Sınıf Ortamında Rutin Olmayan Matematik Problemi Çözme: Didaktik Durumlar Teorisine Dayalı Bir Uygulama Örneği

Matematik öğretim programlarında ve matematik eğitimi literatüründe rutin olmayan problem çözme eylemine büyük önem verilmesine rağmen çalışmalar öğrencilerin rutin olmayan problemlerin çözümündeki başarılarının oldukça düşük olduğunu göstermektedir. Çıkış noktası kavramsal öğrenmenin şartlarını belirlemek olan Didaktik Durumlar Teorisi (DDT) rutin olmayan problem çözme etkinlikleri için önemli bir potansiyele sahiptir. Bu çalışmanın amacı teorinin söz konusu potansiyelini sınıf ortamı bağlamında incelemektir. Çalışmada öncelikle problem çözmeye ilişkin literatür, DDT’nin prensipleri ve kavramları verilerek, problem çözme yaklaşımı sınıf ortamı bağlamında tartışılmış, sonrasında bu prensip ve yaklaşımlar bir uygulama örneği ile desteklenmiştir. Nitel araştırma yöntemlerinin kullanıldığı bu uygulama bir devlet ortaokulunun 6. sınıfında okuyan 24 öğrenciyle gerçekleştirilmiştir. Yaklaşık 2 ders saatinde gerçekleştirilen uygulamanın verileri video kaydı ve öğrenci çalışma kağıtları aracılığıyla toplanmıştır. Veriler teorinin belirlediği aşamalara göre analiz edilmiştir. Tasarlanan ortamın öğrencilerin sezgisel stratejiler geliştirmesini desteklediği ve öğrencilerin tasarlanan ortamda karşılıklı etkileşim içinde ve muhakeme yoluyla yeni bilgilere ulaştıkları görülmüştür. Ayrıca DDT’nin sınıf ortamında öğrencilerin problem çözme yaklaşımlarıyla ilgili ortam tasarımı, öğretmen ve öğrencilerin rolleri açısından birçok avantaj sağladığı belirlenmiştir.

Anahtar Kelimeler:

Didaktik Durumlar Teorisi, sınıf ortamında problem çözme, rutin olmayan problem, 6. sınıf

Non-routine Mathematical Problem Solving in Classroom Environment: An Example Based Upon Theory of Didactical Situations

Despite the fact that great importance is attached to the practice of solving non-routine problems in mathematics curriculums and literature of mathematical education, studies show that the success of the students in non-routine problem solving is considerably low. Theory of Didactical Situations (TDS), starting point of which is to define the conditions of meaningful learnings, has a substantial potential for non-routine problem solving activities. The aim of this study is to analyze the aforementioned potential of the theory in a classroom environment. Within the scope of the study, first of all, literature in relation to problem solving and the approach of problem solving were discussed in terms of classroom environment by giving the principles and concepts of TDS, and in the sequel, these principles and approaches were supported through an application example. This application through which qualitative research method were used was conducted with 24 students who studying their 6th grade education in a public school. Data of application which was performed in approximately 2 courses were collected via video records and students’ work sheets. The data were analyzed in accordance with the steps specified by theory. It was seen that the designed environment has supported the students in terms of developing heuristic problem solving strategies and students have reached new knowledge in the designed environment by interacting with each other and through the way of reasoning. Additionally, environment design of TDS in relation to problem solving activities in classroom environment is reported to have provided a lot of advantages for the roles of teachers and students.

Keywords:

Theory of Didactical Situations, problem solving in classroom environment, non-routine problem, 6th grade,

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