Creating Design Principles of a Learning Environment for Teaching Vector Spaces

Year 2021, Volume: 12 Issue: 1, 244 - 289, 05.02.2021

Gökay Açıkyıldız , Temel Kösa

https://doi.org/10.16949/turkbilmat.860627

Abstract

In this study, determining the design principles of a technology-supported learning environment for teaching vector spaces by taking into account the representation languages defined by Hillel (2000), Harel's (2000) pedagogical principles and Sierpinska's (2000) thinking modes on Linear Algebra teaching were intended to be established. The research is a design-based research and three cycles were conducted to determine the design principles for the learning environment. The study group of the first cycle consists of 51, the second cycle's working group was 44, and the third cycle's study group consisted of 11 teacher candidates. The data of the research were obtained by field notes and video recordings. By analyzing the field notes and video recordings, design principles for the learning environment were determined after the first two cycles in light of the literature. The third cycle was carried out with the determined design principles, and the design principles were revised in line with the opinions of the teacher candidates and the course teacher after the application with the reports obtained during the application process. Design principles in the light of the results obtained from the research are as follows ; the use of technology, usage of modes of description, tasks, worksheets, the role of the teacher and group work. It is thought that a learning environment that will be created by paying attention to these design principles will contribute to the pre-service teachers' differentiation and use of different languages, the development of thinking styles, and to meet the principles of concreteness, necessity and generalizability.

Keywords

Linear algebra, vector spaces, learning environment, design principles, technology, desing-based research

Vektör Uzaylarının Öğretimine Yönelik Bir Öğrenme Ortamının Tasarım İlkelerini Oluşturma

Abstract

Bu çalışmada Lineer Cebir öğretimi üzerine Hillel’in (2000) tanımladığı temsil dilleri, Harel’in (2000) pedagojik prensipleri ve Sierpinska’nın (2000) düşünme biçimleri göz önünde bulundurularak vektör uzaylarının öğretimine yönelik teknoloji destekli bir öğrenme ortamının tasarım ilkelerinin belirlenmesi amaçlanmıştır. Araştırma, tasarım tabanlı bir araştırma olup öğrenme ortamına yönelik tasarım ilkelerinin belirlenmesi için üç döngü gerçekleştirilmiştir. Birinci döngünün çalışma grubunu 51, ikinci döngünün çalışma grubunu 44 ve üçüncü döngünün çalışma grubunu 11 öğretmen adayı oluşturmaktadır. Araştırmanın verileri alan notları ve video kayıtları ile elde edilmiştir. Alan notları ve video kayıtları analiz edilerek literatür ışığında ilk iki döngü sonrasında öğrenme ortamına yönelik tasarım ilkeleri belirlenmiştir. Belirlenen tasarım ilkeleriyle üçüncü döngü gerçekleştirilmiş, uygulama sürecinde elde edilen raporlar ile uygulama sonrasında öğretmen adayları ve ders öğretmenin görüşleri doğrultusunda tasarım ilkeleri revize edilerek son halini almıştır. Araştırmadan elde edilen sonuçlar ışığında tasarım ilkeleri; teknoloji kullanımı, temsil dillerinin kullanımı, ödevler, çalışma yaprakları, öğretmenin rolü ve grup çalışması şeklinde ortaya çıkmıştır. Belirlenen bu tasarım ilkelerine dikkat edilerek oluşturulacak bir öğrenme ortamının öğretmen adaylarının farklı dilleri ayırt etmesine ve kullanmasına, düşünme biçimlerinin gelişimine katkı sağlayacağı ve somutluk, gereklilik ve genellenebilirlik prensiplerinin karşılanmasında yardımcı olacağı düşünülmektedir.

Keywords

Lineer cebir, vektör uzayları, öğrenme ortamı, tasarım ilkeleri, teknoloji, tasarım tabanlı araştırma

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