Abstract

Amaç: Bu çalışma bir devlet lisesinde öğrenim gören üç 11. sınıf öğrencisinin tek değişkenli doğrusal denklemlere dair kullandıkları söylemsel rutinleri inceleyen bir durum çalışmasıdır. Bu çalışmanın amacı, Commognitive bakış açısıyla söylemsel rutinlerin yapısını ortaya koyarak öğrencilerin doğrusal denklemlere ilişkin cebirsel anlayışlarını araştırmaktır. Yöntem: Bu bağlamda araştırmanın verileri 40 ila 60 dakika süren yarı-yapılandırılmış bireysel görüşmeler aracılığıyla toplanmış ve öğrencilerin matematiksel iletişimlerini detaylı bir şekilde yakalamak amacıyla iki kamerayla kayıt altına alınmıştır.  Bu araştırmada öğrencilerin doğrusal denklemlere ilişkin matematiksel söylemlerinde ortaya koydukları rutinler; ritüel ve keşif türleri bağlamında sınıflandırılmış ve bu rutinleri nasıl kullandıkları incelenerek veriler analiz edilmiştir. Bulgular: Araştırmanın bulguları, öğrencilerin tek değişkenli doğrusal denklemlere ilişkin rutinlerinin çoğunlukla ritüel olduğunu ortaya koymuş ve öğrencilerin matematiksel anlatılar üretmekten ziyade katı prosedürleri uygulamaya odaklandıklarını göstermiştir.  Nitekim, öğrenciler çoğunlukla uyguladıkları prosedürler üzerine söylemlerde bulunmuş; bu söylemler de onların denklemleri birer matematiksel nesne olarak değil, manipüle edilebilir sembol dizileri olarak ele aldıklarını göstermiştir. Bununla birlikte, katılımcıların bir denklemin çözüm kümesi ve bu kümenin elemanları hakkında konuştukları bazı söylemlerde, sınırlı da olsa keşif rutinlerine başvurdukları gözlemlenmiştir.  Bu rutinler bulgularda, öğrencilerin denklemleri birer matematiksel nesne olarak ele aldıkları ve denklemler hakkında matematiksel anlatılar ürettikleri söylemsel rutinler olarak öne çıkmıştır. Sonuç: Araştırmanın bulgularından yola çıkarak değişken ve eşitlik kavramları ile görev durumunun içeriğinin cebirsel anlayışın oluşmasında önemli bir rol oynadığını sonucuna ulaşılmıştır. Bu nedenle, doğrusal denklemler bağlamında, öğrencilerin değişken, eşitlik, denklem ve bir denklemin çözümü gibi kavramları matematiksel nesneler olarak nasıl işlev gördüklerine dair geliştirecekleri anlayışın, onları keşif rutinlerini kullanmaya teşvik edeceği düşünülmektedir.

Keywords

• Söylemsel rutinler
• Ritüel rutinler
• Keşif rutinleri
• Doğrusal denklemler
• Lise öğrencileri

High School Students’ Discursive Routines in the Context of Linear Equations

Abstract

Purpose: This case study explores the discursive routines of three 11th-grade students from a public high school as they engaged with single-variable linear equations. Specifically, it aims to reveal the nature and structure of their participation in mathematical discourse and to examine how their algebraic understanding of linear equations is constructed from a commognitive perspective.  Method: A qualitative case study design was employed. Data were collected via semi-structured individual interviews, lasting between 40 and 60 minutes, and recorded using two cameras to capture the students’ mathematical communication in detail. The analysis focused on how students participated in mathematical discourse, particularly using ritual and exploration routines.  Findings: The findings reveal that students mainly relied on ritual routines, concentrating on performing rigid procedures rather than producing mathematical narratives. Their discourse centered on calculations, treating equations as sequences of symbols to manipulate rather than as mathematical objects. Exploration routines—which involve making sense of mathematical discourses—were infrequent but emerged primarily during discussions about the solution set and its elements.  Conclusion: The findings emphasize the significance of the variable, equal sign, and task situation in constructing algebraic understanding.    Therefore, in the context of linear equations, these findings suggest that students’ developing understanding of how concepts such as variables, equality, equations, and solution sets function as mathematical objects may encourage them to engage in exploration routines.

Keywords

• Discursive routines
• Ritual routines
• Exploration routines
• Linear equations
• High school students

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