Turkish Adaptation of the Mathematical Resilience Scale for 4th Grade Primary Schools Students: A Validity and Reliability Study

Öz

Primary school students’ attitudes toward coping with difficulties in mathematics learning may affect their academic achievement in later educational stages. Therefore, it is important to evaluate students’ responses to mathematical challenges. This study aims to examine the validity and reliability of the Turkish adaptation of the Mathematical Resilience Scale developed by Kooken, Welsh, McCoach, Johnston-Wilder ve Lee (2016) for use with 4th grade primary school students. The study group consists of 1,098 fourth-grade students from various regions of Türkiye. To assess construct validity, confirmatory factor analysis (CFA) was conducted, and the original 21-item, three-factor structure (value, struggle, and growth) was confirmed in the Turkish version. The Cronbach’s alpha reliability coefficients for the subdimensions ranged between .76 and .78. The findings indicate that the Turkish version of the scale is a valid and reliable instrument for measuring the mathematical resilience levels of primary school students at this age group.

Anahtar Kelimeler

• Factor analysis
• primary school
• mathematical resilience
• scale

Matematiksel Yılmazlık Ölçeği’nin İlkokul 4. Sınıf Öğrencileri İçin Türkçe’ye Uyarlanması: Geçerlik- Güvenirlik Çalışması

Öz

İlkokul öğrencilerinin matematik öğrenme sürecinde karşılaştıkları güçlüklerle başa çıkma tutumları, ileri eğitim kademelerindeki akademik başarılarını etkileyebilmektedir. Bu nedenle öğrencilerin matematiksel zorluklar karşısında sergiledikleri tutumların değerlendirilmesi önemlidir. Bu çalışmanın amacı, Kooken, Welsh, McCoach, Johnston-Wilder ve Lee (2016) tarafından geliştirilen Matematiksel Yılmazlık Ölçeği’nin Türkçeye uyarlanarak ilkokul 4. sınıf öğrencileri için geçerlik ve güvenirliğini incelemektir. Araştırmanın çalışma grubunu, Türkiye genelinde öğrenim gören 1098 dördüncü sınıf öğrencisi oluşturmaktadır. Ölçeğin yapı geçerliliği doğrulayıcı faktör analizi (DFA) ile test edilmiş ve üç faktörlü (değer, mücadele, gelişim) 21 maddelik özgün yapı Türkçe formda doğrulanmıştır. Ölçeğin alt boyutlarına ait Cronbach’s Alpha güvenirlik katsayılarının .76 ile .78 arasında değiştiği belirlenmiştir. Elde edilen bulgular, ölçeğin bu yaş grubunda kullanılabilecek geçerli ve güvenilir bir ölçme aracı olduğunu göstermektedir.

Anahtar Kelimeler

• Faktör analizi
• ilkokul
• matematiksel yılmazlık
• ölçek.

Etik Beyan

Necmettin Erbakan Üniversitesi Sosyal ve Beşeri Bilimler Etik Kurulu 21.03.2025 tarih 2025/231 karar tarihi ile etik onay alınmıştır.

Kaynakça

1. Agustin, N., Noto, M. S., & Dewi, I. L. K. (2022). Construction of student mathematics resilience through the development of sainsmatika-based teaching materials. International Electronic Journal of Mathematics Education, 17(2), em0683. https://doi.org/10.29333/iejme/11835
2. Apostolidu, M., & Johnston-Wilder, S. (2023). Breaking through the fear: Exploring the mathematical resilience toolkit with anxious FE students. Research in Post-Compulsory Education, 28(2), 330-347. doi.org/10.1080/13596748.2023.2206704
3. Atahan, Ş., & Mert Uyangör, S. (2024). The development of the mathematical resilience scale: Validity andreliability study. Acta Didactica Napocensia, 17(2), 77-88, https://doi.org/10.24193/adn.17.2.6
4. Attami, D., & Indriati, D. (2020, August). Mathematical resilience and mathematical problem-solving ability in Junior High School. In Journal of Physics: Conference Series (Vol. 1613, No. 1, p. 012028). IOP Publishing. https://doi.org/10.1088/1742-6596/1613/1/012028
5. Awofala, A. O. (2021). A validation of the mathematical resilience scale for twelfth graders through confirmatory factor analysis and its relationship with achievement in mathematics in Nigeria. SN Social Sciences, 1(8), 204. https://doi.org/10.1007/s43545-021-00212-8
6. Bandura, A. (1989). Human agency in social cognitive theory. American Psychologist, 44, 1175–1184. https://doi.org/10.1037/0003-066X.44.9.1175
7. Boaler, J. (2013). Ability and mathematics: The mindset revolution that is reshaping education. FORUM, 55(1), 143–152. https://doi.org/10.2304/forum.2013.55.1.143
8. Brown, T. A. (2015). Confirmatory factor analysis for applied research (2nd ed.). Guilford Press.

9. Büyüköztürk, Ş., Kılıç Çakmak, E., Akgün, Ö. E., Karadeniz, Ş., & Demirel, F. (2012). Örnekleme yöntemleri. Pegem Akademi.
10. Büyüköztürk, Ş, Kılıç Çakmak, E, Akgün, Ö. E, Karadeniz, Ş, & Demirel, F. (2020). Bilimsel araştırma yöntemleri (28. baskı). Pegem Akademi.
11. Byrne, B. M. (2012). Structural equation modeling with Mplus: Basic concepts, applications, and programming. Routledge.
12. Comrey, A. L., & Lee, H. B. (2013). A first course in factor analysis. Psychology press.
13. 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(1): 7. https://doi.org/10.7275/jyj1-4868
14. Çetin, Ş, Durmaz, B, & Girit, D. (2018). Matematiksel yılmazlık/dayanıklılık ölçeğini Türkçeye uyarlama çalışması. In Proceedings of the Fifth International Eurasian Educational Research Congress (s. 875–881). Anı Publishing.
15. Deniz, K. Z. (2007). Psikolojik ölçme aracı uyarlama. Ankara Üniversitesi Eğitim Bilimleri
16. Fakültesi Dergisi, 40 (1), 1-16.
17. Dweck, C.S. (1999). Self-theories: Their Role in Motivation, Personality, and Development (1nd ed.). Psychology Press. https://doi.org/10.4324/9781315783048
18. Field, A. (2009). Discovering statistics using SPSS: Book plus code for E version of text (Vol. 896). SAGE Publications Limited.
19. Goodall, J. & Johnston-Wilder, S. (2015) Overcoming mathematical helplessness and developing mathematical resilience in parents: An illustrative case study. Creative Education, 6, 526-535. doi: 10.4236/ce.2015.65052.
20. George, D, & Mallery, P. (2010). SPSS for Windows step by step: A simple guide and reference (4nd ed.). Allyn & Bacon.
21. Gürefe, N, & Akçakin, V. (2018). The Turkish adaptation of the mathematical resilience scale: Validity and reliability study. Journal of Education and Training Studies, 6(4), 38-47. https://doi.org/10.11114/jets.v6i4.2992.
22. Hair, J. F, Black, W. C, Babin, B. J, & Anderson, R. E. (2010). Multivariate data analysis (7th ed.). Pearson.
23. Hambleton, R. K. (2005). Issues, designs, and technical guidelines for adapting tests into multiple languages and cultures. In R. K. Hambleton, P. F. Merenda, & C. D. Spielberger (Eds.), Adapting educational and psychological tests for cross-cultural assessment (pp. 3–38). Lawrence Erlbaum Associates.
24. Henseler, J., Ringle, C.M. & Sarstedt, M. (2015). A new criterion for assessing discriminant validity in variance-based structural equation modeling. J. of the Acad. Mark. Sci. 43, 115–135 (2015). https://doi.org/10.1007/s11747-014-0403-8
25. Hoyle, R. H. (Ed.). (2014). Handbook.of structural equation modeling. Guilford Punblications.
26. Hu, L. T., & Bentler, P. M. (1999). Cutoff criteria for fit indexes in covariance structure analysis: Conventional criteria versus new alternatives. Structural Equation Modeling, 6(1), 1–55.
27. Hutauruk, A. J. B, & Priatna, N. (2017). Mathematical resilience of mathematics education students. In Journal of Physics: Conference Series (Vol. 895, No. 1, p. 012067). IOP Publishing. https://doi.org/10.1088/1742-6596/895/1/012067.
28. Johnston-Wilder, S., & Lee, C. (2010, 1-4 September). Developing mathematical resilience. [Conference session]. Paper presented at the British Educational Research Association (BERA), University of Warwick.
29. Johnston-Wilder, Sue, Lee, Clare & Mackrell, Kate (2021) Addressing mathematics anxiety through developing resilience: building on self-determination theory. Creative Education, 12 pp. 2098-2115. doi:10.4236/ce.2021.129161
30. Karasar, N. (2007). Bilimsel araştırma yöntemi: kavramlar, ilkeler, teknikler. Nobel Yayın Dağıtım.
31. Kline, R. B. (2016). Principles and practice of structural equation modeling (4th ed.). Guilford Press.
32. Kooken, J., Welsh, M. E., McCoach, D. B., Johnston-Wilder, S., & Lee, C. (2016). Development and validation of the mathematical resilience scale. Measurement and Evaluation in Counseling and Development, 49(3), 217-242. https://doi.org/10.1177/0748175615596782.
33. Kooken, J., & Costelnock, J. (2024). Mathematical Resilience in elementary school: Validation of a tool to support student success.
34. Lee, C., & Johnston-Wilder, S. (2014). Mathematical resilience: What is it and why is it important? In S. Chinn (Ed.), The Routledge International Handbook of Dyscalculia and Mathematical Learning Difficulties (pp. 337–345). Routledge.
35. Lee, C., & Johnston Wilder, S. (2017). The construct of mathematical resilience. In U. X. Eligio (Ed.), Understanding emotions in mathematical thinking and learning (pp. 269–291). Academic Press. https://doi.org/10.1016/B978-0-12-802218-4.00010-8
36. Lee, C., & Ward-Penny, R. (2021). Agency and fidelity in primary teachers’ efforts to develop mathematical resilience. Teacher Development, 26(1), 75–93. https://doi.org/10.1080/13664530.2021.2006768
37. Luthar, S. S., Cicchetti, D., & Becker, B. (2000). The construct of resilience: A critical evaluation and guidelines for future work. Child development, 71(3), 543-562. https://doi.org/10.1111/1467-8624.00164
38. Marcoulides, G. A., & Schumacher, R. E. (2011). Advanced structural equation modeling: Issues and techniques. Routledge.
39. Meirong, Z., & Mustafa, Z. (2025). The Chinese adaptation of the mathematical resilience scale among high school students: Validity and reliability study. Edelweiss Applied Science and Technology, 9(3), 864–880. https://doi.org/10.55214/25768484.v9i3.5359
40. Neumann, I., Jeschke, C., & Heinze, A. (2021). First year students’ resilience to cope with mathematics exercises in the university mathematics studies. Journal für Mathematik-Didaktik, 42(2), 307-333. https://doi.org/10.1007/s13138-020-00177-w
41. Oszwa, U. (2022). Mathematical resilience as a conceptual framework for school practice. Multidisciplinary Journal of School Education, 11(1 (21), 99-114. https://doi.org/10.35765/mjse.2022.1121.05
42. Patton, M. Q. (2014). Nitel araştırma ve değerlendirme yöntemleri. (Bütün, S. ve Demir, S. B., Çev.). Ankara: PegemA Akademi.
43. Pekdemir, Ü., Yazıcı, H., Altun, F., & Tosun, C. (2019). Matematikte akademik yılmazlık ölçeği’nin Türk kültürüne uyarlanması. Turkish Journal of Computer and Mathematics Education (TURCOMAT), 10(1), 217-231. https://doi.org/10.16949/turkbilmat.446722
44. Piaget, J. (1972). Intellectual evolution from adolescence to adulthood. Human Development, 15(1), 1–12. https://doi.org/10.1159/000271225
45. Ramirez, G., Gunderson, E. A., Levine, S. C., & Beilock, S. L. (2016). Math anxiety, working memory, and math achievement in early elementary school. Journal of Cognition and Development, 17(2), 178–193. https://doi.org/10.1080/15248372.2015.1088772.
46. Ricketts, S. N., Engelhard, G., Jr., & Chang, M. L. (2015). Development and validation of a scale to measure academic resilience in mathematics. European Journal of Psychological Assessment, 31(4), 243–251. https://doi.org/10.1027/1015-5759/a000274
47. Robinson, J. P., Shaver, P. R., & Wrightsman, L. S. (1991). Measures of personality and social psychological attitudes. Academic Press.
48. Stevens, J. P. (2009). Applied multivariate statistics for the social sciences (5th ed.). Routledge. https://doi.org/10.4324/9780203843130
49. Sümer, N. (2000). Yapısal eşitlik modelleri: Temel kavramlar ve örnek uygulamalar. Türk Psikoloji Yazıları, 3(6), 49–74.
50. Szczygieł, M., & Kutt, M. (2025). The psychometric properties of the Polish-language version of the mathematical resilience scale. Journal of Numerical Cognition, 11, 1-22. https://doi.org/10.5964/jnc.13251
51. Tabachnick, B. G., & Fidell, L. S. (2013). Using multivariate statistics (6th ed.). Pearson.
52. Yeager, D., & Dweck, C. (2012). Mindsets that promote resilience: When students believe that personal characteristics can be developed. Educational Psychologist, 47, 302–314. https://doi.org/10.1080/00461520.2012.722805
53. Xenofontos, C., & Mouroutsou, S. (2023). Resilience in mathematics education research: A systematic review of empirical studies. Scandinavian Journal of Educational Research, 67(7), 1041-1055. https://doi.org/10.1080/00313831.2022.2115132
54. West, S. G., Finch, J. F., & Curran, P. J. (1995). Structural equation models with nonnormal variables: Problems and remedies. In R. H. Hoyle (Ed.), Structural equation modeling: Concepts, issues, and applications (pp. 56–75). Sage Publications Inc.
55. Williams, G. (2014). Optimistic problem-solving activity: Enacting confidence, persistence, and perseverance. ZDM, 46, 407-422. https://doi.org/10.1007/s11858-014-0586-y