Abstract

Educators have long emphasized the importance of relating mathematics to everyday life situations. During the primary school years, mathematical modeling activities play an important role in this regard. Through a mathematical modeling activity prepared in accordance with the length and area measurement learning outcomes in the primary school 4th-grade mathematics curriculum, the purpose of this study was to determine students' mathematical modeling competencies. The study adopted a qualitative approach using a teaching experiment model. The study involved three students selected from 33 in a state primary school through criterion sampling. Farmer Uncle Hüseyin model eliciting activity (MEA) was given to the focus group to work on, and the whole process was videotaped. Each video recording was transcribed in detail. Transcriptions, student handouts, and researcher field notes were analyzed using the mathematical modeling competencies cycle developed by Blum and Kaiser and adapted by Maaß (2006). Modeling competencies of students were found to be at different levels. Based on the study, the students' warm-up activities, the context of the MEA, and their previous modeling experiences all contributed to the students' representation of different levels of modeling competency. Due to the frequent use of multiple-choice questions in their classrooms, students also had difficulty interpreting qualitative data and understanding the mathematical task they were given.

Keywords

References

• An, I., & Oh, Y. (2018). An analysis of mathematical modeling process and mathematical reasoning ability by group organization method. Journal of Elementary Mathematics Education in Korea, 22(4), 497-516.
• Aydın-Güç, F. (2015). Examining mathematical modeling competencies of teacher candidates in learning environments designed to improve mathematical modeling competencies [Unpublished doctoral dissertation]. Karadeniz Tecnical University, Trabzon.
• Baki, A. (2014). Kuramdan uygulamaya matematik eğitimi [Mathematics education from theory to practice]. Harf Pub.
• Baltacı, A. (2017). Miles-Huberman model in qualitative data analysis. Ahi Evran University Institute of Social Sciences Journal, 3 (1), 1-14.
• Biccard, P. (2010). An investigation into the development of mathematical modelling competencies of grade 7 learners [Unpublished Master’s thesis]. Stellenbosch University, South Africa.
• Biccard, P. & Wessels, D. C. J. (2011). Documenting the development of modelling competencies of grade 7 mathematics students. International Perspectives on the Teaching and Learning of Mathematical Modelling, 1(5), 375-383.
• Blomhøj, M. & Jensen, T.H. (2003). Developing mathematical modelling competence: Conceptual clarification veeducational planning. Teaching Mathematics and Its Applications, 22(3), 123-139. https://doi.org/10.1093/teamat/22.3.123
• 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
• Blum, W. (2015). Quality teaching of mathematical modelling: What do we know? What can we do?. In S. J. Cho (Ed.), The proceedings of the 12th international congress on mathematical education—intellectual and attitudinal challenges (pp. 73–96). Springer. https://doi.org/10.1007/978-3-319-12688-3_9
• Borromeo Ferri, R. (2006). Theoretical and empirical differentiations of phases in the modelling process. Zentralblatt für Didaktik der Mathematik (ZDM), 38(2), 86-95. doi.org/10.1007/BF02655883
• Bukova-Güzel, E. (2011). An examination of pre-service mathematics teachers’ approaches to construct and solve mathematical modelling problems. Teaching Modelling and Its Applications, 39, 19-36. https://doi.org/10.1093/teamat/hrq015
• Bukova Güzel, E. (2016). Matematik eğitiminde matematiksel modelleme [Mathematical modeling in mathematics education]. Pegem Akademi.
• Canbazoğlu, H. B., & Tarım, K. (2021). A teaching process for mathematical modeling in primary school. Buca Faculty of Education Journal, 51, 210-225. https://doi.org/10.53444/deubefd.825361
• Chan, C. M. E., Ng, K. E. D., Widjaja, W. & Seto, C. (2012). Assessment of primary students‘ mathematical modelling competencies. Journal of Science And Mathematics Education in Southeast Asia, 23(2), 146-178.
• Çakmak-Gürel, Z. (2018). The investigation of mathematical modelling processes of pre-service mathematics teachers with cognitive perspective [Unpublished doctoral dissertation]. Atatürk University, Erzurum.
• Çavuş Erdem, Z. & Gürbüz, R. (2018). Examining the 7th grade students’ surface area calculation knowledges and skills in mathematical modelling activities based learning environments. Adıyaman University Journal of Education Sciences, 8(2), 86-115.
• Çiltaş, A. (2011). The effect of the mathematical modeling method in teaching the sequences and series on the learning and modeling skills of prospective elementary mathematics teachers [Unpublished doctoral dissertation]. Atatürk University, Erzurum.
• Deniz, D. & Akgün, L. (2016). The sufficiency of high school mathematics teachers’ to design activities appropriate to model eliciting activities design principles. Karaelmas Journal of Educational Sciences, 4, 1-14.
• Deniz, Ş. (2020). Investigation of mathematical modelling processes in stem education through model eliciting activities of middle school students [Unpublished master’s thesis]. Mersin University, Mersin.
• Doerr, H. M. ve English, L. D. (2003). A modeling perspective on students‘ mathematical reasoning about data. Journal for Research in Mathematics Education, 34(2), 110–136. https://doi.org/10.2307/30034902
• Doğan, M. F., Gürbüz, R., Çavuş Erdem, Z. and Şahin, S. (2018). STEM eğitimine geçişte bir araç olarak matematiksel modelleme [Mathematical modeling as a tool for transition to STEM education]. In R. Gürbüz & M. F. Doğan (Eds.), Matematiksel modellemeye disiplinler arası bakış: Bir STEM yaklaşımı [An interdisciplinary view of mathematical modeling: A STEM approach] (pp. 43-56). Pegem Akademi.
• English, L. D. & Watters, J.J. (2004). Mathematical modelling with young children. In M. J. Hoines & A. B Fuglestad (Eds.), Proceedings of the 28th Annual Conference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 335 342). PME.
• English, L. D. (2006a). Mathematical modeling in the primary school: Children's construction of a consumer guide. Educational studies in mathematics, 63(3), 303-323. doi.org/10.1007/s10649-005-9013-1
• English, L. D. (2006b). Introducing young children to complex systems through modeling. In Grootenboer, P., Zevenbergen, R. & Chinnappan, M. (Eds.), 29th Annual Conference of the Mathematics Education Research Group of Australasia (pp.195-202). MERGA.
• English, L. D. (2009). Promoting interdisciplinarity through mathematical modelling. Zentralblatt für Didaktik der Mathematik (ZDM), 41(1–2), 161–181. https://doi.org/10.1007/s11858-008-0106-z
• English, L. D. (2015). Learning through modelling in the primary years. In Lee, N. G. & Ng, K.E.D. (Eds.), Mathematical Modelling: From Theory To Practice (pp. 99-124). National Intstitute of Education, Nanyang Technological University.
• Haines C. & Crouch R. (2007). Mathematical Modelling and Applications: Ability and Competence Frameworks. In Blum W., Galbraith P.L., Henn HW., & Niss M. (Eds.) Modelling and Applications in Mathematics Education (pp.417-424). New ICMI Study Series, Springer.
• Hıdıroğlu, Ç. N., & Bukova Güzel, E. (2016). Transitions between cognitive and metacognitive activities in mathematical modelling process within a technology enhanced environment. Necatibey Faculty of Education Electronic Journal of Science & Mathematics Education, 10(1), 313-350.
• Hıdıroğlu, Ç. N. (2022). Mathematics student teachers’ task design processes: The case of History, Theory, Technology, and Modeling. Journal of Pedagogical Research, 6(5), 17-53. https://doi.org/10.33902/JPR.202217094
• Işık, N. (2016). The effect of mathematical modelling activities on difficulty perception and success of numbers domain in primary school 4th class [Unpublished doctoral dissertation]. Necmettin Erbakan University, Konya.
• İncikabı, S. (2020). Investigation of reflections of mathematical modeling activities on the mathematical modeling efficacy and teaching experiences of prospective primary school mathematics teachers [Unpublished doctoral dissertation]. Kastamonu University, Kastamonu.
• Ji, X. (2012). A quasi-experimental study of high school students’mathematics modelling competence [Paper presentation]. 12. International Congress on Mathematical Education, Korea, Seoul.
• Ko, C. & Oh, Y. (2015). The effects of mathematical modeling activities on mathematical problem solving and mathematical dispositions. Journal of Elementary Mathematics Education in Korea, 19(3), 347-370.
• Leiss, D., Schukajlo, S., Blum, W., Messner, R. & Pekrun, R. (2010). The role of the situation model in mathematical model- Task analyses, student competencies, and interventions. Journal Für Mathematik- Didaktik, 31(1), 119-141. doi.org/10.1007/s13138-010-0006
• Lesh, R., Hoover, M., Hole, B., Kelly, A., & Post, T. (2000). Principles for developing thought-revealing activities for students veteachers. In A.Kelly, & R. Lesh. (Eds.) Handsbook of Resarch Design in Mathematics and Science Education (pp.591-645). Lawrence Erlbaum Associates.
• Lesh, R. A., & Doerr, H. M. (2003). Foundations of models vemodeling perspective on mathematics teaching, learning, and problem solving. In R. Lesh & H. M. Doerr (Eds.), Beyond constructivism: Models vemodeling perspectives on mathematics problem solving, learning, and teaching (pp. 3-33). Lawrence Erlbaum Associates.
• Lesh, R., & Caylor, B. (2007). Introduction to the special issue: Modeling as application versus modeling as a way to create mathematics. International Journal of computers for mathematical Learning, 12(3), 173-194.
• Maaß, K. (2006). What are modelling competencies?. ZDM, 38(2), 113-142. https://doi.org/10.1007/BF02655885
• Maaß, K. (2007). Modelling tasks for low achieving students – first results of an empirical study. In D. Pitta-Pantazi, & G. Philippou (Eds.), Proceedings of the fifth congress of the European society for research in mathematics education (pp. 2120-2129). University of Cyprus.
• Ministry of National Education [MoNE]. (2011). TIMSS 2011 ulusal matematik ve fen raporu: 4. Sınıflar [TIMSS 2011 national math and science report: 4^th Grades]. Author. Retrieved July, 22, 2022 from http://odsgm.meb.gov.tr/test/analizler/docs/timss/TIMSS-2011-4-Sinif%20Raporu.pdf
• Ministry of National Education [MoNE]. (2018a). PISA-Uluslararası öğrenci değerlendirme programı [PISA-International student assessment program]. Author. Retrieved July, 22, 2022 from http://pisa.meb.gov.tr/
• Ministry of National Education [MoNE]. (2018b). İlkokul matematik dersi öğretim programı: 1, 2, 3, 4, 5, 6, 7 ve 8. Sınıflar [Primary school mathematics curriculum: Grades 1, 2, 3, 4, 5, 6, 7, and 8]. Author.
• Ministry of National Education [MoNE]. (2015a). 2015 PISA ulusal raporu [2015 PISA national report]. Author. Retrieved July, 22, 2022 from https://odsgm.meb.gov.tr/www/2015-pisa-ulusal-raporu/icerik/204
• Ministry of National Education [MoNE]. (2015b). İlkokul matematik dersi öğretim programı:1, 2, 3 ve 4. sınıflar [Primary school mathematics curriculum: Grades 1,2,3,4]. Author.
• Miles, H. B. & Huberman, A. M. (1994). Qualitative data analysis. Sage.
• OECD. (2019). PISA 2018 Assessment and analytical framework. Author.
• Özaltun Çelik, Ö. & Bukova Güzel, E. (2018). Students’ quantitative reasoning while engaging in a mathematical modeling task designed for learning linear function. Adıyaman University Journal of the Faculty of Education, 8(2), 53-85.
• Özer, A. Ö. & Bukova Güzel, E. (2016). Mathematical modelling problems from the viewpoint of students, prospective teachers and teachers. Manisa Celal Bayar University Journal of Faculty of Education, 4(1), 57-73.
• Patton, M. Q. (2015). Purposeful sampling and case selections: Overview of strategies and options. Sage.
• Sekerak, J. (2010). Phases of mathematical modelling and competence of high school students. The Teaching of Mathematics, 13(2), 105-112.
• Sriraman, B. (2005). Conceptualizing the notion of model eliciting [Paper presentation]. Fourth Congress of the European Society for Research in Mathematics Education, Sant Feliu de Guíxols, Spain.
• Steffe, L. P. (1991). The constructivist teaching experiment: Implication and illustrations. In E. von Glasersfeld (Ed.), Radical constructivism in mathematics education (pp. 177–194). Kluver.
• Steffe, L. P. & Thompson, P. W. (2000). Teaching experiment methodology: Underlying principles and essential elements. In R. Lesh and A. E. Kelly (Eds.). Handbook of research design in mathematics and science education (pp. 267– 307). Lawrence Erlbaum.
• Suh, J. M., Matson, K. & Seshaiyer, P. (2017). Engaging elementary students in the creative process of mathematizing their world through mathematical modeling. Education Sciences, 7(2), 62. https://doi.org/10.3390/educsci7020062
• Şahin, N. (2014). Fourth grade primary school students' modeling processes [Unpublished master’s thesis]. Ondokuz Mayıs University, Samsun.
• Şahin, N. (2019). Determining and evaluating of primary 4th-grade school students' cognitive modelling competencies [Unpublished doctoral dissertation]. Ondokuz Mayıs University, Samsun.
• Şahin, S., Doğan, M. F., Gürbüz, R. & Çavuş-Erdem, Z. (2017). Öğretmen adaylarının matematiksel modelleme problemi hazırlama becerileri [Pre-service teachers' skills in preparing mathematical modeling problems]. In A. Baki (Ed.), 3^rd International Symposium of Turkish Computer and Mathematics Education (pp. 582- 584). Bilmat Education Services.
• 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. https://doi.org/10.12738/estp.2017.1.0038
• Şahin, N. & Eraslan, A. (2018). How To Apply Model Eliciting Activities In Primary School? Journal of Education Theory and Practical Research, 4(1), 99-117.
• Şen-Zeytun, A. (2013). An ınvestigation of prospective teachers’ mathematical modeling processes vetheir views about factors affecting these processes [Unpublished doctoral dissertation]. Middle East Tecnical University, Ankara.
• Tekin Dede, A. (2015). Developing students' modelling competencies in mathematics lessons: An action research study [Unpublished doctoral dissertation]. Dokuz Eylül University, İzmir.
• Tekin Dede A., & Yılmaz S. (2013). İlköğretim matematik öğretmeni adaylarının modelleme yeterliliklerinin incelenmesi [Examination of modeling competencies of primary school mathematics teacher candidates]. Turkish Journal of Computer and Mathematics Education, 4(3), 185-206.
• Tekin Dede A., & Yılmaz S. (2016). Mathematization competencies of pre-service elementary mathematics teachers in the mathematical modelling process. International Journal of Education in Mathematics, Science and Technology, 4(4), 284-298.
• Ulu, M. (2017). Examining the mathematical modeling processes of primary school 4th-grade students: Shopping problem. Universal Journal of Educational Research, 5(4), 561-580.
• Watters, J. J., English, L. D., & Mahoney, S. (2004). Mathematical modeling in the elementary school [Paper presentation]. American Educational Research Association Annual meeting, San Diego.
• Yıldırım, A. & Şimşek, H. (2013). Sosyal bilimlerde nitel araştırma yöntemleri [Qualitative research methods in the social sciences]. Seçkin.
• Zubi,I., A., Peled, I., & Yarden, M. (2018). Children with mathematical difficulties cope with modelling tasks: what develops? International Journal of Mathematical Education in Science and Technology. https://doi.org/10.1080/0020739X.2018.1527404

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