Investigation of Prospective Primary School Teachers’ Knowledge of The Meaning of Division

Yıl 2020, Cilt: 28 Sayı: 2, 931 - 946, 20.03.2020

Reyhan Tekin Sitrava Zeynep Özel Ahmet Işık

https://doi.org/10.24106/kefdergi.697844

Öz

The aim of this study is to examine knowledge of the prospective primary school teachers about the meaning of division and modeling of division depending on this meaning. For this purpose, a case study method which is one of the qualitative research methods was used and the study was conducted with 25 prospective classroom teachers determined by purposive sampling method. The data of the study was collected in two stages by means of “The Meaning of Division Operation” questionnaire consisting of two open-ended questions and semi-structured interviews. According to findings, it is seen that more than half of the prospective primary school teachers did not have sufficient knowledge about the learning outcome, “s/he uses the meaning of grouping and partition meaning at division operation” presented at 2nd grade level. Approximately one-third of prospective teachers knew both meanings of division operation and they can distinguish between the meaning of division operation. On the other hand, it shows that about half of the prospective primary school teachers had modeling knowledge, approximately one third of them had insufficient modeling knowledge and the rest of them did not have modeling knowledge. Since the prospective teachers had insufficient knowledge of division, it has great importance to increase their knowledge in the courses at Primary School Education Program. It might be provided to prospective teachers to get experience in teaching division operation and to get feedback from their mentor teachers at Methods of Teaching Mathematics I-II course.

Anahtar Kelimeler

content knowledge, the meaning of division operation, modeling of division operation, prospective primary school teachers

Sınıf Öğretmeni Adaylarının Bölme İşleminin Anlamına Dair Alan Bilgilerinin İncelenmesi

Öz

Bu çalışmanın amacı sınıf öğretmeni adaylarının bölme işleminin anlamına ve bu anlama bağlı olarak bölme işleminin modellenmesine ilişkin bilgilerinin incelenmesidir. Bu amaç doğrultusunda, nitel araştırma yöntemlerinden durum çalışması yöntemi kullanılmış ve amaçlı örneklem yöntemi ile belirlenen 25 sınıf öğretmeni adayı ile çalışma yürütülmüştür. Çalışmanın verileri açık uçlu 2 problemden oluşan “Bölme İşleminin Anlamı” soru seti ile yarı-yapılandırılmış görüşmeler vasıtasıyla iki aşamada toplanmıştır. Elde edilen bulgular doğrultusunda, sınıf öğretmeni adaylarının yarısından fazlasının ilkokul 2. sınıf düzeyinde yer alan “Bölme işleminde gruplama ve paylaştırma anlamlarını kullanır” kazanımına ilişkin yeterli bilgiye sahip olmadığı görülmüştür. Öğretmen adaylarının yaklaşık üçte biri bölme işleminin farklı anlamlarını bilmekte ve verilen problemin bölme işleminin hangi anlamını içerdiğini ayırt edebilmektedir. Diğer taraftan, çalışmaya katılan sınıf öğretmeni adaylarının yaklaşık yarısının bölme işleminin modellenmesine yönelik yeterli bilgiye sahip olduğunu, yaklaşık üçte birinin bölme işleminin modellenmesine yönelik bilgilerinin yetersiz olduğunu ve kalanının da bölme işleminin modellenmesine yönelik yeterli bilgiye sahip olmadığını göstermektedir. Sınıf öğretmeni adaylarının bölme işlemine yönelik alan bilgileri eksik olduğu için, sınıf öğretmenliği programında yer alan derslerde alan bilgilerinin artırılması büyük önem taşımaktadır. Öğretmenlik Uygulaması I-II derslerinde bu konuları anlatma deneyimi yaşamaları ve rehber öğretmenlerinden bu konularda geri bildirim alarak öğretmen adaylarının alan bilgilerinin güçlendirilmesi sağlanabilir.

Anahtar Kelimeler

alan bilgisi, bölme işleminin anlamı, bölme işleminin modellenmesi, sınıf öğretmeni adayları

Kaynakça

• Ambrose, R., Baek, J.-M. & Carpenter, T.P. (2003) Children’s invention of multiplication and division algorithms. In A. Baroody & A. Dowker (Eds.), The development of arithmetic concepts and skills: Recent research and theory. Mahwah, NJ: Erlbaum. Anghileri, J. (1989). An investigation of young children's understanding of multiplication. Educational Studies in Mathematics, 20(4), 367-385. Baki, M. (2013). Pre-service classroom teachers' mathematical knowledge and instructional explanations associated with division. Education and Science, 38(167), 300-311. Ball, D. L. (1990a). The mathematical understandings that prospective teachers bring to teacher education. The Elementary School Journal, 90(4), 449-466. Ball, D. L. (1990b). Prospective elementary and secondary teachers' understanding of division. Journal for Research in Mathematics Education, 132-144. Ball, D. L., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching. Journal of Teacher Education, 59(5), 389-407. Baturo, A., & Nason, R. (1996). Student teachers' subject matter knowledge within the domain of area measurement. Educational Studies in Mathematics, 31(3), 235-268. Baykul, Y. (2017). Ortaokulda matematik öğretimi (5-8. sınıflar). Ankara, Turkey: Pegem Akademi. Blum, W. (2002). ICMI Study 14: Applications and modeling in mathematics education- Discussion Document. Educational Studies in Mathematics, 51(1/2), 149-171. Boaler, J., & Staples, M. (2008). Creating mathematical futures through an equitable teaching approach: The case of Railside School. Teachers College Record, 110(3), 608-645. Borko, H., & Putnam, R. T. (1996). Learning to teach. In D. C. Berliner & R. C. Calfee (Eds.), Handbook of educational psychology (pp. 673-708). New York, NY, US: Macmillan Library Reference Usa; London, England: Prentice Hall International. Bryant, P. (1997). Mathematical understanding in the nursery school years. In T. Nunes & P. Bryant, (Eds.), Learning and teaching mathematics: An international perspective (pp. 53-67). East Sussex, UK: Psychology Press. Cohen, D. K., Raudenbush, S. W., & Ball, D. L. (2003). Resources, instruction, and research. Educational Evaluation and Policy Analysis, 25(2), 119-142. Contreras, J. M., Batanero, C., Díaz, C., & Fernandes, J. A. (2011). Prospective teachers’ common and specialized knowledge in a probability task. In Seventh Congress of the European Society for Research in Mathematics Education (pp. 766-775). European Society for Research in Mathematics Education. Çiltaş, A. & Işık, A. (2012). Matematiksel modelleme yönteminin akademik başarıya etkisi. Çağdaş Eğitim Dergisi Akademik, 2, 57-67. Dreyfus, T., & Eisenberg, T. (1996). On different facets of mathematical thinking. In R. J. Sternberg & T. Ben-Zeev (Eds.), The nature of mathematical thinking (pp. 253–284). Mahwah, NJ: Lawrence Erlbaum Downton, A. (2008, June). Links between children’s understanding of multiplication and solution strategies for division. In Proceedings of the 31st annual conference of the mathematics education research group of Australia (pp. 171-178). Sydney, New South Wales, Australia: MERGA. Erbaş, A. K., Kertil, M., Çetinkaya, B., Çakıroğlu, E., Alacacı, C., & Baş, S. (2014). Matematik eğitiminde matematiksel modelleme: Temel kavramlar ve farklı yaklaşımlar. Kuram ve Uygulamada Eğitim Bilimleri, 14(4), 1-21. Even, R. (1990). Subject matter knowledge for teaching and the case of functions. Educational Studies in Mathematics, 21(6), 521-544. Fennema, E., & Franke, M. L. (1992). Teachers' knowledge and its impact. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning: A project of the National Council of Teachers of Mathematics (pp. 147-164). New York, NY, England: Macmillan Publishing Co, Inc.Fischbein, E., Deri, M., Nello, M. S., & Merino, M. S. (1985). The role of implicit models in solving verbal problems in multiplication and division. Journal for Research in Mathematics Education, 16, 3–17Graeber, A. O., Tirosh, D., & Glover, R. (1989). Preservice teachers' misconceptions in solving verbal problems in multiplication and division. Journal for Research in Mathematics Education, 20(1), 95-102. Hiebert, J. & Wearne, D. (1988). Instruction and cognitive change in mathematics. Educational Psychologist, 23, 105-117. Hill, H. C., & Lubienski, S. T. (2007). Teachers' mathematics knowledge for teaching and school context: A study of California teachers. Educational Policy, 21(5), 747-768. Hill, H. C., Schilling, S. G., & Ball, D. L. (2004). Developing measures of teachers’ mathematics knowledge for teaching. The Elementary School Journal, 105(1), 11-30. İdil, F. H., & Narlı, S. (2019). Ortaokul matematik öğretmenlerinin uzmanlık alan bilgilerinin matematiksel hatalar bağlamında incelenmesi. International Journal of New Trends in Arts, Sports & Science Education (IJTASE), 8(3), 67-84. İşleyen, T., & Işık, A. (2003). Conceptual and procedural learning in mathematics. Research in Mathematical Education, 7(2), 91-99. Jacobs, V. R., Lamb, L. L., & Philipp, R. A. (2010). Professional noticing of children's mathematical thinking. Journal for Research in Mathematics Education, 169-202. Kaasila, R., Pehkonen, E., & Hellinen, A. (2010). Finnish pre-service teachers’ and upper secondary students’ understanding of division and reasoning strategies used. Educational Studies in Mathematics, 73(3), 247-261. Kouba, V. L. (1989). Children's solution strategies for equivalent set multiplication and division word problems. Journal for Research in Mathematics Education, 147-158. Kouba, V. L., & Franklin, K. (1993). Multiplication and division: Sense making and meaning. In J. Jansen (Eds.), Research Ideas for the Classroom Early Childhood Mathematics (pp. 103-126). New York: Macmillan Publishing Company. Livy, S., & Vale, C. (2011). First year pre-service teachers' mathematical content knowledge: Methods of solution to a ratio question. Mathematics Teacher Education and Development, 13(2), 22-43. Mewborn, D. S. (2003). Teaching, teachers’ knowledge, and their professional development. A Research Companion to Principles and Standards for School Mathematics, 45-52. Miles, M.B. ve Huberman, A.M. (1994). Qualitative data analysis: An expanded source book (2nd ed.). Thousand Oaks, California: SAGE. Milli Eğitim Bakanlığı [MEB]. (2009). İlköğretim matematik dersi 1–5. sınıflar öğretim programı. Ankara, Türkiye: MEB. Milli Eğitim Bakanlığı [MEB]. (2018). Matematik dersi öğretim programı (İlkokul ve Ortaokul 1, 2, 3, 4, 5, 6, 7 ve 8. sınıflar). Ankara, Türkiye: MEB. Mousley, J. (2000). Understanding multiplication concepts. Australian Primary Mathematics Classroom, 5 (3), 26–28. Muşlu, M. & Çiltaş, A. (2016). Doğal sayılarda işlemler konusunun öğretiminde matematiksel modelleme yönteminin öğrenci başarısına etkisi. Bayburt Eğitim Fakültesi Dergisi, 11(2), 329-343. National Council of Teachers of Mathematics. (2014). Principles to actions: Ensuring mathematics success for all. Reston, VA: National Council of Teachers of Mathematics. Piaget, J. (1977). Epistemology and psychology of functions. Dordrecht, Netherlands: D. Reidel Publishing Company. Pilkington, R. (2001). Analysing educational dialogue interaction: Towards models that support learning. International Journal of Artificial Intelligence in Education, 12, 1-7. Post, T., Wachsmuth, I., Lesh, R., & Behr, M. (1985). Order and equivalence of rational numbers: A cognitive analysis. Journal for Research in Mathematics Education, 16(1), 18–36. Roche, A., & Clarke, D. M. (2013). Primary teachers’ representations of division: Assessing mathematical knowledge that has pedagogical potential. Mathematics Education Research Journal, 25(2), 257-278. Rowland, T., Huckstep, P., & Thwaites, A. (2003). The knowledge quartet. Proceedings of the British Society for Research into Learning Mathematics, 23(3), 97-102. Rowland, T., Huckstep, P., & Thwaites, A. (2005). Elementary teachers’ mathematics subject knowledge: The knowledge quartet and the case of Naomi. Journal of Mathematics Teacher Education, 8(3), 255-281. Rowland, T., Jared, L., & Thwaites, A. (2011). Secondary mathematics teachers’ content knowledge: The case of Heidi. In Proceedings of the Seventh Congress of the European Society for Research in Mathematics Education (pp. 2827-2837). Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational researcher, 15(2), 4-14. Silver, E. A. (1986). Using conceptual and procedural knowledge: A focus on relationships. In J. Hiebert (Ed.), Conceptual and procedural knowledge: The case of mathematics (pp. 181-189). Hillsdale, NJ: Lawrence Elrbaum. Simon, M. A. (1993). Prospective elementary teachers' knowledge of division. Journal for Research in Mathematics education, 233-254. Stake, R. E. (2010). Qualitative research: Studying how things work. Guilford Press. Steffe, L. P. (1988). Children’s construction of number sequences and multiplying schemes. Number Concepts and Operations in the Middle Grades, 2, 119-140. Stein, M.K., Smith, M.S., & Remillard, J. (2007). How curriculum influences student learning. In Lester, F.K. (Ed.), Second handbook of research on mathematics teaching and learning (pp. 319-370). Greenwich, CT: Information Age Publishing. Stein, M. K., & Lane, S. (1996). Instructional tasks and the development of student capacity to think and reason: An analysis of the relationship between teaching and learning in a reform mathematics project. Educational Research and Evaluation, 2(1), 50-80. Tekin Sitrava, R. (2018). An investigation of prospective mathematics teachers' knowledge of basic algorithms with whole numbers: A case of Turkey. European Journal of Educational Research, 7(3), 513-528. Tirosh, D. (2000). Enhancing prospective teachers' knowledge of children's conceptions: The case of division of fractions. Journal for research in Mathematics Education, 5-25. Tirosh, D., & Graeber, A. O. (1991). The Effect of Problem Type and Common Misconceptions on Preservice Elementary Teachers' Thinking about Division. School Science and Mathematics, 91(4), 157-63. Yin, Robert K. (2014). Case study research: Design and methods. Los Angeles, CA: Sage. Yüksek Öğretim Kurumu [YÖK]. (2007). Eğitim fakültesi öğretmen yetiştirme lisans programları. Ankara, Türkiye: YÖK.