Sınıf Öğretmenlerinin Matematiksel Problem Çözme Hakkındaki İnançları

Year 2020, , 35 - 46, 30.10.2020

Emel Topbaş Tat

https://doi.org/10.32433/eje.797714

Abstract

Bu çalışmanın amacı, öğretmenlerin matematiksel problem çözme konusundaki inançlarını incelemektir. Bu araştırmada nitel araştırma yöntemlerinden fenomenoloji kullanılmıştır. Araştırma on sınıf öğretmeni ile gerçekleştirilmiştir. Veriler görüşmeler aracılığıyla toplanmış ve içerik analizi kullanılarak analiz edilmiştir. Matematiksel problem çözmenin doğası, matematiksel problem çözmenin önemi, sınıf ortamında problem çözme süreci, problem çözme becerisi, çözüm yolunu öğretme, bir problemin farklı çözüm yolları, anlamanın önemi ve problem kurmanın önemi araştırmanın sekiz temasıdır.

Keywords

Problem çözme, inanç, sınıf öğretmeni

Elementary Teachers’ Beliefs about Mathematical Problem Solving

Abstract

The purpose of this study is to investigate teachers’ beliefs about mathematical problem solving. In this study, phenomenology was used to gain an insight about the elementary classroom teachers’ beliefs about mathematical problem solving. To collect data, interviews were conducted with ten elementary teachers. The data were analyzed through content analysis. According to analysis, the nature of mathematical problem solving, the importance of mathematical problem solving, problem solving process in classroom environment, problem solving ability, teaching the correct procedure to solve problems, several ways of solving a problem, the importance of understanding, and the importance of problem posing are eight themes of the study. 

Keywords

Problem solving, beliefs, elementary teachers

References

• Andrews, P., & Xenofontos, C. (2015). Analysing the relationship between the problem-solving-related beliefs, competence and teaching of three Cypriot primary teachers. Journal of Mathematics Teacher Education, 18, 299–325.
• Bogdan, R. C., & Biklen, S. K. (1998). Qualitative research for education: An introduction to theory and methods. Boston: Allyn and Bacon.
• Borko, H., & Shavelson, R. J. (1990). Teacher decision making. In B. F. Jones & L. Idol (Eds.), Dimensions of thinking and cognitive instruction (pp. 311–346). Hillsdale, NJ: Lawrence Erlbaum Associates, Inc.
• Brown, N.M. (2003). A Study of elementary teachers’ abilities, attitudes, and beliefs about problem solving. Dissertation Abstracts International, 64(10), 3620.
• Callejo, M. L., & Vila, A. (2009). Approach to mathematical problem-solving and students’ belief systems: Two case studies. Educational Studies in Mathematics, 72, 111–126.
• Carpenter, T. P., & Fennema, E. (1991). Research and cognitively guided instruction. In E. Fennema, T. P. Carpenter, & S. J. Lamon (Eds.), Integrating research on teaching and learning mathematics (pp. 1–16). Albany, NY: State University of New York Press.
• Chapman, O. (1997). Metaphors in the teaching of mathematical problem solving. Educational Studies in Mathematics, 32, 201–228.
• Charles, R., & Lester, F. (1982). Teaching problem solving: What, why and how. Palo Alto, CA: Dale Seymour Publications.
• Chen, L., Dooren, W. V., & Verschaffel, L. (2011). An investigation on Chinese teachers’ realistic problem solving abilities and beliefs. Journal of Mathematics Education, 4(2), 80–96.
• De Corte, E. (2003).Transfer as the productive use of acquired knowledge, skills, and motivations. Current Directions in Psychological Science, 12(4), 142–146.
• Deringöl, Y. (2018). Sınıf öğretmeni adaylarının matematik problemi çözmeye yönelik inançları ile problem kurma özyeterlik inançlarının incelenmesi [Examination of problem solving beliefs and problem posing self-efficacy beliefs of prospective classroom teachers]. Türk Bilgisayar ve Matematik Eğitimi Dergisi, 9(1), 31–53.
• Dossey, J. A., Mullis, I. V. S., Lindquist, M. M., & Chambers, D. L. (1988). The Mathematics report card: Are we measuring up? Trends and achievement based on the 1986 national assessment. Princeton, N.J.: Educational Testing Service.
• Emenaker, C. (1996). A problem-solving based mathematics course and elementary teachers’ beliefs. School Science and Mathematics, 96(2), 75–84.
• 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.
• Ford, M. I. (1994). Teachers’ beliefs about mathematical problem solving in the elementary school. School Science and Mathematics, 94(6), 314–322.
• Giovanni, P., & Sangcap, A. (2010). Mathematics-related beliefs of Filipino college students: Factors affecting mathematics and problem solving performance. Procedia Social and Behavioral Sciences, 8, 465–475.
• Hacıömeroğlu, G. (2011). Sınıf öğretmeni adaylarının matematiksel problem çözmeye ilişkin inançlarını yordamada epistemolojik inançlarının incelenmesi [Examining elementary preservice teachers’ epistemological beliefs as predictors of beliefs about mathematical problem solving]. Buca Eğitim Fakültesi Dergisi, 30, 206–220.
• Hart, L. C. (2002). Preservice teachers’ beliefs and practice after participating in an integrated content/methods course. School Science and Mathematics, 102(1), 4–14.
• Jonassen, D. H. (2000). Toward a design theory of problem solving. Educational Technology Research and Development, 48(4), 63–85.
• Kayan, F., & Çakıroğlu, E. (2008). İlköğretim matematik öğretmen adaylarının matematiksel problem çözmeye yönelik inançları [Preservice elementary mathematics teachers’ mathematical problem solving beliefs]. Hacettepe Üniversitesi Eğitim Fakültesi Dergisi, 35, 218–226.
• Kloosterman, P. (2002). Beliefs about mathematics and mathematics learning in the secondary school: Measurement and implications for motivation. In G. C. Leder, E. Pehkonen, & G. Törner (Eds.), Beliefs: A hidden variable in mathematics education? (pp. 247–269). Dordrecht: Kluwer Academic Publishers.
• Kloosterman, P., & Stage, F. K. (1992). Measuring beliefs about mathematical problem solving. School Science and Mathematics, 92(3), 109–115.
• Lesh, R., & Zawojewski, J. S. (2007). Problem solving and modeling. In F. Lester, (Ed.), Second Handbook of Research on Mathematics Teaching and Learning (pp. 763–804), Charlotte, NC: Information Age Publishing.
• Lester, F. K. (1994). Musings about mathematical problem-solving research: 1970-1994. Journal for Research in Mathematics Education, 25(6), 660–675.
• Lester, F. K. (2013). Thoughts about research on mathematical problem-solving instruction. The Mathematics Enthusiast, 10(1), 245–278.
• Levin, B. B., He, Y., & Allen, M. H. (2013). Teacher beliefs in action: A cross-sectional, longitudinal follow-up study of teachers' personal practical theories. The Teacher Educator, 48(3), 201-217.
• Marshall, C., & Rossman, G. B. (2006). Designing qualitative research. Thousand Oaks, CA: Sage.
• Mason, L. (2003). High school students’ beliefs about maths, mathematical problem solving, and their achievement in maths: A cross-sectional study. Educational Psychology, 23(1), 73–85.
• Ministry of National Education (2013). Ortaokul matematik dersi (5, 6, 7 ve 8. Sınıflar) öğretim programı. Ankara: Talim ve Terbiye Kurulu Başkanlığı.
• NCTM (2000). Principles and standards for school mathematics, Reston, VA: Author.
• Patton, M. Q. (1990). Qualitative evaluation and research methods. Newbury Park, CA: Sage.
• Polya, G. (1953). On teaching problem solving. In H. F. Fehr (Ed.), The Learning of mathematics: Its theory and practice (pp. 228–270). 21st yearbook of the NCTM. Reston, VA: NCTM.
• Polya, G. (1981). Mathematical discovery: On understanding, learning and teaching problem solving. New York: Wiley.
• Posamentier, A. S., & Krulik, S. (1998). Problem-solving strategies for efficient and elegant solutions. California: Corwin Press.
• Putnam, R. T., Heaton, R. M., Prawat, R. S., & Remillard, J. (1992). Teaching mathematics for understanding: Discussing case studies of four fifth-grade teachers. The Elementary School Journal, 93(2), 213–228.
• Reys, R., Suydam, M., Lindquist, M., & Smith, N. (1998). Helping children learn mathematics. Boston: Allyn and Bacon.
• Richardson, V. (1996). The role of attitudes and beliefs in learning to teach, In J. Sikula (Ed.) Handbook of research on teacher education (pp.102-119). New York: Macmillan.
• Sağlam, Y., & Dost, Ş. (2014). Pre service science and mathematics teachers’ beliefs about mathematical problem solving. Procedia Social and Behavioral Sciences, 116, 303–306.
• Schoenfeld, A. (1988). When good teaching leads to bad results: The disasters of 'well-taught' mathematics courses. Educational Psychologist, 23(2), 145–166.
• Schommer-Aikins, M., Duell, O. K., & Hutter, R. (2005). Epistemological beliefs, mathematical problem-solving beliefs, and academic performance of middle school students. The Elementary School Journal, 105(3), 289–304.
• Topbaş-Tat, E. (2018). Problem solving instruction: Prospective mathematics teachers’ opinions and problem solving processes. International Journal of Eurasia Social Sciences, 9(32), 960–990.
• Ünlü, M., & Sarpkaya Aktaş, G. (2016). İlköğretim matematik öğretmen adaylarının problem kurma özyeterlik ve problem çözmeye yönelik inançları [Pre-service elementary mathematics teachers’ self-efficacy beliefs about problem posing and beliefs about problem solving]. Abant İzzet Baysal Üniversitesi Eğitim Fakültesi Dergisi, 16(4), 2040–2059.
• Wijaya, A., Van den Heuvel-Panhuizen, M., & Doorman, M. (2015). Teachers’ teaching practices and beliefs regarding context-based tasks and their relation with students’ difficulties in solving these tasks. Mathematics Education Research Journal, 27(4), 637–662.
• Yıldırım, A., & Şimsek, H. (2006). Sosyal bilimlerde nitel araştırma yöntemleri [Qualitative research methods in social sciences]. Ankara: Seçkin yayıncılık.