Matematiksel Görevlerin Uygulanmasında İletişim Stratejileri ve Bilişsel Talep Kavramı: Sınıf İçi Yansımalar

Yıl 2020, Cilt: 35 Sayı: 4, 759 - 779, 31.10.2020

Defne Yabaş Sertel Altun

Öz

Matematik derslerinde uygulanan öğrenme görevleri, öğrencilere sunduğu öğrenme olanakları bakımından farklılık gösterebilmektedir. Bilişsel talep kavramı, bir öğrenme görevinin öğrenciye sunduğu, akıl yürütme, problem çözme vb. olanakları tanımlamaktadır. Bilişsel talep düzeyinin, öğretmenin görevi öğrencilere sunmasından, öğrencilerin görevi tamamlayana dek geçen süreçte değişebildiği belirtilmiştir. Değişimde rol oynayan öğrenme desteği sunma, öğrenciyi açıklama yapma, savunma, sorgulama ve yorum yapma yönünde cesaretlendirme vb. faktörler sınıf-içi iletişim ile ilişkilidir. Bu nedenle, öğretmenin görevi öğrencilere hangi detayları vererek sunduğu, öğrencilere uygulama süresince nasıl bir öğrenme desteği sağladığı, öğrencilerin fikirlerini tartışmalarına ne kadar olanak verdiği, öğrenme görevinin bilişsel talep düzeyinin sürdürülmesinde önemlidir. Buradan hareketle, çalışmada, bilişsel talep ve matematiksel iletişim kavramlarının bir matematiksel görevin uygulanmasında nasıl bir etkileşim gösterdiğinin incelenmesi amaçlanmıştır. İstanbul’da bir özel okuldaki iki dördüncü sınıf öğretmeni ve 37 öğrencinin katıldığı araştırmada örnek olay yöntemi kullanılmıştır. Dördüncü sınıf matematik dersi kesirler ünitesi öğretim sürecine ilişkin ders gözlemleri iki farklı şubede gerçekleştirilmiştir. Ders gözlemlerinden elde edilen veriler araştırmacıların alan notları ile desteklenmiş ve içerik analizi yöntemi ile veriler çözümlenmiştir. Bulgular, matematiksel iletişim ve bilişsel talep kavramlarının uygulamada karşılıklı bir etkileşim oluşturduğuna ve matematiksel görevlerin öğrencide olumlu kazanımlar ortaya çıkarmasında, seçilen görevin bilişsel talep düzeyi, uygulama sırasında öğretmenin yönlendirici davranışları ve oluşturduğu matematiksel iletişim ortamının etkili olduğuna işaret etmiştir.

Anahtar Kelimeler

matematiksel iletişim, bilişsel talep, matematik öğretimi, öğrenme görevleri

Communication Strategies and Cognitive Demand in Mathematical Task Enactment: Reflections from the Classroom

Öz

Learning opportunities presented to students through various mathematical tasks can differ. Cognitive demand concept defines the degree of thinking, reasoning and problem-solving opportunities offered to students through a mathematical task. Over a class period, the cognitive demand of a mathematical task can change in set-up and implementation phases. Scaffolding, encouraging students to give explanations, justification, questioning and making comments, etc. are factors associated with the change in cognitive demand. These factors are also related to in-class mathematical communication. Therefore, cognitive demand of tasks can be affected from teachers’ task presentation, guidance provided, and environment created for mathematical discussions. From this point on, the study aims to explore the interactions between cognitive demand and mathematical communication during the enactment of a mathematical task. Employing a case study design, the study included two 4th grade teachers and their 37 students from a private school in İstanbul. Data from classroom observations were complemented with the researchers’ field notes. Results indicated that, cognitive demand and mathematical communication had a reciprocal relationship during enactment, and to achieve positive results with students, cognitive demand level of chosen mathematical tasks, guiding behavior of teachers and mathematical communication environment should be considered.

Anahtar Kelimeler

Mathematical communication, cognitive demand, teaching mathematics, learning tasks

Kaynakça

• Baxter, J. A., Woodward, J., & Olson, D. (2001). Effects of reform-based mathematics instruction on low achievers in five third-grade classrooms. The Elementary School Journal, 101(5), 529-547.
• Blum, W., & Ferri, R. B. (2009). Mathematical modelling: Can it be taught and learnt?. Journal of Mathematical Modelling and Application, 1(1), 45-58.
• Boaler, J., & Brodie, K. (2004). The importance, nature and impact of teacher questions. In D. E. McDougall, J A. Ross (Eds.), Proceedings of the twenty-sixth annual Meeting of the North American Chapter of the International Group for Psychology of Mathematics Education (pp. 773-782).
• Boesen, J., Helenius, O., Bergqvist, E., Bergqvist, T., Lithner, J., Palm, T., Palmberg, B. (2014). Developing Mathematical Competence: From the Intended to the Enacted Curriculum. The Journal of Mathematical Behavior, 33, 72-87.
• Boston, M. D. (2013). Connecting Changes in Secondary Mathematics Teachers’ Knowledge to Their Experiences in a Professional Development Workshop. Journal of Mathematics Teacher Education,16(1), 7-31.
• Brendefur, J., & Frykholm, J. (2000.) Promoting mathematical communication in the classroom: Two preservice teachers' conceptions and practices. Journal of Mathematics Teacher Education, 3 (2), 125-153.
• Bruce, C.D. (2007). Student interaction in the math classroom: Stealing ideas or building understanding. What works?Research into practice. Toronto: Literacy and Numeracy Secreteriat.
• Chapin, S. H., O'Connor, C., & Anderson, N. C. (2009). Classroom discussions: Using math talk to help students learn, grades K-6. Sausalito, CA: Math Solutions.
• Collopy, R. (2003). Curriculum Materials as a Professional Development Tool: How a Mathematics Textbook Affected Two Teachers' Learning. The Elementary School Journal, 103(3), 287-311.
• Cooke, B. D., & Buchholz, D. (2005). Mathematical communication in the classroom: A teacher makes a difference. Early Childhood Education Journal, 32 (6), 365-369.
• Creswell, J. W. (2012). Educational Research: Planning, Conducting, And Evaluating Quantitative and Qualitative Research. 4.bs. Boston: Pearson.
• Creswell, J. W., & Miller, D. L. (2000). Determining Validity in Qualitative Inquiry. Theory Into Practice, 39(3), 24-130.
• Doyle, W. (1988). Work in mathematics classes: The context of students' thinking during instruction. Educational Psychologist, 23 (2), 167-180.
• Eskelson, S. L. (2013). Exploring the relationship between teachers’ participation in modified lesson study cycles and their implementation of high-level tasks. Unpublished doctoral dissertation, University of Pittsburgh School of Education, Pittsburgh, USA.
• Fan, L., Qi, C., Liu, X., Wang, Y., & Lin, M. (2017). Does a transformation approach improve students’ ability in constructing auxiliary lines for solving geometric problems? An intervention-based study with two Chinese classrooms. Educational Studies in Mathematics, 96(2), 229-248.
• Franke, M. L., Webb, N. M., Chan, A. G., Ing, M., Freund, D., & Battey, D. (2009). Teacher questioning to elicit students’ mathematical thinking in elementary school classrooms. Journal of Teacher Education, 60 (4), 380-392. [Available online, Sage Journals database at: https://journals.sagepub.com], Retrieved on September 15, 2017
• Georgius, K. (2013). Planning and enacting mathematical tasks of high cognitive demand in the primary classroom. Unpublished doctoral dissertation, University of Nebraska Graduate College, Lincoln, USA.
• Gresalfi, M., Martin, T., Hand, V., & Greeno, J. (2009). Constructing competence: An analysis of student participation in the activity systems of mathematics classrooms. Educational Studies in Mathematics, 70 (1), 49-70.
• Guba, E. G., & Lincoln Y.V. (1982). Epistemological and Methodological Bases Of Naturalistic Inquiry. Educational Technology Research and Development, 30(4), 233-252.
• Henningsen, M., & Stein, M.K. (1997). Mathematical tasks and student cognition: Classroom-based factors that support and inhibit high-level mathematical thinking and reasoning. Journal for Research in Mathematics Education, 28 (5), 524-549.
• Imm, K., & Stylianou, D. A. (2012). Talking mathematically: An analysis of discourse communities. The Journal of mathematical behavior, 31(1), 130-148.
• Jung, H. Y., & Reifel, S. (2011). Promoting children's communication: a kindergarten teacher's conception and practice of effective mathematics instruction. Journal of Research in Childhood Education, 25(2), 194-210.
• Kysh, J., Thompson, A., & Vicinus, P. (2007). From the editors: welcome to the "MT" 2007 focus issue: Mathematical discourse. The Mathematics Teacher, 101 (4), 245-245.
• Lamon, S. (2001). Presenting and Representing: From Fractions to Rational Numbers, In Albert A. Cuoco, & Frances R. Curcio (Eds.), The Roles of Representation in School Mathematics (pp. 146-165). Reston, The National Council of Teachers of Mathematics
• Lee, C. (2006). Language for learning mathematics: Assessment for learning in practice. UK: McGraw-Hill Education.
• Leino, J. (1990). Knowledge and learning in mathematics. In L. P. Steffe, & T. Wood (Eds.), Transforming children’s mathematics education: International perspectives (pp. 41-46). Mahwah, NJ: Lawrence Erlbaum Associates.
• Lloyd, G. M. (1999). Two Teachers' Conceptions of a Reform-Oriented Curriculum: Implications for Mathematics Teacher Development. Journal of Mathematics Teacher Education, 2(3), 227-252.
• Masingila, J. O., Olanoff, D., & Kimani, P. M. (2018). Mathematical knowledge for teaching teachers: knowledge used and developed by mathematics teacher educators in learning to teach via problem solving. Journal of Mathematics Teacher Education, 21(5), 429-450.
• Milli Eğitim Bakanlığı. (2018). Matematik Dersi Öğretim Programı:İlkokul ve Ortaokul 1,2,3,4,5,6,7 ve 8.Sınıflar. Ankara.
• Mooney, C., Briggs, M., Fletcher, M., McCullouch, J., & Hansen, A. (2012). Primary mathematics: Teaching theory and practice (6th ed.). Exeter:Learning Matters.
• Palincsar, A. S., Anderson, C., & David, Y. M. (1993). Pursuing Scientific Literacy in The Middle Grades Through Collaborative Problem Solving. The Elementary School Journal, 93(5), 643-658.
• Pape, S. J., Bell C. V., & Yetkin, I. E. (2003). Developing mathematical thinking and self-regulated learning: A teaching experiment in a seventh-grade mathematics classroom. Educational Studies in Mathematics, 53(3), 179-202.
• Pettersen, A., & Nortvedt, G.A. (2017). Identifying Competency Demands in Mathematical Tasks: Recognising What Matters. International Journal of Science and Mathematics Education, Online First March 2017, 1-17.
• Remillard, J. T. (1999). Curriculum Materials in Mathematics Education Reform: A Framework for Examining Teachers' Curriculum Development. Curriculum Inquiry, 29(3), 315-342.
• Remillard, J. T., & Bryans, M.B. (2004). Teachers' Orientations Toward Mathematics Curriculum Materials: Implications for Teacher Learning. Journal for Research in Mathematics Education, 35(5), 352-388.
• Resnick, L. B., & Zurawsky, C. (2006). Do the math: Cognitive demand makes a difference. Research Points, 4 (2), 1-4.
• Schoenfeld, A. H. (1994). Reflections on doing and teaching mathematics. In A. H. Schoenfeld (Ed.), Mathematical thinking and problem solving (pp. 53-70). Mahwah, NJ: Lawrence Erlbaum Associates.
• Sfard, A. (2001). There is more to discourse than meets the ears: looking at thinking as communicating to learn more about mathematical learning. Educational Studies in Mathematics, 46 (1-3), 13-57.
• Silver, E. A., & Smith, M. S. (1996). Building discourse communities in mathematics classrooms. In P. C. Elliot, M. J. Kenney (Eds.), Yearbook: Communication in Mathematics K–12 and Beyond (pp. 20-28). Reston, VA: NCTM
• Son, J. W., & Kim, O. K. (2016). Curriculum enactment patterns and associated factors from teachers’ perspectives. Mathematics Education Research Journal, 28 (4), 585-614.
• Spillane, J. P., & Zeuli, J. S. (1999). Reform and teaching: Exploring patterns of practice in the context of national and state mathematics reforms. Educational Evaluation and Policy Analysis, 21(1), 1-27.
• Stake, R. E. (1995). The art of case study research. Thousand Oaks, CA: Sage.
• Stein, M. K., & Smith, M.S. (1998). Mathematical tasks as a framework for reflection: From research to practice. Mathematics Teaching in the Middle School, 3 (4), 268-275. [Available online at:https://nctm.org], Retrieved on September 15, 2017
• Stein, M. K., Engle, R. A., Smith, M. S., & Hughes. E. K. (2008). Orchestrating productive mathematical discussions: Five practices for helping teachers move beyond show and tell. Mathematical Thinking and Learning, 10 (4), 313-340.
• Stein, M. K., Grover, B. W., & Henningsen, M. (1996). Building student capacity for mathematical thinking and reasoning: An analysis of mathematical tasks used in reform classrooms. American Educational Research Journal, 33 (2), 455-488.
• Stein, M. K., Smith, M. S., Henningsen, M. A., & Silver, E. A. (2009). Implementing standards-based mathematics instruction: A casebook for professional development. New York, NY: Teachers College Press.
• Tekkumru-Kisa, M., Schunn, C., Stein, M. K., & Reynolds, B. (2017). Change in thinking demands for students across the phases of a science task: An exploratory study. Research in Science Education. Published Online First, 1-25.
• Trafton, P. R., & Claus, A. S. (1994). A changing curriculum for a changing age. In C. A. Thornton, & N. S. Bley (Eds.), Windows of opportunity mathematics for students with special needs (pp. 19-39). Reston, VA: National Council of Teachers of Mathematics.
• Truxaw, M. P., & DeFranco, T. (2008). Mapping mathematics classroom discourse and its implications for models of teaching. Journal for Research in Mathematics Education 39 (5), 489-525.
• Varol, F., & Farran, D. C. (2006). Early mathematical growth: How to support young children’s mathematical development. Early Childhood Education Journal, 33 (6), 381-387.
• Viseu, F., & Oliveira, I. B. (2017). Open-ended tasks in the promotion of classroom communication in mathematics. International Electronic Journal of Elementary Education, 4(2), 287-300.
• Wasburn, M.H. (2007). Mentoring Women Faculty: An Instrumental Case Study of Strategic Collaboration. Mentoring & Tutoring, 15 (1), 57-72.
• Wijaya, A., van den Heuvel-Panhuizen, M., & Doorman, M. (2015). Opportunity-to-learn context-based tasks provided by mathematics textbooks. Educational studies in Mathematics, 89(1), 41-65.
• Yıldırım, A., & Şimşek, H. (2004). Sosyal Bilimlerde Nitel Araştırma Yöntemleri(4.bs). Ankara:Seçkin