Publication: Matematik öğretmen adaylarının ispat yapma süreçlerinin incelenmesi
Abstract
MATEMATİK ÖĞRETMEN ADAYLARININ İSPAT YAPMA SÜREÇLERİNİN İNCELENMESİ Matematik eğitiminde ispatın, önemi ve rolü nedeniyle özellikle ileri matematik derslerinde çok üzerinde durulan ve vakit harcanan bir konu olduğu bilinmektedir. İspat üzerinde çok durulan, çok vakit harcanan bir konu olmasına rağmen öğretmen adayları ve üniversite öğrencileri lisans derslerinde karşılaştıkları teoremlerin ispatlarını yapmada ve anlamada zorluk çekmektedirler. Bu üzerinde düşünülmesi gereken bir durumdur. Özellikle ileride öğretmen olacak bireylerin ispatları anlaması ve kavraması önemlidir. Matematik öğretmen adaylarının ispata bakış açılarının ve ispat yapma süreçlerinin incelendiği bu araştırma Marmara Üniversitesi Atatürk Eğitim Fakültesi Matematik Öğretmenliği Bölümünde 2012-2013 yılında eğitim gören 73 öğrenci ile yürütülmüştür. Çalışmada öğretmen adaylarına, ispata ilişkin genel görüşlerini ölçmeye yönelik bir ölçek ve ispat süreçlerini incelemeye yönelik matematiksel ispat gerektiren sorular sorulmuştur. Adayların bu sorulara yazılı olarak cevap verdiği kâğıtlar üzerinden adaylarla yarı yapılandırılmış mülakat yapılmıştır. Elde edilen veriler nitel analiz yöntemlerinden betimsel istatistik yardımıyla analiz edilmiştir. Öğretmen adaylarının ispat süreçlerinin incelendiği bu çalışmada, öğretmen adaylarının ispat yöntemlerini ezbere kullanmaya çalıştıkları, ispat yaparken doğru yöntemi seçmekte zorlandıkları, sürece tam olarak hâkim olmadıkları ve yöntemler hakkında eksik ve yanlış bilgilere sahip oldukları tespit edilmiştir. Teorem İspatlama, Matematiksel İspat, İspat Yöntemleri, Matematik Eğitimi, İspat Yapma Güçlükleri, İspat Yapma Süreci.
ANALYSING THE PROCESS OF PROSPECTIVE MATH TEACHERS’ DOING MATHEMATICAL PROOF It is commonly known that doing Mathematical proof is an area focused and worked on a lot due to its significant role in Mathematics education. Although it is of much importance, prospective teachers and undergraduates have difficulty in doing and understanding of proofs of theorems they encounter in Math classes. This situation raises some question marks and necessitates deep thoughts about the underlying reasons since it is of great importance for prospective Math teachers to digest how to do Math proofs in Mathematics education. This study is aimed at analyzing especially prospective Math teachers’ viewpoints and the process they undergo while doing Math proof. Through the aim of this research, 73 students were chosen as samples from Marmara University, the faculty of education, the department of Mathematics education. To measure prospective Math teachers’ general thoughts and ideas and to analyze the process they went through while doing proof, mathematical proof questions were asked. Based on the answers students gave to these Mathematical proof questions, semi-structured interviews were conducted. The data obtained was analyzed through descriptive statistics which is one of the qualitative analysis methods. In this study focused on analyzing prospective Math teachers’ proof processes, it was found that students did not fully digest the proof methods and it was just rote learning; they had difficulty in choosing the correct proof method; they did not have a full grasp of the proof processes and they had missing and wrong information about proof methods. Key words: Theorem Proving, Mathematical Proof, Proof Methods, Mathematics Education, Difficulties in Doing Proof, The Process of Doing Proof
ANALYSING THE PROCESS OF PROSPECTIVE MATH TEACHERS’ DOING MATHEMATICAL PROOF It is commonly known that doing Mathematical proof is an area focused and worked on a lot due to its significant role in Mathematics education. Although it is of much importance, prospective teachers and undergraduates have difficulty in doing and understanding of proofs of theorems they encounter in Math classes. This situation raises some question marks and necessitates deep thoughts about the underlying reasons since it is of great importance for prospective Math teachers to digest how to do Math proofs in Mathematics education. This study is aimed at analyzing especially prospective Math teachers’ viewpoints and the process they undergo while doing Math proof. Through the aim of this research, 73 students were chosen as samples from Marmara University, the faculty of education, the department of Mathematics education. To measure prospective Math teachers’ general thoughts and ideas and to analyze the process they went through while doing proof, mathematical proof questions were asked. Based on the answers students gave to these Mathematical proof questions, semi-structured interviews were conducted. The data obtained was analyzed through descriptive statistics which is one of the qualitative analysis methods. In this study focused on analyzing prospective Math teachers’ proof processes, it was found that students did not fully digest the proof methods and it was just rote learning; they had difficulty in choosing the correct proof method; they did not have a full grasp of the proof processes and they had missing and wrong information about proof methods. Key words: Theorem Proving, Mathematical Proof, Proof Methods, Mathematics Education, Difficulties in Doing Proof, The Process of Doing Proof