Cebirsel kavram ve genellemelerinin, soyutlama sürecine uygun öğretiminin tasarımı, uygulanması ve değerlendirilmesi
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Date
2021-02-22
Authors
Yılmaz, Rümeysa
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Journal ISSN
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Publisher
Bursa Uludağ Üniversitesi
Abstract
Matematiksel kavram ve genellemelerin öğretiminde, soyutlama sürecinin analizinden yararlanılması, soyutlamaya olan ilginin artarak devam etmesine yol açmış bulunmaktadır. Öğrencilerin soyutlama süreçlerini inceleyen araştırmacılar; bireysel araştırmalara ağırlık vermişler, bu durum sınıf ortamında soyutlama süreçlerini incelemenin önemini arttırmıştır. Bu araştırmanın amacı ise 6. sınıftan başlayarak 6. ve 7. sınıf öğrencilerinin cebirsel kavram ve genellemeleri oluşturma ve soyutlama süreçlerinin incelenmesi, süreç içerisinde hazırlanan öğretim tasarımının soyutlama sürecine katkısının belirlenmesidir. Araştırma karma yöntem araştırması modelinde olup iki aşamadan oluşmuştur. İlk aşamada tasarım tabanlı araştırma modeli, ikinci aşamada ise durum çalışması modeli kullanılmış olup, yarı boylamsal bir çalışmadır. Çalışma 2017-2018 yılları arasında iki yıl boyunca Bursa Setbaşı Ortaokulunda biri deney grubu diğeri ise kontrol grubu olarak belirlenen 32’şer kişilik iki grupta toplam 64 öğrenciyle gerçekleştirilmiştir. Uygulama öncesi öğrencilerin cebir kavram ve genellemeleri bilgisini ölçmek için Chelsea Cebir Tanılama Testi (CCTT) uygulanmıştır. Altıncı ve yedinci sınıf müfredatındaki cebir kavram ve genellemeleri belirlenerek, bu kavram ve genellemelerin soyutlanma süreçlerini incelemeye imkân verecek öğretim tasarımı hazırlanmış ve pilot çalışması yapılarak eksikler tespit edilerek giderilmiş, hazırlanan öğretim tasarımı deney grubu öğrencilerine uygulanmıştır. Uygulama sonrası CCTT, SBT1 (Soyutlama Becerileri Testi), SBT2 ve SBT3 testleri yapılarak sonuçları analiz edilmiş ve öğrencilerin soyutlama süreçleri RBC+C modeliyle ayrıntılı olarak incelenmiştir. Yapılan ön ve son testler arasındaki gelişim nicel analizle belirlenmiştir. Öğrencilerin soyutlama süreçlerini derinlemesine analiz etmek için deney grubundan seçilen 2 düşük, 3 orta ve 4 yüksek başarı düzeyine sahip odak grup öğrencilerinin uygulamanın her aşamasında etkinlik kâğıtları, yapılan ön ve son testlerin nitel analizleri belirlenen tematik soyutlama göstergeleri çerçevesinde yapılmıştır. Göstergelerin RBC+C (Recognizing, Building with Construction, Consolidation) modelindeki gibi alındığında bazı durumları ayrıntılı analize imkân vermediğinden, detaylandırması yapılmıştır. Araştırmada kullanılan SBT2, SBT3 ve CCTT ön ve son testlerinin nicel analiz sonuçlarına bakıldığında, öğrencilerin 6. ve 7. sınıftaki uygulamalar sonrası, soyutlama becerilerindeki gelişimde anlamlı farklılıklar elde edildiği görülmüştür. Ayrıntılı analiz yapılmak için seçilen odak grubu öğrencilerinden elde edilen etkinlik kâğıtları ve testlerin nitel analizinde de soyutlama becerilerinin geliştiği gözlemlenmiştir. Öğrencilerden orta ve yüksek başarı düzeyine sahip öğrencilerin oluşturma ve pekiştirme basamaklarına ulaştığı gözlemlenmiştir. Başarı düzeyi düşük öğrencilerin ise yanlış oluşturmaya sahip olabildikleri ya da yardımcı tanımayla kısmi doğru oluşturmaya ulaştıkları gözlemlenmiştir. Araştırmanın ikinci aşamasında odak grup öğrencilerinden elde edilen nitel veriler analiz edildiğinde pekiştirme basamağına ulaşıp ulaşamayan öğrencilerin derinlemesine analizinde başarı düzeyi yüksek ve orta öğrencilerin pekiştirme basamağına ulaşabildikleri, düşük başarı düzeyine sahip öğrencilerin ise kısmi doğru oluşturma basamağında kaldıklarından dolayı pekiştiremedikleri sonucuna varılmıştır. Araştırma sonuncunda hazırlanan öğretim tasarımının öğrencilerin soyutlama becerilerini geliştirdiği sonucuna varılmıştır. RBC+C modelinin tanılama aracı olmasının yanında, bilgilendirici ve tasarımı aracı olarak da kullanılabileceği sonucuna ulaşılmıştır. Elde edilen bu sonuçlara göre soyutlama becerilerinin geliştirilme sürecinde öğretime ve gelecekte yapılacak çalışmalara yönelik önerilerde bulunulmuştur.
The use of abstraction analysis in the teaching of mathematical concepts and generalizations has led to an increasing interest in abstraction. Those who investigate students' abstraction processes; They trained personal research, which increased the importance of examining classroom analysis. The aim of this study is to examine the processes of creating algebraic concepts and generalizations and abstraction processes of 6th and 7th grade students starting from the 6th grade and determining the contribution of the design of encryption method to the abstraction process by experimenting. The research is in mixed method research model and consists of two stages. The designbased research model was used in the first stage, and the case study model was used in the second stage, and it is a semi-longitudinal study. The study was conducted for two years between 2017 and 2018 in Bursa Setbaşı Secondary School with a total of 64 students in two groups, one of which was determined as the experimental group and the other as the control group. Chelsea Algebra Diagnostic Test (CCTT) was applied before the application to measure the students' knowledge of algebra concepts and generalizations. By determining the concepts and generalizations of algebra in the curriculum in the sixth and seventh grades, an instructional design was prepared that would allow to examine the abstraction processes of these concepts and generalizations, and the deficiencies were identified and eliminated through a pilot study, and the instructional design was applied to the experimental group students. After the application, CCTT, SBT1 (Abstraction Skills Test), SBT and SBT3 tests were performed, the results were analyzed, and the abstraction processes of the students were examined in detail with the RBC + C model. The development between the pre and posttests was determined by quantitative analysis. In order to analyze the abstraction processes of the students in depth, the activity papers of the focus group students with 2 low, 3 medium and 4 high achievement levels selected from the experimental group, and the qualitative analysis of the pre and post tests were carried out within the framework of the determined thematic abstraction indicators. Some of the situations when the indicators are taken as in the RBC + C model do not allow for detailed analysis, so they are detailed. Considering the quantitative analysis results of the SBT2, SBT3 and CCTT pre and post tests used in the study, it was seen that significant differences were obtained in the development of abstraction skills of the students after the applications in 6th and 7th grade. It was observed that abstraction skills developed in the qualitative analysis of the activity papers and tests obtained from the focus group students selected for detailed analysis. It has been observed that students with medium and high achievement levels have reached the stages of formation and reinforcement. It has been observed that students with low level of success may have false positional forms or achieved partial correct constructions with helpful recognition. In the second stage of the study, when the qualitative data obtained from the focus group students were analyzed, it was concluded that the students with high success level and middle students could reach the reinforcement step, while the students with low achievement level could not reinforce it because they remained at the partial correct formation step. It was concluded that the instructional design prepared at the end of the study improved the abstraction skills of the students. It was concluded that the RBC + C model can be used as an informative and design tool as well as a diagnostic tool. According to these results, suggestions were made for teaching and future studies in the process of developing abstraction skills.
The use of abstraction analysis in the teaching of mathematical concepts and generalizations has led to an increasing interest in abstraction. Those who investigate students' abstraction processes; They trained personal research, which increased the importance of examining classroom analysis. The aim of this study is to examine the processes of creating algebraic concepts and generalizations and abstraction processes of 6th and 7th grade students starting from the 6th grade and determining the contribution of the design of encryption method to the abstraction process by experimenting. The research is in mixed method research model and consists of two stages. The designbased research model was used in the first stage, and the case study model was used in the second stage, and it is a semi-longitudinal study. The study was conducted for two years between 2017 and 2018 in Bursa Setbaşı Secondary School with a total of 64 students in two groups, one of which was determined as the experimental group and the other as the control group. Chelsea Algebra Diagnostic Test (CCTT) was applied before the application to measure the students' knowledge of algebra concepts and generalizations. By determining the concepts and generalizations of algebra in the curriculum in the sixth and seventh grades, an instructional design was prepared that would allow to examine the abstraction processes of these concepts and generalizations, and the deficiencies were identified and eliminated through a pilot study, and the instructional design was applied to the experimental group students. After the application, CCTT, SBT1 (Abstraction Skills Test), SBT and SBT3 tests were performed, the results were analyzed, and the abstraction processes of the students were examined in detail with the RBC + C model. The development between the pre and posttests was determined by quantitative analysis. In order to analyze the abstraction processes of the students in depth, the activity papers of the focus group students with 2 low, 3 medium and 4 high achievement levels selected from the experimental group, and the qualitative analysis of the pre and post tests were carried out within the framework of the determined thematic abstraction indicators. Some of the situations when the indicators are taken as in the RBC + C model do not allow for detailed analysis, so they are detailed. Considering the quantitative analysis results of the SBT2, SBT3 and CCTT pre and post tests used in the study, it was seen that significant differences were obtained in the development of abstraction skills of the students after the applications in 6th and 7th grade. It was observed that abstraction skills developed in the qualitative analysis of the activity papers and tests obtained from the focus group students selected for detailed analysis. It has been observed that students with medium and high achievement levels have reached the stages of formation and reinforcement. It has been observed that students with low level of success may have false positional forms or achieved partial correct constructions with helpful recognition. In the second stage of the study, when the qualitative data obtained from the focus group students were analyzed, it was concluded that the students with high success level and middle students could reach the reinforcement step, while the students with low achievement level could not reinforce it because they remained at the partial correct formation step. It was concluded that the instructional design prepared at the end of the study improved the abstraction skills of the students. It was concluded that the RBC + C model can be used as an informative and design tool as well as a diagnostic tool. According to these results, suggestions were made for teaching and future studies in the process of developing abstraction skills.
Description
Keywords
Bağlamdan soyutlama (AiC), RBC+C modeli, Soyutlama süreçleri, Kısmi doğru yapılar (PaCC), Abstraction in context (AiC), RBC+C model, Abstraction process, Partially correct constructs (PaCC)
Citation
Yılmaz, R. (2021). Cebirsel kavram ve genellemelerinin, soyutlama sürecine uygun öğretiminin tasarımı, uygulanması ve değerlendirilmesi. Yayınlanmamış doktora tezi. Bursa Uludağ Üniversitesi Eğitim Bilimleri Enstitüsü.