Investigation of the relationship between learning concepts and mathematical thinking of secondary school students with canonical correlation analysis

Ahsen Filiz 1 * , Mevhibe Kobak Demir 2
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1 Biruni University, Istanbul, TURKEY
2 Balıkesir University, Balikesir, TURKEY
* Corresponding Author
EUR J SCI MATH ED, Volume 13, Issue 4, pp. 273-288. https://doi.org/10.30935/scimath/17247
Published: 08 October 2025
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ABSTRACT

In this study, the relationship between secondary school students’ conceptions of learning and their mathematical thinking was examined. The study was conducted with 311 secondary school students using relational survey model. The data were collected with the learning conceptions scale and mathematical thinking scale, and the relationship between the variables was evaluated by canonical correlation analysis. The results revealed that there was a high level of relationship between students’ learning conceptions and mathematical thinking skills. It was determined that the sub-dimensions of learning conceptions, knowledge acquisition and use, and personal changes had a moderate inverse effect on mathematical thinking. In addition, the tendency for higher-order thinking sub-dimension made the highest contribution to the model but had an inverse relationship with learning conceptions. These findings provide important clues to understand the effect of learning conceptions on mathematical thinking.
Keywords: sustainable education, learning conceptions, mathematical thinking, canonical correlation analysis, secondary school students

CITATION

Filiz, A., & Kobak Demir, M. (2025). Investigation of the relationship between learning concepts and mathematical thinking of secondary school students with canonical correlation analysis. European Journal of Science and Mathematics Education, 13(4), 273-288. https://doi.org/10.30935/scimath/17247

REFERENCES

  • Afifi, A., & Clark, V. (2004). Computer-aided multivariate analysis. Chapman & Hall/CRC.
  • Alamdarloo, G. H., Moradi, S., & Dehshiri, R. G. (2013). The relationship between students’ conceptions of learning and their academic achievement. Psychology, 4(1), 44–49. https://doi.org/10.4236/psych.2013.41006
  • Albayrak, A. S. (2010). Kanonik korelasyon analizi [Canonical correlation analysis]. In Ş. Kalaycı (Ed.), SPSS uygulamalı çok değişkenli istatistik teknikleri (pp. 234–255). Asil Yayın Dağıtım.
  • Anderson, L. W., & Krathwohl, D. R. (Eds.). (2001). A taxonomy for learning, teaching, and assessing: A revision of Bloom’s taxonomy of educational objectives. Longman.
  • Ashcraft, M. H., & Kirk, E. P. (2001). The relationships among working memory, math anxiety, and performance. Journal of Experimental Psychology: General, 130(2), 224–237. https://doi.org/10.1037/0096-3445.130.2.224
  • Aygün, Y., Orbay, K., & Aydın Güç, F. (2021). Üstün yetenekli tanısı konulmuş ve konulmamış öğrencilerin matematiksel düşünme süreçlerinin karşılaştırılması [Comparison of mathematical thinking processes of gifted and non-gifted students]. Milli Eğitim Dergisi, 50(229), 337–362.
  • Bahadır, F., Yılmaz, A., & Bahar, H.H. (2025). İlköğretim öğrencilerinin öğrenme anlayışlarının incelenmesi [Examining primary school students’ learning concepts]. Eğitim Yansımaları, 9(1), 1–13. https://doi.org/10.70740/eduref.1637902
  • Bahçivan, E., & Kapucu, S. (2014). Adaptation of conceptions of learning science questionnaire into Turkish and science teacher candidates’ conceptions of learning science. European Journal of Science and Mathematics Education, 2(2), 106–118. https://doi.org/10.30935/scimath/9404
  • Baş, G. (2013). İlköğretim öğrencilerinin öğrenme anlayışları ölçeği: Geçerlik ve güvenirlik çalışması [Primary school students’ learning conceptions scale: A validity and reliability study]. Abant İzzet Baysal Üniversitesi Eğitim Fakültesi Dergisi, 13(1), 97–115.
  • Beattie, V., Collins, B., & McInnes, B. (1997). Deep and surface learning: A simple or simplistic dichotomy? Accounting Education, 6(1), 1–12. https://doi.org/10.1080/096392897331587
  • Benli, F. B., & Gürtaş, K. (2021). Ortaokul 7. sınıf öğrencilerinin rasyonel sayılar konusundaki matematiksel düşünme ve problem çözme becerilerinin incelenmesi [Examining the mathematical thinking and problem-solving skills of 7th grade secondary school students on rational numbers]. Pearson Journal, 6(15), 552–562. https://doi.org/10.46872/pj.418
  • Beşoluk, Ş., & Önder, İ. (2010). Öğretmen adaylarının öğrenme yaklaşımları, öğrenme stilleri ve eleştirel düşünme eğilimlerinin incelenmesi [Examining prospective teachers’ learning approaches, learning styles, and critical thinking tendencies]. İlköğretim Online, 9(2), 679–693.
  • Biggs, J. (1987). Student approaches to learning and studying. Australian Council for Educational Research. https://eric.ed.gov/?id=ED308201
  • Biggs, J., Kember D., & Leung, D. Y. P. (2001). The revised two factor study process questionnaire. British Journal of Educational Psychology, 71(1), 133–149. https://doi.org/10.1348/000709901158433
  • Boaler, J. (2002). Learning from teaching: Exploring the relationship between reform curriculum and equity. Journal for Research in Mathematics Education, 33(4), 239–258. https://doi.org/10.2307/749740
  • Bordens, K. S. & Abbott, B. B. (2011). Research design and methods: A process approach. The McGraw-Hill Companies.
  • Bransford, J. D., Zech, L., Schwartz, D., Barron, B., & Vye, N. (2012). Fostering mathematical thinking in middle school students: Lessons from research. In R. J. Sternberg, & T. Ben-Zeev (Eds.), The nature of mathematical thinking (pp. 45–70). Routledge.
  • Büyüköztürk, Ş. (2012). Veri analizi el kitabı [Data analysis handbook] (17. Baskı). Pegem Akademi.
  • Cai, J. (2003). Singaporean students’ mathematical thinking in problem-solving and problem posing: An exploratory study. International Journal of Mathematical Education in Science and Technology, 34(5), 719–737. https://doi.org/10.1080/00207390310001595401
  • Çankaya, S. (2005). Kanonik korelasyon analizi ve hayvancılıkta kullanımı [Canonical correlation analysis and its use in animal husbandry] [Unpublished PhD thesis]. Çukurova Üniversitesi.
  • Case, J. (2004). Between deep and surface: Procedural approaches to learning in engineering education contexts. Studies in Higher Education, 29(6), 605–615. https://doi.org/10.1080/0307507042000261571
  • Chan, K. W. & Elliott, R. G. (2004). Relational analysis of personal epistemology and conceptions about teaching and learning. Teaching and Teacher Education, 20, 817–831. https://doi.org/10.1016/j.tate.2004.09.002
  • Chin, C., & Brown, D. E. (2000). Learning in science: A comparison of deep and surface approaches. Journal of Research in Science Teaching, 37(2), 109–138. https://doi.org/10.1002/(SICI)1098-2736(200002)37:2<109::AID-TEA3>3.0.CO;2-7
  • Cohen, J., Cohen, P., West, S. G., & Aiken, L. S. (2003). Applied multiple regression/correlation analysis for the behavioral sciences. Lawrence Erlbaum Associates.
  • Creswell, J. W. (2017). Araştırma deseni nitel, nicel ve karma yöntem yaklaşımları [Research design: Qualitative, quantitative and mixed method approaches]. Eğiten Kitap.
  • Demetriou, A., Kazi, S., Makris, N., & Spanoudis, G. (2020). Cognitive ability, cognitive self-awareness, and school performance: From childhood to adolescence. Intelligence, 79, Article 101432. https://doi.org/10.1016/j.intell.2020.101432
  • Demetriou, A., Makris, N., Tachmatzidis, D., Kazi, S., & Spanoudis, G. (2019). Decomposing the influence of mental processes on academic performance. Intelligence, 77, Article 101404. https://doi.org/10.1016/j.intell.2019.101404
  • Dowker, A. (2005). Individual differences in arithmetic: Implications for psychology, neuroscience and education. Psychology Press. https://doi.org/10.4324/9780203324899
  • Düzgün, C., & İpek, A. S. (2023). Sekizinci sınıf öğrencilerinin üslü ifadelerle ilgili matematiksel düşünme süreçlerinin incelenmesi [Examining eighth grade students’ mathematical thinking processes related to exponential expressions]. MANAS Sosyal Araştırmalar Dergisi, 12(4), 1249–1269. https://doi.org/10.33206/mjss.1272950
  • Entwistle, N. (2009). Teaching for understanding at university: Deep approaches and distinctive ways of thinking. Palgrave Macmillan.
  • Entwistle, N., & McCune, V. (2004a). The conceptual bases of study strategy inventories. Educational Psychology Review, 16(4), 325–345. https://doi.org/10.1007/s10648-004-0003-0
  • Entwistle, N., & McCune, V. (2004b). The nature of learning in higher education: A review of research on the understanding of student learning in different contexts. Studies in Higher Education, 29(2), 1–25.
  • Entwistle, N., & Peterson, E. (2004). Conceptions of learning and knowledge in higher education: Relationships with study behaviour and influences of learning environments. International Journal of Educational Research, 41(6), 407–428. https://doi.org/10.1016/j.ijer.2005.08.009
  • Ersoy, E., & Başer, N. (2013). Matematiksel düşünme ölçeğinin geliştirilmesi [Development of a mathematical thinking scale]. Kastamonu Eğitim Dergisi, 21(4), 1471–1486.
  • Everitt, B., & Hothorn, T. (2011). An introduction to applied multivariate analysis with R. Springer. https://doi.org/10.1007/978-1-4419-9650-3
  • Fan, X. (1996). Canonical correlation analysis as a general analytic model. In B. Thompson (Ed.), Advances in social science methodology (pp. 71–94). JAI.
  • Fan, X. (1997). Canonical correlation analysis and structural equation modeling: What do they have in common? Structural Equation Modeling, 4, 65–79. https://doi.org/10.1080/10705519709540060
  • Ferdianto, F., Sukestiyarno, Y. L., & Widowati, I. J. (2022). Mathematical thinking process on numeracy literacy problems for middle school students. Journal of Positive School Psychology, 6(8), 6909–6923.
  • Gray, A. (1997). Contructivist teaching and learning. SSTA Research Centre. https://saskschoolboards.ca/wp-content/uploads/97-07.htm
  • Hair Jr, J. F., Black, W. C, Babin, B. J., & Anderson, R. E. (2010). Multivariate data analysis. Prentice Hall.
  • Härdle, W. K., & Simar, L. (2012). Applied multivariate statistical analysis. Springer. https://doi.org/10.1007/978-3-642-17229-8
  • Hasbek, G. (2020). Ortaokul öğrencilerinin öğrenme yaklaşımları ile değerlendirme uygulamalarına yönelik algıları arasındaki ilişkilerin kanonik korelasyon analizi ile incelenmesi [Examining the relationships between middle school students’ perceptions of learning approaches and assessment practices using canonical correlation analysis] [Unpublished master’s thesis]. Sivas Cumhuriyet Üniversitesi.
  • Henson, R. K. (2000). Demystifying parametric analyses: Illustrating canonical correlation as the multivariate general linear model. Multiple Linear Regression Viewpoints, 26(1), 11–19.
  • Holmes, J. (2012). Exploring cognitive styles in learning mathematics. Routledge.
  • Huo, Y., & Budescu, D. V. (2009). An extension of dominance analysis to canonical correlation analysis. Multivariate Behavioral Research, 44, 688–709. https://doi.org/10.1080/00273170903187673
  • İlhan Beyaztaş, D. & Senemoğlu, N. (2015). Başarılı öğrencilerin öğrenme yaklaşımları ve öğrenme yaklaşımlarını etkileyen faktörler [Learning approaches of successful students and factors affecting learning approaches]. Eğitim ve Bilim, 40(179), 193–216. https://doi.org/10.15390/EB.2015.4214
  • Karasar, N. (2005). Bilimsel araştırma yöntemi: Kavramlar ilkeler teknikler [Scientific research method: Concepts, principles, techniques]. Nobel Yayıncılık.
  • Kember, D. (1997). A reconceptualisation of the research into university academics’ conceptions of teaching. Learning and Instruction, 7(3), 255–275. https://doi.org/10.1016/S0959-4752(96)00028-X
  • Kılıç, H., Tunç Pekkan, Z., & Karatoprak, R. (2013). Materyal kullanımının matematiksel düşünme becerisine etkisi [The effect of material use on mathematical thinking skills]. Eğitimde Kuram ve Uygulama, 9(4), 544–556.
  • Kline, R.B. (2011). Principles and practice of structural equation modeling. The Guilford Press.
  • Kükey, E., Aslaner, R., & Tutak, T. (2019). Matematiksel düşünmenin varsayımda bulunma bileşenine yönelik olarak ortaokul öğrencilerinin kullandıkları problem çözme stratejilerinin incelenmesi [Examining the problem solving strategies used by middle school students regarding the hypothesizing component of mathematical thinking.]. Journal of Computer and Education Research, 7(13), 146–170. https://doi.org/10.18009/jcer.535610
  • Leech, N. L. Barlett, K. C. & Morgan, G. A. (2005). SPSS for intermediate statistics: Use and interpretation. Lawrence Erlbaum Associates.
  • Lim, C. S., & Hwa, T. Y. (2006). Promoting mathematical thinking in the Malaysian classroom: Issues and challenges. In Proceedings of the Meeting of the APEC–Tsukuba International Conference.
  • Marton, F., & Säljö, R. (1976). On qualitative differences in learning: I–Outcome and process. British Journal of Educational Psychology, 46(1), 4–11. https://doi.org/10.1111/j.2044-8279.1976.tb02980.x
  • Murphy, P. E. L. (2016). Student approaches to learning, conceptions of mathematics, and successful outcomes in learning mathematics. In L. Wood, & Y. Breyer (Eds.), Success in higher education (pp. 75–93). Springer. https://doi.org/10.1007/978-981-10-2791-8_5
  • Olkun, S., & Toluk Uçar, Z. (2014). İlköğretimde etkinlik temelli matematik öğretimi [Activity-based mathematics teaching in primary education] (6. Baskı). Eğiten Kitap.
  • Pedhazur, E. J. (1997). Multiple regressions in behavioral research: Explanation and prediction. Holt, Rinehart & Winston.
  • Pugh, R. C., & Hu, Y. (1991). Use and interpretation of canonical correlation analysis in journal of educational research articles: 1978-1989. Journal of Research, 84(3), 147–152. https://doi.org/10.1080/00220671.1991.10886008
  • Rencher, C. A. (2002). Methods of multivariate analysis. John Wiley & Sons, Inc. https://doi.org/10.1002/0471271357
  • Saltanat, B., Guldana, A., Lazzat, K., Fang, Y., Tevfik, H., & Khang, L. (2023). Improving students’ cognitive processes to enhance the quality of education. In Proceedings of the Materials of International Practical Internet Conference “Challenges of Science”. https://doi.org/10.31643/2023.06
  • Schaathun, H. G. (2022). On understanding in mathematics. Teaching Mathematics and Its Applications, 41(4), 318–328. https://doi.org/10.1093/teamat/hrac016
  • Sherry, A., & Henson, R. K. (2005) Conducting and interpreting canonical correlation analysis in personality research: A user-friendly primer. Journal of Personality Assessment, 84(1), 37–48. https://doi.org/10.1207/s15327752jpa8401_09
  • Skemp, R. R. (1976). Relational understanding and instrumental understanding. Mathematics Teaching, 77(1), 20–26.
  • Skemp, R. R. (2006). Relational understanding and instrumental understanding. Mathematics Teaching in the Middle School, 12(2), 88–95. https://doi.org/10.5951/MTMS.12.2.0088
  • Stacey, K. (2006). What is mathematical thinking and why is it important? University of Melbourne. https://www.criced.tsukuba.ac.jp/math/apec/apec2007/paper_pdf/Kaye%20Stacey.pdf
  • Stangor, C. (2010). Research methods for the behavioral sciences. Wadsworth.
  • Stevens, J. P. (2009). Applied multivariate statistics for the social sciences. Routledge.
  • Tabachnick, B. G., & Fidell, L. S. (2007). Using multivariate statistics. Pearson.
  • Thompson, B. (2000). Canonical correlation analysis. In L. G. Grimm, & P. R. Yarnold (Eds.), Reading and understanding more multivariate statistics. American Psychological Association.
  • Trigwell, K., & Prosser, M. (1991). Improving the quality of student learning: The influence of learning context and student approaches to learning on learning outcomes. Higher Education, 22(3), 251–266. https://doi.org/10.1007/BF00132290
  • Tsai, C. C. (2004). Conceptions of learning science among high-school students in Taiwan: A phenomenographic analysis. International Journal of Science Education, 26(14), 1733–1750. https://doi.org/10.1080/0950069042000230776
  • Tüzün, M., & Cihangir, A. (2020). Ortaokul öğrencilerinin matematiksel düşünme aşamaları ile matematik öz yeterlikleri arasındaki ilişkinin incelenmesi [Examining the relationship between secondary school students’ mathematical thinking stages and their mathematical self-efficacy]. Ahmet Keleşoğlu Eğitim Fakültesi Dergisi, 2(2), 210–228. https://doi.org/10.38151/akef.2020.5
  • Varmuza, K., & Filzmoser, P. (2009). Introduction to multivariate statistical analysis in chemometrics. CRC Press. https://doi.org/10.32614/CRAN.package.chemometrics
  • Yıldırım, D., & Yavuzsoy Köse, N. (2017). Ortaokul öğrencilerinin çokgen problemlerindeki matematiksel düşünme süreçleri [Mathematical thinking processes of middle school students in polygon problems]. Abant İzzet Baysal Üniversitesi Eğitim Fakültesi Dergisi, 18(1), 605–633. https://doi.org/10.17240/aibuefd.2018..-362044
  • Yılmaz, B., M., & Orhan, F. (2011). Ders çalışma yaklaşımı ölçeği’nin türkçe formunun geçerlik ve güvenirlik çalışması [Validity and reliability study of the Turkish form of the study approach scale]. Eğitim ve Bilim, 36(159), 69–83.