PROBLEM SOLVING INSTRUCTION: PROSPECTIVE MATHEMATICS TEACHERS’ OPINIONS AND PROBLEM SOLVING PROCESSES

The main purpose of this research is to examine the problem solving processes of prospective elementary mathematics teachers and to identify how the problem solving instruction affects prospective teachers’ problem solving processes. It is also aimed to investigate the prospective teachers’ opinions about problem solving process and problem solving instruction. This qualitative study was conducted with the participation of 36 prospective elementary mathematics teachers enrolled in an elective course entitled as Problem solving in 2016-2017 academic year. At the beginning and at the end of the semester, prospective mathematics teachers were asked to pose and solve a problem. At the end of the problem solving course, interviews were conducted with seven prospective mathematics teachers. Descriptive analysis method was used for data analysis. The results of the research showed that before the problem solving course, prospective mathematics teachers did not follow problem solving steps and solved the problems they wrote by using equations. After the problem solving course, they have begun to apply the problem solving steps and strategies explained to them during the lessons. It was also determined that prospective teachers had positive opinions about problem solving instruction. Similarly, prospective mathematics teachers stated that problem solving course has enabled a lot of experience and valuable knowledge which would be useful to them in profession of teaching and increased their success and self-confidence.

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Altun, M. (1995). İlkokul 3, 4 ve 5. sınıf öğrencilerinin problem çözme davranışları üzerine bir çalışma. Yayınlanmamış Doktora Tezi, Hacettepe Üniversitesi, Ankara.

Altun, M. ve Arslan, Ç. (2006). “İlköğretim öğrencilerinin problem çözme stratejilerini öğrenmeleri üzerine bir çalışma.” Uludağ Üniversitesi Eğitim Fakültesi Dergisi, XIX(1): 1–21.

Arslan, Ç. (2002). İlkoğretim yedinci ve sekizinci sınıf öğrencilerinin problem çözme stratejilerini kullanabilme düzeyleri üzerine bir çalışma. Yayınlanmamış Yüksek Lisans Tezi, Uludağ Üniversitesi, Bursa.

Arslan, Ç. & Altun, M. (2007). “Learning to solve non-routine mathematical problems.” Elementary Education Online, 6(1): 50–61.

Ay, Z.S. & Bulut, S. (2014). "Experimental study on mathematical problem solving approach with pre-service elementary teachers." Pamukkale Üniversitesi Eğitim Fakültesi Dergisi, 36: 45–57.

Aydoğdu, M. ve Ayaz, M. F. (2008). "Matematikte öğrencilere problem çözme yeteneğinin kazandırılması." E- Journal of New World Sciences Academy, 3(4): 588–596.

Ball, D. L., Thames, M. H., & Phelps, G. C. (2008). “Content knowledge for teaching: What makes it special?” Journal of Teacher Education, 59(5): 389–407.

Baykul, Y. (2014). Ortaokulda matematik öğretimi (5-. Sınıflar). Ankara: Pegem Akademi.

Bayrakdar, Z., Deniz, D., Akgün, L., & İşleyen, T. (2011). “Problem solving approaches of mathematics teacher candidates in PISA 2003.” Procedia Social and Behavioral Sciences, 15: 3334–3337.

Briggs, C. (1986). Learning how to ask: A sociolinguistic appraisal of the role of the interview in social science research. Cambridge University Press.

Cai, J. (2003). “Singaporean students’ mathematical thinking in problem solving and problem posing: An exploratory study.” International Journal of Mathematical Education in Science and Technology, 34(5): 719–737.

Cankoy, O. ve Darbaz, S. (2010). "Problem kurma temelli problem çözme öğretiminin problemi anlama başarısına etkisi." Hacettepe Üniversitesi Eğitim Fakültesi Dergisi, 38: 11–24.

Çalışkan, S. (2007). Problem çözme stratejileri öğretiminin fizik başarısı, tutumu, özyeterliği üzerindeki etkileri ve strateji kullanımı. Yayınlanmamış Doktora Tezi, Dokuz Eylül Üniversitesi, İzmir.

Chapman, O. (2012). “Prospective elementary school teachers’ ways of making sense of mathematical problem posing.” PNA, 6 (4): 135–146.

Charles R. & Lester, F. (1982). Teaching problem solving: What, why and how. Palo Alto, CA: Dale Seymour Publications.

Charles, R. I., & Lester, F. K. (1984). “An evaluation of a process-oriented instructional program in mathematical problem solving in grades 5 and 7.” Journal for Research in Mathematics Education, 15(1): 15–34.

Crespo, S. (2003). “Learning to pose mathematical problems: Exploring changes in teachers’ practices.” Educational Studies in Mathematics, 52: 243–270.

Çömlekoğlu, G. (2001). Öğretmen adaylarının problem çözme becerilerine hesap makinesinin etkisi. Yayınlanmamış Yüksek Lisans Tezi, Balıkesir üniversitesi, Balıkesir.

Dede, Y. (2004). "Öğrencilerin cebirsel sözel problemleri denklem olarak yazarken kullandıkları çözüm stratejilerinin belirlenmesi." Educational Science and Practice, 4(6): 175–192.

Dede, Y. ve Yaman, S. (2005). "Matematik öğretmen adaylarının matematiksel problem kurma ve problem çözme becerilerinin belirlenmesi." Eğitim Araştırmaları, 5: 41–56.

Demircioğlu, H., Argün, Z., & Bulut, S. (2010). "A case study: Assessment of preservice secondary mathematics teachers’ metacognitive behaviour in the problem-solving process." ZDM Mathematics Education, 42: 493–502.

Dooren, W. V., Verschaffel, L., & Onghena, P. (2003). “Pre-service teachers’ preferred strategies for solving arithmetic and algebra word problems.” Journal of Mathematics Teacher Education, 6: 27–52.

English, L. D. (2003). Problem posing in elementary curriculum. In F. Lester, & R. Charles (Eds.), Teaching mathematics through problem solving. Reston, Virginia: National Council of Teachers of Mathematics.

Franke, M. L., & Kazemi, E. (2001). “Learning to teach mathematics: Focus on student thinking.” Theory into Practice, 40(2): 102–109.

Gagne, R. M. (1980). The conditions of learning. New York: Holt, Rinehart, & Winston.

Gonzales, N. A. (1998). “A Blueprint for Problem Posing.” School Science & Mathematics, 9(8): 448–456.

Harskamp E., & Suhre C. (2007). "Schoenfeld’s problem solving theory in a student controlled learning environment." Computers & Education, 49: 822–839.

Herr, T., & Johnson K. (1994). Problem solving strategies: Crossing the river with dogs. USA: Key Curriculum Press.

Higgins, K. M. (1997). "The effect of long instruction in mathematical problem solving on middle school students’ attitudes, beliefs and abilities." Journal of Experimental Education, 66(1): 5–24.

Işık, C. ve Kar, T. (2012). "Sınıf öğretmeni adaylarının problem kurma becerileri." Mehmet Akif Ersoy Üniversitesi Eğitim Fakültesi Dergisi, 12(23): 190–214.

Jitendra, A. K., Griffin, C. C., Buchman, A. D., & Sczesniak, E. (2007). “Mathematical problem solving in third- grade classrooms.” The Journal of Educational Research, 100(5): 282–302.

Jonassen, D. H. (2000). “Toward a design theory of problem solving.” Educational Technology Research and Development, 48(4): 63–85.

Kayaaslan, A. (2006). İlköğretim 4. ve 5. sınıf öğrencilerinin matematiğin doğası ve matematik öğretimi hakkındaki inançları. Yayınlanmamış Yüksek Lisans Tezi, Gazi Üniversitesi, Ankara.

Kayan, F. ve Çakıroğlu, E. (2008). “İlköğretim matematik öğretmen adaylarının problem çözmeye yönelik inançları.” Hacettepe Üniversitesi Eğitim Fakültesi Dergisi, 35: 218–226.

Kılıç, Ç. (2013). "Sınıf öğretmeni adaylarının farklı problem kurma durumlarında sergilemiş oldukları performansın belirlenmesi." Kuram ve Uygulamada Eğitim Bilimleri, 13(2): 1195–1211.

Kılıç, Ç. (2014). "Sınıf öğretmenlerinin problem kurmayı algılayış biçimlerinin belirlenmesi." Kastamonu Eğitim Dergisi, 22(1): 203–214.

Kilpatrick, J. (1987). Problem formulating: Where do good problems come from? In Schoenfeld, A. H. (Ed.). Cognitive Science and Mathematics Education (pp. 123–147). NJ, Lawrence Erlbaum.

Korkmaz, E. ve Gür, H. (2006). “Öğretmen adaylarının problem kurma becerilerinin belirlenmesi.” Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 8 (1): 64–74.

Labuda, C. B. (2004). The impact of a professional development program on the implementation of problem- solving strategies in the classroom. Yayınlanmamış Doktora Tezi, University of Houston, Houston, USA.

Lee, S. K. (1982). “Fourth graders’ heuristic problem-solving behavior.” Journal for Research in Mathematics Education, 13(2): 110–123.

Leikin, R. (2007). Habits of mind associated with advanced mathematical thinking and solution spaces of mathematical tasks. Proceedings of the Fifth Conference of the European Society for Research in Mathematics Education. University of Cyprus, Larnaca, Cyprus.

Lester, F. K. (1994). "Musings about mathematical problem solving research: 1970-1994." Journal for Research in Mathematics Education, 25(6): 660–675.

Lin, P. J. (2004). Supporting teachers on designing problem-posing tasks as a tool of assessment to understand students’ mathematical learning. In M. J. Hoines & A. B. Fuglestad (Eds.), Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education, Vol. 3 (pp. 257– 264). July 14-18. Bergen University College.

MEB (2016a). PISA 2015 Ulusal Raporu. Ankara: Milli Eğitim Bakanlığı Ölçme, Değerlendirme ve Sınav Hizmetleri Genel Müdürlüğü.

MEB (2016b). TIMSS 2015 Ulusal Matematik ve Fen Ön Raporu. Ankara: Milli Eğitim Bakanlığı Ölçme, Değerlendirme ve Sınav Hizmetleri Genel Müdürlüğü.

NCTM (2000). Principles and standards for school mathematics, Reston, VA: National Council of Teachers of Mathematics Pub.

Miles, M. B. & Huberman, A. M. (1994). Qualitative data analysis. Thousand Oaks, CA: Sage Publication.

Patton, M. Q. (1987). How to use qualitative methods in evaluation. Newbury Park, CA: Sage.

Phye, G. D. (2001). “Problem-solving instruction and problem-solving transfer: The correspondence issue.” Journal of Educational Psychology, 93(3): 571-578.

Polya, G. (1973). How to solve it: A new aspect of mathematical method. Princeton, NJ: Princeton University Press.

Posamentier, A. S., & Krulik, S. (1998). Problem-solving strategies for efficient and elegant solutions. California: Corwin Press.

Posluoğlu, Z. Y. (2002). İlkoğretim matematik dersinde problem çözme becerisinin kazandırılmasında işbirliğine dayalı öğrenme yaklaşımının etkililiği. Yayınlanmamış Yüksek Lisans Tezi, Gazi Üniversitesi, Ankara.

Reys, R., Suydam, M., Lindquist, M., & Smith, N. (1998). Helping children learn mathematics (5th ed). Boston: Allyn and Bacon.

Rizvi, N. F. (2004). “Prospective teachers’ ability to pose word problems.” International Journal for Mathematics Teaching and Learning, 12: 1-22.

Schoenfeld, A. H. (1979). “Explicit heuristic training as a variable in problem-solving performance.” Journal for Research in Mathematics Education, 10(3): 173-187.

Schoenfeld, A. (1985). Mathematical problem solving. New York: Academic Press.

Schoenfeld, A.H. (1992). Learning to think mathematically: Problem solving, metacognition, and sense making in mathematics. In D.A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 334-368). New York, NY: Macmillan.

Silver, E. A. (1994). “On mathematical problem solving.” For the Learning of Mathematics. 14(1): 19-28.

Soylu, Y. ve Soylu, C. (2006). “Matematik derslerinde başarıya giden yolda problem çözmenin rolü.” İnönü Üniversitesi Eğitim Fakültesi Dergisi, 7(11): 97-111.

Stoyanova, E. (1998). Problem posing in mathematics classrooms, In A. McIntosh & N. Ellerton (Eds), Research in Mathematics Education: A contemporary perspective (pp. 164-185). Edith Cowan University: MASTEC.

Tertemiz, N. ve Sulak, S. E. (2013). "İlköğretim beşinci sınıf öğrencilerinin problem kurma becerilerinin incelenmesi." İlköğretim Online, 12(3): 713-729.

Thompson, A. G. (1989). Learning to teach mathematical problem solving: Changes in teacher's conceptions and beliefs. In R. I. Charles & E. A. Silver (Eds.), Research Agenda for Mathematics Education Vol 3 (pp. 232-243). The Teaching and Assessing of Mathematical Problem Solving. Reston, VA: Lawrence Erlbaum & National Council of Teachers of Mathematics.

Toluk-Uçar, Z. (2009). “Developing pre-service teachers understanding of fractions through problem posing.” Teaching and Teacher Education, 25: 166-175.

Toptaş, V. ve Gözel, E. (2017). “ Sınıf öğretmeni adaylarının özyeterlik İle matematiksel problem çözmeye yönelik inançları.”, Kırıkkale Üniversitesi Sosyal Bilimler Dergisi, 7(2): 439-460.

TTKB (2009). İlköğretim matematik dersi 1.-5. sınıflar öğretim programı. Ankara: Milli Eğitim Bakanlığı.

TTKB (2013). Ortaokul matematik dersi (5, 6, 7 ve 8. Sınıflar) öğretim programı. Ankara: Milli Eğitim Bakanlığı.

Turhan, B. ve Güven, M. (2014). “Problem kurma yaklaşımıyla gerçekleştirilen matematik öğretiminin problem çözme başarısı, problem kurma becerisi ve matematiğe yönelik görüşlere etkisi.” Çukurova Üniversitesi Eğitim Fakültesi Dergisi, 43(2): 217-234.

Xin, P. Y. (2007). “Word problem solving tasks in textbooks and their relation to student performance.” The Journal of Educational Research, 100(6): 347-359.

Yazgan, Y. (2007). "Dördüncü ve beşinci sınıf öğrencilerinin rutin olmayan problem çözme stratejileriyle İlgili gözlemler." İlköğretim Online, 6(2): 249-263.

Yıldırım, A. ve Şimşek, H. (2006). Sosyal bilimlerde nitel araştırma yöntemleri. (6. Baskı) Ankara: Seçkin Yayıncılık.

Yıldız, V. (2008). Investigation of the change in sixth grade students’ problem solving abilities, attitude towards problem solving and attitude toward mathematics after mathematics instruction based on Polya’s problem solving steps. Yayınlanmamış Yüksek Lisans Tezi, Orta Doğu Teknik Üniversitesi, Ankara.