Middle School Students' Approaches to Optimization: Insights into Mathematical Modeling and Real-World Problem Solving

Year 2025, Volume: 12 Issue: 1, 174 - 194

Rüveyda Karaman Dündar , İleyda Arslan , İlayda Mengi

Abstract

This study investigates middle school students' perspectives on optimization problems in mathematics, focusing on their problem-solving processes and learning experiences. Optimization involves finding the best solution under specific constraints or maximizing/minimizing an objective function, a concept closely related to mathematical modeling. This process is designed to develop essential skills, such as logical reasoning, prediction, argumentation, and critical thinking, by framing real-world situations as mathematical challenges. Although existing research on students' problem-solving with optimization problems primarily involves high school or university students, recent studies emphasize the necessity of introducing optimization concepts earlier in education.
This study administered four optimization problems to 16 middle school students to explore their experiences and opinions. Data were collected through observations, feedback forms, and individual interviews and analyzed using descriptive and content analysis methods. The findings reveal that students limited prior exposure to optimization problems significantly contributes to their challenges. While students generally understand the optimization problems, their performance varies notably, especially in assumption-making and mathematical calculations.
The study underscores the need for systematically integrating optimization problems into the middle school curriculum to enhance students' problem-solving skills and critical thinking. It suggests incorporating mathematical modeling with optimization tasks could improve students' abstraction and problem-solving abilities. Future research could investigate the effects of optimization problems on students' problem-solving skills and mathematical understanding.
ÖZ
Bu çalışma, ortaokul öğrencilerinin matematikteki optimizasyon problemlerine yönelik görüşlerini ve çözüm süreçlerini incelemeyi amaçlamaktadır. Optimizasyon, belirli kısıtlamalar altında en iyi çözümü bulmayı veya bir amaç fonksiyonunu maksimize/minimize etmeyi içeren bir süreç olup, matematiksel modelleme ile doğrudan ilişkilidir. Bu süreç, öğrencilere mantıksal akıl yürütme, tahmin etme, muhakeme yapma ve eleştirel düşünme gibi temel becerileri kazandırır. Optimizasyon problemleri, gerçek dünya durumlarını matematiksel modelleme problemleri olarak ele alır ve bu bağlamda önemli bir eğitimsel değer taşır. Mevcut literatürde optimizasyon problemleri genellikle lise veya üniversite seviyesinde incelenmiş olup, ortaöğretim düzeylerinde bu kavramların daha detaylı öğretilmesi gerektiği önerilmiştir.
Bu bağlamda, bu çalışmada dört optimizasyon problemi 16 ortaokul öğrencisine uygulanmış ve öğrencilerin bu problemleri çözme süreçleri ile görüşleri derinlemesine incelenmiştir. Veriler, gözlemler, geri bildirim formları ve birebir görüşmeler yoluyla toplanmış ve betimsel ile içerik analizi yöntemleri kullanılarak değerlendirilmiştir. Bulgular, öğrencilerin optimizasyon problemlerine yönelik sınırlı ön bilgiye sahip olmalarının, çözüm süreçlerinde karşılaştıkları zorlukları önemli ölçüde artırdığını göstermektedir. Öğrenciler, optimizasyon problemlerini genel olarak anlamalarına rağmen, performansları özellikle varsayım yapma ve matematiksel hesaplamalar aşamalarında değişkenlik göstermektedir.
Çalışmanın sonuçları, optimizasyon problemlerinin ortaokul müfredatına sistematik bir şekilde entegre edilmesinin önemini vurgulamaktadır. Matematiksel modelleme ile optimizasyon problemlerinin entegrasyonunun, öğrencilerin soyutlama becerilerini ve problem çözme yeteneklerini artırabileceği öngörülmektedir. Gelecekteki araştırmalar, optimizasyon problemlerinin öğrencilerin problem çözme becerileri ve matematiksel anlayışları üzerindeki etkilerini inceleyebilir.

Keywords

Mathematical education, mathematical modeling, optimization problems, middle school students.

Ethical Statement

Etik Kurul Onay Belgesi sisteme yüklenmiştir.

Supporting Institution

TÜBİTAK

Project Number

1919B012308984

Thanks

This study is based upon the “Optimization Concepts from the Perspective of Middle School Students” project supported by the Scientific and Technological Research Council of Turkey (TÜBİTAK; Project No: 1919B012308984). Any opinions, findings, conclusions, or recommendations expressed in this study are those of the authors and do not necessarily reflect the views of TÜBİTAK.

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