An Analysis of the Qualities of the Problems Posed by the Students in a Seventh Grade Mathematics Course Assisted by the Problem Posing Approach

Yıl 2021, Cilt: 8 Sayı: 2, 13 - 30, 30.06.2021

Katibe Gizem Yığ , Zeynep Ay

https://doi.org/10.33200/ijcer.795390

Cited By: 1

Öz

In this study, it is primarily aimed to determine the qualities of the problems posed by the students in a mathematics class delivered through the problem-posing approach and to examine the mean scores of the students obtained from these qualifications. The linear equations topic at the seventh grade was taught using the problem-posing approach. The study was designed as a case study and involved twenty students as participants. The data were collected using thirteen problem-posing tasks. At the first step of the study, a problem-posing evaluation rubric was developed. The rubric involved the following criteria: clarity, mathematical accuracy, contextual originality, originality in terms of mathematical relations, complexity level and pertinence to situation qualifications. Then, this rubric was used to identify the qualities of these problems. It was also employed to determine whether or not the mean scores of the participants significantly differed based on the objectives stated. The findings of the study suggest that in parallel to the participants’ improvement on the objectives, their mean scores on contextual originality, originality in terms of mathematical relations, and complexity also improved. It is concluded that the integrity of the problem-posing approach into the educational program will improve the qualities of the problems developed by the participants.

Anahtar Kelimeler

problem posing, linear equations, Problem posing evaluation rubric, qualities of the problems

Kaynakça

• Andrade, H. G. (2000). Using rubrics to promote thinking and learning. Educational Leadership, 57(5), 13-19.
• Karaaslan, K. G. (2018). Problem kurma yaklaşımıyla desteklenen bir matematik sınıfında öğrencilerin cebir öğrenmelerinin ve problem kurma becerilerinin incelenmesi. [Investigation of students' algebra learning and problem posing skills in a mathematics classroom supported by problem posing approach] (Unpublished doctoral dissertation). Hacettepe Üniversitesi, Eğitim Bilimleri Enstitüsü, Ankara.
• Birgin, O., Kutluca, T., & Gürbüz, R. (2008). The effects of computer assisted instruction on the students’ achievement in mathematics at seventh grade. 8th International Educational Technology Conference Proceeding (879-882). Ankara: Nobel Yayın Dağıtım.
• Bonotto, C. (2013). Artifacts as sources for problem-posing activities. Educational Studies in Mathematics, 83(1), 37-55.
• Bonotto, C., & Dal Santo, L. (2015). On the relationship between problem posing, problem solving, and creativity in the primary school. In F. M. Singer, N. F. Ellerton, J.F. Cai (Eds.), Mathematical Problem Posing (103-123). Springer, New York, NY.
• Cai, J., & Hwang, S. (2019). Learning to teach through mathematical problem posing: Theoretical considerations, methodology, and directions for future research. International Journal of Educational Research. Online first doi:10.1016/j.ijer.2019.01.001
• Cai, J., Hwang, S., Jiang, C., & Silber, S. (2015). Problem-posing research in mathematics education: Some answered and unanswered questions. In F. M. Singer, N. F. Ellerton, J.F. Cai (Eds.), Mathematical Problem Posing (3-34). Springer, New York.
• Cai, J., Moyer, J. C., Wang, N., Hwang, S., Nie, B., & Garber, T. (2013). Mathematical problem posing as a measure of curricular effect on students' learning. Educational Studies in Mathematics, 83(1), 57-69.
• Canköy, O. (2014). Interlocked problem posing and children’s problem posing performance in free structured situations. International Journal of Science and Mathematics Education, 12(1), 219-238.
• Canadas, M. C., Molina, M., & Rio, A. (2018). Meanings given to algebraic symbolism in problem-posing. Educational Studies in Mathematics, 98(1), 19-37.
• Çelik, D. & Güneş, G. (2013). Farklı sınıf düzeyindeki öğrencilerin harfli sembolleri kullanma ve yorumlama seviyeleri [Different grade students’ use and interpretation of literal symbols]. Kuram ve Uygulamada Eğitim Bilimleri, 13(2), 1157-1175.
• Çetinkaya, A. (2017). İlköğretim 8. sınıf öğrencilerinin problem kurma becerilerinin incelenmesi [An investigatıon of problem posing skills of elemantary school 8th grade students] (Yayınlanmamış yüksek lisans tezi). Erciyes Üniversitesi, Eğitim Bilimleri Enstitüsü, Kayseri.
• De Bock, D., Van Dooren, W., Janssens, D., & Verschaffel, L. (2002). Improper use of linear reasoning: An in-depth study of the nature and the irresistibility of secondary school students' errors. Educational Studies in Mathematics, 50(3), 311-334.
• Erbaş, A. K., Çetinkaya, B. & Ersoy, Y. (2009). Öğrencilerin basit doğrusal denklemlerin çözümünde karşılaştıkları güçlükler ve kavram yanılgıları [Student difficulties and misconceptions in solving simple linear equations]. Education and Science, 34(152), 44-59.
• Hadjidemetriou, C., & Williams, J. (2002). Children's graphical conceptions. Research in Mathematics Education, 4(1), 69-87.
• Hattikudur, S., Prather, R. W., Asquith, P., Alibali, M. W., Knuth, E. J., & Nathan, M. (2012). Constructing graphical representations: Middle schoolers' intuitions and developing knowledge about slope and y‐intercept. School Science and Mathematics, 112(4), 230-240.
• Işık, C. & Kar, T. (2012). 7. sınıf öğrencilerinin kesirlerde toplama işlemine kurdukları problemlerin analizi [Analyzing Problems Posed by 7th Grade Students for Addition Operation with Fractions]. İlköğretim Online, 11(4), 1021-1035.
• Kaba, Y., & Şengül, S. (2016). Developing the Rubric for Evaluating Problem Posing (REPP). International Online Journal of Educational Sciences, 8(1).
• Klaassen, K., & Doorman, M. (2015). Problem posing as providing students with content-specific motives. In F. M. Singer, N. F. Ellerton, J.F. Cai (Eds.), Mathematical Problem Posing (215-240). Springer, New York, NY.
• Korkmaz, E., & Gür, H. (2006). Determining of prospective teachers’ problem posing skills. Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 8(1), 64- 74.
• Kwek, M. L. (2015). Using problem posing as a formative assessment tool. In F. M. Singer, N. F. Ellerton, J.F. Cai (Eds.), Mathematical Problem Posing (273-292). Springer, New York, NY.
• Kwek, M. L., & Lye, W. L. (2008). Using problem-posing as an assessment tool. Proceedings of the 10th Asia-Pacific Conference on Giftedness. Singapore. Retrieved on June 1, 2016 from http://hkage.org.hk/en/events/080714_10th_APCG.htm
• Leinhardt, G., Zaslavsky, O., & Stein, M. K. (1990). Functions, graphs, and graphing: Tasks, learning, and teaching. Review of Educational Research, 60(1), 1-64.
• Leung, S. S. (1993). Mathematical problem posing: The influence of task formats, mathematics knowledge, and creative thinking. In Proceedings of the 17th PME Conference (Vol. 3, pp. 33-40).
• McDonald, P. A., & Smith, J. M. (2020). Improving mathematical learning in Scotland's Curriculum for Excellence through problem posing: an integrative review. The Curriculum Journal, 31(3), 398-435.
• Mielicki, M. K., & Wiley, J. (2016). Alternative representations in algebraic problem solving: When are graphs better than equations? The Journal of Problem Solving, 9(1), 1.
• Miles, M. B., & Huberman, A. M. (2015). Analizde ilk adımlar. (A. Ersoy, Çev.), Nitel veri analizi içinde (50-89) [Qualitative data analysis] S. Akbaba Altun ve A. Ersoy (Çev. Ed.). Ankara: Yayın Akademi.
• MoNE (2013). İlköğretim matematik dersi 5-8. sınıflar öğretim programı [Primary schools mathematics education programs for grades 5-8]. T.C. Milli Eğitim Bakanlığı Talim ve Terbiye Kurulu Başkanlığı, Ankara.
• Nirawati, R., Fatimah, S., & Irma, A. (2020). Analysis of multi-representation ability to solve algebra problem. Journal of Physics: Conference Series 1657 (2020) 012075. IOP Publishing. https://iopscience.iop.org/article/10.1088/1742-6596/1657/1/012075.
• Özgen, K., Aydın, M., Geçici, M. E., & Bayram, B. (2017). Sekizinci sınıf öğrencilerinin problem kurma becerilerinin bazı değişkenler açısından incelenmesi [Investigation of problem posing skills of eighth grade students in terms of some variables]. Turkish Journal of Computer and Mathematics Education (TURCOMAT), 8(2), 323-351.
• Sezgin Memnun, D. (2011). İlköğretim altıncı sınıf öğrencilerinin analitik geometrinin koordinat sistemi ve doğru denklemi kavramlarını oluşturması süreçlerinin araştırılmas [The investigation of sixth grade students? construction of coordinate system and linear equation concepts of the analytical geometry using constructivism and realistic mathematics education].(Unpublished doctoral dissertation). Uludağ Üniversitesi, Eğitim Bilimleri Enstitüsü, Bursa.
• Silver, E. A. & Cai, J. (1996). Analysis of aritmetic problem posing by middle school. Journal for Research in Mathematics Education, 27, 521.
• Silver, E., & Cai, J. (2005). Assessing students' mathematical problem Posing. Teaching Children Mathematics, 12(3), 129-135.
• Silver, E.A. (1993). On mathematical problem posing. In Proceedings of the 17. International Conference of Mathematics Education (Vol. I, pp. 66-85).
• Singer, F. M., Ellerton, N., & Cai, J. (2013). Problem-posing research in mathematics education: New questions and directions. Educational Studies in Mathematics, 83(1), 1-7.
• Stoyanova, E. (2003). Extending students' understanding of mathematics via problem posing. Australian Mathematics Teacher, 59(2), 32-40.
• Stoyanova, E., & Ellerton, N. F. (1996). A framework for research into students’ problem posing in school mathematics. Technology in Mathematics Education, 518-525.
• Toluk-Uçar, Z. (2009). Developing pre-service teachers understanding of fractions through problem posing. Teaching and Teacher Education, 25, 166–175.
• Turanlı, N., Keçeli, V., & Türker, N. K. (2007). Ortaöğretim ikinci sınıf öğrencilerinin karmaşık sayılara yönelik tutumları ile karmaşık sayılar konusundaki kavram yanılgıları ve ortak hataları [The secondary school second grade students’ attitudes towards complex numbers their misconceptions abaut and common errors in complex numbers]. Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 9(2), 135-149.
• Vacc, N. N. (1993). Implementing the professional standards for teaching mathematics: Questioning in the mathematics classroom. Arithmetic Teacher, 41(2), 88-92.
• Wilkie, K. J. (2016). Students’ use of variables and multiple representations in generalizing functional relationships prior to secondary school. Educational Studies in Mathematics, 93(3), 333-361.
• Yenilmez, K. & Yaşa, E. (2008). İlköğretim öğrencilerinin geometrideki kavram yanılgıları [Primary school students’ misconceptions about geometry]. Uludağ Üniversitesi Eğitim Fakültesi Dergisi, 21(2), 461-483.