Sorun Aynı - Kavramlar; Kitle Aynı - Öğretmen Adayları

Öğretmenlerin matematiksel kavramları anlamaları ve bunları kullanma becerileri birçok araştırmaya konu Olmuştur. Bu çalışma öğretmen adaylarına kesirlerde görüş bildirmek kavramsal anlamalar nelere, nasıl odaklandıklarını incelemektedir. 2004-2005 ve 2005-2006 akademik yılları Türkiye Orta Anadolu bir büyükşehir üniversitesinde sınıf öğretmenliğinde kayıtlı bulunulan 153 tane son sınıf, sınıf öğretmeni adayına dönemin başladığı ilk derslerde açık uçlu sorulardan oluşan bir sınav sınavı uygulanmış. Uygulamada sorulan bir yerde kesirlerde bölme işlemiyle ilgili olup " 4 3 2 1 2 ÷ işlemi ile modellenebilen (veya çözülebilen) sözel bir problem yazınız "biçimindedir. Bu soru, klasik anlamdaki işlem sonucuna yönelik sorulardan farklı ya da kesirler ve bölme kavramlarını analiz etmeyi talep ettiği için adayların bilgi ve nasıl akıl yürüttükleri ortaya çıkarılmış etkili olmuş. Yapilmis analizler, öğretmen adaylarının anlam bakımından kesirler, bölme ve birİŞler ilgili bir çok kavramda eksikliğinin ortaya çıkarmıştır.

Anahtar Kelimeler:

Kavramsal anlama, muhakeme, kesirlerde bölme, öğretmen adayları, değerlendirme

Working on the Same Problem – Concepts; With the Usual Subjects – Prospective Elementary Teachers

The purpose of current study was to shed light on what concepts or ideas prospective elementary teachers drew on (and how) when they reasoned about problems related to division of fractions. The participants were 153 senior prospective elementary teachers who registered for a mathematics-methods course either during the 2004-2005 or 2005- 2006 academic year. The participants were from a metropolitan city university located in the central part of Turkey. The study was based on an open-ended written assessment item administered during the very first class of the semester before any teaching. One of the applied open-ended questions was: “Write a real-world problem that would be solved or modeled by 4 3 2 1 2 ÷ .” A question like this requires a detailed analysis of the concepts of division and fractions as opposed to getting a single numeric result. Such a question, to some extent, provided an opportunity to investigate these teachers’ reasoning about division and fractions. The results showed that prospective elementary teachers had significant difficulties in thinking about fractions, division, and units.

Keywords:

Conceptual understanding, reasoning, division of fractions, prospective elementary teachers, assessment,

PDF

___

Armstrong, B. E., & Bezuk, N. (1995). Multiplication and division of fractions: The search for meaning. In J. Sowder & B. P. Schappelle (Eds.), Providing a foundation for teaching mathematics in the middle grades (pp. 85-119). Albany, NY: State University of New York Press.
Ball, D. L. (1990). Prospective elementary and secondary teachers' understanding of division. Journal for Research in Mathematics Education, 21(2), 132-144.
Bell, A., Swan, M., & Taylor, G. (1981). Choice of operations in verbal problems with decimal numbers. Educational Studies in Mathematics, 12, 399-420.
Fishbein, E., Deri, M., Nello, M. S., & Marino, M. S. (1985). The role of implicit models in solving verbal problems in multiplication and division. Journal for Research in Mathematics Education, 16(1), 3-17.
Graeber, A. O., Tirosh, D., & Glover, R. (1986). Preservice teachers' misconceptions in solving verbal problems in multiplication and division. Journal for Research in Mathematics Education, 95-102.
Greer, B. (1987). Nonconservation of multiplication and division involving decimals (Brief Report). Journal for Research in Mathematics Education, 18(1), 37-45.
Ma, L. (1999). Knowing and teaching elementary mathematics: Teachers' understanding of fundamental mathematics in China and the United States. Mahwah, NJ: Lawrence Erlbaum Associates, Inc.
Silver, E. A., Shapiro, L. J., & Deutsch, A. (1993). Sense making and the solution of division problems involving remainders: An examination of middle school students' solution processes and their interpretations of solutions. Journal for Research in Mathematics Education, 24(2), 117-135.
Simon, M. A. (1993). Prospective elementary teachers' knowledge of division. Journal for Research in Mathematics Education, 24(3), 233-254.
Sowder, J. T., Armstrong, B., Lamon, S., Simon, M. A., Sowder, L., & Thompson, A. (1998). Educating teachers to teach multiplicative structures in the middle grades. Journal of Mathematics Teacher Education, 1(2), 127-155.
Tirosh, D., & Graeber, A. O. (1989). Preservice elementary teachers' explicit beliefs about multiplication and division. Educational Studies in Mathematics, 20(1), 79-96.
Thompson, P. W. (1993). Quantitative reasoning, complexity, and additive structures. Educational Studies in Mathematics, 25(3), 165-208.
Toluk, Z., & Middleton, J. A. (2004). The development of children’s understanding of quotient: A Teaching experiment. International Journal for Mathematics Teaching and Learning, 5(10).Online: http://www.cimt.plymouth.ac.uk/journal/default.htm
Tzur, R., & Timmerman, M. (1997). Why do we invert and multiply? Elementary teachers' struggle to conceptualize division of fractions. In J. A. Dossey, J. O. Swafford, M. Parmantie & A. E. Dossey (Eds.), Proceedings of the 19th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 553-559). Bloomington-Normal, IL: Eric Clearinghouse for Science, Mathematics, and Environmental Education.
Zembat, . Ö. (2004). Conceptual development of prospective elementary teachers: The case of division of fractions, The Pennsylvania State University, University Park, unpublished PhD thesis.