Pre-service Mathematics Teachers’ Mathematical Modeling Experiences: Modeling Cycle Phases, Challenges, and Modeling Routes

Year 2026, Issue: Erken Görünüm [Online First], 1 - 31

Muhammet Şahal , Ahmet Şükrü Özdemir

https://doi.org/10.9779/pauefd.1340106

Abstract

Mathematical modeling is one of the prominent research areas in mathematics education for solving complex real-life problems. This study aims to reveal the mathematical modeling phases performed by pre-service mathematics teachers, the phases they have difficulties, and the modeling routes they follow in modeling cycles. In this case study, twenty-one pre-service mathematics teachers worked in groups on three modeling problems. We obtained the data from student notebooks, solution tracking templates, and audio and video recordings. We analyzed them using content analysis and transferred them to the modeling cycle, allowing us to see “modeling routes”. Most modeling routes were “irregular” and “completed.” In the modeling routes, pre-service mathematics teachers were successful in terms of “mental representation of the situation”, “creating the real model”, and “mathematical result(s)”. The most skipped phases in the modeling cycles were “creating a mathematical model,” “interpreting the real results,” and the “validation” phases. Furthermore, while they reported difficulties in “creating the mathematical model,” none of the pre-service mathematics teachers reported in the “interpretation” and “validation” phases. The study results are expected to shed light on mathematical modeling applications in the education of pre-service teachers and contribute to the literature on the difficulties encountered.

Keywords

mathematical modeling, modeling cycle, modeling routes, pre-service math teacher, mathematical modeling problems

Matematik Öğretmen Adaylarının Matematiksel Modelleme Deneyimleri: Modelleme Döngüsü Aşamaları, Zorluklar ve Modelleme Rotaları

Abstract

Matematiksel modelleme karmaşık gerçek yaşam problemlerinin çözümü için matematik eğitiminde öne çıkan araştırma alanlarından biridir. Çalışmanın amacı ortaokul matematik öğretmeni adaylarının hangi modelleme aşamalarını deneyimlediklerini, modelleme aşamalarında karşılaştıkları zorlukları ve modelleme döngülerinde ortaya çıkan rotaları incelemektir. Bu bağlamda durum çalışması ile yürütülen araştırmada yirmi bir ortaokul matematik öğretmeni adayı gruplar halinde üç modelleme problemi üzerinde çalışmıştır. Katılımcıların not defterlerinden, çözüm izleme şablonlarından, ses ve video kayıtlarından elde edilen veriler içerik analizi yöntemiyle analiz edilmiştir ve “modelleme rotalarını” görünür kılan modelleme döngüsüne aktarılmıştır. Gruplarda ortaya çıkan modelleme rotalarının çoğu “düzensiz” ve “tamamlanmış” kategorisinde değerlendirilmiştir. Modelleme rotalarında öğretmen adaylarının “durumun zihinsel temsili”, “gerçek model oluşturma” ve “matematiksel çözüm/sonuç” aşamalarında başarılı oldukları görülmüştür. Modelleme döngülerinde en fazla atlanan aşamaların “matematiksel model”, “gerçek sonuçları yorumlama” ve “doğrulama” aşamaları olduğu ortaya çıkmıştır. Ayrıca atlanan aşamalardan matematiksel “model aşamasına” dair öğretmen adaylarının zorluk yaşadıklarını belirttikleri görülürken; “gerçek sonuçları yorumlama” ve “doğrulama” aşamalarına dair zorluk yaşadıklarını belirten herhangi bir ifade görülmemiştir. Çalışmadan elde edilen sonuçların öğretmen adaylarının eğitiminde matematiksel modelleme uygulamalarına ışık tutacağı ve karşılaşılan zorluklara ilişkin literatüre katkıda bulunacağı düşünülmektedir.

Keywords

matematiksel modelleme, modelleme döngüsü, modelleme rotaları, öğretmen adayları, matematiksel modelleme problemleri

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