Review of Mathematical Modeling Research: A Descriptive Content Analysis Study

Yıl 2023, Cilt: 17 Sayı: 2, 994 - 1025, 02.01.2024

İbrahim Çetin Mustafa Aydın Şerife Bilgiç

https://doi.org/10.17522/balikesirnef.1321365

Öz

Recently, mathematical models and modeling practices have become popular in associating mathematics with real-life problems and, hence understanding this relationship. Accordingly, the mathematical modeling skill has been adopted in the standards and by researchers. Understanding the use of mathematical modeling in the learning and teaching processes of mathematics education will contribute to the future of the field. This study aimed to review the trends in mathematical modeling literature using leading research studies. This study reviewed the various types of studies indexed in the Web of Science database between 2000 and 2021 regarding how they addressed modeling. As well as mathematical modeling approaches used, the studies were reviewed in terms of basic characteristics such as publication year, sample, and research method. We evaluated studies using a form developed by the researchers, and the study revealed an increase in the number of studies over the years, and the studies were conducted mostly with pre-service teachers. In addition, we observed that research studies employed mostly small samples to closely monitor the modeling process.

Anahtar Kelimeler

mathematical modeling, mathematics, modeling, mathematics education, descriptive content analysis

Matematiksel Modelleme Araştırmalarının İncelenmesi: Betimleyici Bir İçerik Analizi Çalışması

Öz

Matematiğin gerçek yaşamdaki problemlerle ilişkilendirilmesi ve anlamlandırılmasında matematiksel modeller ve modelleme uygulamaları gün geçtikçe daha da benimsenir hale gelmiştir. Bu doğrultuda bir yetkinlik olarak geliştirilen matematiksel modelleme becerisi ise hem standartlar arasında hem de araştırmacılar tarafında yer edinmiştir. Özellikle matematik eğitiminde öğrenme ve öğretme süreçlerinde matematiksel modellemenin kullanımının anlaşılması bu çalışmaların geleceği için katkı sağlayacaktır. Bu araştırmada matematik eğitiminde modelleme çalışmalarına ilişkin eğilimlerin önde gelen çalışmalar üzerinden değerlendirilmesi amaçlanmıştır. Web of Science veri tabanında indekslenen araştırmalarla yürütülen çalışmada 2000-2021 yılları arasındaki farklı türdeki araştırmaların modelleme çalışmalarını hangi yönleriyle ele aldığı incelenmiştir. Bu çalışmalarda kullanılan matematiksel modelleme yaklaşımlarının yanı sıra araştırmalar yıl, örneklem ve kullanılan yöntem gibi temel özellikleri bakımından ele alınmıştır. Araştırmacılar tarafından geliştirilen form üzerinden değerlendirilen çalışmalar yıllara göre bu çalışmalarda beklendiği gibi bir artış meydana geldiğini, öğretmen adayları ile çoğunlukla araştırmaların yürütüldüğünü göstermiştir. Ayrıca araştırmada modelleme sürecinin yakından izlenmesi amacıyla çoğunlukla daha küçük araştırma grupları ile çalışmaların yürütüldüğü görülmüştür. Eğitsel modelleme ve gerçekçi modelleme yaklaşımlarının incelenen araştırmalarda öne çıkan modelleme yaklaşımları olduğu görülmüştür. Araştırma sonuçları, öğrencilerin sorumlu vatandaş olabilmeleri ve toplumsal gelişmelere katılım sağlayabilmeleri için bir yetkinlik olarak görülen modelleme becerisine ilişkin çalışmaların literatürde halen sınırlı bir yer tuttuğunu göstermiştir.

Anahtar Kelimeler

matematiksel modelleme, matematik, modelleme, matematik eğitimi, betimsel içerik analizi

Kaynakça

• Albayrak, E., & Çiltaş, A. (2017). Türkiye’de matematik eğitimi alanında yayınlanan matematiksel model ve modelleme araştırmalarının betimsel içerik analizi. Uluslararası Türk Eğitim Bilimleri Dergisi, 2017(9), 258-283.
• Amit, M. (1999). Mathematics for all: Millennial vision or feasible reality. In Z. Usiskin (Ed.), Developments in school mathematics around the World (Vol. 4, pp. 23–35). National Council of Teachers of Mathematics
• Asempapa, R. S., & Brooks, G. P. (2020). Factor analysis and psychometric evaluation of the mathematical modeling attitude scale for teachers of mathematics. Journal of Mathematics Teacher Education, 25, 131-161. https://doi.org/10.1007/s10857-020-09482-0
• Australia Ministry of Education, (2008). Australian curriculum, http://www.australiancurriculum.edu.au/mathematics/rationale
• Aztekin, S., & Taşpınar Şener, Z. (2015). The Content Analysis of Mathematical Modelling Studies in Turkey: A Meta-synthesis Study. Education & Science, 40(178), 139-161. https://doi.org/10.15390/eb.2015.4125
• Bal, A. P., & Doganay, A. (2014). Improving primary school prospective teachers' understanding of the mathematics modelling process. Educational Sciences: Theory and Practice, 14(4), 1375-1384. https://doi.org/10.12738/estp.2014.4.2042
• Barquero, B., Bosch, M., & Romo, A. (2018). Mathematical modelling in teacher education: dealing with institutional constraints. ZDM, 50(1), 31-43. https://doi.org/10.1007/s11858-017-0907-z
• Berry, J., & Houston, K. (1995). Mathematical modelling. Bristol: J.W. Arrowsmith Ltd.
• Blum, W. (2011). Can modelling be taught and learnt? Some answers from empirical research. Trends in teaching and learning of mathematical modelling: ICTMA14, 15-30.
• Blum, W., & Ferri, R. B. (2009). Mathematical modelling: Can it be taught and learnt? Journal of Mathematical Modelling and Application, 1 (1), 45-58.
• Blum, W., & Leiβ, D. (2007). How do students and teachers deal with mathematical modelling problems? The example “Filling up”. In C. Haines et al. (Eds.), Mathematical modelling (ICTMA 12): Education, engineering and economics (pp. 222–231). Chichester: Horwood. https://doi.org/10.1533/9780857099419.5.221
• Blum, W., & Niss, M. (1991). Applied mathematical problem solving, modelling, applications, and links to other subjects—State, trends and issues in mathematics instruction. Educational studies in mathematics, 22(1), 37-68.
• Bukova Güzel, E. (2016). Matematik eğitiminde matematiksel modelleme [Mathematical modeling in mathematics education: For researchers, educators and students]. Ankara: Pegem Akademi.
• Chamberlin, S. A., & Moon, S. M. (2008). How does the problem-based learning approach compare to the model-eliciting activity approach in mathematics? International Journal for Mathematics Teaching and Learning, 9(3), 78-105.
• Chan, C. M. E. (2013). Initial Perspectives of Teacher Professional Development on Mathematical Modelling in Singapore: Conceptions of Mathematical Modelling. In International Perspectives on the Teaching and Learning of Mathematical Modelling (pp. 405–413). Springer Netherlands. https://doi.org/10.1007/978-94-007-6540-5_34
• Chang, Y. P., Krawitz, J., Schukajlow, S., & Yang, K. L. (2020). Comparing German and Taiwanese secondary school students’ knowledge in solving mathematical modelling tasks requiring their assumptions. ZDM, 52(1), 59-72. https://doi.org/10.1007/s11858-019-01090-4
• Çavuş Erdem, Z. (2018). Matematiksel modelleme etkinliklerine dayalı öğrenim sürecinin alan ölçme konusu bağlamında incelenmesi [Investigation Of The Learning Process Based On Mathematical Modeling Activities In The Context Of Area Measurement] (Doctoral dissertation, Adıyaman Üniversitesi).
• Çekmez, E. (2020). Using dynamic mathematics software to model a real-world phenomenon in the classroom. Interactive Learning Environments, 28(4), 526-538. https://doi.org/10.1080/10494820.2019.1674882
• Cevikbas, M., Kaiser, G., & Schukajlow, S. (2022). A systematic literature review of the current discussion on mathematical modelling competencies: State-of-the-art developments in conceptualizing, measuring, and fostering. Educational Studies in Mathematics, 1-32. https://doi.org/10.1007/s10649-021-10104
• Ciltas, A., & Isik, A. (2013). The Effect of Instruction through Mathematical Modelling on Modelling Skills of Prospective Elementary Mathematics Teachers. Educational Sciences: Theory and Practice, 13(2), 1187-1192.
• Damlamian, A., Rodrigues, J. F., & Stra¨ßer, R. (Eds.). (2013). Educational interfaces between mathematics and industry. Report on an ICMI-ICIAM-study. Cham: Springer.
• Dawn, N. K. E. (2018). Towards a professional development framework for mathematical modelling: The case of Singapore teachers. ZDM, 50(1), 287-300. https://doi.org/10.1007/s11858-018-0910-z
• Dewolf, T., Van Dooren, W., Hermens, F., & Verschaffel, L. (2015). Do students attend to representational illustrations of non-standard mathematical word problems, and, if so, how helpful are they? Instructional Science, 43(1), 147-171. https://doi.org/10.1007/s11251-014-9332-7
• Doruk, B. K. (2012). Mathematical Modeling Activities as a Useful Tool for Values Education. Educational Sciences: Theory and Practice, 12(2), 1667-1672.
• Doruk, B., & Umay, A. (2011). The effect of mathematical modeling on transferring mathematics into daily life. Hacettepe University Journal of Education, 41, 124-135
• Durand-Guerrier, V., Hochmuth, R., Nardi, E., & Winsløw, C. (Eds.). (2021). Research and development in university mathematics education: Overview produced by the international network for didactic research in university mathematics.
• Durand-Guerrier, V., Hochmuth, R., Nardi, E., & Winsløw, C. (Eds.). (2021). Research and development in university mathematics education: Overview produced by the international network for didactic research in university mathematics.
• English, L. D., & Watters, J. J. (2005). Mathematical modeling in third-grade classrooms. Mathematics Education Research Journal, 16, 59-80
• Eraslan, A. (2012). Prospective Elementary Mathematics Teachers' Thought Processes on a Model Eliciting Activity. Educational Sciences: Theory and Practice, 12(4), 2964-2968.
• Eraslan, A., & Kant, S. (2015). Modeling Processes of 4th-Year Middle-School Students and the Difficulties Encountered. Educational Sciences: Theory and Practice, 15(3), 809-824. https://doi.org/10.12738/estp.2015.3.2556
• Erbaş, A. K., Kertil, M., Çetinkaya, B., Çakıroğlu, E., Alacacı, C., & Baş, S. (2014). Matematik eğitiminde matematiksel modelleme: Temel kavramlar ve farklı yaklaşımlar [Mathematical modeling in mathematics education:Basic concepts and approaches]. Educational Sciences: Theory and Practice, 14(4), 1607–1627. https://doi.org/10.12738/estp.2014.4.2039
• Er-sheng, D. (1999). Mathematics curriculum reform facing the new century in China. In Z. Usiskin (Ed.), Developments in school mathematics around the world (Vol. 4, pp. 58–69). Reston, VA: National Council of Teachers of Mathematics.
• Ferri, R. B. (2006). Theoretical and empirical differentiations of phases in the modelling process. ZDM, 38, 86-95.
• Ferruzzi, E. C., & Almeida, L. M. W. (2013). Modelagem matema´tica no ensino de matema´tica para engenharia. Revista Brasileira de Ensino de Cieˆncia e Tecnologia, [Mathematical Modeling in Teaching Mathematics for Engineering], 6(1), 153–172
• Frejd, P., & Bergsten, C. (2016). Mathematical modelling as a professional task. Educational Studies in Mathematics, 91(1), 11-35. https://doi.org/10.1007/s10649-015-9654-7
• Frejd, P., & Bergsten, C. (2018). Professional modellers’ conceptions of the notion of mathematical modelling: ideas for education. ZDM, 50(1), 117-127. https://doi.org/10.1007/s11858-018-0928-2
• Freudenthal, H. (1991). Revisiting mathematics education. Dordrecht, The Netherlands: Kluwer Academic Publishers.
• Gainsburg, J. (2013). Learning to model in engineering. Mathematical Thinking and Learning, 15(4), 259-290.
• Galbraith, P. (2012). Models of modelling: Genres, purposes or perspectives. Journal of Mathematical Modelling and application, 1(5), 3-16.
• Galbraith, P. L., & Clatworthy, N. J. (1990). Beyond standard models—meeting the challenge of modelling. Educational Studies in Mathematics, 21(2), 137-163.
• Galleguillos, J., & de Carvalho Borba, M. (2018). Expansive movements in the development of mathematical modeling: analysis from an Activity Theory perspective. ZDM, 50(1), 129-142. https://doi.org/10.1007/s11858-017-0903-3
• Hankeln, C. (2020). Mathematical modeling in Germany and France: A comparison of students’ modeling processes. Educational Studies in Mathematics, 103(2), 209-229. https://doi.org/10.1007/s10649-019-09931-5
• Hart, L. C., Smith, S. Z., Swars, S. L., & Smith, M. E. (2009). An examination of research methods in mathematics education (1995-2005). Journal of Mixed Methods Research, 3(1), 26-41. https://doi.org/10.1177/1558689808325771
• Hernandez-Martinez, P., & Vos, P. (2018). “Why do I have to learn this?” A case study on students’ experiences of the relevance of mathematical modelling activities. ZDM, 50(1), 245-257. https://doi.org/10.1007/s11858-017-0904-2
• Hickendorff, M. (2013). The effects of presenting multidigit mathematics problems in a realistic context on sixth graders' problem solving. Cognition and Instruction, 31(3), 314-344. https://doi.org/10.1080/07370008.2013.799167
• Hidayat, R., Zamri, S. N. A. S., & Zulnaidi, H. (2018). Does mastery of goal components mediate the relationship between metacognition and mathematical modelling competency? Educational Sciences: Theory & Practice, 18(3), 579-604. https://doi.org/10.12738/estp.2018.3.0108
• Hwang, G. J., & Tsai, C. C. (2011). Research trends in mobile and ubiquitous learning: A review of publications in selected journals from 2001 to 2010. British Journal of Educational Technology, 42(4), E65-E70. https://doi.org/10.1111/j.1467-8535.2011.01183.x
• Jacobs, G. J., & Durandt, R. (2016). Attitudes of pre-service mathematics teachers towards modelling: a South African inquiry. Eurasia journal of mathematics, science and technology education, 13(1), 61-84. https://doi.org/10.12973/eurasia.2017.00604a
• Jones, G. A., Langrall, C. W., Thornton, C. A., & Nisbet, S. (2002). Elementary students’ access to powerful mathematical ideas. In L. D. English (ed.), Handbook of international research in mathematics education, 113-141. Mahwah, NJ: Lawrence Erlbaum. https://doi.org/10.4324/9780203930236.ch6
• Kaiser, G. (2005). Mathematical Modelling in School – Examples and Experiences. In Kaiser, G. Henn, H.-W. (Eds.), Mathematikunterricht im Spannungsfeld von Evaluation und Evolution (pp. 99-108) Hildesheim: Franzbecker.
• Kaiser, G., & Sriraman, B. (2006). A global survey of international perspectives on modelling in mathematics education. ZDM – The International Journal on Mathematics Education, 38(3), 302-310. https://doi.org/10.1007/bf02652813
• Kaiser, G., Blomhøj, M., & Sriraman, B. (2006). Towards a didactical theory for mathematical modelling. ZDM– The International Journal on Mathematics Education, 38(2), 82- 85. https://doi.org/10.1007/bf02655882
• Kapur, J. N. (1982). The art of teaching the art of mathematical modelling. International Journal of Mathematical Education in Science and Technology, 13(2), 185-192. https://doi.org/10.1080/0020739820130210
• Karali, D., & Durmus, S. (2015). Primary school pre-service mathematics teachers’ views on mathematical modeling. Eurasia Journal of Mathematics, Science and Technology Education, 11(4), 803-815. https://doi.org/10.12973/eurasia.2015.1440a
• Kertil, M., Çetinkaya, B., Erbaş, A. K., & Çakıroğlu, E. (2016). Matematik eğitiminde matematiksel modelleme [Mathematical modeling in mathematics education]. In E. Bingölbali, S. Arslan, & İ. Ö. Zembat (Eds.), Matematik eğitiminde teoriler [Theories in mathematics education] (pp. 539–563). Ankara: Pegem Akademi.
• Kitchenham, B., Brereton, O. P., Budgen, D., Turner, M., Bailey, J., & Linkman, S. (2009). Systematic literature reviews in software engineering–a systematic literature review. Information and software technology, 51(1), 7-15. https://doi.org/10.1016/j.infsof.2008.09.009
• Kim, S. H., & Kim, S. (2010). The effects of mathematical modeling on creative production ability and self-directed learning attitude. Asia Pacific Education Review, 11(2), 109-120. https://doi.org/10.1007/s12564-009-9052-x
• Kjeldsen, T. H., & Blomhøj, M. (2013). Developing students’ reflections on the function and status of mathematical modeling in different scientific practices: History as a provider of cases. Science & Education, 22(9), 2157-2171. https://doi.org/10.1007/s11191-012-9555-4
• Krutikhina, M. V., Vlasova, V. K., Galushkin, A. A., & Pavlushin, A. A. (2018). Teaching of mathematical modeling elements in the mathematics course of the secondary school. Eurasia Journal of Mathematics, Science and Technology Education, 14(4), 1305-1315. https://doi.org/10.29333/ejmste/83561
• Laudares, J. B., & Lachini, J. (2005). O uso da matema´tica em cursos de engenharia na perspectiva dos docentes de disciplinas te´cnicas. Revista de Ensino de Engenharia, 24(1), 39–45. https://doi.org/10.15552/2236-0158/abenge.v24n1p39-45
• Lehrer, R., & Schauble, L. (2003). Origins and evaluation of model-based reasoning in mathematics and science. In R. Lesh, & H. M. Doerr (Eds.), Beyond constructivism: Models and modelling perspectives on mathematics problem solving, learning, and teaching (pp. 59-70). Mahwah, NJ: Lawrence Erlbaum.
• Lesh, R., & Doerr, H. M. (2003). Foundations of a models and modeling perspective on mathematics teaching, learning, and problem solving. In R. Lesh, & H. M. Doerr (Eds.), Beyond constructivism: Models and modeling perspectives on mathematics problem solving, learning, and teaching (pp. 3-33). Mahwah, NJ: Lawrence Erlbaum.
• Lesh, R., & Harel, G. (2003). Problem solving, modeling, and local conceptual development. Mathematical thinking and learning, 5(2-3), 157-189.
• Lesh, R., & Zawojewski, J. S. (2007). Problem solving and modeling. In F. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 763-804). Information Age Publishing.
• Lingefjärd, T. (2013). Teaching mathematical modelling in teacher education: Efforts and results. in mathematical modelling with multidisciplinary applications (pp. 57–80). John Wiley & Sons, Inc. https://doi.org/10.1002/9781118462706.ch4
• Maaß, K. (2006). What are modelling competencies? ZDM – The International Journal on Mathematics Education, 38(2), 113–142.
• MEB (2018). Ortaokul ve İmam Hatip Ortaokulu Matematik Uygulamaları Dersi (5, 6, 7 ve 8. Sınıflar) Öğretim Programı. Ankara. Talim ve Terbiye Kurulu Başkanlığı.
• Mentzer, N., Huffman, T., & Thayer, H. (2014). High school student modeling in the engineering design process. International Journal of Technology and Design Education, 24(3), 293-316. https://doi.org/10.1007/s10798-013-9260-x
• Ministry Of Education Singapore (2007). Mathematics Syllabus Primary. Retrieved from https://www.moe.gov.sg/docs/defaultsource/document/education/syllabuses/sciences/fi-les/mathematics_syllabus_primary_1_to_6.pdf.
• National Council of Teachers of Mathematics (NCTM). (2000). Principles and standards for school mathematics. Author.
• Niss, M. (2017). Obstacles related to structuring for mathematization encountered by students when solving physics problems. International Journal of Science and Mathematics Education, 15(8), 1441-1462. https://doi.org/10.1007/s10763-016-9754-6
• Niss, M., Blum, W., & Galbraith, P. L. (2007). Introduction. In W. Blum, P. Galbraith, H. Henn, & M. Niss (Eds.), Modelling and applications in mathematics education: The 14th ICMI study (pp. 3-32). New York: Springer
• Orey, D. C., & Rosa, M. (2018). Developing a mathematical modelling course in a virtual learning environment. ZDM, 50(1), 173-185. https://doi.org/10.1007/s11858-018-0930-8
• Organisation for Economic Co-operation and Development. (2013). PISA 2012 results in focus: What 15-year-olds know and what they can do with what they know. Paris, OECD. Retrieved from https://www.oecd.org/pisa/keyfindings/pisa-2012-results-overview.pdf
• Paolucci, C., & Wessels, H. (2017). An examination of pre-service teachers’ capacity to create mathematical modeling problems for children. Journal of Teacher Education, 68(3), 330-344. https://doi.org/10.1177/0022487117697636
• Pollak, H. O. (1979). The interaction between mathematics and other school subjects. New trends in mathematics teaching IV, 232-248.
• Rojano, T. (2015). Students’ access to mathematics learning in the middle and junior secondary schools. In Handbook of International Research in Mathematics Education (pp. 231-250). Routledge. https://doi.org/10.4324/9780203448946-14
• Şahin, N., & Eraslan, A. (2016). Modeling processes of primary school students: The crime problem. Egitim ve Bilim, 41(183). https://doi.org/10.15390/eb.2016.6011
• Schukajlow, S., Kaiser, G., & Stillman, G. (2018). Empirical research on teaching and learning of mathematical modelling: a survey on the current state-of-the-art. ZDM, 50(1), 5-18. https://doi.org/10.1007/s11858-018-0933-5
• Schwarz, B., Wissmach, B., & Kaiser, G. (2008). “Last curves not quite correct”: Diagnostic competence of future teachers with regard to modelling and graphical representations. ZDM – The International Journal on Mathematics Education, 40(5), 777–790. https://doi.org/10.1007/s11858-008-0158-0
• Stillman, G. A., Blum, W., & Biembengut, M. S. (2015). Cultural, social, cognitive and research influences on mathematical modelling education. Mathematical modelling in education research and practice: Cultural, social and cognitive influences, 1-32.
• Şen Zeytun, A., Çetinkaya, B., & Erbaş, A. K. (2017). Understanding prospective teachers’ mathematical modeling processes in the context of a mathematical modeling course. Eurasia Journal of Mathematics Science and Technology Education. 13(33), s. 691-722. https://doi.org/10.12973/eurasia.2017.00639a
• Sevinc, S., & Lesh, R. (2018). Training mathematics teachers for realistic math problems: a case of modeling-based teacher education courses. ZDM, 50(1), 301-314. https://doi.org/10.1007/s11858-017-0898-9
• Shahbari, J. A., & Peled, I. (2015). Resolving cognitive conflict in a realistic situation with modeling characteristics: Coping with a changing reference in fractions. International Journal of Science and Mathematics Education, 13(4), 891-907. https://doi.org/10.1007/s10763-014-9509-1
• Shahbari, J. A., & Tabach, M. (2020). Features of modeling processes that elicit mathematical models represented at different semiotic registers. Educational Studies in Mathematics, 105(2), 115-135. https://doi.org/10.1007/s10649-020-09971-2
• Siller, H. S., & Greefrath, G. (2010). Mathematical modelling in class regarding to technology. In Durand-Guerrier, V., Soury-Lavergne, S., &Arzarello, F. (Eds.), Proceedings of the Sixth Congress of the European Society for Research in Mathematics Education (pp. 2136-2145). France: INRP.
• Tezer, M., & Cumhur, M. (2017). Mathematics through the 5E instructional model and mathematical modelling: The geometrical objects. Eurasia Journal of Mathematics, Science and Technology Education, 13(8), 4789-4804. https://doi.org/10.12973/eurasia.2017.00965a
• Urhan, S., & Dost, Ş. (2018). Analysis of ninth grade mathematics course book activities based on model-eliciting principles. International Journal of Science and Mathematics Education, 16(5), 985-1002. https://doi.org/10.1007/s10763-017-9808-4
• Villarreal, M. E., Esteley, C. B., & Smith, S. (2018). Pre-service teachers’ experiences within modelling scenarios enriched by digital technologies. ZDM, 50(1), 327-341. https://doi.org/10.1007/s11858-018-0925-5
• Wake, G. (2014). Making sense of and with mathematics: The interface between academic mathematics and mathematics in practice. Educational Studies in Mathematics, 86(2), 271-290. https://doi.org/10.1007/s10649-014-9540-8
• Yenilmez, K., & Yıldız, Ş. (2019). Matematiksel Modelleme İle İlgili Lisansüstü Tezlerin Tematik İçerik Analizi. [Thematic Content Analysis Of Graduate Theses Related to Mathematical Modelling]. Eskişehir Osmangazi Üniversitesi Sosyal Bilimler Dergisi, 20, 1-22. https://doi.org/10.17494/ogusbd.548180
• Yükseköğretim Kurulu Başkanlığı [Higher Education Council]. (2018). Öğretmen Yetiştirme Lisans Programları [Teacher Training Undergraduate Programs]. Ankara Üniversity Publishing.
• Zapata-Grajales, F. N., Cano-Velásquez, N. A., & Villa-Ochoa, J. A. (2017). Art and geometry of plants: Experience in mathematical modelling through projects. Eurasia Journal of Mathematics, Science and Technology Education, 14(2), 585-603. https://doi.org/10.12973/ejmste/76958
• Zawojewski, J., Lesh, R., & English, L. (2003). A Model and Modelling Perspective on the Role of Small Group Learning. Beyond constructivism, 337-358.