Preservice Teachers' Knowledge of Students' Cognitive Processes About the Division of Fraktions

Bu çalışmanın amacı ilköğretim matematik öğretmen adaylarının ilköğretim öğrencilerinin kesirlerde bölmeye ilişkin sahip olabilecekleri kavram yanılgıları ve karşılaştıkları zorluklar hakkındaki bilgilerini incelemektir. Ayrıca, öğretmen adaylarının bu kavram yanılgıları ve zorlukların olası sebepleri hakkındaki bilgileri ve bu zorlukları gidermeye yönelik sundukları stratejileri incelemektir. Çalışma 2004-2005 bahar dönemi sonunda bir devlet üniversitesinde öğretmen yetiştirme programına devam eden son sınıf ilköğretim matematik öğretmen adayları ile nitel durum çalışması yapılarak gerçekleştirilmiştir. Çalışmanın sonuçları, öğretmen adaylarının öğrencilerin kesirlerde bölmeyle ilgili kavram yanılgılarının dört ana başlıkta toplanabileceğini göstermiştir. Ayrıca, sonuçlar öğretmen adaylarının öğrencilerin karşılaştıkları zorlukları giderebilmek için birçok strateji geliştirdiklerini göstermiştir. Bulgular, içerik ve pedagoji ağırlıklı derslerin, öğretmen adaylarının öğrencilerin matematiksel kavramları anlamaya ilişkin bilgilerinin gelişmesindeki önemini ortaya koymuştur.

Öğretmen Adaylarının Kesirlerde Bölmeye İlişkin Öğrencilerin Bilişsel Süreçleri Hakkındaki Bilgileri

The purpose of this study was to examine preservice mathematics teachers’ knowledge about common (mis)conceptions and difficulties of elementary students. In addition, it was aimed to investigate preservice teachers’ knowledge about the possible sources of these misconception/difficulties, and their suggested strategies to overcome those difficulties. Data was collected from senior preservice elementary mathematics teachers enrolled in a teacher education program at a public university at the end of the spring semester of 2004-2005. Qualitative case study design was used to collect the data. Results revealed that preservice teachers’ knowledge on difficulties that elementary students might have could be grouped under four headings. In addition, preservice teachers suggested various strategies that can be used to overcome students’ difficulties on division of fractions. Research study revealed the importance of content-pedagogy rich courses on preservice teachers’ knowledge related to students’ understanding of mathematics concepts.

PDF

___

Ashlock, R. D. (1990). Error patterns in computation. New York: Macmillan.
Ball, D. L. (1990). Prospective elementary and secondary teachers’ understanding of division. Journal for Research in Mathematics Education, 21, 132-144.
Ball, D. L. (1991). Research on teaching mathematics: Making subject-matter knowledge part of the equation. Research on Teaching Mathematics, 2, 1-48.
Ball, D. L., & McDiarmid, G. W. (1990). The subject-matter preparation of teachers. In W. R. Houston (Ed.), Handbook of research on teacher education: A project of the Association of Teachers (pp. 437-449). New York: MacMillan.
Barash, A., & Klein, R. (1996). Seventh grades students’ algorithmic, intuitive and formal knowledge of multiplication and division of non negative rational numbers. In L. Puig, & A. Gutiérrez (Eds.), Proceedings of the 20th conference of the International Group for the Psychology of Mathematics Education. Valencia, Spain: University of Valencia, 35-42.
Behr, M. J., Lesh, R., Post, T., & Silver, E. A. (1983). Rational number concepts. In R. Lesh, & M. Landau (Eds.), Acquisition of mathematics concepts and processes (pp. 91-126). New York: Academic Press.
Crespo, S., & Nicol, C. (2006). Challenging pre-service teachers’ mathematical understanding: The case of division by zero. School Science and Mathematics, 106(2), 84-97.
Fischbein, E. (1987). Intuition in science and mathematics: An educational approach. Dordrecht, The Netherlands: Reidel.
Fischbein, E., Deri, M., Nello, M., & Marino, M. (1985). The role of implicit models in solving verbal problems in multiplication and division. Journal for Research in Mathematics Education, 16, 3-17.
Graeber, A., Tirosh, D., & Glover, R. (1989). Preservice teachers’ misconceptions in solving verbal problems in multiplication and division. Journal for Research in Mathematics Education, 20, 95-102.
Grossman, P. L. (1989). A study in contrast: Sources of pedagogical content knowledge for secondary English. Journal of Teacher Education, 40, 24-31.
Grossman, P. L. (1990). The making of a teacher: Teacher knowledge and teacher education. New York: Teachers College Press, Columbia University.
Haser, Ç. & Ubuz, B. (2003). Students’ conceptions of Fractions: A study of 5th grade students. Hacettepe Üniversitesi Eğitim Fakültesi Dergisi, 24, 64-69.
Hill, H. C., Rowan, B., & Ball, D. L. (2005). Effects of teachers’ mathematical knowledge for teaching on student achievement.American Educational Research Journal, 42, 371-406.
Lederman, N. G., Gess-Newsome, J., & Latz, M. S. (1994). The nature and development of pre-service science teachers’conceptions of subject matter and pedagogy. Journal of Research in Science Teaching, 31(2), 129-146.
Lincoln, Y. S., & Guba, E. G. (1985). Naturalistic Inquiry. Thousand Oaks, California: Sage Publications.
Mack, N. K. (1990). Learning fractions with understanding: Building on informal knowledge. Journal for Research in Mathematics Education, 21, 16-32.
Merriam, S. B. (1998). Qualitative research and case study applications in education (Rev. ed.). Jossey-Bass, Inc., San Francisco.
Seale, C. (1999). Quality in qualitative research. Qualitative Inquiry, 5(4), 465-478.
Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4-14.
Shulman, L. S. (1987). Knowledge and teaching: Foundations of the new reform. Harvard Educational Review, 57(1), 1-22.
Stake, R. E. (1995). The art of case study research. Thousand Oaks, California: Sage Publications.
Stenbacka, C. (2001). Qualitative research requires quality concepts of its own. Management Decision, 39, 551-555.
Şandır, H., Ubuz, B. ve Argün, Z. (2007). 9th grade students’ difficulties in arithmetic operations, ordering numbers, solving equations and inequalities. Hacettepe Üniversitesi Eğitim Fakültesi Dergisi, 32, 274-281.
Tirosh, D. (2000). Enhancing prospective teacher’ knowledge of children’s conceptions: The case of division of fractions.Journal for Research in Mathematics Education, 31(1), 5-25.
Tirosh, D., Fischbein, E., Graeber, A., & Wilson, J. (1993). Conceptual adjustments in progressing from whole to rational numbers. Final report of the United States-Israel Binational Science Grant, Tel Aviv, Israel: Tel-Aviv University.