Publication: Bilgisayar cebiri sistemi destekli öğretimin farklı düşünme yapısındaki öğrencilerin integral konusundaki temsil dönüşüm süreçlerine etkisi
Abstract
BİLGİSAYAR CEBİRİ SİSTEMİ DESTEKLİ ÖĞRETİMİN FARKLI DÜŞÜNME YAPISINDAKİ ÖĞRENCİLERİN İNTEGRAL KONUSUNDAKİ TEMSİL DÖNÜŞÜM SÜREÇLERİNE ETKİSİ Bu çalışma ile Bilgisayar Cebiri Sistemi (BCS) destekli öğretimin, integral konusundaki yeterliklere ve özel olarak da temsil dönüşüm süreçlerine etkisi, düşünme yapısı farklılıkları bağlamında değerlendirilmiştir. Araştırma nitel yorumlayıcı paradigmaya sahip çoklu durum çalışmasıdır. Araştırmanın çalışma grubunu, bir devlet üniversitesinin ilköğretim matematik öğretmenliği ikinci sınıf programındaki Analiz I dersine kayıtlı 84 öğrenci oluşturmaktadır. Çalışma grubundaki öğrenciler arasından yansız atama ile oluşturulan uygulama gruplarının birinde geleneksel öğretim (n=42), diğerinde BCS destekli öğretim (n=42) deseni takip edilerek, altı haftalık uygulama süreci tamamlanmıştır. Öğretim süreci sonundaki çıktıları değerlendirmek üzere ön ve son ölçme araçları kullanılmıştır. Araştırmada elde edilen veriler sınıflandırma yöntemi ve betimsel istatistik teknikleri kullanılarak içerikleri üzerinden analiz edilmiş ve yorumlanmıştır. Çalışma sonuçları, BCS grubunun limit-integral ilişkisi, integralin geometrik yorumu ve integral uygulamaları öğrenme alanlarında; geleneksel grubun türev-integral ilişkisi ve integrasyon hesabı öğrenme alanlarında yüksek yeterliğe sahip olduğunu göstermiştir. BCS destekli öğretim süreci sonrasında, öğrencilerin grafik temsiline yönelik dönüşüm başarıları daha fazla artarken, hem BCS grubundaki hem geleneksel gruptaki öğrencilerin nümerik temsiline yönelik dönüşüm başarılarının düşük olduğu belirlenmiştir. Geleneksel grupta, cebirsel yaklaşımlar düşünme yapısından bağımsız olarak baskın şekilde tercih edilirken; BCS grubundaki analitik öğrenciler cebirsel, harmonik öğrenciler cebirsel ile birlikte grafiksel, görsel öğrenciler ise grafiksel çözüm yaklaşımlarını daha sık tercih etmiştir. Çalışma kapsamında elde edilen diğer bulgular, ilgili alan yazını ışığında tartışılarak, öğrenme ortamlarının düzenlenmesine yönelik çeşitli önerilerde bulunulmuştur. Anahtar Sözcükler: Bilgisayar Cebiri Sistemleri, Çoklu Temsiller, Matematiksel Düşünme Yapısı, İntegral Konusundaki Yeterlikler
THE EFFECT OF A COMPUTER ALGEBRA SYSTEM SUPPORTED TEACHING ON PROCESSES OF REPRESENTATIONAL TRANSITION IN INTEGRAL TOPICS OF STUDENTS WITH DIFFERENT TYPES OF THINKING This study is evaluated the effect of Computer Algebra System (CAS) supported teaching on the efficiencies about integral and especially, on the processes of representational transition in terms of mathematical thinking types. The research is a multiple case study having qualitative paradigm. The participants were 84 students who were registered for the course Analysis I at the second year of the undergraduate program of primary mathematics teaching in a state university. After research group has randomly assigned into two groups, the six-week teaching process was completed by following traditional approach (n = 42) or CAS supported design (n = 42) in one of the groups which was chosen randomly. Pre and post assessment tools were used to determine the teaching output of implementations. The data gained in the study were analyzed and interpreted through classification method and descriptive statistical techniques in terms of content. The results showed that CAS group has high efficiency on the learning of limit-integral relations, geometric interpretation of integral and integral applications; whereas traditional group has higher efficiency on the learning of derivative-integral relations and integration techniques. While students’ success of transition for the graphical representation increased more after the process of CAS supported teaching, it was observed that students’ success of transition for the numerical representation in both groups were low. In traditional group while algebraic approaches, independent from thinking structure, were dominantly preferred; analytical students preferred algebraic, harmonic students preferred graphical with algebraic and visual students preferred graphical solution approaches more frequently in CAS group. Other findings in the context of the study were discussed based on the literature and some suggestions for designing learning environments were presented. Key Words: Computer Algebra System, Multiple Representation, Types of Mathematical Thinking, Efficiencies in Integral
THE EFFECT OF A COMPUTER ALGEBRA SYSTEM SUPPORTED TEACHING ON PROCESSES OF REPRESENTATIONAL TRANSITION IN INTEGRAL TOPICS OF STUDENTS WITH DIFFERENT TYPES OF THINKING This study is evaluated the effect of Computer Algebra System (CAS) supported teaching on the efficiencies about integral and especially, on the processes of representational transition in terms of mathematical thinking types. The research is a multiple case study having qualitative paradigm. The participants were 84 students who were registered for the course Analysis I at the second year of the undergraduate program of primary mathematics teaching in a state university. After research group has randomly assigned into two groups, the six-week teaching process was completed by following traditional approach (n = 42) or CAS supported design (n = 42) in one of the groups which was chosen randomly. Pre and post assessment tools were used to determine the teaching output of implementations. The data gained in the study were analyzed and interpreted through classification method and descriptive statistical techniques in terms of content. The results showed that CAS group has high efficiency on the learning of limit-integral relations, geometric interpretation of integral and integral applications; whereas traditional group has higher efficiency on the learning of derivative-integral relations and integration techniques. While students’ success of transition for the graphical representation increased more after the process of CAS supported teaching, it was observed that students’ success of transition for the numerical representation in both groups were low. In traditional group while algebraic approaches, independent from thinking structure, were dominantly preferred; analytical students preferred algebraic, harmonic students preferred graphical with algebraic and visual students preferred graphical solution approaches more frequently in CAS group. Other findings in the context of the study were discussed based on the literature and some suggestions for designing learning environments were presented. Key Words: Computer Algebra System, Multiple Representation, Types of Mathematical Thinking, Efficiencies in Integral