Mathematical Modeling Process as an Activity Requiring Creativity

Yıl 2026, Cilt: 23 Sayı: 1 , 1 - 24 , 24.04.2026

Deniz Kaya , Tamer Kutluca

https://doi.org/10.33711/yyuefd.1788468

https://izlik.org/JA24RR75JX

Öz

The aim of this study is to address creativity as a measurable and conceptually assessable dimension by incorporating it into the processes of modeling competence. For this purpose, real-world problem situations requiring creativity were employed to evaluate the enriched structure. Usefulness, fluency, and originality were indicators of creativity in solving real-world problems. The study was conducted by addressing both qualitative and quantitative dimensions of the research process. The research participants consist of 60 students taking the modeling course in mathematics teaching at the undergraduate level. The participants, selected through criterion sampling, completed their work individually during the data collection process. The findings of the study revealed that students’ mathematical modeling (MM) competencies varied depending on the difficulty level and content structure of the tasks. A significant and consistent relationship was identified among the dimensions of usefulness, fluency, and originality in students' performance across all tasks. Overall, the findings reveal that creativity indicators—such as usefulness, fluency, and originality—should be integrated into the structure of MM competencies, and they contribute to opening a new avenue for future modeling studies in this direction.

Anahtar Kelimeler

Conceptualization , creativity , mathematical modeling , preservice mathematics teacher

Etik Beyan

This research was carried out with the permission of Nevşehir Hacı Bektaş Veli University Publication Ethics Board with the decision numbered 2022.13.431 dated 26.12.2022.

Yaratıcılık Gerektiren Bir Aktivite Olarak Matematiksel Modelleme Süreci

https://izlik.org/JA24RR75JX

Öz

Bu çalışmanın amacı, yaratıcılığı modelleme yeterlik süreçlerine dahil ederek ölçülebilir ve kavramsal olarak değerlendirilebilir bir boyut olarak ele almaktır. Bu amaç doğrultusunda, zenginleştirilmiş yapının değerlendirilmesi için yaratıcılık gerektiren gerçek dünya problem durumları kullanılmıştır. Gerçek dünya problemlerin çözüm sürecindeki yaratıcılık göstergeleri olarak yararlık, akıcılık ve orijinallik dikkate alınmıştır. Çalışma, araştırma sürecinin hem nitel hem de nicel boyutları dikkate alınarak yürütülmüştür. Araştırmanın katılımcıları lisans düzeyinde matematik öğretiminde modelleme dersini alan 60 lisans öğrenciden oluşmaktadır. Ölçüt örnekleme yöntemiyle belirlenen katılımcılar, veri toplama sürecinde çalışmalarını bireysel olarak gerçekleştirmiştir. Çalışmanın bulguları, öğrencilerin matematiksel modelleme (MM) yeterliklerinin, görevlerin zorluk düzeyi ve içerik yapısına bağlı olarak değişiklik gösterdiğini ortaya koymuştur. Tüm görevlerde öğrencilerin performansları incelendiğinde, yararlık, akıcılık ve orijinallik boyutları arasında anlamlı ve tutarlı ilişkiler belirlenmiştir. Genel olarak elde edilen sonuçlar, yararlılık, akıcılık ve özgünlük gibi yaratıcılık göstergelerinin MM yeterliklerinin yapısına dahil edilmesi gerektiğini ortaya koymakta ve bu doğrultuda yapılacak modelleme araştırmaları için yeni bir alan açmaktadır.

Anahtar Kelimeler

Kavramsallaştırma , yaratıcılık , matematiksel modelleme , matematik öğretmeni adayı

Etik Beyan

Bu araştırma, 26.12.2022 tarihli ve 2022.13.431 sayılı kararıyla Nevşehir Hacı Bektaş Veli Üniversitesi Bilimsel Araştırmalar ve Yayın Etik Kurulu'nun izniyle gerçekleştirilmiştir.

Kaynakça

• Acquah, E. O., & Szelei, N. (2020). The potential of modelling culturally responsive teaching: Pre-service teachers’ learning experiences. Teaching in Higher Education, 25(2), 157-173. https://doi.org/10.1080/13562517.2018.1547275
• Altman, D. G. (1991). Practical statistics for medical research. Chapman and Hall.
• Amabile, T. M. (1996). Creativity in context: Update to the social psychology of creativity. West-View Press.
• Asempapa, R. S. (2018). Assessing teachers’ knowledge of mathematical modeling: Results from an initial scale development. Journal of Mathematics Education, 11(1), 1-16. https://doi.org/10.26711/007577152790017
• Barker, A. (2002). The alchemy of innovation: Perspectives from the leading edge. Spiro Press.
• Blomhøj, M., & Jensen, T. H. (2007). What’s all the fuss about competencies? Experiences with using a competence perspective on mathematics education to develop the teaching of mathematical modelling. In Modelling and applications in mathematics education: The 14th ICMI study (pp. 45-56). Springer.
• Blomhøj, M., & Jensen, T. (2003). Developing mathematical modelling competence: Conceptual clarification and educational planning. Teaching Mathematics and Its Applications, 22(3), 123-139. https://doi.org/10.1093/teamat/22.3.123
• Blum, W. (2011). Can modelling be taught and learnt? Some answers from empirical research. In G. Kaiser, W. Blum, R. Borromeo Ferri, & G. Stillman (Eds), Trends in teaching and learning mathematical modelling (pp. 15-30). Springer. https://doi.org/10.1007/978-94-007-0910-2_3
• Blum, W., & Leiß, D. (2007). How do students and teachers deal with mathematical modelling problems? The example sugaloaf und the DISUM project. In C. Haines, P. L. Galbraith, W. Blum, & S. Khan (Eds.), Mathematical modelling (ICTMA12)-Education, Engineering and Economics. Horwood Publishing.
• Blum, W., & Leiß, D. (2005). Modellieren im Unterricht mit der "Tanken"-Aufgabe. Mathematik Lehren, 128, 18-21.
• Blum, W., & Kaiser, G. (1997). Vergleichende empirische Untersuchungen zu mathematischen Anwendungsfähigkeiten von englischen und deutschen Lernenden. Unpublished application to Deutsche Forschungsgesellschaft.
• Borromeo Ferri, R. (2018). Learning how to teach mathematical modelling in school and teacher education. Springer.
• Borromeo Ferri, R. (2006). Theoretical and empirical differentiations of phases in the modelling process. Zentralblatt für Didaktik der Mathematik 38(2), 86-95. https://doi.org/10.1007/BF02655883
• Borromeo Ferri, R., & Blum, W. (2014). Barriers and motivations of primary teachers for implementing modelling in mathematics lessons. In B. Ubuz, C. Haser, & M. A. Mariotti (Eds.), Proceedings of CERME 8 (pp. 1000-1009). Middle East Technical University.
• Bukova-Güzel, E. (Ed.) (2021). Mathematical modeling in mathematics education. For researchers, educators and students (4th ed.). Pegem Akademi Publishing.
• 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
• Chamberlin, S. A., & Moon, S. M. (2005). Model-eliciting activities as a tool to develop and identify creatively gifted mathematicians. Journal of Secondary Gifted Education, 17(1), 37-47. https://doi.org/10.4219/jsge-2005-393
• Clement, J. (2000) Analysis of clinical interviews: Foundations and model viability. In R, Lesh, & A. Kelly, (Eds.), Handbook of research methodologies for science and mathematics education (pp. 341-385). Lawrence Erlbaum Publishing.
• Council of Higher Education (CoHE) (2023). Elementary mathematics teaching undergraduate program. Retrieved from https://www.yok.gov.tr/kurumsal/idari-birimler/egitim-ogretim-dairesi
• English, L. D. (2009). Promoting interdisciplinarity through mathematical modelling. ZDM Mathematics Education, 41(1), 161-181. https://doi.org/10.1007/s11858-008-0106-z
• Feldman, D. H. (1999). The development of creativity. In R. J. Sternberg (Ed.), Handbook of creativity (pp. 169-186). Cambridge University Press.
• Freudenthal, H. (1991). Revisiting mathematics education. Kluwer Academic.
• Galbraith, P., & Stillman, G. (2006). A framework for identifying student blockages during transitions in the modelling process. Zentralblatt für Didaktik der Mathematik 38(2), 143-162. https://doi.org/10.1007/BF02655886
• Greefrath, G., & Vorhölter, K. (2016). Teaching and learning mathematical modelling: Approaches and developments from German speaking countries. In G. Greefrath, & K. Vorhölter (Eds.), Teaching and learning mathematical modelling (pp. 1-42). Springer. https://doi.org/10.1007/978-3-319-45004-9_1
• Guilford, J. P. (1977). Way beyond the IQ. Creative Synergistic Associates.
• Guilford, J. P. (1950). Creativity. American Psychologist, 5(9), 444-454. http://dx.doi.org/10.1037/h0063487
• Hébert, T. P., Cramond, B., Neumeister, K. L. S., Millar, G., & Silvian, A. F. (2002). E. Paul Torrance: His life, accomplishments, and legacy. Research monograph series. National Research Center on the Gifted and Talented, Storrs. Retrieved from https://eric.ed. gov/?id=ED480289
• Ikeda, T., & Stephens, M. (1998). The influence of problem format on students’ approaches to mathematical modelling. In P. Galbraith, W. Blum, G. Booker, & I. Huntley (Eds.), Mathematical modelling, teaching and assessment in a technology-rich world (pp.223-232). Horwood Publishing.
• Jensen, T. H. (2007). Assessing mathematical modelling competency. In C. P. Haines, P. Galbraith, W. Blum & S. Khan (Eds.), Mathematical modelling (ICTMA 12): Education, engineering and economics (pp. 141–148). Horwood Publishing.
• Kaiser, G. (2017). The teaching and learning of mathematical modelling. In J. Cai (Ed.), Compendium for research in mathematics education (pp. 267–291). National Council of Teachers of Mathematics.
• Kaiser, G. (2007). Modelling and modelling competencies in school. In C. Haines, P. Galbraith, W. Blum, & S. Khan (Eds.), Mathematical modelling (ICTMA12) education, engineering and economics (pp. 110-119). Horwood Publishing.
• Kaiser, G., & Brand, S. (2015). Modelling competencies: Past development and further perspectives. In G. A. Stillman, W. Blum, & M. S. Biembengut (Eds.), Mathematical modelling in education research and practice: Cultural, social and cognitive influences (pp. 129-149). Springer.
• Kaiser, G., Blomhøj, M., & Sriraman, B. (2006). Towards a didactical theory for mathematical modelling. Zentralblatt für Didaktik der Mathematik, 38(2), 82-85. https://doi.org/10.1007/BF02655882
• Kaiser, G., & Schwarz, B. (2006). Mathematical modelling as bridge between school and university. ZDM Mathematics Education, 38(2), 196-208. https://doi.org/10.1007/BF02655889
• Kattou, M., Kontoyianni, K., Pitta-Pantazi, D., & Christou, C. (2013). Connecting mathematical creativity to mathematical ability. ZDM Mathematics Education, 45(2), 167-181. https://doi.org/10.1007/s11858-012-0467-1
• Klavir, R., & Gorodetsky, M. (2011). Features of creativity as expressed in the construction of new analogical problems by intellectually gifted students. Creative Education, 2(3), 164-173. https://doi.org/10.4236/ce.2011.23023
• Leikin, R. (2013). Evaluating mathematical creativity: The interplay between multiplicity and insight. Psychological Test and Assessment Modeling, 55(4), 385-400.
• Leikin, R., & Lev, M. (2013). Mathematical creativity in generally gifted and mathematically excelling adolescents: What makes the difference? ZDM Mathematics Education, 45(2), 183-197. https://doi.org/10.1007/s11858-012-0460-8
• Lesh, R., Hoover, M., Hole, B., Kelly, A., & Post, T. (2000). Principles for developing thought-revealing activities for students and teachers. In A. Kelly & R. Lesh (Eds.), Handbook of research in mathematics and science education (pp. 113-149). Erlbaum Publishing.
• Lu, X., Cheng, J., Xu, B., & Wang, Y. (2019). Xuesheng shuxue jianmo suyang de pingjia gongju yanjiu [A research of the assessment tool of students’ mathematical modelling competency]. Kecheng Jiaocai Jiaofa [Curriculum, Teaching Materials, and Method], 39(2), 100-106.
• Lu, X., & Kaiser, G. (2022a). Creativity in students’ modelling competencies: Conceptualisation and measurement. Educational Studies in Mathematics, 109(2), 287-311. https://doi.org/10.1007/s10649-021-10055-y
• Lu, X., & Kaiser, G. (2022b). Can mathematical modelling work as a creativity‑demanding activity? An empirical study in China. ZDM Mathematics Education, 54(1), 67-81. https://doi.org/10.1007/s11858-021-01316-4
• Ludwig, M., & Xu, B. (2010). A comparative study of modelling competencies among Chinese and German students. Journal für Mathematik-Didaktik, 31(1), 77-97. https://doi.org/10.1007/s13138-010-0005-z
• Maaß, K. (2006). What are modelling competencies? Zentralblatt für Didaktik der Mathematik, 38(2), 113-142. https://doi.org/10.1007/BF02655885
• Mann, E. L. (2006). Creativity: The essence of mathematics. Journal for the Education of the Gifted, 30(2), 236-260. https://doi.org/10.4219/jeg-2006-264
• Mayring, P. (2014). Qualitative content analysis: Theoretical foundation, basic procedures and software solution. Klagenfurt. Retrieved from https://nbnresolving.org/urn:nbn:de:0168-ssoar-395173
• National Council of Teachers of Mathematics (NCTM) (2020). NCTM 2020 standards for mathematics teacher preparation. Retrieved from https://www.nctm.org/caep/
• Niss, M., & Blum, W. (2020). The learning and teaching of mathematical modelling. Routledge. https://doi.org/10.4324/9781315189314
• Osborn, A. (1953). Applied imagination: Principles and procedures of creative problem solving. Charles Scribner's Sons.
• Pitta Pantazi, D., Kattou, M., & Christou, C. (2018). Mathematical creativity: Product, person, process and press. In F. M. Singer (Ed.), Mathematical creativity and mathematical giftedness: Enhancing creative capacities in mathematically promising students (pp. 27-53). Springer.
• Preiser, S. (1976). Kreativitätsforschung [Research on creativity]. Wissenschaftliche Buchgesellschaft.
• Renzulli, J. S. (2012). Reexamining the role of gifted education and talent development for the 21st century: A four-part theoretical approach. Gifted Child Quarterly 56(3), 150-159. https://doi.org/10.1177/0016986212444901
• Robinson, K. (2011). Out of our minds: Learning to be creative. Capstone Publishing.
• Runco, M. A. (2010). Divergent thinking, creativity, and ideation. In J. C. Kaufman & R. J. Sternberg (Eds.), The Cambridge handbook of creativity (pp. 413-446). Cambridge University Press.
• Schukajlow, S., Krug, A., & Rakoczy, K. (2015). Effects of prompting multiple solutions for modelling problems on students’ performance. Educational Studies in Mathematics, 89(3), 393-417. https://doi.org/10.1007/s10649-015-9608-0
• Silver, E. A. (1997). Fostering creativity through instruction rich in mathematical problem solving and problem posing. Zentralblatt für Didaktik der Mathematik, 29(3), 75-80. https://doi.org/10.1007/s11858-997-0003-x
• Sriraman, B. (2009). The characteristics of mathematical creativity. ZDM Mathematics Education, 41(1-2), 13-27. https://doi.org/10.1007/s11858-008-0114-z
• Stillman, G. A. (2019). State of the art on modelling in mathematics education-lines of inquiry. In G. A. Stillman, & J. Brown (Eds.) Lines of inquiry in mathematical modelling research in education. ICME-13 monographs. Springer. https://doi.org/10.1007/978-3-030-14931-4_1
• Stillman, G., Kaiser, G., Blum, W., & Brown, J. (Eds.). (2013). Teaching mathematical modeling: Connecting research to practice. Springer.
• Torrance, E. P. (1998). The Torrance test of creative thinking norms‐technical manual figural, forms A and B. Scholastic Testing Service, Inc.
• Torrance, E. P. (1988). The nature of creativity as manifest in its testing. In R. J. Sternberg (Ed.), The nature of creativity: Contemporary psychological perspectives (pp. 43-75). Cambridge University Press.
• Torrance, E. P. (1966). Torrance tests of creative thinking: Directions manual and scoring guide. Personnel Press.
• Van Harpen, X. Y., & Sriraman, B. (2013). Creativity and mathematical problem posing: An analysis of high school students’ mathematical problem posing in China and the USA. Educational Studies in Mathematics, 82(2), 201-221. https://doi.org/10.1007/s10649-012-9419-5
• Vorhölter, K. (2018). Conceptualization and measuring of metacognitive modelling competencies: Empirical verification of theoretical assumptions. ZDM Mathematics Education, 50(1-2), 343-354. https://doi.org/10.1007/s11858-017-0909-x
• Wessels, H. (2014). Levels of mathematical creativity in model-eliciting activities. Journal of Mathematical Modelling and Application, 1(9), 22-40.