A systematic review of the best practices for teaching mathematical modelling in education context

Riyan Hidayat 1 * , Ahmad Fauzi Mohd Ayub 1, Mohd Afifi Bin Bahurudin Setambah 2, Nurul Hijja Mazlan 3
More Detail
1 Department of Science and Technical Education, Faculty of Educational Studies, Universiti Putra Malaysia, Serdang, Selangor, MALAYSIA
2 Fakulti Pembangunan Manusia, Universiti Pendidikan Sultan Idris, Tanjung Malim, Perak, MALAYSIA
3 Faculty of Computer and Mathematical Sciences, Universiti Teknologi MARA, Shah Alam, Selangor, MALAYSIA
* Corresponding Author
EUR J SCI MATH ED, Volume 13, Issue 4, pp. 255-272. https://doi.org/10.30935/scimath/17155
Published Online: 24 September 2025, Published: 01 October 2025
OPEN ACCESS   767 Views   1073 Downloads
Download Full Text (PDF)

ABSTRACT

This research aims to examine recent studies on the dimensions necessary for developing mathematical modelling instruction and established frameworks used in teaching mathematical modelling. The study followed the steps outlined as such: identification, screening, eligibility, inclusion, and data analysis throughout three search engines: ERIC, ScienceDirect, and Scopus. The study followed the preferred reporting items for systematic reviews and meta-analysis (PRISMA) protocol and found 18 articles related to the topic. The findings showed that a well-balanced approach to implementing the three dimensions of teaching mathematical modelling; design of activity, pedagogy, and assessment systems which enhances the teaching and learning experience. The findings of the systematic literature review showed that most authors emphasized the authenticity and uniqueness of activities, highlighting the importance of engaging learners with interesting tasks. Finally, authors from Hong Kong, Australia, and Germany have been widely active in developing frameworks and dimensions for teaching mathematical modelling as they emphasize the application of modelling in secondary schools. A key significance of this study is that reviewing effective frameworks for designing mathematical modelling tasks, teaching modelling lessons, and assessing students’ work can help educators improve their lessons and create a better classroom environment.
Keywords: education, framework, mathematical modelling, PRISMA, systematic review, teaching

CITATION

Hidayat, R., Mohd Ayub, A. F., Setambah, M. A. B. B., & Mazlan, N. H. (2025). A systematic review of the best practices for teaching mathematical modelling in education context. European Journal of Science and Mathematics Education, 13(4), 255-272. https://doi.org/10.30935/scimath/17155

REFERENCES

  • Alibekova, J. D., Ashirbaev, N.K., & Meirbekova, G. (2023). Orta mektepte oqushylardy qoldanbaly esepterdі shygaruga oqytudagy matematikalyq modeldeu adіsі [The method of mathematical modeling in teaching solving applied problems to secondary school students]. Iasaui Universitetіnіn Habarshysy, 4(130), 329–343. https://doi.org/10.47526/2023-4/2664-0686.27
  • Ang, K. C. (2015). Mathematical modelling in Singapore schools: A framework for instruction. In N. H. Lee, & K. E. D. Ng (Eds.), Mathematical modelling–From theory to practice (pp. 57–72). World Scientific Publishing Company. https://doi.org/10.1142/9789814546928_0004
  • Aniskin, V. N., & Rakhmatullina, D. K. (2023). Mathematical modeling as a method of forming cognitive universal learning actions and competences of students in the conditions of a holistic educational environment. Natural Science Series, 29(3), Article 7992. https://doi.org/10.18287/2541-7525-2023-29-3-79-92
  • Araújo, J. D. L., & Lima, F. H. D. (2020). The mathematization process as object-oriented actions of a modelling activity system. Bolema: Boletim de Educação Matemática, 34(68), 847–868. https://doi.org/10.1590/1980-4415v34n68a01
  • Barquero, B., & Ferrando, I. (2024). Teacher education for mathematical modelling: Exploring the experiences of secondary school teachers in two courses. ZDM Mathematics Education, 56, 1109–1122. https://doi.org/10.1007/s11858-024-01609-4
  • Blum, W. (2015). Quality teaching of mathematical modelling: What do we know, what can we do? In S. J. Cho (Ed.), Proceedings of the 12th International Congress on Mathematical Education (pp. 73–98). Springer. https://doi.org/10.1007/978-3-319-12688-3_9
  • Blum, W. H.-J., & Borromeo Ferri, R. (2009). Mathematical modelling: Can it be taught and learnt? International Journal of Mathematical Education in Science and Technology, 40(1), 1–13.
  • Blum, W., Galbraith, P. L., Henn, H. W., & Niss, M. (2007). Modelling and applications in mathematics education. Springer. https://doi.org/10.1007/978-0-387-29822-1
  • Borromeo Ferri, R. (2018). Learning how to teach mathematical modeling in school and teacher education. Springer Cham. https://doi.org/10.1007/978-3-319-68072-9
  • Borromeo Ferri, R., & Blum, W. (2010). Mathematical modelling in teacher education–Experiences from a modelling seminar. In Proceedings of the CERME 6.
  • Brignardello-Petersen, R., Santesso, N., & Guyatt, G. H. (2024). Systematic reviews of the literature: An introduction to current methods. American Journal of Epidemiology, 194(2), Article kwae232. https://doi.org/10.1093/aje/kwae232
  • Cevikbas, M., Kaiser, G., & Schukajlow, S. (2021). 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, 205–236. https://doi.org/10.1007/s10649-021-10104-6
  • Dede, A. T., & Güzel, E. B. (2023). Developing a framework to support teachers’ implementation of mathematical modelling. International Journal of Mathematical Education in Science and Technology, 56(2), 181–207. https://doi.org/10.1080/0020739X.2023.2204098
  • Delić-Zimić, A., & Destović, F. (2018). Mathematical modeling and statistical representation of experimental access. In S. Avdaković (Ed.), Advanced technologies, systems, and applications III: IAT 2018 (pp. 36–48). Springer. https://doi.org/10.1007/978-3-030-02574-8_4
  • Diefes-Dux, H. A., Zawojewski, J. S., Hjalmarson, M. A., & Cardella, M. E. (2012). A framework for analyzing feedback in a formative assessment system for mathematical modeling problems. Journal of Engineering Education, 101(2), 375–406. https://doi.org/10.1002/j.2168-9830.2012.tb00054.x
  • Dogan, M. F. (2020). Evaluating pre-service teachers’ design of mathematical modelling tasks. International Journal of Innovation in Science and Mathematics Education, 28(1), 44–59. https://doi.org/10.30722/IJISME.28.01.004
  • Egamov, M., Sharipov, E., Shodiev, S., & Abdiraxmonov, A. (2024). Application of mathematical modeling in probability theory and mathematical statistics. E3S Web Conferences, 583, Article 06017. https://doi.org/10.1051/e3sconf/202458306017
  • Fulton, E. W., Wickstrom, M. H., Carlson, M. A., & Burroughs, E. A. (2019). Teachers as learners: Engaging communities of learners in mathematical modelling through professional development. In G. A. Stillman, & J. P. Brown (Eds.), Lines of inquiry in mathematical modelling research in education (pp. 145–158). ICME-13 Monographs. https://doi.org/10.1007/978-3-030-14931-4_7
  • Geiger, V., Galbraith, P., Niss, M., & Delzoppo, C. (2021). Developing a task design and implementation framework for fostering mathematical modelling competencies. Educational Studies in Mathematics, 109, 313–336. https://doi.org/10.1007/s10649-021-10039-y
  • Greefrath, G., Siller, H.-S., Klock, H., & Wess, R. (2021). Pre-service secondary teachers’ pedagogical content knowledge for the teaching of mathematical modelling. Educational Studies in Mathematics, 109(3), 383–407. https://doi.org/10.1007/s10649-021-10038-z
  • Guerrero-Ortiz, C., & Borromeo Ferri, R. (2022). Pre-service teachers’ challenges in implementing mathematical modelling: Insights into reality. PNA, 16(4), 309–341. https://doi.org/10.30827/pna.v16i4.21329
  • Henn, H. W. (2007). Modelling pedagogy – overview. In W. Blum, P. L. Galbraith, H. W. Henn & M. Niss (Eds.), Modelling and applications in mathematics education: The 14th ICMI Study (pp. 321–324). Springer. https://doi.org/10.1007/978-0-387-29822-1_33
  • Hidayat, R., Hermandra, & Ying, S. T. D. (2023). The sub-dimensions of metacognition and their influence on modeling competency. Humanities and Social Sciences Communications, 10(1), Article 763. https://doi.org/10.1057/s41599-023-02290-w
  • Hidayat, R., Idris, W. I. W., Qudratuddarsi, H., & Rahman, M. N. A. (2021a). Validation of the mathematical modeling attitude scale for Malaysian mathematics teachers. Eurasia Journal of Mathematics, Science and Technology Education, 17(12), Article em2047. https://doi.org/10.29333/ejmste/11375
  • Hidayat, R., Zamri, S. N. A. S., Zulnaidi, H., Abdullah, M. F. N. L., & Adnan, M. (2021b). The interrelationships between metacognition and modeling competency: The moderating role of the academic year. European Journal of Educational Research, 10(4), 1853–1866. https://doi.org/10.12973/eu-jer.10.4.1853
  • Hodgson, L., & Wilkie, K. (2022). Modelling lessons for more than imitation: Investigating teachers’ reactions and decompositions of unfamiliar practices. Journal of Mathematics Teacher Education, 25, 749–775. https://doi.org/10.1007/s10857-021-09516-1
  • Jabar, J. M., Hidayat, R., Samat, N. A., Rohizan, M. F. H., Rosdin, N. A., Salim, N., & Norazhar, S. A. (2022). Augmented reality learning in mathematics education: A systematic literature review. Journal of Higher Education Theory and Practice, 22(15). https://doi.org/10.33423/jhetp.v22i15.5570
  • Jensen, T. H. (2007). Assessing mathematical modelling competency. In C. Haines, P. Galbraith, W. Blum, & S. Khan (Eds.), Mathematical Modelling (ICTMA 12): Education, Engineering and Economics (pp. 141–148). Horwood.
  • Kaiser, G., & Grünewald, S. (2015). Promotion of mathematical modelling competencies in the context of modelling projects. In Mathematical modelling: From theory to practice (pp. 21–39). https://doi.org/10.1142/9789814546928_0002
  • Kannadass, P., Hidayat, R., Siregar, P. S., & Husain, A. P. (2023). Relationship between computational and critical thinking towards modelling competency among pre-service mathematics teachers. TEM Journal, 12(3), 1370–1382. https://doi.org/10.18421/tem123-17
  • Leong, K. E. (2014). Mathematical modelling in the Malaysian secondary curriculum. Learning Science and Mathematics Online Journal, 8, 66–74.
  • Lesh, R., & Doerr, H. M. (2003). Beyond constructivism: A models & modeling perspective on mathematics problem solving, learning, and teaching. Mahwah. https://doi.org/10.4324/9781410607713
  • Lo, C.-K., Huang, X., & Cheung, K.-L. (2022). Toward a design framework for mathematical modeling activities: An analysis of official exemplars in Hong Kong mathematics education. Sustainability, 14, Article 9757. https://doi.org/10.3390/su14159757
  • Lopes, A. R., & Reis, P. (2022). Contributions of mathematical modelling for learning differential equations in the remote teaching context. Acta Scientiae, 24(2), 1–15. https://doi.org/10.17648/acta.scientiae.7011
  • Lu, X., & Kaiser, G. (2022). Can mathematical modelling work as a creativity-demanding activity? An empirical study in China. ZDM: The International Journal on Mathematics Education, 54(1), 67–81. https://doi.org/10.1007/s11858-021-01316-4
  • Luczak, R., & Erwin, R. (2023). Mathematical modeling: A study of multidisciplinary benefits in the math classroom. Teaching Mathematics and its Applications: An International Journal of the IMA, 42(4), 325–342. https://doi.org/10.1093/teamat/hrac021
  • Maaß, K. (2006). What are modelling competencies? ZDM Mathematics Education, 38(2), 113–142. https://doi.org/10.1007/BF02655885
  • Maaß, K., Geiger, V., Ariza, M. R., & Goos, M. (2019). The role of mathematics in interdisciplinary STEM education. ZDM–Mathematics Education, 51(7), 869–884. https://doi.org/10.1007/s11858-019-01100-5
  • McGrane, C. (2020). Mathematical tasks: The bridge between teaching and learning. John Catt Educational.
  • Mohamed Shaffril, H. A., Samsuddin, S. F., & Abu Samah, A. (2021). The ABC of systematic literature review: The basic methodological guidance for beginners. Quality & Quantity, 55(4), 1319–1346. https://doi.org/10.1007/s11135-020-01059-6
  • Mohd Saad, M. R., Mamat, S., Hidayat, R., & Othman, A. J. (2023). Integrating technology-based instruction and mathematical modelling for STEAM-based language learning: A sociocultural and self-determination theory perspective. International Journal of Interactive Mobile Technologies, 17(14), 55–80. https://doi.org/10.3991/ijim.v17i14.39477
  • Moher, D., Shamseer, L., Clarke, M., Ghersi, D., Liberati, A., Petticrew, M., & Stewart, L. A. (2015). Preferred reporting items for systematic review and meta-analysis protocols (PRISMA-P) 2015 statement. Systematic Reviews, 4(1), 1–9. https://doi.org/10.1186/2046-4053-4-1
  • Ng, K. E. D. (2013). Teacher readiness in mathematical modelling: Are there differences between pre-service and in-service teachers? In G. A. Stillman, G. Kaiser, W. Blum, & J. P. Brown (Eds.), Teaching mathematical modelling: Connecting to research and practice (pp. 339–348). Springer. https://doi.org/10.1007/978-94-007-6540-5_28
  • Nowell, L. S., Norris, J. M., White, D. E., & Moules, N. J. (2017). Thematic analysis. International Journal of Qualitative Methods, 16(1), Article 160940691773384. https://doi.org/10.1177/1609406917733847
  • Oh, P. S., & Oh, S. J. (2011). What teachers of science need to know about models: An overview. International Journal of Science Education, 33(8), 1109–1130. https://doi.org/10.1080/09500693.2010.502191
  • Özbek, A., & Köse, H. (2022). Determination of psychometric characteristics of mathematical modeling competencies scale: Gifted and talented youth. Ankara Üniversitesi Eğitim Bilimleri Fakültesi Özel Eğitim Dergisi, 23(4), 1–19. https://doi.org/10.21565/ozelegitimdergisi.874247
  • Palm, T. (2002). The realism of mathematical school tasks–Features and consequences [PhD thesis, Umeå University].
  • Pelemeniano, A. P., & Siega, M. H. (2023). Integrating mathematical modeling of real-life problems: A contextualized approach to developing instructional material in basic calculus. International Journal of Membrane Science and Technology, 10(3), 149–163. https://doi.org/10.15379/ijmst.v10i3.1498
  • Peter, K., Dunn, M., & Marshman, M. (2020). Teaching mathematical modelling: A framework to support teachers’ choice of resources. Teaching Mathematics and its Applications: An International Journal of the IMA, 39(2), 127–144. https://doi.org/10.1093/teamat/hrz008
  • Pollak, H. (2011). What is mathematical modelling? In H. Gould (Ed.), Mathematical modelling handbook (pp. vi–x). COMAP.
  • Reit, X.-R., & Ludwig, M. (2015). An approach to theory-based modelling tasks. In G. A. Stillman, W. Blum, & M. S. Biembengut (Eds.), Mathematical modelling in education research and practice: Cultural, social, and cognitive influences (pp. 81–91). Springer. https://doi.org/10.1007/978-3-319-18272-8_6
  • Rezaei, J., & Asghary, N. (2024). Teaching differential equations through a mathematical modelling approach: The impact on problem-solving and the mathematical performance of engineering undergraduates. International Journal of Mathematical Education in Science and Technology, 55(5), 781–799. https://doi.org/10.1080/0020739X.2024.2307397
  • Siller, H.-S., & Greefrath, G. (2020). Modelling tasks in central examinations based on the example of Austria. In G. A. Stillman, G. Kaiser, & C. E. Lampen (Eds.), Mathematical modelling education and sense-making (pp. 383–392). Springer, Cham. https://doi.org/10.1007/978-3-030-37673-4_33
  • Stillman, G., Brown, J. P., Edwards, I., & Galbraith, P. (2007). A framework for success in implementing mathematical modelling in the secondary classroom. In J. Watson, & K. Beswick (Eds.), Mathematics: Essential Research, Essential Practice. Proceedings of the 30th Annual conference of the Mathematics Education Research Group of Australasia (pp. 688–707). Mathematics Education Research Group of Australasia.
  • Tangkawsakul, S., Thaikam, W., & Ugsonkid, S. (2024). Bridging gaps: Pre-service mathematics teachers’ handling the difficulties in posing real-world mathematical problems. Journal of Education and Learning, 13(3), Article 133. https://doi.org/10.5539/jel.v13n3p133
  • Tober, M. (2011). PubMed, ScienceDirect, Scopus or Google Scholar–Which is the best search engine for an effective literature research in laser medicine? Medical Laser Application, 26(3), 139–144. https://doi.org/10.1016/j.mla.2011.05.006
  • Turkish Ministry of National Education. (2009). Primary education school mathematics lesson (6-8 grades) education program. Ankara, Turkey: Headship of Public Books Printing House.
  • Wei, Y., Zhang, Q., & Guo, J. (2022). Can mathematical modelling be taught and learned in primary mathematics classrooms: A systematic review of empirical studies. Education Sciences, 12(12), Article 923. https://doi.org/10.3390/educsci12120923
  • Wess, R., Klock, H., Siller, H.-S., & Greefrath, G. (2021). Measuring professional competence for the teaching of mathematical modelling. In F. K. S. Leung, G. A. Stillman, G. Kaiser, & K. L. Wong (Eds.), Mathematical modelling education in east and west (pp. 249–260). Springer. https://doi.org/10.1007/978-3-030-66996-6_21
  • Wickstrom, M. H., & Arnold, E. G. (2023). Investigating secondary pre-service teachers as teachers and learners of mathematical modeling. Teaching Mathematics and Its Applications: An International Journal of the IMA, 42(1), 86–107. https://doi.org/10.1093/teamat/hrab031
  • Wohlin, C., Kalinowski, M., Romero Felizardo, K., & Mendes, E. (2022). Successful combination of database search and snowballing for identification of primary studies in systematic literature studies. Information and Software Technology, 147, Article 106908. https://doi.org/10.1016/j.infsof.2022.106908
  • Wright, T., & Pullen, S. (2007). Examining the literature: A bibliometric study of ESD journal articles in the Education Resources Information Centre Database. Journal of Education for Sustainable Development, 1(1), 77–90. https://doi.org/10.1177/097340820700100114