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Journals / Necatibey Eğitim Fakültesi Elektronik Fen ve Matematik Eğitimi Dergisi / 2025 / Cilt: 19 Sayı: 2

Examination of Mathematical Work Performed in Mathematical Modelling Task in the Light of MWS: The Case of Pre-Service Elementary Mathematics Teachers

Matematiksel Modelleme Görevinde Yapılan Matematiksel Çalışmaların MÇA Işığında İncelenmesi: İlköğretim Matematik Öğretmen Adayları Örneği

Ozan Deniz Kıyıcı(TC Milli Eğitim Bakanlığı Tekirdağ)0000-0002-4426-8581
Filiz Tuba Dikkartın Övez(BALIKESIR UNIVERSITY, NECATİBEY FACULTY OF EDUCATION)0000-0003-2646-5327
Pages
393–426
Publication Date
2025-12-29
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

The findings reveal that pre-service teachers frequently employed components of the epistemological plane during the problem comprehension and simplification stages of the modeling cycle.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:Mathematical modeling plays a crucial role for bridging the gap between mathematics and real-life contexts.
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Key Findings & Data:Employing a qualitative case study design, the research involved 15 pre-service teachers selected through criterion sampling.
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Conclusion & Impact:The findings reveal that pre-service teachers frequently employed components of the epistemological plane during the problem comprehension and simplification stages of the modeling cycle.
🔬Design:Modeling & Simulation
📍Scope:Comprehensive Sample
⚙️Variables:Matematiksel çalışma alanı · matematiksel modelleme · matematiksel çalışma

Abstract

Mathematical modeling plays a crucial role for bridging the gap between mathematics and real-life contexts. The theory of Mathematical Working Spaces (MWS) provides a suitable framework for analyzing the mathematical modeling process by incorporating both epistemological and cognitive dimensions of mathematical work. This study investigates the mathematical work carried out by pre-service elementary mathematics teachers as they engage with modeling-based mathematical tasks, interpreted the lens of MWS. Employing a qualitative case study design, the research involved 15 pre-service teachers selected through criterion sampling. Data were collected via video recordings and written documents capturing the participants’ solution processes, which were guided by exploratory questions. The data were analyzed descriptively, focusing on the components of the MWS framework. The findings reveal that pre-service teachers frequently employed components of the epistemological plane during the problem comprehension and simplification stages of the modeling cycle. The mathematization stage predominantly took place within the semiotic-instrumental plane, while the ‘working mathematically’ stage involved actions spanning across multiple planes. Future research may explore the instructional practices of pre-service teachers as they implement mathematical modeling in classroom environment, guided by the principles of MWS theory.

Özet

Matematiksel modelleme, gerçek yaşam durumları ile matematik arasındaki köprüyü kurmak için önemli bir süreçtir. Matematiksel Çalışma Alanları teorisi, matematiksel çalışmanın epistemolojik ve bilişsel taraflarını ele alarak matematiksel modelleme sürecinin açıklanmasında uygun bir araç olarak görülmektedir. Bu çalışmada, modelleme etkinliği içeren matematiksel görevlerin çözümü için ilköğretim matematik öğretmen adayları tarafından gerçekleştirilen matematiksel çalışmalar Matematiksel Çalışma Alanları teorisi doğrultusunda incelenmiştir. Nitel araştırma yöntemlerinden durum çalışması deseninin temel alındığı çalışmada, ölçüt örnekleme ile belirlenen 15 ilköğretim matematik adayı ile gerçekleştirilmiştir. Yönlendirilmiş keşif çalışma soruları ile desteklenen matematiksel modelleme etkinliği probleminin çözüm sürecine ilişkin veriler video kayıtları ve çözüm süreçlerini içeren dokümanlar ile elde edilmiştir. Elde edilen veriler Matematiksel Çalışma Alanları teorisinin bileşenleri temel alınarak betimsel olarak yorumlanmıştır. Çalışmanın sonucunda, matematiksel modelleme döngüsünün problemi anlama ve basitleştirme aşamalarında öğretmen adayları tarafından sıklıkla epistemolojik düzlem bileşenlerinin kullanıldığı, matematikselleştirme aşamasının ağırlıklı olarak semiyotik-enstrümantal düzlemde gerçekleştirildiği, matematiksel olarak çalışma aşamasının farklı düzlemlerde gerçekleştirilen eylemler ile yürütüldüğü görülmüştür. İleriki çalışmalarda, matematiksel modellemeyi sınıf ortamına aktaracak öğretmen adaylarının gerçekleştireceği öğretim uygulamalarının Matematiksel Çalışma Alanları teorisi çerçevesinde incelenmesine yönelik çalışmalar gerçekleştirilebilir.

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Cite This Article

Kıyıcı, O. D., Övez, F. T. D. (2025). Examination of Mathematical Work Performed in Mathematical Modelling Task in the Light of MWS: The Case of Pre-Service Elementary Mathematics Teachers. Necatibey Eğitim Fakültesi Elektronik Fen ve Matematik Eğitimi Dergisi, Cilt: 19 Sayı: 2, 393–426. https://doi.org/10.17522/balikesirnef.1626066

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References (46)

  1. Abrams, J. P. (2001). Mathematical modeling: Teaching the open-ended application of mathematics. In A. A. Cuoco & F. R. Curcio (Eds.), The teaching mathematical modeling and the of representation (pp. 269-282). NCTM.
  2. Altun, M. (2020). Matematik okuryazarlığı el kitabı: yeni nesil soru yazma ve öğretim düzenleme teknikleri. Alfa Aktüel.
  3. Ang, K. C. (2010). Teaching and learning mathematical modelling with technology. Electronic Proceedings of the 15th Asian Technology Conference in Mathematics, Malaysia. https://repository.nie.edu.sg/server/api/core/bitstreams/3e930bcf-707e-480f-acd7-9d17c2037cd6/content
  4. Blum, W., & Leiß, D. (2007). How do students’ and teachers deal with modelling problems? In P. Haines, P. Galbraith, W. Blum, & S. Khan (Eds.), Mathematical modelling: Education, engineering and economics (pp. 222-231). Horwood. https://doi.org/10.1533/9780857099419.5.221
  5. Borromeo Ferri, R. (2006). Theoretical and empirical differentiations of phases in the modelling process. ZDM, 38(2), 86-95. https://doi.org/10.1007/BF02655883
  6. Bukova Güzel, E., Tekin-Dede, A., Hıdıroğlu, Ç., Kula-Ünver, S., & Özaltun-Çelik, A. (2016). Matematik eğitiminde matematiksel modelleme: Araştırmacılar, eğitimciler ve öğrenciler için. Pegem Akademi.
  7. Büyüköztürk, Ş., Kılıç-Çakmak, E., Akgün, Ö., Karadeniz, Ş., & Demirel, F. (2008). Eğitimde bilimsel araştırma yöntemleri. Pegem Akademi.
  8. Chamberlin, S. A., & Moon, S. M. (2005). Model-eliciting activities as a tool to develop and identify creatively gifted mathematicians. Journal of Secondary Gifted Education, 17(1), 37-47. https://doi.org/10.4219/jsge-2005-393
  9. 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 (Publication No. 301126) [Doctoral dissertation, Atatürk University]. Council of Higher Education Thesis Center.
  10. Darses, F. (2001). Providing ergonomists with techniques for cognitive work analysis. Theoretical Issues in Ergonomics Science, 2(3), 268–277. https://doi.org/10.1080/14639220110104952
  11. Delgadillo, E., Viola, F., & Vivier, L. (2017). Choosing a mathematic working space in a modelling task: the influence of teaching. CERME 10, Ireland. https://hal.science/hal-01933475v1
  12. Derouet, C. (2019). La fonction de densité au carrefour entre probabilités et analyse. Une ingénierie didactique en classe de terminale scientifique. Actes du séminaire national de didactique des mathématiques 2017, 174-193.
  13. Derouet, C., Kuzniak, A., Laval, D., Delgadillo, E. M., Moutet, L., Nechache, A., Parzysz, B., & Vivier, L. (2017). Modeling tasks and mathematical work. CERME 10, Ireland. https://hal.science/hal-01933419v1
  14. Erlandson, D. A., Harris, E. L., Skipper, B. L., & Allen, S. D. (1993). Doing naturalistic inquiry: A guide to methods. Sage.
  15. Flores Salazar, J. V., & Almonacid Adriano, A. I. (2020). Espacio de trabajo matemático: una tarea de modelización sobre función cuadrática. Transformación, 16(2), 256-274.
  16. Gómez-Chacón, I. M., & Kuzniak, A. (2015). Spaces for geometric work: Figural, instrumental, and discursive geneses of reasoning in a technological environment. International Journal of Science and Mathematics Education, 13(1), 201-226. https://doi.org/10.1007/s10763-013-9462-4
  17. Hall, J., & Lingefjard, T. (2016). Mathematical modeling: applications with GeoGebra. John Wiley & Sons.
  18. Hankeln, C., & Hersant, M. (2020). Processus de modélisation et processus de problématisation en mathématiques à la fin du lycée. Éducation & didactique, 3, 39-67. https://doi.org/10.4000/educationdidactique.7776
  19. Henríquez Rivas, C., Ponce, R., Carrillo-Yáñez, J., Climent, N., & Espinoza-Vásquez, G. (2021). Trabajo matemático de un profesor basado en tareas y ejemplos propuestos para la enseñanza. Enseñanza de las Ciencias, 39(2), 0123-0142. https://doi.org/10.5565/rev/ensciencias.3210
  20. Henríquez Rivas, C., Verdugo Hernández, P., & Valenzuela Barrera, Y. (2023). Trabajo matemático de estudiantes de educación técnica profesional en un contexto interdisciplinar. Uniciencia, 37(1), 1-24. https://doi.org/10.15359/ru.37-1.25
  21. Henríquez-Rivas, C., & Kuzniak, A. (2021). Profundización en el trabajo geométrico de futuros profesores en entornos tecnológicos y de lápiz y papel. Bolema: Boletim de Educação Matemática, 35(71), 1550-1572. https://doi.org/10.1590/1980-4415v35n71a15
  22. Herget, W., & Torres-Skoumal, M. (2007). Picture (im) perfect mathematics! In W. Blum, P. Galbraith, H. Henn, & M. Niss (Eds.), Modelling and applications in mathematics education: The 14th ICMI study (pp. 379-386). Springer.
  23. Hidayat, R., & Iksan, Z. H. (2018). Mathematical modelling competency for Indonesian students in mathematics education programmes. Creative Education, 9(15), 2483-2490. https://doi.org/10.4236/ce.2018.915187
  24. Korkmaz, E. (2010). Middle school prospective maths and elementary school prospective teachers' views about mathematical modelling and their mathematical modelling competency (Publication No. 275237)[Doctoral Dissertation, Balıkesir University]. Council of Higher Education Thesis Center.
  25. Kuzniak, A. (2014). Understanding geometric work through its development and its transformations. In S. Rezat, M. Hattermann, & A. Peter-Koop (Eds.), Transformation - a fundamental idea of mathematics education (pp. 311-325). Springer. https://doi.org/10.1007/978-1-4614-3489-4_15
  26. Kuzniak, A. (2022). The theory of mathematical working spaces—theoretical characteristics. In Kuzniak, A., Montoya-Delgadillo, E., Richard, P.R. (eds), Mathematical work in educational context (pp. 3-31). https://doi.org/10.1007/978-3-030-90850-8_1
  27. Kuzniak, A., & Nechache, A. (2021). On forms of geometric work: a study with pre-service teachers based on the theory of Mathematical Working Spaces. Educational Studies in Mathematics, 106(2), 271-289. https://doi.org/10.1007/s10649-020-10011-2
  28. Kuzniak, A., & Richard, P. R. (2014). Spaces for mathematical work: Vievpoints and perspectives. RELIME, 17(4-1), 17-27. https://doi.org/10.12802/relime.13.1741b
  29. Kuzniak, A., Tanguay, D., & Elia, I. (2016). Mathematical working spaces in schooling: an introduction. ZDM, 48(6), 721-737. https://doi.org/10.1007/s11858-016-0812-x
  30. Lagrange, J. B. (2021). Les espaces de travail connectés: une perspective nouvelle pour la modélisation dans le secondaire? Canadian Journal of Science, Mathematics and Technology Education, 21(1), 9-28. https://doi.org/10.1007/s42330-020-00130-6
  31. Lagrange, J. B., Huincahue, J., & Psycharis, G. (2022). Modeling in education: New perspectives opened by the theory of Mathematical Working Spaces. In A. Kuzniak, E. Montoya-Delgadillo, ve P. R. Richard (Eds.), Mathematical work in educational context: The perspective of the theory of mathematical working spaces (pp. 247-266). Springer International. https://doi.org/10.1007/978-3-030-90850-8_11
  32. Lesh, R., & Doerr, H. (2003). Foundations of a models and modeling perspective on mathematics teaching and learning. In R. Lesh & H. Doerr (Eds.), Beyond constructivism: A models and modeling perspective on mathematics teaching, learning, and problem solving. Lawrence Erlbaum.
  33. Mason, J. (1988). Modelling: What do we really want pupils to learn. Hodder & Stoughton.
  34. Miles, M. B., & Huberman, A. M. (1994). Qualitative data analysis: An expanded sourcebook. Sage.
  35. Ministry of National Education [MoNE], (2018). Matematik dersi öğretim programı. Ankara.
  36. Ministry of National Education [MoNE], (2023). PISA 2022 Türkiye raporu. https://pisa.meb.gov.tr/meb_iys_dosyalar/2024_03/21120745_26152640_pisa2022_rapor.pdf
  37. Ministry of National Education [MoNE], (2024). Türkiye yüzyılı maarif modeli öğretim programları ortak metni. https://hoshaberio.meb.k12.tr/meb_iys_dosyalar/76/01/721342/dosyalar/2024_06/11231346_2024programortakmetinonayli.pdf
  38. Moutet, L. (2019). The extended theoretical framework of mathematical working space (extended MWS): potentialities in physics. Eleventh Congress of the European Society for Research in Mathematics Education, Netherlands.
  39. Nechache, A. (2018). L’articulation des genèses de l’espace de travail mathématique dans la résolution de tâches probabilistes faisant appel à la modélisation. Menon-Journal of Educational Research-online, 4th Thematic Issue, 93-104.
  40. Paolucci, C., & Wessels, H. (2017). An examination of preservice teachers’ capacity to create mathematical modeling problems for children. Journal of Teacher Education, 68(3), 330-344. https://doi.org/10.1177/0022487117697636
  41. Pinkstone, J. (2020). Rome's Colosseum to get a £9 million high-tech retractable floor so visitors can stand in the centre of the arena and feel like gladiators. https://www.dailymail.co.uk/sciencetech/article-9082233/Romes-Colosseum-high-tech-retractable-floor.html
  42. Psycharis, G., Kafetzopoulos, G. I., & Lagrange, J. B. (2021). A framework for analyzing students’ learning of function at the upper-secondary level: Connected working spaces and abstraction in context. In Mathematics Education in the Digital Age (pp. 150-167). Routledge.
  43. Reyes Avendaño, C. G. (2020). Enseignement et apprentissage des fonctions numériques dans un contexte de modélisation et de travail mathématique [Doctoral dissertation, Université Paris Cité]. HAL science ouverte. https://hal.science/tel-03211997/
  44. Tekin-Dede, A., & Bukova-Güzel, E. (2018). A rubric development study for the assessment of modeling skills. The Mathematics Educator, 27(2), 33-72. https://doi.org/10.63301/tme.v27i2.2040
  45. Verdugo Hernández, P., Huincahue, J., Cumsille, P., & Nechache, A. (2023). Articulación entre modelización y espacios de trabajo matemático. Análisis de una Tarea bajo el ciclo de Blomhøj en Educación Superior. Acta Scientiae, 24(7), 146-175. https://doi.org/10.17648/acta.scientiae.7135
  46. Yıldırım, A., & Şimşek, H. (2021). Sosyal bilimlerde nitel araştırma yöntemleri. Şeçkin.