Matematiksel Modellemeyi Anlamak

Year 2025, Volume: 4 Issue: 1, 61 - 83, 16.12.2025

Ebru Ergül , Neşe Işık Tertemiz

Abstract

Bu çalışmanın amacı, matematiksel modellemenin eğitim bağlamında sıkça karşılaşılan kavramsal belirsizliklerini gidermek ve “doğru anlama”yı destekleyen uygulanabilir ve bütüncül bir çerçeve sunmak adına matematiksel modelleme kavramını tanımlamak, döngüleri hakkında bilgi vermek, matematiksel modelleme yeterlikleri, nitelikli matematiksel modelleme etkinliklerinin ayırt edici özellikleri ile matematiksel modelleme sürecinin yürütülmesi ve değerlendirilmesini açıklamaktır. Çalışmada, matematiksel modellemenin problem çözmede izlenecek özel bir yol olduğu, matematiksel modelleme yeterliklerinin yalnızca bilişsel alt becerilerden ibaret olmadığı; bilişsel, üstbilişsel, duyuşsal ve sosyal boyutları içeren çok bileşenli bir yetkinlik alanı olduğu ortaya konulmaktadır. Matematiksel modelleme etkinliklerinin seçimi ve tasarımına yönelik farklı kuramsal çerçevelerin bütünleştirilmesiyle, bu etkinliklerin öğretim programıyla uyumlu, gerçek yaşamla ilişkili, açık uçlu, çoklu çözüme imkân veren ve öğrencilerin düşünme süreçlerini görünür kılan görevler olarak yapılandırılması gerektiği vurgulanmaktadır. Ayrıca matematiksel modelleme sürecinin planlanması, yürütülmesi ve rubrikler, öz–akran değerlendirme, projeler, gözlemler ve yazılı testler gibi çoklu araçlarla değerlendirilmesine ilişkin ilkeler sunulmaktadır.

Keywords

Matematik Eğitimi , Matematiksel Modelleme , Problem Çözme

Understanding Mathematical Modelling

Abstract

The purpose of this study is to clarify the conceptual ambiguities frequently encountered in the educational use of mathematical modeling and to propose a practical and comprehensive framework that supports a “correct understanding” of the construct. To this end, the study aims to define mathematical modeling, present major modeling cycles, describe mathematical modeling competencies, outline the distinguishing characteristics of high-quality modeling tasks, and explain how the modeling process is implemented and assessed. The study highlights that mathematical modeling constitutes a specific pathway for problem solving and that modeling competencies extend beyond cognitive subskills; rather, they represent a multifaceted domain that encompasses cognitive, metacognitive, affective, and social dimensions. By integrating various theoretical frameworks on the selection and design of modeling tasks, the study underscores that such tasks must be aligned with the curriculum, grounded in real-life contexts, open-ended in nature, allow for multiple solution approaches, and make students’ thinking processes visible. Furthermore, the study outlines principles for planning, conducting, and evaluating the mathematical modeling process using multiple assessment tools, including rubrics, self- and peer assessment, projects, observations, and written tests.

Keywords

Mathematics Education , Mathematical Modelling , Problem-solving

References

• Abay, S., & Gökbulut, Y. (2017). Sınıf öğretmeni adaylarının matematiksel modelleme becerileri: Fermi problemleri uygulamaları. Uluslararası Türk Eğitim Bilimleri Dergisi, (9), 65-83. https://dergipark.org.tr/tr/pub/goputeb/issue/34356/379918#article_cite
• Abrams, J. P. (2001). Mathematical modeling: Teaching the open-ended application of mathematics. In The teaching of mathematical modeling and the role of representation (pp. 269–282). National Council of Teachers of Mathematics.
• Ang, K. C. (2010). Implementing mathematical modelling in the mathematics classroom: The Singapore experience. ZDM – Mathematics Education, 42(3), 247–256.
• Anhalt, C., & Cortez, R. (2015). Mathematical modeling: A structured process. Mathematics Teacher, 108(6), 446–452.
• Asempapa, R. S. (2015). Mathematical modelling: Essential for elementary and middle school students. Journal of Mathematics Education, 8(1), 16-29. https://journalofmathed.scholasticahq.com/article/90005-mathematical-modeling-essential-for-elementary-and-middle-school-students
• Berry, J. S. & Davies, A. (1996). “Written Reports”. In C. R. Haines & S. Dunthorne (Eds.), Mathematics Learning and Assessment: Sharing Innovative Practices, s. 3.3–3.11. London: Arnold.
• Berry, J., & Houston, K. (1995). Mathematical modelling. Stanley Thornes Publishers.
• Biccard, P., & Wessels, D. C. J. (2011). Documenting the development of modelling competencies of grade 7 mathematics students. In G. Kaiser, W. Blum, R. Borromeo-Ferri, & G. Stillman (Eds.), Trends in teaching and learning of mathematical modelling: ICTMA14 (pp. 375–383). Dordrecht: Springer.
• 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). Boston: Springer.
• Blum, W., & Borromeo-Ferri, R. (2009). Mathematical modelling: Can it be taught and learnt?. Journal of mathematical modelling and application, 1(1), 45-58. https://eclass.uoa.gr/modules/document/file.php/MATH601/3rd%20%26%204rth%20unit/3rd%20unit_Modelling%20cycle.pdf
• Blum, W., & Kaiser, G. (1997). Vergleichende empirische Untersuchungen zu mathematischen Anwendungsfähigkeiten von englischen und deutschen Lernenden. Unpublished application to Deutsche Forschungsgemeinschaft, University of Kassel, Kassel.
• Blum, W., & Leiß, D. (2007). Deal with modelling problems. Mathematical Modelling: Education, Engineering and Economics-ICTMA, 12, 222.
• Borromeo-Ferri, R. (2006). Theoretical and empirical differentiations of phases in the modelling process. ZDM, 38(2), 86–95. https://doi.org/10.1007/BF02655883
• Bukova-Güzel, E. (2021). Matematik eğitiminde matematiksel modelleme (4. Baskı), Ankara: Pegem.
• Canbazoğlu, H. B., & Tarım, K. (2021). İlkokulda matematiksel modelleme için bir öğretim çerçevesi. Dokuz Eylül Üniversitesi Buca Eğitim Fakültesi Dergisi, (51), 210-225. https://doi.org/10.53444/deubefd.825361
• 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, 109(2), 205–236. https://doi.org/10.1007/s10649-021-10104-6
• Chamberlin, S. A., & Coxbil, E. (2012). Using model-eliciting activities to introduce upper elementary students to statistical reasoning and mathematical modeling. In L. Hatfield & R. Mayes (Eds.), Quantitative reasoning and mathematical modeling: A driver for STEM-integrated education and teaching in context (pp. 169–179). Laramie: WISME.
• Chamberlin, S. A., & Coxbil, E. (2012). Using model eliciting activities to introduce upper elementary students to statistical reasoning and mathematical modeling. In L. Hatfield & R. Mayes (Eds.), Quantitative reasoning and mathematical modeling: A driver for STEM-integrated education and teaching in context (pp. 169–179). Laramie: WISME.
• 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
• Consortium for Mathematics and Its Applications (COMAP) & Society of Industrial and Applied Mathematics (SIAM). (2016). Guidelines for Assessment and Instruction in mathematical modeling education. Philadelphia: COMAP & SIAM.
• Doerr, H.M. (1997). Experiment, simulation and analysis: an integrated instructional approach to the concept of force. International Journal of Science Education, 19(3), 265-282, DOI: 10.1080/0950069970190302.
• Dost, Ş. (2023). Matematik eğitiminde modelleme etkinlikleri (2. Baskı). Ankara: Pegem.
• Du, W., Wijaya, T. T., Cao, Y., & Li, X. (2025). What factors influence secondary students’ active participation in mathematics classrooms: A theory of planned behavior perspective. Acta Psychologica, 251, 103876. https://doi.org/10.1016/j.actpsy.2025.103876
• Eğitim Bilişim Ağı. (2023). İlkokul matematik ders kitapları. https://ders.eba.gov.tr/ders/proxy/VCollabPlayer_v0.0.992/index.html#/main/vcEbaSearch/2/ders%2520kitab%25C4%25B1%2520/1?pageSize=24 sayfasından erişilmiştir.
• English, L. D., & Watson, J. M. (2018). Modelling with authentic data in sixth grade. ZDM- Mathematics Education, 50(1-2), 103–115. http://dx.doi.org/10.1007/s11858-017-0896-y
• English, L. D., & Watters, J. J. (2005). Mathematical modelling in the early school years. Mathematics Education Research Journal, 16(3), 59-80. https://doi.org/10.1007/BF03217401 Eraslan, A. (2011). İlköğretim matematik öğretmen adaylarının model oluşturma etkinlikleri ve bunların matematik öğrenimine etkisi hakkındaki görüşleri. İlköğretim Online, 10(1), 365-377. https://dergipark.org.tr/tr/pub/ilkonline/issue/8593/106870
• Eraslan, A., & Şahin, N. (2023).İlkokul ve ortaokulda etkinlik örnekleriyle matematiksel modelleme (3. Baskı). Ankara: Pegem.
• Erbaş, A. K., Çetinkaya, B., Alacacı, C., Aydoğan Yenmez, A., Çakıroğlu, E., Kertil, M., Didiş, M. G., … Korkmaz, H. (2024). Lise matematik konuları için günlük hayattan modelleme soruları (2. Baskı). Ankara: Türkiye Bilimler Akademisi.
• Erbaş, A. K., Kertil, M., Çetinkaya, B., Çakıroğlu, E., Alacacı, C., & Baş, S. (2014). Matematik eğitiminde matematiksel modelleme: Temel kavramlar ve farklı yaklaşımlar. Kuram ve Uygulamada Eğitim Bilimleri, 14(4), 1-21. DOI: 10.12738/estp.2014.4.2039
• Francis, D. C., Hong, J., Bharaj, P. K., Schutz, P., & Yu, B. (2025). Advancing mathematics teacher development through holistic individualized coaching: A multiphase mixed methods study. Methods in Psychology, 14, 100456. https://doi.org/10.1016/j.metps.2025.100456
• Frejd, P. (2013). Modes of modelling assessment-A literature review. Educational Studies in Mathematics, 84, 413-438. https://www.jstor.org/stable/43589797
• Galbraith, P. L., & Stillman, G. (2006). A framework for identifying student blockages during transitions in the modelling process. ZDM – Mathematics Education, 38(2), 143–162. https://doi.org/10.1007/BF02655886
• Gould, H. (2013). Teachers’ conceptions of mathematical modeling. Unpublished dissertation. Teachers College Columbia University, New York.
• Göktepe-Yıldız, S. (2020). Reflections from the pre-service teachers’ geometric modeling design process: Is it half the base or the height?, International Journal of Educational Studies in Mathematics, 7(4), 250-270. https://doi.org/10.17278/ijesim.812035
• Greefrath, G. (2020). Mathematical modelling competence. Selected current research developments. Avances de Investigación en Educación Matemática, (17), 38-51. DOI: 10.35763/aiem.v0i17.303
• Haines, C., & Crouch, R. (2001). Recognizing constructs within mathematical modelling. Teaching Mathematics and Its Applications: International Journal of the IMA, 20(3), 129-138. https://doi.org/10.1093/teamat/20.3.129
• Haines, C., Crouch, R., & Davies, J (2001). Understanding students’ modelling skills. In J. Matos, W. Blum, K. Houston, & S. Carreira (Eds.), Modelling and mathematics Education, ICTMA 9: Applications in science and technology (pp. 366–380). Chichester: Horwood.
• Hankeln, C., Adamek, C., & Greefrath G. (2019). Assessing sub-competencies of mathematical modelling. Development of a new test instrument. In G. A. Stillman, & J. P. Brown (Eds.), Lines of inquiry in mathematical modelling research in education (pp. 143–160). Cham: Springer.
• Hıdıroğlu, Ç. N. (2012). Teknoloji destekli ortamda matematiksel modelleme problemlerinin çözüm süreçlerinin analiz edilmesi: Yaklaşım ve düşünme süreçleri üzerine bir açıklama. Yüksek Lisans Tezi, Dokuz Eylül Üniversitesi Eğitim Bilimleri Enstitüsü, İzmir.
• Hıdıroğlu, Ç. N. (2015). Teknoloji destekli ortamda matematiksel modelleme problemlerinin çözüm süreçlerinin analizi: Bilişsel ve üstbilişsel yapılar üzerine bir açıklama. Doktora Tezi, Dokuz Eylül Üniversitesi Eğitim Bilimleri Enstitüsü, İzmir.
• Hidayat, R., Ayub, A. F. M., & Bahurudin Setambah, M. A. (2025). Modelling for secondary mathematics teacher: Insight from expert. Universiti Putra Malaysia Institutional Repository. http://psasir.upm.edu.my/id/eprint/119260
• Houston, K. (2007). Assessing the “phases” of mathematical modelling. In Modelling and applications in mathematics education: The 14th ICMI study (pp. 249-256). Boston: Springer.
• Ikeda, T., & Stephens, M. (1998). Some characteristics of students' approaches to mathematical modelling in the curriculum based on pure mathematics. Journal of Science Education in Japan, 22(3), 142-154. https://doi.org/10.14935/jssej.22.142
• Işık-Tertemiz, N., & Ergan, S. N. (2024). Understanding mathematics and process skills in primary school. In Y. İnel, B. Kılcan, & T. Çetin (Eds.), Contemporary educational tendencies in the 2nd century of the Republic of Türkiye: Research and practices (pp.437-485). Ankara: Pegem.
• Izard, J., Crouch, R., Haines, C., Houston, K., & Neill, N. (2003). Assessing the impact of teaching mathematical modelling: Some implications. In C. Haines, P. Galbraith, W. Blum, & S. Khan (Eds.), Mathematical Modelling: Education, Engineering and Economics – ICTMA 12 (pp. 165-177). Sawston: Woodhead.
• Kaiser, G. (2007). Modelling and modelling competencies in school. In C. Haines, P. Galbraith, W. Blum, & S. Khan (Eds.), Mathematical modelling: Education, engineering and economics (pp. 110–119). Chichester: Horwood.
• Kaiser, G., & Maaß, K. (2007). Modelling in lower secondary mathematics classroom—problems and opportunities. In W. Blum, P. L. Galbraith, H.-W. Henn & M. Niss (Eds.), Modelling and Applications in Mathematics Education: The 14th ICMI Study (pp. 99–108). New York: Springer.
• Kaiser, G., & Schwarz, B. (2006). Mathematical modelling as a bridge between school and university. ZDM- Mathematics Education, 38, 196-208. https://doi.org/10.1007/BF02655889
• Kapur, J. N. (1982). The art of teaching the art of mathematical modeling. International Journal of Mathematical Education in Science and Technology, 13(2), 185-192. https://doi.org/10.1080/0020739820130210
• Kertil, M. (2008). Matematik öğretmen adaylarının problem çözme becerilerinin modelleme sürecinde incelenmesi. Yüksek Lisans Tezi, Marmara Üniversitesi Eğitim Bilimleri Enstitüsü, İstanbul.
• Kertil, M., Çetinkaya, B., Erbaş, A. K., & Çakıroğlu, E. (2016). Matematik eğitiminde matematiksel modelleme. E. Bingölbali, S. Arslan & İ. Ö. Zembat (Ed.), Matematik eğitiminde teoriler içinde (s. 539-560), Ankara: Pegem.
• Kılıç, Z. (2020). Farklı disiplinler ile ilişkilendirme bağlamında matematiksel modelleme etkinliklerinin geliştirilmesi ve uygulanması: Ortaokul öğrencileri örneklemesi. Yüksek Lisans Tezi, Dicle Üniversitesi Eğitim Bilimleri Enstitüsü, Diyarbakır.
• Lehrer, R., & Schauble, L. (2007). A developmental approach for supporting the epistemology of modelling. In Modelling and applications in mathematics education: The 14th ICMI study (pp. 153-160). Boston: Springer. Leong, K. E. (2012). Assessment of mathematical modeling. Journal of Mathematics Education at Teachers College, 3(1), 61–65. https://ssrn.com/abstract=2431553
• Lesh, R., & Doerr, H. M. (2003). Foundations of a models and modelling perspective on mathematics teaching, learning, and problem solving. In Beyond constructivism (pp. 3-33). London: Routledge.
• 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.), Research Design in Mathematics and science education. (pp. 591-646). Mahwah: Lawrence Erlbaum.
• Lingefjärd, T. (2007). Mathematical modelling in teacher education—Necessity or unnecessarily. In Modelling and applications in mathematics education: The 14th ICMI study (pp. 333-340). Boston: Springer.
• 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. (2004). Mathematisches modellieren im unterricht: Ergebnisse einer empirischen studie. Franzbecker, Germany: Hildesheim.
• Maaß, K. (2006). What are modelling competencies? ZDM- Mathematics Education, 38(2), 113-142. https://doi.org/10.1007/BF02655885
• Mason, J. (1988). Modelling: What do we really want pupils to learn? In D. Pimm (Ed.), Mathematics, Teachers and Children. (pp. 201-215). London: Hodder & Stoughton.
• Millî Eğitim Bakanlığı. (2011a). Ölçme, değerlendirme ve sınav hizmetleri genel müdürlüğü. http://odsgm.meb.gov.tr/test/analizler/docs/timss/TIMSS-2011-4-Sinif%20Raporu.pdf sayfasından erişilmiştir.
• Millî Eğitim Bakanlığı. (2011b). Ölçme, değerlendirme ve sınav hizmetleri genel müdürlüğü. https://odsgm.meb.gov.tr/meb_iys_dosyalar/2017_06/23161945_timss_2015_on_raporu.pdf sayfasından erişilmiştir.
• Millî Eğitim Bakanlığı. (2015). Ölçme, değerlendirme ve sınav hizmetleri genel müdürlüğü. https://odsgm.meb.gov.tr/www/2015-pisa-ulusal-raporu/icerik/204 sayfasından erişilmiştir.
• Millî Eğitim Bakanlığı. (2018). Matematik dersi öğretim programı (ilkokul ve ortaokul 1, 2, 3, 4, 5, 6, 7 ve 8. Sınıflar http://mufredat.meb.gov.tr/Dosyalar/201813017165445-MATEMATİK%20ÖĞRETİM%20PROGRAMI%202018v.pdf sayfasından erişilmiştir.
• Millî Eğitim Bakanlığı (2024a). PISA 2022 Türkiye raporu. https://pisa.meb.gov.tr/meb_iys_dosyalar/2024_03/21120745_26152640_pisa2022_rapor.pdf sayfasından erişilmiştir.
• Millî Eğitim Bakanlığı. (2024b). TIMSS 2023 Türkiye raporu. https://odsgm.meb.gov.tr/meb_iys_dosyalar/2024_12/23102111_timss2023rapor2012kapakli.pdf sayfasından erişilmiştir.
• Millî Eğitim Bakanlığı. (2024c). İlkokul matematik dersi öğretim programı (1, 2, 3 ve 4. Sınıflar). https://mufredat.meb.gov.tr sayfasından erişilmiştir.
• Miranda, A., & Sgreccia, N. (2025). Covariational instruction and MWS–AI integration: Modeling teacher–AI interactions in math education. Book of Abstracts, HELMeTO 2025, University of Naples Federico II, 234–236. https://www.iris.unina.it/retrieve/c4d83188-e30e-4794-b055-3b5f9568bb8a/BOA_HELMETO_2025_con_ISBN_compressed.pdf#page=234
• Mousoulides, N. G. (2007). The modeling perspective in the teaching and learning of mathematical problem solving (Doctoral dissertation, University of Cyprus).
• Müller, G., & Wittmann, E. (1984). Der Mathematikunterricht in der Primarstufe. Braunschweig: Vieweg. National Research Council. (1989). Everybody counts: A report to the nation on the future of mathematics education. National Academy Press.
• Niss, M. A., & Jensen, T. H. (2011). Competencies and mathematical learning: Ideas and inspiration for the development of mathematics teaching and learning in Denmark. Denmark: English Edition.
• Niss, M., Blum, W., & Galbraith, P. (2007). Introduction. In W. Blum, P. L. Galbraith, H. W. Henn, & M. Niss (Eds.), Modelling and applications in mathematics education. The 14th ICMI study (pp. 3–32). Cham: Springer.
• Niss, M., & Blum, W. (2020). The learning and teaching of mathematical modelling. London: Routledge. Organisation for Economic Co-operation and Development. (2019). PISA 2018 results (Volume I): What students know and can do. OECD Publishing. https://doi.org/10.1787/5f07c754-en
• Penrose, O. (1978). How can we teach mathematical modelling? Journal of Mathematical Modelling for Teachers, 1(2), 31-42.
• Pollak, H.O. (1978), On Mathematics Application and Real Problem Solving*. School Science and Mathematics, 78: 232-239. https://doi.org/10.1111/j.1949-8594.1978.tb09351.x
• 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
• Shekhmirzova, A. M., & Gribina, L. V. (2024). Developing emotional intelligence through mathematical modelling projects. International Journal of Advanced Studies in Education and Sociology, 12(3), 45–58. https://elibrary.ru/item.asp?id=54098572
• Spain Ministry of Education. (2023). Curriculum planning and development division (CPDD). Retrieved from https://www.moe.gov.tt/curriculum-guides/
• Stark, R. M., & Nichols, R. L. (2005). Mathematical foundations for design: Civil engineering systems. New York: Dover.
• Stohlmann, M. (2019). In-service teachers’ understanding of mathematical modeling. The 118th Annual convention of the School Science and Mathematics Association. Salt Lake City, UT: SSMA.
• Şahin, N., & Eraslan, A. (2018). İlkokulda model oluşturma etkinlikleri nasıl uygulanmalı?. Eğitim Kuram ve Uygulama Araştırmaları Dergisi, 4(1), 99-117. https://dergipark.org.tr/tr/pub/ekuad/issue/35893/412071
• Şimşeker, M., & Güzel, E. B. (2025). Metacognitive actions displayed by a science high school student during the mathematical modeling process. Turkish Journal of Mathematics Education, 5(1), 45–62. https://tujme.org/index.php/tujme/article/view/162
• Tang, J., Zheng, Y., Wijaya, T. T., Su, M., & Listiawan, T. (2025). Determinants of student discussion participation in the mathematical collaborative problem-solving process using PLS-SEM and FsQCA. Scientific Reports, 15, 21086. https://doi.org/10.1038/s41598-025-21086-3
• Tekin-Dede, A., & Bukova-Güzel, E. (2018). A rubric development study for the assessment of modeling skills. The Mathematics Educator, 27(2), 33-72. DOI: 10.63301/tme.v27i2.2040
• Toluk, Z., & Olkun, S. (2002). Türkiye'de matematik eğitiminde problem çözme: İlköğretim 1- 5. sınıflar matematik ders kitapları. Kuram ve Uygulamada Eğitim Bilimleri, 2(2), 563-581.
• Tutak, T., & Güder, Y. (2014). Matematiksel modellemenin tanımı, kapsamı ve önemi. Turkish Journal of Educational Studies, 1(1), 173-190. https://dergipark.org.tr/tr/pub/turkjes/issue/34150/377625 Türker-Biber, B., & Yetkin-Özdemir, İ. E. (2015). Matematik öğretiminde matematiksel modelleme yaklaşımı. Cito Eğitim: Kuram ve Uygulama, 27, 39-50.
• Ulu, M. (2017). Errors made by elementary fourth grade students when modelling word problems and the elimination of those errors through scaffolding. International Electronic Journal of Elementary Education, 9(3), 553-580. https://iejee.com/index.php/IEJEE/article/view/176
• Verschaffel, L., Greer, B., & De Corte, E. (2002). Everyday knowledge and mathematical modeling of school word problems. In Symbolizing, modeling and tool use in mathematics education (pp. 257–276). Springer.
• Vorhölter, K., Greefrath, G., Borromeo Ferri, R., Leiß, D., & Schukajlow, S. (2019). Mathematical modelling. In Traditions in German-speaking mathematics education research (pp. 91-114). Cham: Springer.
• Voskoglou, M. G. (2006). The use of mathematical modelling as a tool for learning mathematics. Quaderni di Ricerca in Didattica (Scienze Matematiche), 16, 121–130.
• Zawojewski, J. S., Lesh, R., & English, L. D. (2003). A models and modelling perspective on the role of small group learning. In R. A. Lesh & H. Doerr (Eds.), Beyond constructivism: Models and modeling perspectives on mathematics problem solving, learning, and teaching (pp. 337–358). Mahwah: Lawrence Erlbaum.
• Zheng, S. X., & Leong, K. E. (2025). Metacognition’s mediating effect on undergraduate achievement goals and mathematical modelling competency. International Journal of Instruction, 18(2), 455-472. https://doi.org/10.29333/iji.2025.18225a
• Zubi, I. A., Peled, I., & Yarden, M. (2019). Children with mathematical difficulties cope with modelling tasks: what develops?. International Journal of Mathematical Education in Science and Technology, 50(4), 506-526. DOI: 10.1080/0020739X.2018.1527404