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

Year 2017, Volume: 14 Issue: 1, 140 - 181, 15.01.2017

Mustafa Gök Abdulkadir Erdoğan

Abstract

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.

Keywords

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

Abstract

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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