Abstract

The purpose of this study is to investigate the reflections that arise during the implementation of mathematical modeling activities with third-grade primary school students. To achieve this goal, a case study methodology was employed. The study consisted of 9 third-grade students (average age 8), selected through purposive sampling from a public primary school. In the 5-week preparatory phase preceding the main intervention, a distinct mathematical modeling activity was implemented each week to facilitate students' acquisition of foundational knowledge and experience on. Subsequently, a focus group consisting of three students was selected using criterion sampling. These students engaged with a mathematical modeling problem entitled 'The Healthy Money Saving Problem,' developed by the authors, under carefully structured problem-solving environments and processes. The entire process was video recorded, and the dialogues were transcribed verbatim. These transcriptions, along with the students' individual work sheets, were analyzed in alignment with the modeling cycle framework. The results indicate that students engaged in collaborative group work, where they generated and critically discussed mathematical ideas, interpreted and analyzed data, used relationships between data points, and applied mathematical concepts to real-world problems. Furthermore, they developed multiple solution strategies and were able to discard unsuitable approaches. The students also employed a range of mathematical skills such as problem solving, critical thinking, and reasoning throughout the process. Additionally, the students integrated informal knowledge (the knowledge students acquire outside of school) into the modeling process and made efforts to generalize their models to validate their applicability in real-life contexts.

Keywords

References

• Berry, J., & Houston, K. (1995). Mathematical modelling. J.W. Arrowsmith Ltd.
• Blum, W. (2002). ICMI Study 14: Applications and modelling in mathematics education- discussion document. Zentralblatt Fur Didaktik Der Mathematik, 34(5), 229-339. https://doi.org/10.1007/BF02655826
• Blum, W., & Ferri, B. R. (2009). Mathematical modeling: Can it be taught and learnt? Journal of Mathematical Modeling and Applications, 1(1), 45-58.
• Blum, W., & Niss, M. (1991). Applied mathematical problem solving, modelling, application and links to other subjects-state, trends, and issues in mathematics instruction. Educational Studies in Mathematics, 22(1), 37-68. https://doi.org/10.1007/BF00302716
• Borromeo Ferri, R. (2018). Learning how to teach mathematical modeling in school and teacher education. Springer.
• Carlson, M. A., Wickstrom, M. H., Burroughs, E. A., & Fulton, E. W. (2016). A case for mathematical modelling in the elementary school classroom. In C. R. Hirsch & A. R. McDuffie (Eds.), Mathematical modeling and modeling mathematics (pp. 121-129). National Council of Teachers of Mathematics.
• Çepni, S. (2016). PISA ve TIMSS mantığını ve sorularını anlama [Understanding the logic and questions of PISA and TIMSS]. Pegem Publishing.
• De Corte, E. (2004). Mainstreams and perspectives in research on learning mathematics from instruction. Applied Psychology, 53, 279-310. https://doi.org/10.1111/j.1464-0597.2004.00172.x
• Dindyal, J. (2010). Word problems and modelling in primary school mathematics. In B. Kaur, & J. Dindyal (Eds.), Mathematical applications and modelling (94-111). World Scientific.
• Doruk, B. K. (2010). The effects of mathematical modeling on transferring mathematics into daily life (Publication no. 265182) [Doctoral dissertation, Hacettepe University]. Council of Higher Education Thesis Center.
• English, L. D. (2006). Mathematical modeling in the primary school: children's construction of a consumer guide. Educational Studies in Mathematics, 63(3), 303-323. https://doi.org/10.1007/s10649-005-9013-1
• English, L. D., & Watters, J. J. (2004). Mathematical modelling with young children. In M. J. Hoines & A. B. Fuglestad (Eds.), Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education, Vol. 2 (pp. 335–342). PME.
• English, L. D., & Watters, J. (2005). Mathematical modelling in the early school years. Mathematics Education Research Journal, 16(3), 59-80. https://doi.org/10.1007/BF03217401
• 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, 1–23. https://doi.org/10.1007/s10649-021-10039-y
• Haines, C. R., & Crouch, R. M. (2010). remarks on a modelling cycle and interpretting behaviours. In R. A. Lesh, C. R. Haines, P. L. Galbraith, & A. Hurford (Eds.), Modeling students’ mathematical modelling competencies: The ICTMA-13 study (pp. 145-154). Springer.
• Jablonski, S., et al. (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
• Koç, D., & Elçi, A. N. (2022). The effect of mathematical modeling instruction on pre-service primary school teachers’ problem‑solving skills and attitudes towards mathematics. Journal of Pedagogical Research, 6(4), 111–129. https://doi.org/10.33902/JPR.202217783
• Leiss, D., Schukajlow, S., Blum, W., Messner, R., & Pekrun, R. (2010). The role of the situation model in mathematical modelling-task analyses, student competencies and teacher interventions. Journal für Mathematik-Didaktik, 31, 119-141.
• Lesh, R. A., & Doer, H. M. (2003). Foundations of a models and modelling perspective on mathematics teaching, learning, and problem solving. In R. A. Lesh & H. M. Doerr (Eds.), Beyond constructivism: A models and modeling perspective on mathematics problem solving, learning and teaching (pp. 3–33). Lawrence Erlbaum Associates.
• Lesh, R. A., Hamilton, E., & Kaput, J. J. (2007). Foundations for the future in mathematics education. Lawrence Erlbaum.
• Lesh, R. A., Post, T., & Behr, M. (1987). Representations and translations among representations in mathematics learning and problem solving. In C. Janvier (Ed.), Problems of representations in the teaching and learning of mathematics (pp. 33-40). Lawrence Erlbaum.
• Lesh, R. A., & Zawojewski, J. S. (2007). Problem solving and modeling. In F. Lester (Ed.), Second handbook of research on mathematics teaching and learning: a project of the national council of teachers of mathematics (pp. 763–804). Information Age Publishing.
• Lincoln, Y. S., & Guba, E. G. (1985). Naturalistic Inquiry. Sage.
• Merriam, S. B., & Tisdell, E. J. (2016). Qualitative research: a guide to design and implementation. Jossey-Bass.
• Miles, M. B., & Huberman, A. M. (1994). Qualitative data analysis: An expanded sourcebook. Sage.
• Ministry of National Education [MoNE]. (2013). PISA 2002 projesi ulusal ön raporu [PISA 2002 project national preliminary report]. Author. http://yegitek.meb.gov.tr
• Ministry of National Education [MoNE]. (2018). İlkokul matematik
• (1-4. Sınıflar) dersi öğretim programı [Mathematics curriculum for primary school: Grades 1–4]. Author.
• Mousoulides, N. (2007). A modeling perspective in the teaching and learning of mathematical problem solving [Unpublished Doctoral Dissertation]. University of Cyprus, Cyprus.
• Ofem, U. J., Ovat, S. V., Ntah, H., Ani, M. I., & Nwinyinya, E. (2024). Modelling achievement in mathematics: The predictive role of affective variables among students. Journal of Pedagogical Sociology and Psychology, 6(2), 78-97. https://doi.org/10.33902/jpsp.202426613
• Organisation for Economic Cooperation and Development [OECD]. (2019a). PISA 2018 assessment and analytical framework. Author.
• Organisation for Economic Cooperation and Development [OECD]. (2019b). PISA 2018 results volume I: What students know and can do. Author.
• Patton, M. Q. (2015). Qualitative research and evaluation methods. Sage.
• Pollak, H. (2007). Mathematical modeling-A conversation with Henry Pollak. In W. Blum, P. L. Galbraith, H-W, Henn, & M. Niss (Eds.), Modelling and applications in mathematics education. The 14th ICMI Study (pp. 109-120). Springer.
• Stillman, G., Brown, J., & Galbraith, P. (2009). Identifying challenges within transition phases of mathematical modeling activities at Year 9. In R. A. Lesh, P. L. Galbraith, C. R. Haines, & A. Hurford (Eds.), Modeling Students’ Mathematical Modeling Competencies: ICTMA‑13 (pp. 385–398). Springer. https://doi.org/10.1007/978-1-4419-0561-1_33
• Swetz, F., & Hartzler J. S. (1991). Mathematical modeling in the secondary school curriculum. NCTM.
• Şahin, N. (2019). Determining and evaluating of primary 4th-grade school students' cognitive modelling competencies (Publication no. 601972) [Doctoral dissertation, On Dokuz Mayıs University]. Council of Higher Education Thesis Center.
• Şahin, N., & Eraslan, A. (2017). Fourth-grade elementary school students’ thought processes and challenges encountered during the butter beans problem. Educational Sciences: Theory & Practice, 17(1), 105–127.
• Tekin, A. (2012). Mathematics teachers’ views concerning model eliciting activities, developmental process and the activities themselves (Publication no. 317671) [Master’s thesis, Dokuz Eylül University]. Council of Higher Education Thesis Center.
• Tekin Dede, A. T., Bukova Güzel, E. (2013). Secondary mathematics teachers' views regarding model eliciting activities and applications of them in mathematics courses. Bartın University Journal of Faculty of Education, 2(1), 300-322.
• Thomas, K., & Hart, J. (2010). Pre-service teacher perceptions of model eliciting activities. In R. A. Lesh, P. L. Galbraith, C. R. Haines, & A. Hurford (Eds.), Modeling students’ mathematical modeling competencies (pp. 531-539). Springer Science and Business Media. https://doi.org/10.1007/978-1-4419-0561-1_46
• Ulu, M. (2017). Examining the mathematical modeling processes of elementary school 4th grade students: Shopping problem. Universal Journal of Educational Research, 5(4), 561-580. https://doi.org/10.13189/ujer.2017.050406
• Watters, J. J., English, L. D., & Mahoney, S. (2004, April). Mathematical modeling in the elementary school [Paper presentation]. American Educational Research Association Annual Meeting, San Diego.
• Wess, R., Klock, H., Siller, H. S., & Greefrath, G. (2021). Mathematical modelling. In R. Wess, H. Klock, H. Siller, & G. Greefrath (Eds.), Measuring professional competence for the teaching of mathematical modelling. Springer. https://doi.org/10.1007/978-3-030-78071-5_1

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