Matematik Öğretmen Adaylarının Problem Çözme ve Problem Kurma Becerilerinin İncelenmesi: İnanç ve Öz Yeterliğin Aracı Rolü

Year 2025, Issue: 65, 248 - 267, 19.09.2025

Mustafa Zeki Aydoğdu , Abdullah Faruk Kılıç , Tugay Kaçak

https://doi.org/10.9779/pauefd.1530235

Abstract

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.

Keywords

Problem çözme , Problem kurma , Problem çözme inancı , Problem kurma öz yeterliği , Aracılık analizi

Ethical Statement

Bu araştırma, Trakya Üniversitesi Sosyal ve Beşerî Bilimler Araştırmaları Etik Kurulu’nun 27.03.2024 tarihli 2024/03 sayılı kararı ile alınan izinle yürütülmüştür.

Investigation of Mathematics Teacher Candidates' Problem Solving and Problem Posing Abilities: The Mediating Role of Belief and Self-Efficacy

Abstract

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

Keywords

Problem-solving , Problem-posing , Problem-solving beliefs , Problem-posing self-efficacy Mediation analysis

Ethical Statement

This research was conducted with the permission of Trakya University Social and Human Sciences Research Ethics Committee with the decision numbered 2024/03 and dated 27.03.2024.

References

• AERA, APA, & NCME. (2014). Standards for educational and psychological testing. American Educational Research Association.
• 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.
• 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
• 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
• 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
• 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
• 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.
• Brookhart, S. M., & Nitko, A. J. (2015). Educational assesment of students (7th ed.). Pearson.
• Brown, T. A. (2015). Confirmatory factor analysis for applied research (2nd ed.). The Guilford Press.
• 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
• 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
• 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
• 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
• 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
• 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
• 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
• 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.
• 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
• 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
• 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
• 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.
• 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
• 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.
• 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
• Ergin, A. S. (2019). 7. Sınıf öğrencilerinin geometride problem kurma süreçlerinin incelenmesi ve yaratıcılıklarına etkisinin araştırılması [Yayımlanmamış doktora tezi]. Dokuz Eylül Üniversitesi.
• Ergin, A. S., & Türnüklü, E. (2019). 7. Sınıf öğrencilerinin kurdukları geometri problemlerinde yaratıcılıklarının incelenmesi. Eğitim ve Öğretim Araştırmaları Dergisi, 8(1), 27-38.
• 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
• 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.
• 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
• 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
• 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
• 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
• 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
• Hayes, A. F. (2018). Introduction to mediation, moderation, and conditional process analysis: A regression-based approach (2nd edition). The Guilford Press.
• 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
• 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
• 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
• 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.
• 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
• Kayan, F., & Çakıroğlu, E., (2008). Preservice elementary mathematics teachers' mathematical problem solving beliefs. Hacettepe Egitim Dergisi, 35(35), 218-226.
• 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
• 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
• Kline, R. B. (2016). Principle and practice of structural equation modeling (4th ed.). The Guilford Press.
• 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
• 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
• 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
• 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
• 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
• 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
• 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.
• 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
• 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
• Lorenzo-Seva, U., Timmerman, M. E. & Kiers, H. A. L. (2023). Factor (Version 12.04.02) [Software].
• MacKinnon, D. P. (2008). Introduction to statistical mediation analysis (1st ed.). Routledge. https://doi.org/10.4324/9780203809556
• 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
• 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
• Nicolau, A. A., & Philippou, G. N. (2007). Efficacy beliefs, problem posing and mathematics achievement (D. Pitta-Pantazi & G. N. Philippou, Ed.; ss. 308-317).
• 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
• Özgen, K., & Bayram, B. (2019). Problem kurma öz yeterlik ölçeğinin geliştirilmesi. İlköğretim Online, 663-680. https://doi.org/10.17051/ilkonline.2019.562029
• 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
• 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
• 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
• Pajares, F. (1996). Self-efficacy beliefs in academic settings. Review of Educational Research, 66(4), 543. https://doi.org/10.2307/1170653
• Philippou, G., Charalambous, C., & Christou, C. (2001). Efficacy in problem posing and teaching problem posing (M. Heuvel-Panhuizen, Ed.; C. 4, pp. 41-48).
• 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.
• 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
• 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
• 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
• 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
• 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
• 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.
• Tabachnick, B. G., & Fidell, L. S. (2019). Using multivariate statistics (7th ed.). Pearson.
• 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
• 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).
• 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.
• 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
• 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
• 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
• 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
• 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