Öğretmen Adaylarının Problem Kurma Becerilerinin Orantısal Akıl Yürütme Gerektiren Durumlar Bağlamında İncelenmesi

Yıl 2017, Cilt: 8 Sayı: 1, 130 - 160, 03.04.2017

İbrahim Bayazit , Servet Merve Kırnap-dönmez

https://doi.org/10.16949/turkbilmat.303759

Cited By: 5

Öz

Bu çalışmada ortaokul matematik öğretmeni
adaylarının problem kurma yeterlikleri incelenmektedir. Konunun, doğal
ortamında ve katılımcıların perspektifinden incelenmesi için araştırmada örnek
olay metodu kullanılmıştır. Araştırmaya 162 öğretmen adayı katılmıştır. Veriler
10 adet açık uçlu soru içeren yazılı sınav ve sonrasında 8 katılımcıyla
yürütülen yarı-yapılandırılmış görüşmelerden elde edilmiştir. Toplanan veriler
içerik ve söylem analizi teknikleri kullanılarak analiz edilmiştir. Sonuçlar,
katılımcıların yeniden düzenleme sorularından hareketle problemler oluşturmada
başarılı olduklarını; ancak bunu yaparken büyük oranda bağlam ve değer
değiştirme tekniklerini kullandıklarını göstermektedir. Yarı-yapılandırılmış ve
serbest problem kurma durumlarında başarının düştüğü görülmüştür. Oluşturulan
problemlerin muhakeme gerektiren nitel karakterli sorular olmaktan ziyade nicel
veriler içeren, özgünlük ve yaratıcılıktan uzak, doğru ve ters orantı
algoritmalarının direkt uygulanmasıyla çözülebilecek türden rutin karakterli
sorular olduğu görülmüştür. Bulgular, öğretmen adaylarının problem kurma
konusundaki yetersizliklerinin pedagojik temelli olabileceğine işaret
etmektedir. Bu nedenle lisans eğitimi kapsamında problem kurma etkinliklerine
yer verilmesinin sorunun çözümüne katkı sağlayacağı söylenebilir.

Anahtar Kelimeler

Öğretmen adayları, problem kurma, orantısal akıl yürütme, yeniden düzenleme, yarı-yapılandırılmış ve serbest problem kurma durumları

Prospective Teachers’ Proficiencies at Problem Posing in the Context of Proportional Reasoning

Öz

This study investigates
prospective elementary school teachers’ proficiencies at problem posing. The
research employed qualitative case study method in order to examine the case in
its natural setting and from the participants’ perspectives. The research was
carried out with 162 prospective elementary mathematics teachers. A written
exam, which included 10 open-ended tasks, was administered to the participants;
and then semi-structured interview was conducted with 8 participants. Data were
analyzed through content and discourse analysis methods. The results indicated
that most of the participants were not proficient enough at posing conceptually
rich and cognitively challenging problems. They displayed relatively better
success at generating problems through re-formulation tasks; yet, they did this
by changing story of the original tasks or the numerical values in it. Their
success declined gradually when they were generating problems from
semi-structured and free problem posing situations. The problems that they
constructed excluded mathematical reasoning and creativity; these tasks could
be resolved by the application of rules, procedures and factual knowledge. The
participants’ lack of proficiency at problem posing seems to be resulting from
their educational backgrounds. Thus, it is suggested that engaging prospective
teachers in problem posing activities, especially in semi-structured and free
situations, during their undergraduate education will contribute to the
solution of this problem.    

Anahtar Kelimeler

Prospective teachers, problem posing, proportional reasoning, reformulation, semi-structured and free problem posing situations

Kaynakça

• Abu-Elwan, R. (1999). The development of mathematical problem posing skills for prospective middle school teachers. In A. Rogerson (Ed.), Proceedings of the International conference on Mathematical Education into the 21st Century: Social challenges, Issues and approaches (Vol. II, pp. 1–8). Cairo, Egypt.
• Abu-Elwan, R. (2002). Effectiveness of problem posing strategies on prospective mathematics teachers’ problem solving performance. Journal of Science and Mathematics Education in Southeast Asia, 25(1), 56-69.
• Behr, M., Harel, G., Post, T., & Lesh, R. (1992). Rational number, ratio and proportion. In D. Grouws (Ed.), Handbook on research of teaching and learning (pp. 296–333). New York: McMillan.
• Brown, S. I., & Walter, M. I. (Eds.). (1993). Problem posing in mathematics education. New Jersey: Lawrence Erlbaum Associates.
• Çelik, A. (2010). İlköğretim öğrencilerinin orantısal akıl yürütme becerileri ile problem kurma becerileri arasındaki ilişki (Yayınlanmamış yüksek lisans tezi). Hacettepe Üniversitesi, Eğitim Bilimleri Enstitüsü, Ankara.
• Christou, C., Mousoulides, N., Pittalis, M., Pitta-Pantazi, D., & Sriraman, B. (2005). An empirical taxonomy of problem posing processes. ZDM, 37(3), 149-158.
• Cramer, K., Post, T., & Currier, S. (1993). Learning and teaching ratio and proportion: Research implications. In D. Owens (Ed.), Research ideas for the classroom (pp. 159-178). New York, NY: Macmillan Publishing Company.
• Crespo, S., & Sinclair, N. (2008). What makes a problem mathematically interesting? Inviting prospective teachers to pose better problems. Journal of Mathematics Teacher Education, 11(5), 395–415.
• Dede, Y. ve Yaman, S. (2005). Matematik öğretmen adaylarının matematiksel problem kurma ve problem çözme becerilerinin belirlenmesi. Eğitim Araştırmaları Dergisi, 18, 41-56.
• English, L. D. (1997). The development of fifth-grade children’s problem-posing abilities. Educational Studies in Mathematics, 34, 183-217.
• English, L. D. (1998). Children’s problem posing within formal and informal contexts. Journal for Research in Mathematics Education, 29(1), 83-106.
• Gingsburg, H. P. (1981). The clinical interview in psychological research on mathematical thinking: aims, rationales, techniques. For the Learning of Mathematics, 1(3), 4-11.
• Grundmeier, T. A. (2003). The effects of providing mathematical problem posing experiences for k-8 pre-service teachers: investigating teachers’ beliefs and characteristics of posed problems (Unpublished doctoral dissertation). University of New Hampshire, Durham.
• Kilpatrick, J. (1987): Problem formulating: Where do good problems come from? In A. H. Schoenfeld (Ed.), Cognitive science and mathematics education (pp. 123-147). Hillsdale, NJ: Erlbaum.
• Korkmaz, E. ve Gür, H. (2006). Öğretmen adaylarının problem kurma becerilerinin belirlenmesi. Balıkesir Üniversitesi Fen Bilimleri Enstitü Dergisi, 8(1), 64-74.
• Lamon, S. J. (1995). Ratio and proportion. Elementary didactical phenomenology. In B. P. Schappelle (Ed.), Providing a foundation for teaching mathematics in the middle grades (pp. 167-198). Albany: State University of New York.
• Lavy, I., & Shriki, A. (2007). Problem posing as a means for developing mathematical knowledge of prospective teachers. Proceedings of the 31st Conference of the International Group for the Psychology of Mathematics Education (Vol. 3, pp. 129-136). Seoul: PME.
• Lesh, R., Post, T., & Behr, M. (1988). Proportional reasoning. In J. Hiebert & M. Behr (Eds.), Number concepts and operations in the middle grades (pp. 93-118). Reston, VA: Lawrence Erlbaum.
• Leung, S. K., & Silver, E. A. (1997). The role of task format, mathematics knowledge, and creative thinking on the arithmetic problem posing of prospective elementary school teachers. Mathematics Education Research Journal, 9(1), 5–24.
• Miles, M. B., & Huberman, A. M. (1994). Qualitative data analysis: An expanded source book (2nd ed.). Thousans Oaks, CA: Sage Publication.
• Moses, B., Bjork, E., & Goldenberg, E. P. (1990). Beyond problem solving: Problem posing. In T. J. Cooney, & C. R. Hirsch (Eds.), Teaching and learning mathematics in the 1990s (pp. 82-91). Reston, VA: National Council of Teachers of Mathematics.
• National Council of Teachers of Mathematics [NCTM] (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics.
• National Council of Teachers of Mathematics [NCTM] (1991). Principals and standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics.
• National Council of Teachers of Mathematics [NCTM] (2000). Principles and standard for school mathematics. Reston, VA: National Council of Teachers of Mathematics.
• Patricia, H., Post, T., Behr, M., & Lesh, R. (1990). Qualitative and numerical reasoning about fractions and rates by seventh- and eighth-grade students. Journal for Research in Mathematics Education, 21, 388-402.
• Phillips. N., & Hardy, C. (2002). Discourse analysis: Investigating processes of social construction. United Kingdom, UK: Sage Publication.
• Silver, E. A. (1994). On mathematical problem posing. For the Learning of Mathematics, 14(1), 19–28.
• Silver, E. A., & Cai, J. (1996). An analysis of arithmetic problem posing by middle school students. Journal for Research in Mathematics Education, 27, 521–539.
• Stickles, P. R. (2006). An analysis of secondary and middle school teachers’ mathematical problem posing (Unpublished doctoral dissertation). Indiana University, School of Education, Indiana.
• Trends in International Mathematics and Science Study [TIMSS]. (2011). Mathematics framework: Chapter-1. Retrieved November 15, 2016 from http://timss.bc.edu/timss2011/downloads/TIMSS2011_Frameworks-Chapter1.pdf
• Milli Eğitim Bakanlığı [MEB]. (2013). İlköğretim matematik öğretim programı. Ankara: Milli Eğitim Bakanlığı Yayınları.
• Van de Walle, J. A., Karp, K. S., & Bay-Williams, J. M. (2012). Elementary and middle school mathematics: teaching developmentally (S. Durmuş, Çev. Ed.). Boston: Pearson.
• Yıldırım, A. ve Şimşek, H. (2008). Sosyal bilimlerde nitel araştırma yöntemleri. Ankara: Seçkin Yayıncılık.
• Yin, R. K. (2003). Case study research: design and methods (3rd ed.). Thousand Oaks, CA: Sage.