Matematik Eğitiminde Futschek Modeli Temelinde Algoritmik Düşünme Ölçeği Geliştirilmesi

Öz

Çalışmanın amacı öğrencilerin matematiksel problemleri çözerken süreç içerisinde karşılaştıkları problemi anlama, çözüm yolu oluşturma, strateji geliştirme, hataları fark etme, çözüm planı yapma ve değerlendirme gibi bilişsel süreçleri değerlendirebilecek geçerli ve güvenilir bir algoritmik düşünme ölçeği geliştirmektir. Araştırmacılar tarafından alanyazın incelenerek Futschek’in algoritmik düşünme süreci modeli temelinde beşli likert tipinde 42 maddelik bir taslak ölçek oluşturulmuştur. Geliştirilen taslak ölçek, 2024-2025 eğitim-öğretim yılında Tekirdağ ilinin Kapaklı ilçesindeki üç farklı lisede 9. sınıf öğrencisi olarak öğrenim gören 312 kız ve 221 erkek olmak üzere toplam 533 öğrenciye uygulanmıştır. Verilerin analizinde SPSS 27 ve AMOS 24 kullanılarak madde toplam test korelasyonları, Cronbach Alpha güvenirlik, Sperman-Brown Prophecy güvenirlik, bileşik güvenirlik, test-tekrar test güvenirlik katsayısı bulunmuştur. Bunun yanı sıra hipotez testleri, keşfedici faktör analizi ve doğrulayıcı faktör analizi yapılmıştır. Analizler ve uzman görüşleri sonucunda ölçek 25 madde indirilerek asıl ölçek oluşturulmuştur. Sonuç olarak geliştirilen ölçeğin, öğrencilerin problem çözme süreci içerisinde yaşadıkları zorlukları, karar verme aşamalarındaki tercihlerini, stratejileri etkili kullanıp kullanmadıklarını, algoritmik yeterliliklerini ve farkındalık düzeylerini ölçmek için kapsamlı ve işlevsel bir ölçme aracı olarak katkı sağlayacağı söylenebilir.

Anahtar Kelimeler

• Algoritmik Düşünme
• Algoritma
• Problem Çözme
• Ölçek Geliştirme
• matematik eğitimi

Development of an Algorithmic Thinking Scale Based on the Futschek Model in Mathematics Education

Öz

The aim of the study is to develop a valid and reliable algorithmic thinking scale that can assess cognitive processes such as understanding the problem, creating a solution path, developing strategies, identifying errors, making a solution plan, and evaluating during the process of solving mathematical problems. Based on a review of the literature literature and Futschek's algorithmic thinking process model the researchers designed a draft scale consisting of 42 items on a five-point Likert. The developed draft scale was applied to a total of 533 students, including 312 female and 221 male ninth- grade students, in three different high schools in the Kapaklı district of Tekirdağ province during the 2024-2025 academic year. In the analysis of the data, SPSS 27 and AMOS 24 were used to determine item-total test correlations, Cronbach's Alpha reliability, Spearman-Brown Prophecy reliability, composite reliability, and test-retest reliability coefficients. In addition, hypothesis testings, exploratory factor analysis, and confirmatory factor analysis were performed. As a result of the analyses and expert evaluations, the scale was reduced to 25 items to form the final scale. In conclusion, it can be said that the developed scale is expected contribute as a comprehensive and functional measurement tool to measure the difficulties students experience in the problem-solving processes, their preferences in the decision-making stages, the effectiveness of their strategy use, and their levels of algorithmic competence and awareness.

Anahtar Kelimeler

• Algorithmic Thinking
• Problem Solving
• Algorithm
• Scale Development
• Mathematics Education

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