Özel Yetenekli Ortaokul Öğrencilerinin Gerçekçi Problem Kurma Performanslarının Belirlenmesi

Yıl 2023, Cilt: 25 Sayı: 3, 428 - 440, 29.09.2023

Temel Kösa , Beyzanur Erkan

https://doi.org/10.17556/erziefd.1268395

Öz

Bu araştırmanın amacı özel yetenekli ortaokul öğrencilerinin sınıf düzeyinde kurdukları problemlerin matematiksel geçerlilik, semantik karmaşıklıkları, gerçekçilikleri belirlenmesi ve karşılaştırılmasıdır. Durum çalışması yöntemiyle yürütülen araştırmanın katılımcılarını bir bilim ve sanat merkezinde öğrenim gören 16 altıncı sınıf, beş yedinci sınıf, yedi sekizinci sınıf düzeyinde olmak üzere toplamda 28 özel yetenekli öğrenci oluşturmaktadır. Araştırmada öğrencilerden karmaşık ve gerçek yaşam ile ilişkili matematik problemi kurmaları istenmiştir. Öğrencilerin kurdukları problemler ilk aşamada matematiksel geçerliliğine, ikinci aşamada ise semantik karmaşıklığına ve gerçekçiliğine yönelik analiz edilmiştir. Araştırmada elde edilen sonuçlar, özel yetenekli öğrencilerin geçerli matematik problemleri kurabildiğini göstermiştir. Yine araştırma sonuçları, öğrencilerin problemlerinde farklı semantik yapılara yer veremediği buna karşın gerçekçi matematik problemleri yazabildiklerini göstermiştir. Öğrenciler gerçekçi matematik problemlerinde bağlam seçimlerinin alışveriş, yemek tarifi gibi bağlamlarla sınırlandığı belirlenmiştir. Bu yönüyle öğretmenlerin matematik derslerinde daha fazla gerçek yaşam durumlarına uygun problem kurma ve çözme etkinliklerine yer vermesi gerektiği önerilebilir.

Anahtar Kelimeler

problem kurma, özel yetenekli öğrenciler, matematiksel geçerlilik, semantik karmaşıklık

Determine of Gifted Middle School Students Problem Posing Performance to Real-life Situations

Öz

The study aimed to determine and compare the mathematical validity, semantic complexity, and real-life relationships of problems posed by gifted middle school students in the classroom level. The participants of the research, which was conducted with the case study method, consisted of a total of 28 gifted students, 16 of whom were in the sixth grade, five in the seventh grade, and seven in the eighth grade, studying in a science and art center. In the study, students were asked to pose a complex real-life math problem. The problems posed by the students were analyzed for mathematical validity in the first stage and for semnatic complexity and real-life relationships in the second stage. The study's results showed gifted students could pose valid math problems. Again, the research found that students couldn't incorporate diverse semantic structures in their problems, but they could pose real-life mathematical problems. It has been determined that students context choices are limited to shopping and cooking recipes in real-life math problems. In this respect, it can be suggested that teachers include more problem-posing and solving activities suitable for real-life situations in their mathematics lessons.

Anahtar Kelimeler

problem posing, gifted students, mathematical validity, semantic complexity

Kaynakça

• Ada, K., Demir, F., ve Öztürk, M. (2020). Examination of Sixth Grade Students' Problem-Posing Skills: A Case study. Turkish Journal of Computer and Mathematics Education (TURCOMAT), 11(1), 210-240. https://doi.org/10.17762/turcomat.v11i1.230
• Baki, A. (2020). Matematik tarihi ve felsefesi. Pegem.
• Cai, J. (1998). An investigation of U. S. and Chinese students’ mathematical problem posing and problem solving. Mathematics Education Research Journal, 10(1), 37– 50. https://doi.org/10.1007/BF03217121
• Cai, J., ve Hwang, S. (2002). Generalized and generative thinking in US and Chinese students’ mathematical problem solving and problem posing. The Journal of Mathematical Behavior, 21(4), 401–421. https://doi.org/10.1016/S0732-3123(02)00142-6
• Cai, J., ve Hwang, S. (2020). Learning to teach through mathematical problem posing: Theoretical considerations, methodology, and directions for future research. International Journal of Educational Research. https://doi.org/10.1016/j.ijer.2019.01.001
• Cankoy, O., ve Özder, H. (2017). Generalizability theory research on developing a scoring rubric to assess primary school students' problem posing skills. Eurasia Journal of Mathematics, Science and Technology Education, 13(6), 2423-2439. https://doi.org/10.12973/eurasia.2017.01233a
• Carpenter, T. P., Fennema, E., ve Franke, M. L. (1996). Cognitively guided instruction: A knowledge base for reform in primary mathematics instruction. The Elementary School Journal, 97(1), 3–20. https://doi.org/10.1086/461846
• Chen, L., Van Dooren, W., Chen, Q., ve Verschaffel, L. (2011). An investigation on Chinese teachers’realistic problem posing and problem solving ability and beliefs. International Journal of Science and Mathematics Education, 9(4), 919–948. https://doi.org/10.1007/s10763-010-9259-7
• Chen, L., Van Dooren, W., ve Verschaffel, L. (2015). Enhancing the development of Chinese fifth-graders’ problem-posing and problem-solving abilities, beliefs, and attitudes: a design experiment. In F. M. Singer, N. F. Ellerton, and J. Cai (Eds.), Mathematical problem posing. From research to effective practice (s. 309– 329). Springer. https://doi.org/10.1007/978-1-4614-6258-3_15
• Çetinkaya, A., ve Soybaş, D. (2018). İlköğretim 8. sınıf öğrencilerinin problem kurma becerilerinin incelenmesi. Journal of Theoretical Educational Science, 11(1), 169-200. https://doi.org/10.30831/akukeg.333757
• English, L. D. (1997). Promoting a problem posing classroom. Teaching Children Mathematics, 4(3), 172. https://doi.org/10.5951/TCM.4.3.0172
• Erkan, B. (2021). Problem biçimlendirme: İlköğretim matematik öğretmeni adaylarının düşünme süreçlerinin incelenmesi. [Yüksek lisans tezi]. Recep Tayyip Erdoğan Üniversitesi, Fen Bilimleri Enstitüsü, Rize.
• Gökkurt, B., Örnek, T., Hayat, F., ve Soylu, Y. (2015). Öğrencilerin problem çözme ve problem kurma becerilerinin değerlendirilmesi. Bartın University Journal of Faculty of Education, 4(2), 751-774. https://doi.org/10.14686/buefad.v4i2.5000145637
• Kaba, Y., ve Şengül, S. (2016). Developing the Rubric for Evaluating Problem Posing (REPP). International Online Journal of Educational Sciences, 8(1). https://doi.org/10.15345/iojes.2016.01.002
• Kar, T., ve Erkan, B. (2022). An Examination of Pre-Service Mathematics Teachers’ Problem-Formulation Performances. Investigations in Mathematics Learning, 14(3), 184-198. https://doi.org/10.1080/19477503.2022.2058841
• Kar, T. (2015). Analysis of problems posed by sixth-grade middle school students for the addition of fractions in terms of semantic structures. International Journal of Mathematical Education in Science and Technology, 46(6), 879-894. https://doi.org/10.1080/0020739X.2015.1021394
• Kar, T., Özdemir, E., Öçal, M. F., Güler, G., and İpek, A. S. (2019). Indicators of prospective mathematics teachers’ success in problem solving: the case of creativity in problem posing. In M. Graven, H. Venkat, A. Essien, and P. Vale (Eds.), Proceedings of the 43rd Conference of the International Group for the Psychology of Mathematics Education (Cilt. 2, s. 456–463). Pretoria, South Africa: PU.
• Kattou, M., Kontoyianni, K., Pitta-Pantazi, D. ve Christou, C. (2011). On the comparison between mathematically gifted and non-gifted students’ creative ability. Paper presented at the 19th Biennial World Conference of the WCGTC. Prague, Czech Republic.
• Keşan, C., Kaya, D. ve Güvercin, S. (2010). “The effect of problem posing approach to the gifted student’s mathematical abilities”. International Online Journal of Educational Science, 2(3), 677-787. http://hdl.handle.net/20.500.11787/6854
• Kilpatrick, J. (1987). Problem formulating: Where do good problems come from?. In A. H. Schoenfeld (Ed.), Cognitive science and mathematics education (s. 123-147). NJ: Erlbaum. https://doi.org/10.4324/9780203062685
• Kopparla, M., Bicer, A., Vela, K., Lee, Y., Bevan, D., Kwon, H., ... ve Capraro, R. M. (2019). The effects of problem-posing intervention types on elementary students’ problem-solving. Educational Studies, 45(6), 708–725. https://doi.org/10.1080/03055698.2018.1509785
• Kozaklı-Ülger, T., Bozkurt, I., ve Altun, M. (2022). Analyzing In-Service Teachers' Process of Mathematical Literacy Problem Posing. International Electronic Journal of Mathematics Education, 17(3). https://doi.org/10.29333/iejme/11985
• Kwek, M. L. (2015). Using problem posing as a formative assessment tool. In F. M. Singer, N. F. Ellerton, and J. Cai (Eds.), Mathematical problem posing. From research to effective practice (s. 273-292). Springer. https://doi.org/10.1007/978-1-4614-6258-3_13
• Lee, Y., Capraro, R. M., ve Capraro, M. M. (2018). Mathematics teachers’ subject matter knowledge and pedagogical content knowledge in problem posing. International Electronic Journal of Mathematics Education, 13(2), 75-90. https://doi.org/10.12973/iejme/2698
• Lee, F. L., ve Heyworth, R. (2000). Problem complexity: A measure of problem difficulty in algebra by using computer. Education Journal, 28(1), 85-108.
• Leung, S. S., ve 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. https://doi.org/10.1007/BF03217299
• Marshall, S. P. (1995). Schemas in problem solving. NY: Cambridge University Press. https://doi.org/10.1017/CBO9780511527890
• Miles, M. B., ve Huberman, A. M. (1994). Qualitative data analysis. Sage Publications.
• Miller, R.C., (1990). Discovering mathematical talent. (ERIC Digest No. E482) ERIC Clearinghouse on Disabilities and Gifted Education.
• Milli Eğitim Bakanlığı [MEB], (2018). İlkokul ve Ortaokul 1,2,3,4,5,6,7 ve 8. Sınıflar Öğretim Programı. Ankara: Milli Eğitim Bakanlığı Yayınları.
• National Council of Teachers of Mathematics [NCTM] (2000). Principles and standards for school mathematics. VA: NCTM.
• Öçal, M. F., İpek, A. S., Özdemir, E., ve Kar, T. (2018). Investigation of elementary school students’ problem posing abilities for arithmetic expressions in the context of order of operations. Turkish Journal of Computer and Mathematics Education (TURCOMAT), 9(2), 170-191. https://doi.org/10.17762/turcomat.v9i2.174
• Özdişçi, S., ve Katrancı, Y. (2020). Ortaokul öğrencilerinin problem çözme ve problem oluşturma becerilerinin incelenmesi. Milli Eğitim Dergisi, 49(226), 149-184. https://dergipark.org.tr/tr/pub/milliegitim/issue/54184/732868
• Özgen, K., Aydın, M., Geçici, M. E., ve Bayram, B. (2017). Sekizinci sınıf öğrencilerinin problem kurma becerilerinin bazı değişkenler açısından incelenmesi. Türk Bilgisayar ve Matematik Eğitimi Dergisi, 8(2), 218-243. https://doi.org/10.16949/turkbilmat.322660
• Palm, T. (2006). Word problems as simulations of real-world situations: A proposed framework. For the learning of mathematics, 26(1), 42-47. https://www.jstor.org/stable/40248523
• Palm, T. (2008). Impact of authenticity on sense making in word problem solving. Educational studies in Mathematics, 67, 37-58. https://doi.org/10.1007/s10649-007-9083-3
• Passarella, S. (2022). Real Contexts in Problem-Posing: An Exploratory Study of Students’ Creativity. International Journal of Innovation in Science and Mathematics Education, 30(1). https://doi.org/10.30722/IJISME.30.01.002
• Pelczer, I. ve F. G. Rodriguez, (2010). “Creativity assessment in school settings through problem posing tasks”. The Mathematics Enthusiast. 8(1-2), 383-398. https://doi.org/10.54870/1551-3440.1221 Renzulli, J. S. (1978). What makes giftedness? Reexamining a definition. Phi Delta Kappan, 60(3), 180. http://www.jstor.org/stable/20299281
• Rosli, R., Goldsby, D., ve Capraro, M. M. (2013). Assessing students’ mathematical problem-solving and problem-posing skills. Asian Social Science, 9(16), 54–60. http://dx.doi.org/10.5539/ass.v9n16p54
• Silver, E. A. (1994). On mathematical problem posing. For the Learning of Mathematics, 14(1), 19–28. https://www.jstor.org/stable/40248099
• Silver, E. A., ve Cai, J. (1996). An analysis of arithmetic problem posing by middle school students. Journal for Research in Mathematics Education, 27(5), 521-539. https://doi.org/10.5951/jresematheduc.27.5.0521
• Silver, E. A., ve Cai, J. (2005). Assessing students’ mathematical problem posing. Teaching Children Mathematics, 12(3), 129-135. https://doi.org/10.5951/TCM.12.3.0129
• Singer, F. M., ve Voica, C. (2013). A problem-solving conceptual framework and its implications in designing problem-posing tasks. Educational Studies in Mathematics, 83(1), 9–26. https://doi.org/10.1007/s10649-012-9422-x
• Stake, R. E. (1995). The art of case study research. Sage Publications.
• Stoyanova, E., ve Ellerton, N. F. (1996). A framework for research into students’ problem posing in school mathematics. In P. Clarkson (Ed.), Technology in mathematics education (s. 518-525). Mathematics Education Research Group of Australasia: The University of Melbourne.
• Terzi, A. (2021). Aktif öğrenme çerçevesine dayalı öğretimin 6. Sınıf öğrencilerinin problem çözme ve kurma performanslarının gelişimine etkisi. [Yüksek lisans tezi]. Recep Tayyip Erdoğan Üniversitesi, Fen Bilimleri Enstitüsü, Rize.
• Terzi, A., ve Kar, T. (2022). Development of Turkish sixth-grade students’ problem-posing and-solving skills: an application of the extended active learning framework. Education 3-13, 1-19. https://doi.org/10.1080/03004279.2022.2090592
• Turhan Türkkan, B. (2018). Examination of middle school sixth grade students’ problem posing skills about fraction operations, Inonu University Journal of the Faculty of Education, 19(3), 374-390. https://doi.org/10.17679/inuefd.358159
• Van Harpen, X. Y., ve Sriraman, B. (2013). Creativity and mathematical problem posing: an analysis of high school students’ mathematical problem posing in China and the USA. Educational Studies in Mathematics, 82(2), 201–221. https://doi.org/10.1007/s10649-012-9419-5
• Van Harpen, X. Y., ve Presmeg, N. C. (2013). An investigation of relationships between students’ mathematical problem-posing abilities and their mathematical content knowledge. Educational Studies in Mathematics, 83(1), 117–132. https://doi.org/10.1007/s10649-012-9456-0
• Xie, J., ve Masingila, J. O. (2017). Examining interactions between problem posing and problem solving with prospective primary teachers. A case of using fractions. Educational Studies in Mathematics, 96(1), 101–118. https://doi.org/10.1007/s10649-017-9760-9
• Xu, B., Cai, J., Liu, Q., ve Hwang, S. (2020). Teachers’ predictions of students’ mathematical thinking related to problem posing. International Journal of Educational Research, 102, 101427. https://doi.org/10.1016/j.ijer.2019.04.005
• Yeap, B. H., ve Kaur, B. (2000). Exploring the relationship between mathematical problem posing and problem solving, type of task and grade level. In J. Ee, B. Kaur, N. H. Lee, and B. H. Yeap (Eds.), New ‘Literacies’: Educational response to a knowledge-based society: Proceedings of the ERA-AME-AMIC Joint Conference (s. 605–611). Educational Research Association.
• Yeap, B. H., ve Kaur, B. (2001). Semantic characteristics that make arithmetic word problems difficult. In J. Bobis, B. Perry, and M. Mitchelmore (Eds.), Numeracy and beyond: Proceedings of the 24th Annual Conference of the Mathematics Education Research Group of Australasia Incorporated (s. 555–562). Merga. http://hdl.handle.net/10497/14364
• Yıldırım, A., ve Şimşek, H. (2016). Sosyal bilimlerde nitel araştırma yöntemleri. Seçkin Yayıncılık.