düşünme modellerini dört süreç (tanımlama, karşılaştırma, çıkarım ve yeniden yapılandırma) ile tanımlayan bir çerçeve kullanılmıştır. Öğrenci düşünmesini açıklarken, öğretmen adayları öğrenci ifadelerini tekrarlamış, öğrenci çözümlerindeki önemli noktalara vurgu yapmış, öğrenci çözüm yöntemlerini ayrıntılı bir şekilde açıklamış veya genel çözüm özelliklerine odaklanmıştır. Karşılaştırma sürecinde öğretmen adayları, öğrenci çözümlerini kendi çözümleriyle açık veya üstü kapalı olarak karşılaştırmış, genellikle kendi veya diğer öğretmen adaylarının düşüncelerine odaklanmışlardır. Çıkarım süreci, öğrenci çalışmalarından gelen kanıtları yorumlamayı içermiştir, bazen gerekçe sunmadan çıkarımda bulunmuşlardır. Öğretmen adayları, öğrenci düşünmesini tahmin ederek ve öğrenci düşüncesini dikkate alan problemler oluşturarak yeniden yapılandırma sürecinde bulunmuşlardır. Oluşturdukları modellerle öğrenci düşünmesini tahmin edebilmişlerdir.

Keywords

Matematik eğitimi, Öğretmen adayları, Bilişsel yönlendirmeli öğretim, Öğrenci düşünme modelleri, Oran kavramı

Ethical Statement

Bu araştırma, Hacettepe Üniversitesi Etik Komisyonu’nun 08 Haziran 2021 tarihli E-35853172-300-00001610808 sayılı kararı ile alınan izinle yürütülmüştür.

Supporting Institution

Bu araştırmada herhangi bir kurum, kuruluş ya da kişiden destek alınmamıştır.

Prospective Middle School Mathematics Teachers' Process of Constructing Student Thinking Models on Ratios

Abstract

This study explores the process of prospective teachers developing student thinking models regarding the ratio concept within a research-based pre-service education program. It employs qualitative research methods and involves four final-year prospective middle school mathematics teachers at a state university. The program design incorporates principles of Cognitively Guided Instruction (CGI), featuring tasks that enable prospective teachers to engage with research-based knowledge on ratio concept development in students and its application in instruction. Data for the study comprises recorded interview sessions spanning five meetings and written responses from prospective teachers to the tasks. Analysis employs a framework defining four processes for constructing student thinking models: description, comparison, inference, and restructuring. When describing student thinking, prospective teachers reiterated student statements, emphasized crucial points in student solutions, provided detailed explanations of student solution methods, or focused on general solution characteristics. In the comparison process, prospective teachers explicitly or implicitly compared student solutions with their own, often based on personal thoughts or those of fellow prospective teachers. The inference process involves interpreting evidence from student work, sometimes without providing a rationale. Prospective teachers showed restructuring through anticipating student thinking and posing problems that consider student thought. They anticipated student thinking through the models they created.

Keywords

Mathematics education, Prospective teachers, Cognitively guided instruction, Student thinking models, Ratio concept

References

• Ball, D. L., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching: What makes it special?
• Bartell, T. G., Webel, C., Bowen, B., & Dyson, N. (2013). Prospective teacher learning: recognizing evidence of conceptual understanding. Journal of Mathematics Teacher Education, 16, 57-79.
• Carpenter, T. P., Fennema, E., & Franke, M. L. (1996). Cognitively guided instruction: A knowledge base for reform in primary mathematics instruction. The Elementary School Journal, 97(1), 3-20.
• Carpenter, T. P., Fennema, E., Peterson, P. L., Chiang, C.-P., & Loef, M. (1989). Using knowledge of children’s mathematics thinking in classroom teaching: An experimental study. American Educational Research Journal, 26(4), 499-531.
• Carpenter, T. P., & Levi, L. (2000). Developing Conceptions of Algebraic Reasoning in the Primary Grades. Research Report.
• Clement, D., & Sarama, J. (2004). Learning Trajectories in Mathematics Education. Mathematical Thingking and Learning, 6(2), 81-89. In.
• Clements, D. H., Sarama, J., Spitler, M. E., Lange, A. A., & Wolfe, C. B. (2011). Mathematics learned by young children in an intervention based on learning trajectories: A large-scale cluster randomized trial. Journal for Research in Mathematics Education, 42(2), 127-166.
• Crespo, S. (2000). Seeing more than right and wrong answers: Prospective teachers' interpretations of students' mathematical work. Journal of Mathematics Teacher Education, 3(2), 155-181.
• de la Cruz, J. A. (2016). Changes in One Teacher's Proportional Reasoning Instruction after Participating in a CGI Professional Development Workshop. Universal Journal of Educational Research, 4(11), 2551-2567.
• Didis, M. G., Erbas, A. K., Cetinkaya, B., Cakiroglu, E., & Alacaci, C. (2016). Exploring prospective secondary mathematics teachers’ interpretation of student thinking through analysing students’ work in modelling. Mathematics Education Research Journal, 28, 349-378.
• Franke, M. L., & Kazemi, E. (2001). Learning to teach mathematics: Focus on student thinking. Theory into practice, 40(2), 102-109. Retrieved from http://faculty.washington.edu/ekazemi/theory%20into%20practice.pdf
• Harel, G., Behr, M., Lesh, R., & Post, T. (1994). Invariance of ratio: The case of children's anticipatory scheme for constancy of taste. Journal for Research in Mathematics Education, 25(4), 324-345. Retrieved from http://www.jstor.org/stable/749237 .
• Hill, H. C., Ball, D. L., & Schilling, S. G. (2008). Unpacking Pedagogical Content Knowledge: Conceptualizing and Measuring Teachers' Topic-Specific Knowledge of Students. Journal for Research in Mathematics Education, 39(4), 372-400. doi:10.5951/jresematheduc.39.4.0372
• Hines, E., & McMahon, M. T. (2005). Interpreting middle school students' proportional reasoning strategies: Observations from preservice teachers. School Science and Mathematics, 105(2), 88-105.
• I, J. Y., Martinez, R., & Dougherty, B. (2018). Misconceptions on part-part-whole proportional relationships using proportional division problems. Investigations in Mathematics Learning, 12(2), 67-81. doi:10.1080/19477503.2018.1548222
• Ivars, P., Fernández, C., Llinares, S., & Choy, B. H. (2018). Enhancing noticing: Using a hypothetical learning trajectory to improve pre-service primary teachers’ professional discourse. Eurasia Journal of Mathematics, Science and Technology Education, 14(11), em1599.
• Johnson, K. (2017). A Study of Pre-Service Teachers Use of Representations in Their Proportional Reasoning. Paper presented at the Proceedings of the 39th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, Indianapolis, IN: Hoosier
• Lamon, S. J. (2012). Teaching Fractions and Ratios for Understanding: Essential Content Knowledge and Instructional Strategies for Teachers (3 ed.). New York, NY: Taylor & Francis Group.
• Liang, B. (2021). Learning about and learning from students: Two teachers’ constructions of students’ mathematical meanings through student-teacher interactions. [University of Georgia, Retrieved from https://esploro.libs.uga.edu/esploro/outputs/doctoral/Learning-about-and-learning-from-students/9949375152802959#file-0
• Lobato, J. (2008). When Students Don't Apply the Knowledge You Think They Have, Rethink Your Assumptions about Transfer. In M. Carlson & C. Rasmussen (Eds.), Making the Connection (pp. 289-304): Washington, DC: Mathematical Association of America.
• Lobato, J., Ellis, A., & Zbiek, R. M. (2010). Developing Essential Understanding of Ratios, Proportions, and Proportional Reasoning for Teaching Mathematics: Grades 6-8: ERIC.
• Lobato, J., & Thanheiser, E. (2002). Developing understanding of ratio as measure as a foundation for slope. In B. Litwiller (Ed.), Making sense of fractions, ratios, and proportions: 2002 yearbook (pp. 162-175): National Council of Teachers of Mathematics.
• Martinez, R., & Dougherty, B. (2018). Misconceptions on part-part-whole proportional relationships using proportional division problems.
• Merriam, S. B. (2013). Nitel araştırma: Desen ve uygulama için bir rehber (3. Basım). Ankara: Nobel akademik yayıncılık.
• Miles, M. B., & Huberman, A. M. (1994). Qualitative data analysis: An expanded sourcebook: sage.
• Pişkin Tunç, M. (2016). Pre-service middle school mathematics teachers’ proportional reasoning before and after a practice based instructional module (DOCTOR). Middle East Technical University, Retrieved from http://etd.lib.metu.edu.tr/upload/12620187/index.pdf
• Richardson, K., Miller, S. D., & Reinhardt, J. (2019). Professional Development as an Ongoing Partnership: The Sum Is Greater than Its Parts. School-University Partnerships, 12(1), 45-50.
• Riehl, S. M., & Steinthorsdottir, O. B. (2014). Revisiting Mr. Tall and Mr. Short. Mathematics Teaching in the Middle School, 20(4), 220-228. doi:https://doi.org/10.5951/mathteacmiddscho.20.4.0220
• Sarama, J., Clements, D. H., Wolfe, C. B., & Spitler, M. E. (2016). Professional development in early mathematics: Effects of an intervention based on learning trajectories on teachers’ practices. Nordic Studies in Mathematics Education, 21(4), 29-55.
• Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4-14.
• Simon, M. A. (1995). Reconstructing mathematics pedagogy from a constructivist perspective. Journal for Research in Mathematics Education, 26(2), 114-145.
• Simon, M. A., & Blume, G. W. (1994). Mathematical modeling as a component of understanding ratio-as-measure: A study of prospective elementary teachers. The Journal of Mathematical Behavior, 13(2), 183-197.
• Sztajn, P., Wilson, P. H., Edgington, C., & Confrey, J. (2011). Learning Trajectories and Key Instructional Practices. North American Chapter of the International Group for the Psychology of Mathematics Education.
• Wilson, P. H., Lee, H. S., & Hollebrands, K. F. (2011). Understanding prospective mathematics teachers' processes for making sense of students' work with technology. Journal for Research in Mathematics Education, 42(1), 39-64.
• Wilson, P. H., Mojica, G. F., & Confrey, J. (2013). Learning trajectories in teacher education: Supporting teachers’ understandings of students’ mathematical thinking. The Journal of Mathematical Behavior, 32(2), 103-121.
• Yıldırım, A., & Şimşek, H. (2013). Sosyal bilimlerde nitel araştırma yöntemleri.(9. Genişletilmiş Baskı) Ankara: Seçkin Yayınevi.