Challenges in geometric modelling–A comparison of students’ mathematization with real objects, photos, and 3D models

Simone Jablonski

doi:10.29333/ejmste/14321

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Simone Jablonski ¹ ^*

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¹ Goethe University Frankfurt, Frankfurt, GERMANY^* Corresponding Author

Abstract

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.

Keywords

geometric modelling
mathematizing
reality
tasks
contexts

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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Article Type: Research Article

EURASIA J Math Sci Tech Ed, Volume 20, Issue 3, March 2024, Article No: em2414

https://doi.org/10.29333/ejmste/14321

Publication date: 03 Mar 2024

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References

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. https://doi.org/10.1007/s10639-023-12408-x
Blum, W. (2015). Quality teaching of mathematical modelling: What do we know? What can we do? In S. Cho (Ed.), Proceedings of the 12^th International Congress on Mathematical Education (pp. 73-96). Springer. https://doi.org/10.1007/978-3-319-12688-3_9
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. https://doi.org/10.1533/9780857099419.5.221
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. https://doi.org/10.1007/978-3-319-62968-1_4
Buchholtz, N. (2021). Students’ modelling processes when working with math trails. Quadrante, 30(1), 140-157. https://doi.org/10.48489/quadrante.23699
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. https://doi.org/10.3389/feduc.2023.1142556
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. https://doi.org/10.1007/s11858-019-01090-4
Crompton, H. (2015). Using context-aware ubiquitous learning to support students’ understanding of geometry. Journal of Interactive Media in Education, 2015(1), 13. https://doi.org/10.5334/jime.aq
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. https://doi.org/10.1007/978-3-319-62968-1_6
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. https://doi.org/10.1177/0013164493053001007
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. https://doi.org/10.1007/s11858-018-0924-6
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. https://doi.org/10.1007/s11858-022-01339-5
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. https://doi.org/10.1007/978-3-030-37673-4_23
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. https://doi.org/10.1007/978-3-030-66996-6_13
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. https://doi.org/10.1007/s11858-017-0904-2
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. https://doi.org/10.1007/s10763-022-10323-0
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. https://doi.org/10.1007/s11423-019-09730-y
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. https://doi.org/10.1007/s10649-023-10215-2
Jablonski, S., & Ludwig, M. (2023). Teaching and learning of geometry–A literature review on current developments in theory and practice. Education Sciences, 13, 682. https://doi.org/10.3390/educsci13070682
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. https://doi.org/10.1080/0020739X.2019.1587530
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. https://doi.org/10.1080/01443410.2018.1502413
Ludwig, M., & Jesberg, J. (2015). Using mobile technology to provide outdoor modelling tasks–The MathCityMap–Project. Procedia-Social and Behavioral Sciences, 191, 2776-2781. https://doi.org/10.1016/j.sbspro.2015.04.517
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. https://doi.org/10.1007/s42330-021-00149-3
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. https://doi.org/10.1007/978-3-658-01580-0_6
Schukajlow, S., Kolter, J., & Blum, W. (2015) Scaffolding mathematical modelling with a solution plan. ZDM Mathematics Education, 47, 1241-1254. https://doi.org/10.1007/s11858-015-0707-2
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. https://doi.org/10.1007/s10649-023-10265-6
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. https://doi.org/10.1007/978-94-007-6540-5_30
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. https://doi.org/10.12973/ejmste/76958
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 2^nd International Conference on Digital Technology in Education (pp. 29-36). Association for Computing Machinery. https://doi.org/10.1145/3284497.3284507

How to cite this article

APA

Jablonski, S. (2024). Challenges in geometric modelling–A comparison of students’ mathematization with real objects, photos, and 3D models. Eurasia Journal of Mathematics, Science and Technology Education, 20(3), em2414. https://doi.org/10.29333/ejmste/14321

Vancouver

Jablonski S. Challenges in geometric modelling–A comparison of students’ mathematization with real objects, photos, and 3D models. EURASIA J Math Sci Tech Ed. 2024;20(3):em2414. https://doi.org/10.29333/ejmste/14321

AMA

Jablonski S. Challenges in geometric modelling–A comparison of students’ mathematization with real objects, photos, and 3D models. EURASIA J Math Sci Tech Ed. 2024;20(3), em2414. https://doi.org/10.29333/ejmste/14321

Chicago

Jablonski, Simone. "Challenges in geometric modelling–A comparison of students’ mathematization with real objects, photos, and 3D models". Eurasia Journal of Mathematics, Science and Technology Education 2024 20 no. 3 (2024): em2414. https://doi.org/10.29333/ejmste/14321

Harvard

Jablonski, S. (2024). Challenges in geometric modelling–A comparison of students’ mathematization with real objects, photos, and 3D models. Eurasia Journal of Mathematics, Science and Technology Education, 20(3), em2414. https://doi.org/10.29333/ejmste/14321

MLA

Jablonski, Simone "Challenges in geometric modelling–A comparison of students’ mathematization with real objects, photos, and 3D models". Eurasia Journal of Mathematics, Science and Technology Education, vol. 20, no. 3, 2024, em2414. https://doi.org/10.29333/ejmste/14321