Matematik Okuryazarlığını Yordamada İstatistiksel ve Makine Öğrenmesi Yaklaşımlarının Karşılaştırılması: PISA 2022 Türkiye Örneği

Year 2025, Volume: 16 Issue: 4, 241 - 263, 31.12.2025

Taner Yılmaz , Kübra Atalay Kabasakal

Abstract

Bu çalışma, PISA 2022’ye katılan Türkiye’deki öğrencilerin matematik okuryazarlığını yordamada istatistiksel ve makine öğrenmesi yöntemlerini karşılaştırmaktadır. Bilişsel, duyuşsal ve bağlamsal boyutları yansıtan 13 standartlaştırılmış yordayıcı değişkene ait 6.427 öğrenci verisi kullanılarak çoklu doğrusal regresyon, en küçük mutlak küçültme ve seçim operatörü (LASSO), rassal ormanlar, aşırı gradyan artırma (XGBoost), yapay sinir ağları ve bir yığıt (stacking) modeli 10 katlı çapraz doğrulama tasarımıyla değerlendirilmiştir. Bulgular, yığıt modellerin doğrusal modellere kıyasla daha yüksek doğruluk sağladığını göstermiştir: yığıt modeli en yüksek doğruluğa ulaşmış (fold dışı R²=.319;RMSE=.777), bunu XGBoost (R²=.313) ve rassal ormanlar (R²=.304) izlemiştir. Doğrusal modeller ise daha düşük sonuçlar vermiştir (çoklu doğrusal regresyon R²≈.270; LASSO R²=.273). Ortalama mutlak hata değerleri modeller arasında oldukça benzer bulunmuştur (≈ .633–.658) ve foldlar arası farklar üç ondalıkta yuvarlamadan kaynaklanacak kadar küçüktür. Artık analizleri, yığıt modellerin daha kararlı hata yapısına sahip olduğunu, doğrusal modellerin ise daha belirgin heteroskedastisite gösterdiğini ortaya koymuştur. Tüm modellerde sosyoekonomik durum en güçlü yordayıcı olarak öne çıkmış, bunu matematik özyeterliği ve sınıf disiplini izlemiştir. Bu durum, öğrenci inançlarının ve sınıf ortamının birlikte belirleyici rol oynadığını göstermektedir. Bulgular, yordama başarımı ve değişken önem düzeylerinin belirlenmesinde yığıt gibi birleşik yöntemlerin avantajlarını vurgulamakta ve sosyoekonomik eşitsizliklerin eğitimsel sonuçlar üzerindeki etkisinin sürdüğüne dikkat çekmektedir.

Keywords

matematik okuryazarlığı , makine öğrenmesi , PISA 2022 , yordayıcı modelleme , eğitimsel veri madenciliği

Ethical Statement

Bu çalışma OECD tarafından yayımlanan kamuya açık PISA 2022 verilerini kullanmaktadır; bu nedenle ek bir etik kurul onayına gerek duyulmamıştır.

Supporting Institution

Yok

Project Number

Not applicable

Thanks

Yazarlar, PISA 2022 veri setine erişim sağladığı için OECD’ye teşekkür eder.

Comparison of Statistical and Machine Learning Approaches for Predicting Mathematical Literacy: Evidence from PISA 2022 Türkiye

Abstract

This study compares statistical and machine learning methods for predicting mathematical literacy among students in Türkiye who participated in PISA 2022. Using data on 6,427 students and 13 standardized predictors capturing cognitive, affective, and contextual dimensions, we evaluated multiple linear regression, least absolute shrinkage and selection operator, random forests, extreme gradient boosting, artificial neural networks, and a stacking ensemble within a 10-fold cross-validation design. Ensemble approaches outperformed linear methods: the stacking model achieved the highest accuracy (out-of-fold R² = .319; RMSE = .777), followed closely by extreme gradient boosting (R² = .313) and random forests (R² = .304). Linear models yielded weaker results (multiple linear regression R² ≈ .270; least absolute shrinkage and selection operator R² = .273). Mean absolute error values were nearly identical across models (≈ .633–.658), with minimal between-fold variation due to rounding at three decimals. Residual analyses indicated that ensemble models produced more stable error structures, whereas linear methods showed stronger heteroskedasticity. Across all approaches, socioeconomic status consistently emerged as the strongest predictor, followed by mathematics self-efficacy and disciplinary climate, underscoring the dual roles of student beliefs and classroom environment. These findings highlight the advantages of ensemble methods for predictive performance and variable-importance estimation, emphasizing the ongoing impact of socioeconomic inequalities on educational outcomes.

Keywords

mathematical literacy , machine learning , PISA 2022 , predictive modeling , educational data mining

Ethical Statement

This study uses publicly available PISA 2022 data published by OECD; therefore, no additional ethical approval was required.

Supporting Institution

None

Project Number

Not applicable

Thanks

The authors would like to thank the OECD for providing access to the PISA 2022 dataset.

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