Matematiksel Üst Düzey Düşünme Ölçeği: Türkçeye Uyarlama, Geçerlik ve Güvenirlik Çalışması

Öz

Bu araştırma, 2024 yılında Zhou vd. tarafından geliştirilen “Mathematical Higher Order Thinking Scale” ölçeğinin Türk kültürüne uyarlanarak lise öğrencilerinin matematiksel üst düzey düşünme seviyelerini tespit etmeye yarayan bir ölçme aracı elde etmeyi amaçlamaktadır. Orijinal ölçek, matematiksel eleştirel düşünme, matematiksel yaratıcı düşünme, matematiksel problem çözme ve matematiksel üstbilişsel beceriler olmak üzere toplam 4 boyuttan meydana gelmektedir. Yazarlar, ölçeğin geliştirilme aşamasında her boyut için ayrı ayrı AFA, DFA ve güvenirlik testi uygulamıştır. Bu doğrultuda, ölçek uyarlama aşamasında da aynı adımlar takip edilmiştir. İlgili ölçeğin Türkçeye çevirisi yapılırken geri orijinaline çeviri tekniği kullanılmıştır. Ölçek uyarlama çalışmasının örneklemini 360 lise öğrencisi oluşturmaktadır. Ölçeğin yapı geçerliği ve faktör yapısını incelemek için her boyuta AFA ve DFA uygulanmıştır. Ölçeğin güvenirliğini belirlemek için tüm ölçeğe ve her alt boyuta güvenirlik testi uygulanmıştır. Sonuç olarak Türk kültürüne uyarlanan Matematiksel Üst Düzey Düşünme ölçeğinin geçerli ve güvenilir bir ölçme aracı olduğu sonucu elde edilmiştir.

Anahtar Kelimeler

• Lise öğrencileri
• Matematiksel üst düzey düşünme becerileri
• Ölçek uyarlama

Mathematical Higher Order Thinking Scale: Turkish Adaptation, Validity and Reliability Study

Abstract

This study aims to adapt the “Mathematical Higher Order Thinking Scale” developed by Zhou et al. in 2024 to Turkish culture to obtain a measurement tool to determine the mathematical higher order thinking levels of high school students. The original scale consists of 4 dimensions: mathematical critical thinking, mathematical creative thinking, mathematical problem solving and mathematical metacognitive skills. The authors conducted EFA, CFA and reliability tests separately for each dimension in the development phase of the scale. Accordingly, the same steps were followed in the scale adaptation phase. While translating the scale into Turkish, back-translation technique was used. The sample of the scale adaptation study consisted of 360 high school students. EFA was applied to each dimension to examine the construct validity and factor structure of the scale. EFA and CFA were applied to each dimension to examine the construct validity and factor structure of the scale. To determine the reliability of the scale, reliability test was applied to the whole scale and each sub-dimension. As a result, it was concluded that the Mathematical Higher Order Thinking scale adapted to Turkish culture is a valid and reliable measurement tool.

Keywords

• High school students
• Mathematical higher order thinking skills
• Scale adaptation

References

1. Acar Güvendir, M., Kılıç, A. F. ve Özer Özkan, Y. (2025). Pursuit for scale selection: The journey to finding the right scale. Pamukkale University Journal of Education, 64, 338 373. https://doi.org/10.9779/pauefd.1501330
2. Altun, H. İ. (2024). An action research on the development of algorithmic thinking skills of pre-service preschool teachers. Unpublished master's thesis (Master's thesis - Kırşehir Ahi Evran University) was obtained from the National Thesis Center of the Council of Higher Education. (Thesis No. 909541).
3. Atlıhan, E. (2021). The investigation of the relationship between grade 5 students' problem solving skills and problem posing skills in the context of creativity in patterns thesis Unpublished master's thesis (Master's thesis – Ağrı İbrahim Çeçen University) was obtained from the National Thesis Center of the Council of Higher Education. (Thesis No. 704753).
4. Aydın, Ü. & Öztürk, M. (2024) . The effect of metacognitive training on mathematics achievement and problem solving: a metaanalysis research. Manisa Celal Bayar University Journal of The Faculty of Education, 12(2), 286–304. https://doi.org/10.52826/mcbuefd.1450124
5. Brislin, R. W. (1970). Back-translation for cross-cultural research. Journal of Cross-Cultural Psychology, 1(3), 185–216. https://doi.org/10.1177/135910457000100301
6. Büyüköztürk, Ş. (2007). Handbook of data analysis for social sciences: Statistics, research design, SPSS applications and interpretation (Seventh Edition). PEGEM A Publishing.
7. Carbonneau, K. J., Wong, R. M., & Borysenko, N. (2020). The influence of perceptually rich manipulatives and collaboration on mathematic problem-solving and perseverance. Contemporary Educational Psychology, 61, 101846. https://doi.org/10.1016/j.cedpsych.2020.101846
8. Çanakçı, O. (2008). The development and the evaluation of mathematics problem solving attitude scale Unpublished doctoral thesis (Doctoral thesis – Marmara University) was obtained from the National Thesis Center of the Council of Higher Education. (Thesis No. 231804).

9. Çanakçı, O., & Özdemir, A. Ş. (2011). The construction of mathematics problem solving attitude scale. Abant Izzet Baysal University Faculty of Education Journal. 11(1), 119136.
10. Çelik, E. (2017). Metacognitive Self-Regulation Scale: The reliability and validity study of the Turkish Form. Studies in Psychology, 37(1), 53-71.
11. Çömlekoğlu, G. (2001). The effect of calculators on prospective teachers problem solving skills Unpublished master's thesis (Master's thesis – Balıkesir University) was obtained from the National Thesis Center of the Council of Higher Education. (Thesis No. 112628).
12. Değirmenci, T., & Deringöl, Y. (2024). Validity and Reliability Study of the Problem Solving Scale for Primary Schools. National Education, 53(244), 1849-1872. https://doi.org/10.37669/milliegitim.1262404 DeVellis, R. F. (2017). Scale development: Theory and applications (4th ed.). Sage Publications.
13. Durdukoca, Ş. F., & Arıbaş, S. (2019). Development of metacognitive awareness scale for teacher candidates. Electronic Journal of Social Sciences, (72), 1541-1557. https://doi.org/10.17755/esosder.474601
14. English, L. D., & Halford, G. S. (2012). Mathematics education: Models and processes. Routledge.
15. Fornell, C., & Larcker, D. F. (1981). Evaluating structural equation models with unobservable variables and measurement error. Journal of Marketing Research, 18(1), 39-50. https://doi.org/10.1177/002224378101800104
16. Fortes, E. C., & Andrade, R. R. (2019). Mathematical creativity in solving non-routine problems. The Normal Lights, 13(1), 108-135. https://doi.org/10.56278/tnl.v13i1.1237
17. Furnham, A., Hughes, D. J., & Marshall, E. (2013). Creativity, OCD, narcissism and the Big Five. Thinking Skills and Creativity, 10, 91-98. https://doi.org/10.1016/j.tsc.2013.05.003
18. Goretzko, D., Pham, T. T. H., & Bühner, M. (2021). Exploratory factor analysis: Current use, methodological developments and recommendations for good practice. Current Psychology, 40(7), 3510-3521. https://doi.org/10.1007/s12144-019-00300-2
19. Gümüş, F. Ö., ve Umay, A. (2017). Effect of problem solving strategies ınstruction on preservice elementary mathematics teachers’ conceptual /procedural solution preferences and problem solving performance. Elementary Education Online, 16(2), 746-764. https://doi.org/10.17051/ilkonline.2017.304731
20. Güner, P., & Erbay, H. N. (2021). Metacognitive skills and problem-solving. International Journal of Research in Education and Science, 7(3), 715–734. https://doi.org/10.46328/ijres.1594
21. Güneş, A. M. (2022). The relationship between problem-solving skills, burnout levels and self-efficacy beliefs of school principals. International Journal of Contemporary Educational Research, 9(3), 590-602. https://doi.org/10.33200/ijcer.1080663
22. 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
23. Gürsoy, S. E., ve Çeliköz, N. (2021). Developıng a problem solvıng scale for second grade prımary school students: a valıdıty and relıabılıty study. Mediterranean Journal of Educational Research, 15(36), 128-163. http://doi.org/10.29329/mjer.2020.367.8
24. Hacıömeroğlu, G. (2011). Turkish adaptation of beliefs about mathematical problem solving ınstrument. Dicle University Ziya Gökalp Faculty of Education Journal, (17), 119-132.
25. Hair, J. F., Black, W. C., Babin, B. J., & Anderson, R. E. (2019). Multivariate data analysis (8th ed.). Cengage Learning. Hambleton, R. K., Merenda, P. F., & Spielberger, C. D. (Eds.). (2005). Adapting educational and psychological tests for cross-cultural assessment. Lawrence Erlbaum Associates Publishers.
26. İncikabı, L., Mercimek, O., Ayanoğlu, P., Aliustaoğlu, F., & Tekin, N. (2016). An evaluation of middle school mathematics teaching programs based on tımss cognitive domains. Elementary Education Online, 15(4). https://doi.org/10.17051/io.2016.54792
27. Kaplan, A., & Duran, M. (2016). Mathematical metacognition awareness inventory towards middle school students: validity and reliability study. Ataturk University Kazim Karabekir Faculty of Education Journal, (32), 1-17.
28. Karasar, N. (2000). Scientific research method. Nobel Publications.
29. Kayan, F. (2008). A study on preservice elemantary mathematics teachers’matematical problem solving beliefs. Unpublished master's thesis (Master's thesis – Middle East Technical University) was obtained from the National Thesis Center of the Council of Higher Education. (Thesis No. 218040).
30. Kholid, M. N., Mahmudah, M. H., Ishartono, N., Putra, F. G., & Forthmann, B. (2024). Classification of students’ creative thinking for non-routine mathematical problems. Cogent Education, 11(1), 2394738. https://doi.org/10.1080/2331186X.2024.2394738
31. Kızılkaya, G., & Aşkar, P. (2009). The development of a reflective thinking skill scale towards problem solving. Education and Science, 34(154), 82-92. https://doi.org/10.15390/ES.2009.839
32. Kline, R. B. (2019). Principles and practice of structural equation modeling. Guilford publications.
33. Korkmaz, Ö. & Karakus, U. (2009). The effects of education faculties on students' critical thinking dispositions and levels. Turkish Educational Sciences Journal, 7(4), 879-902.
34. Kurnaz, A. (2019). Planning, implementing and evaluating critical thinking teaching activities. Education Publishing. Lin, C. (2023). Intellectual development and mathematics learning. Springer.
35. Millî Eğitim Bakanlığı [MEB]. (2024). Türkiye Century Education Model: Secondary School Mathematics Course Curriculum (Grades 9–12). Board of Education and Training. https://tymm.meb.gov.tr/ogretim-programlari
36. Monteleone, C., Miller, J., & Warren, E. (2023). Conceptualising critical mathematical thinking in young students. Mathematics Education Research Journal, 35(2), 339–359. https://doi.org/10.1007/s13394-023-00445-1
37. Muncer, G., Higham, P. A., Gosling, C. J., Cortese, S., Wood-Downie, H., & Hadwin, J. A. (2021). A meta-analysis investigating the association between metacognition and math performance in adolescence. Educational Psychology Review, 34, 301–334. https://doi.org/10.1007/s10648-021-09620-x
38. Muyo, M. (2015). Improving mathematical literacy and problem solving abilities of students in Prizren Faculty of Education. Unpublished doctoral thesis (Doctoral thesis – Balıkesir University) was obtained from the National Thesis Center of the Council of Higher Education. (Thesis No. 421402).
39. OECD. (2023). PISA 2022 Results (Volume I): The State of Learning and Equity in Education. OECD Publishing. https://doi.org/10.1787/53f23881-en
40. Özpınar, İ. (2012). Study of developing scales to measure the skills in 6th - 8th grade mathematics curriculum. Unpublished doctoral thesis (Doctoral thesis – Black Sea Technical University) was obtained from the National Thesis Center of the Council of Higher Education. (Thesis No. 344458).
41. Özsoy, G. (2008). Metacognition. The Journal of Turkish Educational Sciences, 6(4), 713-740.
42. Öztürk, M., Demir, Ü., & Akkan, Y. (2021). Investigation of proportional reasoning problem solving processes of seventh grade students: A mixed method research. International Journal on Social and Education Sciences (IJonSES), 3(1), 48–67. https://doi.org/10.46328/ijonses.66
43. Öztürk, M., Sarıkaya, İ., & Yıldız, K. A. (2023). Middle school students’ problem solving performance: Identifying the factors that influence it. International Journal of Science and Mathematics Education, 22, 1363–1379. https://doi.org/10.1007/s10763-023-10423-5
44. Sachdeva, S., & Eggen, P. O. (2021). Learners’ critical thinking about learning mathematics. International Electronic Journal of Mathematics Education, 16(3), em0644. https://doi.org/10.29333/iejme/11003
45. Sadık, R. (2006). The Comparison of success levels in four operations & problem-solving in natural numbers in primary school grade 4 and 5 students who know to play chess and who do not Unpublished master's thesis (Master's thesis – Bolu Abant İzzet Baysal University) was obtained from the National Thesis Center of the Council of Higher Education. (Thesis No. 190239).
46. Samura, A. O. & Juandi, D. (2020). Improving mathematical critical thinking skills through problem-based learning. Journal of Physics: Conference Series, 1521(3), 032102. https://doi.org/10.1088/1742-6596/1521/3/032102
47. 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. 334–370). Macmillan.
48. Sriraman, B. (2009). The characteristics of mathematical creativity. ZDM Mathematics Education, 41, 13–27. https://doi.org/10.1007/s11858-008-0114-z
49. Suherman, S., & Vidákovich, T. (2022). Assessment of mathematical creative thinking: A systematic review. Thinking Skills and Creativity, 44, 101019. https://doi.org/10.1016/j.tsc.2022.101019
50. Suliani, M., Juniati, D., & Lukito, A. (2024). The influence of student’s mathematical beliefs on metacognitive skills in solving mathematical problems. International Journal of Evaluation and Research in Education, 13(3), 1481–1491. https://doi.org/10.11591/ijere.v13i3.27117
51. Süzer, A. (2022). Problem solving skills and processes of primary school students Unpublished master's thesis (Master's thesis – Bartın University) was obtained from the National Thesis Center of the Council of Higher Education. (Thesis No. 713516).
52. Şahinkaya, T., Öztürk, M., & Albayrak, M. (2022). The effects of metacognitive IMPROVE technique on teaching ratio-proportion and developing proportional reasoning skills. Kocaeli University Education Journal, 5(2), 495–516. https://doi.org/10.33400/kuje.1137016
53. Tabachnick, B. G. & Fidell, L. S. (2013). Using Multivariate Statistics (6th ed.). Allyn and Bacon.
54. Topal, M., Topal, N., Görgel, A., Kama, H., & Yağız, N. (2025). Problem based learning and its theoretical foundations: a new approach to the learning process. Socrates Journal of Interdisciplinary Social Studies, 11(49), 46-64. https://doi.org/10.5281/zenodo.14632143
55. Uğurluoğlu, E. (2008). An investigation of elementary students? beliefs and attitudes towards mathematics and mathematical problem solving according to certain variables Unpublished master's thesis (Master's thesis – Eskişehir Osmangazi University) was obtained from the National Thesis Center of the Council of Higher Education. (Thesis No. 177267).
56. Uysal, O. (2007). Evaluation of relation between problem solving skills, anxiety and attitudes of secondary education grade ii students directed towards mathematics course Unpublished doctoral thesis (Doctoral thesis – Dokuz Eylul University) was obtained from the National Thesis Center of the Council of Higher Education. (Thesis No. 211583).
57. Ünal, M., & Aral, N. (2014). Development of problem solving scale in science education: Validity and reliability studies. Education and Science, 39(176), 267-278. http://dx.doi.org/10.15390.EB.2014.3585
58. Yaşar, S. (2022). The effect of storyline-based mathematics problem solving practices on problem solving success, skills and attitudes Unpublished master's thesis (Master's thesis – Bolu Abant İzzet Baysal University) was obtained from the National Thesis Center of the Council of Higher Education. (Thesis No. 769493).
59. Yüksel, M. Y., Tekin, Ö. E., & Kaplaner, K. (2021). The research of the relationship between the problem solving skills & metacognitive awareness of middle school students and the social emotional learning. Çukurova University Faculty of Education Journal, 50(1), 487-506.
60. Zhang, J., Zhou, Y., Jing, B., Pi, Z., & Ma, H. (2024). Metacognition and mathematical modeling skills: The mediating roles of computational thinking in high school students. Journal of Intelligence, 12(6), 55. https://doi.org/10.3390/jintelligence12060055
61. Zhou, Y., Ning, Y., Chen, J., Zhang, W., & Wijaya, T. T. (2024). Development and validation of Mathematical Higher‐Order Thinking Scale for high school students. Psychology in the Schools, 61(8), 3160-3192. https://doi.org/10.1002/pits.23213