TY - JOUR T1 - Matematik Öğretmen Adaylarının Problem Çözme ve Problem Kurma Becerilerinin İncelenmesi: İnanç ve Öz Yeterliğin Aracı Rolü TT - Investigation of Mathematics Teacher Candidates' Problem Solving and Problem Posing Abilities: The Mediating Role of Belief and Self-Efficacy AU - Aydoğdu, Mustafa Zeki AU - Kılıç, Abdullah Faruk AU - Kaçak, Tugay PY - 2025 DA - September Y2 - 2025 DO - 10.9779/pauefd.1530235 JF - Pamukkale Üniversitesi Eğitim Fakültesi Dergisi JO - PUJE PB - Pamukkale Üniversitesi WT - DergiPark SN - 1301-0085 SP - 248 EP - 267 IS - 65 LA - tr AB - Problem çözme ve problem kurma matematik öğretiminin önemli bileşenleri arasında yer almaktadır. Problem çözme ve problem kurma becerilerinin bazı psikolojik değişkenlerle (öz yeterlik, tutumu, inanç, motivasyon, kaygı vb.) ilişkili olduğu yapılan birçok çalışmada ortaya çıkarılmıştır. Mevcut çalışmada ise problem kurma becerisi, problem çözme becerisi, problem çözme inancı ve problem kurma öz yeterliği arasındaki ilişki nicel yöntemle incelenmiştir. Ayrıca problem çözme becerisinin problem kurma becerisi üzerindeki etkisinde problem çözme inancı ve problem kurma öz yeterliğinin aracılık etkisi analiz edilmiştir. Araştırma matematik eğitimi alanında öğrenim gören öğretmen adaylarıyla gerçekleştirilmiş olup araştırma sonucunda problem çözme becerisi ile problem kurma becerisi arasında istatistiksel olarak anlamlı düzeyde ilişki olmadığı bulunmuştur. Korelasyon analizinde problem çözme inancı ile problem kurma özyeterliği arasında pozitif yönlü ve istatistiksel olarak anlamlı düşük düzeyde ilişki tespit edilmiştir. Aracılık analizi sonucunda problem kurma özyeterliği ile problem çözme inancının aracılık etkisi bulunmamıştır. Elde edilen bulgular çalışmanın sonuç bölümünde ilgili literatür doğrultusunda tartışılmıştır. KW - Problem çözme KW - Problem kurma KW - Problem çözme inancı KW - Problem kurma öz yeterliği KW - Aracılık analizi N2 - Problem-solving and problem-posing are among the important components of mathematics teaching. Many studies have revealed that problem-solving and problem-posing abilities are related to some psychological variables (self-efficacy, attitude, belief, motivation, anxiety, etc.). In the current study, the relationship between problem-posing abilities, problem-solving abilities, problem-solving beliefs, and problem-posing self-efficacy was examined quantitatively. In addition, the mediating effect of problem-solving beliefs and problem-posing self-efficacy on the effect of problem-solving ability on problem-posing ability was analyzed. The research was conducted with pre-service teachers studying in the field of mathematics education, and as a result of the research, it was found that there was no statistically significant relationship between problem-solving abilities and problem-posing abilities. In the correlation analysis, a positive and statistically significant low-level relationship was found between problem-solving beliefs and problem-posing self-efficacy. As a result of mediation analysis, no mediation effect was found between problem-posing self-efficacy and problem-solving beliefs. The findings were discussed in the conclusion section of the study in line with the relevant literature CR - AERA, APA, & NCME. (2014). Standards for educational and psychological testing. American Educational Research Association. CR - Altun, M., Memnun, D. S., & Yazgan, Y. (2007). Sınıf öğretmeni adaylarının rutin olmayan matematiksel problemleri çözme becerileri ve bu konudaki düşünceleri. İlköğretim Online, 6(1), 127-143. CR - Aydoğdu, A. S., & Türnüklü, E. (2023). Geometride problem kurmaya dayalı çalışmaların yaratıcılıkla olan ilişkisinin incelenmesi. Trakya Eğitim Dergisi, 13(2), 1434 1450. https://doi.org/10.24315/tred.1257745 CR - Bal, A. P. (2015). Examination of the mathematical problem-solving beliefs and success levels of primary school teacher candidates through the variables of mathematical success and gender. Educational Sciences: Theory & Practice, 15(5), 1373 1390. https://doi.org/10.12738/estp.2015.5.2573 CR - Baran Bulut, D. (2023). Elementary school mathematics teacher candidates’ competence to design model-eliciting activities, beliefs for problem solving, self-efficacy beliefs for problem posing and the relationship between them. e-International Journal of Educational Research, 14(4), 108-125. https://doi.org/10.19160/e-ijer.1280798 CR - Baumanns, L., & Rott, B. (2021). Rethinking problem-posing situations: A review. Investigations in Mathematics Learning, 13(2), 59-76. https://doi.org/10.1080/19477503.2020.1841501 CR - Bonotto, C., & Dal Santo, L. (2015). On the relationship between problem posing, problem solving, and creativity in the primary school. F. M. Singer, N. F. Ellerton, & J. Cai (Ed.), Mathematical problem posing: From research to effective practive (pp. 103-123). Springer. CR - Brookhart, S. M., & Nitko, A. J. (2015). Educational assesment of students (7th ed.). Pearson. CR - Brown, T. A. (2015). Confirmatory factor analysis for applied research (2nd ed.). The Guilford Press. CR - Browne, M. W., & Cudeck, R. (1992). Alternative ways of assessing model fit. Sociological Methods & Research, 21(2), 230-258. https://doi.org/10.1177/0049124192021002005 CR - Cai, J., & 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 CR - Cai, J., & Leikin, R. (2020). Affect in mathematical problem posing: Conceptualization, advances, and future directions for research. Educational Studies in Mathematics, 105(3), 287-301. https://doi.org/10.1007/s10649-020-10008-x CR - 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. https://doi.org/10.1007/s10649-012-9429-3 CR - Cai, J., & Rott, B. (2023). On understanding mathematical problem-posing processes. ZDM – Mathematics Education, 56(1), 61-71. https://doi.org/10.1007/s11858-023-01536-w CR - Cai, J., Koichu, B., Rott, B., & Jiang, C. (2024). Advances in research on mathematical problem posing: Focus on task variables. The Journal of Mathematical Behavior, 76, 101186. https://doi.org/10.1016/j.jmathb.2024.101186 CR - Chen, T., & Cai, J. (2020). An elementary mathematics teacher learning to teach using problem posing: A case of the distributive property of multiplication over addition. International Journal of Educational Research, 102, 101420. https://doi.org/10.1016/j.ijer.2019.03.004 CR - Cifarelli, V. V., & Sevim, V. (2015). Problem posing as reformulation and sense-making within problem solving. In F. Singer, N. F. Ellerton, & J. Cai (Ed.), Mathematical problem posing: From research to effective practice (pp. 177-194). Springer. CR - Costello, A. B., & Osborne, J. (2005). Best practices in exploratory factor analysis: Four recommendations for getting the most from your analysis. Practical Assessment, Research, and Evaluation, 10(7), 1-9. https://doi.org/10.7275/JYJ1-4868 CR - Da Ponte, J. P. & Henriques, A. (2013). Problem posing based on investigation activities by university students. Educational Studies in Mathematics, 83(1), 145–156. https://doi.org/10.1007/s10649-012-9443-5 CR - Deringöl, Y. (2018). Öğretmen adaylarının problem kurma becerilerinin orantısal akıl yürütme gerektiren durumlar bağlamında incelenmesi. Turkish Journal of Computer and Mathematics Education (TURCOMAT), 9(1), 31-53. https://doi.org/10.16949/turkbilmat.336386 CR - Duman, B., Yakar, A., Türkoğlu, I. E., & Yakar, P. (2013). Türkiye’de öğretmen yetiştirme programları çerçevesinde öğretmen adaylarının kişilik tiplerine göre problem çözme becerilerinin incelenmesi. Hacettepe Üniversitesi Eğitim Fakültesi Dergisi, Özel Sayı (1), 121-143. CR - Ellerton, N. F. (1986). Children’s made-up mathematics problems ? A new perspective on talented mathematicians. Educational Studies in Mathematics, 17(3), 261 271. https://doi.org/10.1007/BF00305073 CR - Ergene, Ö. (2023). Problem kurma ve çözme ilişkisi. K. Özgen, T. Kar, S. Çenberci, & Y. Zengin (Ed.), Matematikte Problem Çözme ve Problem Kurma (pp. 283-307). Pegem. CR - Ergene, Ö., & Çaylan Ergene, B. (2024). Posing problems and solving self-generated problems: the case of convergence and divergence of series. International Journal of Mathematical Education in Science and Technology, 55(10), 2573-2600. https://doi.org/10.1080/0020739X.2023.2170292 CR - Ergin, A. S. (2019). 7. Sınıf öğrencilerinin geometride problem kurma süreçlerinin incelenmesi ve yaratıcılıklarına etkisinin araştırılması [Yayımlanmamış doktora tezi]. Dokuz Eylül Üniversitesi. CR - Ergin, A. S., & Türnüklü, E. (2019). 7. Sınıf öğrencilerinin kurdukları geometri problemlerinde yaratıcılıklarının incelenmesi. Eğitim ve Öğretim Araştırmaları Dergisi, 8(1), 27-38. CR - Erkan, B., & Kar, T. (2022). Pre-service mathematics teachers’ problem-formulation processes: Development of the revised active learning framework. The Journal of Mathematical Behavior, 65, 100918. https://doi.org/10.1016/j.jmathb.2021.100918 CR - Fraenkel, J. R., Wallen, N. E., & Hyun, H. H. (2012). How to design and evaluate research in education (8th ed). McGraw-Hill Humanities/Social Sciences/Languages. CR - Gündoğdu Alaylı, F. (2023). Investigation of problem posing situations of sixth grade students. International Journal of Education Technology and Scientific Researches, 8(23), 1683-1720. https://doi.org/10.35826/ijetsar.646 CR - Güven, E. (2017). Müzik Öğretmeni adaylarının problem çözme becerilerinin piyano dersinde karşılaştıkları sorunların çözümüne olan etkilerinin incelenmesi. Abant İzzet Baysal Üniversitesi Eğitim Fakültesi Dergisi, 17(2), 737-756. https://doi.org/10.17240/aibuefd.2017.17.30227-326595 CR - Güven, B., & Çabakçor, B. Ö. (2013). Factors influencing mathematical problem-solving achievement of seventh grade Turkish students. Learning and Individual Differences, 23, 131-137. https://doi.org/10.1016/j.lindif.2012.10.003 CR - Hackett, G., & Betz, N. E. (1989). An exploration of the mathematics self-efficacy/mathematics performance correspondence. Journal for Research in Mathematics Education, 20(3), 261–273. https://doi.org/10.2307/749515 CR - Hair, J. F., Risher, J. J., Sarstedt, M., & Ringle, C. M. (2019). When to use and how to report the results of PLS-SEM. European Business Review, 31(1), 2-24. https://doi.org/10.1108/EBR-11-2018-0203 CR - Hayes, A. F. (2018). Introduction to mediation, moderation, and conditional process analysis: A regression-based approach (2nd edition). The Guilford Press. CR - Horn, J. L. (1965). A rationale and test for the number of factors in factor analysis. Psychometrika, 30(2), 179-185. https://doi.org/10.1007/BF02289447 CR - Howard, M. C. (2016). A review of exploratory factor analysis decisions and overview of current practices: What we are doing and how can we improve? International Journal of Human-Computer Interaction, 32(1), 51-62. https://doi.org/10.1080/10447318.2015.1087664 CR - Hu, L., & Bentler, P. M. (1999). Cutoff criteria for fit indexes in covariance structure analysis: Conventional criteria versus new alternatives. Structural Equation Modeling: A Multidisciplinary Journal, 6(1), 1-55. https://doi.org/10.1080/10705519909540118 CR - Jung, H., & Magiera, M. T. (2021). Connecting mathematical modeling and social justice through problem posing. Mathematical Thinking and Learning, 25(2), 232–251. https://doi.org/10. 1080/10986 065.2021.1966713. CR - Kar, T., Öztürk, F., & Özkaya, M. (2024). Pose, solve and pose cycle: an examination on the change of pre-service mathematics teachers’ problem-posing performances. Teaching Mathematics and its Applications: An International Journal of the IMA, 44(2). 107 131. https://doi.org/10.1093/teamat/hrae010 CR - Kayan, F., & Çakıroğlu, E., (2008). Preservice elementary mathematics teachers' mathematical problem solving beliefs. Hacettepe Egitim Dergisi, 35(35), 218-226. CR - Kılıç, A. F. (2022). Deciding the number of dimensions in explanatory factor analysis: A brief overview of the methods. Pamukkale University Journal of Social Sciences Institute, 51(1), 305-318. https://doi.org/10.30794/pausbed.1095936 CR - Kılıç, A. F., & Doğan, N. (2021). Comparison of confirmatory factor analysis estimation methods on mixed-format data. International Journal of Assessment Tools in Education, 8(1), Article 1. https://doi.org/10.21449/ijate.782351 CR - Kline, R. B. (2016). Principle and practice of structural equation modeling (4th ed.). The Guilford Press. CR - Koichu, B., & Kontorovich, I. (2013). Dissecting success stories on mathematical problem posing: A case of the Billiard Task. Educational Studies in Mathematics, 83(1), 71 86. https://doi.org/10.1007/s10649-012-9431-9 CR - Koichu, B. (2020). Problem posing in the context of teaching for advanced problem solving. International Journal of Educational Research, 102, 101428. https://doi.org/10.1016/j.ijer.2019.05.001 CR - Kontorovich, I. (2024). The road to “good” problems goes through initial responses to stimulating socio-mathematical situations. Journal of Mathematical Behavior, 73, 101135. https://doi.org/10.1016/j.jmathb.2024.101135 CR - Kopparla, M., Bicer, A., Vela, K., Lee, Y., Bevan, D., Kwon, H., Caldwell, C., Capraro, M. M., & 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 CR - Krawitz, J., Hartmann, L., & Schukajlow, S. (2024). Do task variables of self-generated problems influence interest? Authenticity, openness, complexity, and students’ interest in solving self-generated modelling problems. Journal of Mathematical Behavior, 73, 101129. https://doi.org/10.1016/j.jmathb.2024.101129 CR - Kwek, M.L. (2015). Using Problem Posing as a Formative Assessment Tool. In: Singer, F., F. Ellerton, N., Cai, J. (eds) Mathematical Problem Posing. Research in Mathematics Education (ss. 273-292). Springer. https://doi.org/10.1007/978-1-4614-6258-3_13 CR - Leikin, R. (2015). Problem posing for and through investigations in a dynamic geometry environment. F. Singer, N. Ellerton, & J. Cai (Ed.), Problem posing: From research to effective practive (pp. 373-391). Springer. CR - Leikin, R., & Elgrably, H. (2020). Problem posing through investigations for the development and evaluation of proof-related skills and creativity skills of prospective high school mathematics teachers. International Journal of Educational Research, 102, 101424. https://doi.org/10.1016/j.ijer.2019.04.002 CR - Lorenzo-Seva, U., Timmerman, M. E., & Kiers, H. A. L. (2011). The Hull method for selecting the number of common factors. Multivariate Behavioral Research, 46(2), 340 364. https://doi.org/10.1080/00273171.2011.564527 CR - Lorenzo-Seva, U., Timmerman, M. E. & Kiers, H. A. L. (2023). Factor (Version 12.04.02) [Software]. CR - MacKinnon, D. P. (2008). Introduction to statistical mediation analysis (1st ed.). Routledge. https://doi.org/10.4324/9780203809556 CR - Mardia, K. V. (1970). Measures of multivariate skewness and kurtosis with applications. Biometrika, 57(3), 519-530. https://doi.org/10.1093/biomet/57.3.519 CR - Matsko, V. J., & Thomas, J. (2015). Beyond routine: Fostering creativity in mathematics classrooms. F. M. Singer, N. F. Ellerton, & J. Cai (Ed.), Mathematical Problem Posing (pp. 125-139). Springer New York. https://doi.org/10.1007/978-1-4614-6258-3_6 CR - Nicolau, A. A., & Philippou, G. N. (2007). Efficacy beliefs, problem posing and mathematics achievement (D. Pitta-Pantazi & G. N. Philippou, Ed.; ss. 308-317). CR - Özgen, K., Aydın, M., Geçici, M. E., & Bayram, B. (2017). Sekizinci sınıf öğrencilerinin problem kurma becerilerinin bazı değişkenler açısından incelenmesi. Türk Bilgisayar ve Matematik Eğitimi Dergisi (TURCOMAT), 8(2), 323-351. https://doi.org/10.16949/turkbilmat.322660 CR - Özgen, K., & Bayram, B. (2019). Problem kurma öz yeterlik ölçeğinin geliştirilmesi. İlköğretim Online, 663-680. https://doi.org/10.17051/ilkonline.2019.562029 CR - Özgen, K., & Bayram, B. (2020). Ortaokul öğrencilerinin problem kurmaya yönelik beceri ve öz yeterlik inançlarının incelenmesi. Van Yüzüncü Yıl Üniversitesi Eğitim Fakültesi Dergisi, 17(1), 455-485. https://doi.org/10.33711/yyuefd.693817 CR - Pajares, F., & Graham, L. (1999). Self-Efficacy, motivation constructs, and mathematics performance of entering middle school students. Contemporary Educational Psychology, 24(2), 124-139. https://doi.org/10.1006/ceps.1998.0991 CR - Pajares, F., & Miller, M. D. (1994). Role of self-efficacy and self-concept beliefs in mathematical problem solving: A path analysis. Journal of Educational Psychology, 86(2), 193-203. https://doi.org/10.1037/0022-0663.86.2.193 CR - Pajares, F. (1996). Self-efficacy beliefs in academic settings. Review of Educational Research, 66(4), 543. https://doi.org/10.2307/1170653 CR - Philippou, G., Charalambous, C., & Christou, C. (2001). Efficacy in problem posing and teaching problem posing (M. Heuvel-Panhuizen, Ed.; C. 4, pp. 41-48). CR - Rosli, R., Capraro, M. M., Goldsby, D., Gonzalez, E. G., Onwuegbuzie, A. J. & Capraro, R. M. (2015). Middle-grade preservice teachers’ mathematical problem solving and problem posing. İçinde F. Singer, N. Ellerton, & J. Cai (Ed.), Mathematical problem posing: From research to effective practice (ss. 333-354). Springer. CR - Sangcap, P. G. A. (2010). Mathematics-related beliefs of filipino college students: Factors affecting mathematics and problem solving performance. Procedia - Social and Behavioral Sciences, 8, 465-475. https://doi.org/10.1016/j.sbspro.2010.12.064 CR - Savalei, V., & Rhemtulla, M. (2013). The performance of robust test statistics with categorical data. British Journal of Mathematical and Statistical Psychology, 66(2), 201 223. https://doi.org/10.1111/j.2044-8317.2012.02049.x CR - Schober, P., Boer, C. & Schwarte, L. A. (2018). Correlation coefficients: Appropriate use and interpretation. Anesthesia & Analgesia, 126(5), 1763 1768. https://doi.org/10.1213/ANE.0000000000002864 CR - Silber, S. & Cai, J. (2017). Pre-service teachers’ free and structured mathematical problem posing. International Journal of Mathematical Education in Science and Technology, 48(2), 163–184. https://doi.org/10.1080/0020739X.2016.1232843 CR - Silver, E. A., & 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/10.2307/749846 CR - Singer, F. M., & Voica, C. (2015). Is problem posing a tool for identifying and developing mathematical creativity? İçinde F. M. Singer, N. F. Ellerton, & J. Cai (Ed.), Mathematical problem posing (ss. 141-174). Springer. CR - Tabachnick, B. G., & Fidell, L. S. (2019). Using multivariate statistics (7th ed.). Pearson. CR - Terzi, A., & 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, 52(3), 342-360. https://doi.org/10.1080/03004279.2022.2090592 CR - Torp, L., & Sage, S. (2002). Problems as possibilites: Problem-based learning for K-16 education. VA: ASCD. Uysal, İ., & Kılıç, A. F. (2022). Çok değişkenli normallik testleri üzerine bir inceleme. İçinde Ejer Congress (ss. 968-969). CR - Ünlü, M., & Sarpkaya-Aktaş, G. (2016). İlköğretim matematik öğretmen adaylarının problem kurma özyeterlik ve problem çözmeye yönelik inançları. Abant İzzet Baysal Üniversitesi Eğitim Fakültesi Dergisi, 16(4), 2040-2059. CR - Velicer, W. F., (1976). Determining the number of components from the matrix of partial correlations. Psychometrika, 41(3), 321-327. https://doi.org/10.1007/BF02293557 CR - Xie, J. & 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 CR - Xu, B., Cai, J., Liu, Q., & 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 CR - Yang, X., & Xin, Y. P. (2022). Teaching problem posing to students with learning disabilities. Learning Disability Quarterly, 45(4), 280-293. https://doi.org/10.1177/0731948721993117 CR - Zhang, L., Cai, J., Song, N., Zhang, H., Chen, T., Zhang, Z., & Guo, F. (2022). Mathematical problem posing of elementary school students: The impact of task format and its relationship to problem solving. ZDM – Mathematics Education, 54(3), 497-512. https://doi.org/10.1007/s11858-021-01324-4 UR - https://doi.org/10.9779/pauefd.1530235 L1 - https://dergipark.org.tr/tr/download/article-file/4131625 ER -