Challenges in geometric modelling–A comparison of students’ mathematization with real objects, photos, and 3D models
More details
Hide details
Goethe University Frankfurt, Frankfurt, GERMANY
Publication date: 2024-03-03
EURASIA J. Math., Sci Tech. Ed 2024;20(3):em2414
Mathematical modelling aims at contributing to the involvement of reality in mathematics education. As an example, geometric modelling can be implemented by the use of real objects in modelling tasks. Still, (geometric) modelling tasks can be a challenge for students, especially in the transfer from reality to mathematics, which is referred to as mathematization. Since the representation of a real object in tasks might differ, the question arises, which challenges can be observed when working in different task settings. In a study with 19 secondary school students, the task settings (1) outdoors at the real object, (2) indoors with photos of the real object, and (3) indoors with a 3D model of the real object are compared. Based on video recordings, differences concerning the students’ challenges are examined. The results highlight challenges in estimating and measuring when working at the real object, scale and perspective when working with photos and the transfer between representation and object when working with 3D models.
Anđić, B., Maričić, M., Weinhandl, R., Mumcu, F., Schmidthaler, E., & Lavicza, Z. (2024). Metaphorical evolution: A longitudinal study of secondary school teachers’ concepts of 3D modelling and printing in education. Education and Information Technologies.
Blum, W. (2015). Quality teaching of mathematical modelling: What do we know? What can we do? In S. Cho (Ed.), Proceedings of the 12th International Congress on Mathematical Education (pp. 73-96). Springer.
Blum, W., & Leiss, D. (2007). How do students and teachers deal with mathematical modelling problems? In C. Haines, P. Galbraith, W. Blum, & S. Khan (Eds.), Mathematical modelling (pp. 222-231). Woodhead Publishing.
Buchholtz, N. (2017). How teachers can promote mathematising by means of mathematical city walks. In G. Stillman, W. Blum, & G. Kaiser (Eds.), Mathematical modelling and applications (pp. 49-58). Springer.
Buchholtz, N. (2021). Students’ modelling processes when working with math trails. Quadrante, 30(1), 140-157.
Cevikbas, M., Greefrath, G., & Siller, H.-S. (2023). Advantages and challenges of using digital technologies in mathematical modelling education–a descriptive systematic literature review. Frontiers in Education, 8, 1142556.
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 Mathematics Education, 52, 59-72.
Crompton, H. (2015). Using context-aware ubiquitous learning to support students’ understanding of geometry. Journal of Interactive Media in Education, 2015(1), 13.
Doerr, H. M., Ärlebäck, J. B., & Misfeldt, M. (2017). Representations of modelling in mathematics education. In G. Stillman, W. Blum, & G. Kaiser (Eds.), Mathematical modelling and applications (pp. 71-82). Springer.
Field, A. (2016). An adventure in statistics: The reality enigma. SAGE.
Gilpin, A. R. (1993). Table for conversion of Kendall’s tau to Spearman’s rho within the context of measures of magnitude of effect for meta-analysis. Educational and Psychological Measurement, 53, 87-92.
Greefrath, G., Hertleif, C., & Siller, H.-S. (2018). Mathematical modelling with digital tools–A quantitative study on mathematising with dynamic geometry software. ZDM Mathematics Education, 50, 233-244.
Greefrath, G., Siller, H.-S., Vorhölter, K., & Kaiser, G. (2022). Mathematical modelling and discrete mathematics: Opportunities for modern mathematics teaching. ZDM Mathematics Education, 54, 865-879.
Gurjanow, I., & Ludwig, M. (2020). Mathematics trails and learning barriers. In G. Stillman, G. Kaiser, & C. Lampen (Eds.), Mathematical modelling education and sense-making (pp. 265-275). Springer.
Hartmann, L.-M., & Schukajlow, S. (2021). Interest and emotions while solving real-world problems inside and outside the classroom. In F. K. S. Leung, G. A. Stillman, G. Kaiser, & K. L. Wong (Eds.), Mathematical modelling education in east and west (pp. 153-163). Springer.
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 Mathematics Education, 50, 245-257.
Hoth, J., Heinze, A., Huang, H.-M. E., Weiher, D. F., Niedermeyer, I., & Ruwisch, S. (2023). Elementary school students’ length estimation skills–Analyzing a multidimensional construct in a cross-country study. International Journal of Science and Mathematics Education, 21, 1841-1864.
Hwang, W.-Y., Zhao, L., Shadiev, R., Lin, L.-K., Shih, T. K., & Chen, H.-R. (2020). Exploring the effects of ubiquitous geometry learning in real situations. Education Technology Research and Development, 68, 1121-1147.
Jablonski, S. (2023). Is it all about the setting? A comparison of mathematical modelling with real objects and their representation. Educational Studies in Mathematics, 113, 307-330.
Jablonski, S., & Ludwig, M. (2023). Teaching and learning of geometry–A literature review on current developments in theory and practice. Education Sciences, 13, 682.
Jankvist, U. T., & Niss, M. (2019). Upper secondary school students’ difficulties with mathematical modelling. International Journal of Mathematical Education in Science and Technology, 51(4), 467-496.
Krawitz, J., Schukajlow, S., & Van Dooren, W. (2018). Unrealistic responses to realistic problems with missing information: What are important barriers? Educational Psychology, 38, 1221-1238.
Ludwig, M., & Jesberg, J. (2015). Using mobile technology to provide outdoor modelling tasks–The MathCityMap–Project. Procedia-Social and Behavioral Sciences, 191, 2776-2781.
Mayring, P. (2000). Qualitative content analysis. Forum: Qualitative Social Research, 1(2).
Ramírez-Montes, G., Henriques, A., & Carreira, S. (2021). Undergraduate students’ learning of linear algebra through mathematical modelling routes. Canadian Journal of Science, Mathematics and Technology Education, 21, 357-377.
Schukajlow, S. (2013). Lesekompetenz und mathematisches Modellieren [Reading skills and mathematical modeling]. In R. Borromeo Ferri, G. Greefrath, & G. Kaiser (Eds.), Mathematisches Modellieren für Schule und Hochschule. Realitätsbezüge im Mathematikuntericht [Mathematical modeling for schools and universities. Reality references in mathematics lessons] (pp. 125-143). Springer.
Schukajlow, S., Kolter, J., & Blum, W. (2015) Scaffolding mathematical modelling with a solution plan. ZDM Mathematics Education, 47, 1241-1254.
Schukajlow, S., Krawitz, J., Kanefke, J., Blum, W., & Rakoczy, K. (2023). Open modelling problems: Cognitive barriers and instructional prompts. Educational Studies in Mathematics, 114, 417-438.
Stillman, G., Brown, J., Faragher, R., Geiger, V., & Galbraith, P. (2013). The role of textbooks in developing a socio-critical perspective on mathematical modelling in secondary classrooms. In G. Sillman, G. Kaiser, W. Blum, & J. Brown (Eds.), Teaching mathematical modelling: Connecting to research and practice (pp. 361-372). Springer.
Zapata-Grajales, F. N., Cano-Velásquez, N. A., & Villa-Ochoa, J. A. (2018). Art and geometry of plants: Experience in mathematical modelling through projects. EURASIA Journal of Mathematics, Science and Technology Education, 14(2), 585-603.
Zhao, L., Hwang, W.-Y., Shadiev, R., Lin, L.-K., Shih, T. K., & Chen, H.-R. (2018). Exploring the effects of ubiquitous geometry learning in real situations. In Proceedings of the 2nd International Conference on Digital Technology in Education (pp. 29-36). Association for Computing Machinery.
Journals System - logo
Scroll to top