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.
Highlights
Linear algebra is an important study area in mathematics that examines vectors, vector spaces, linear transformations, linear equation systems and matrices
The findings obtained as a result of the application of the learning environment designed for the teaching of vector spaces in two cycles are discussed under the titles of study story and revisions
The findings for the first two cycles, along with the results obtained in the analysis of field notes and video recordings, and the regulations and changes decided to be made in the first and second cycles are presented
Summary
Linear algebra is an important study area in mathematics that examines vectors, vector spaces, linear transformations, linear equation systems and matrices. The fact that it is a course that offers students the opportunity to make mathematical abstraction is shown among the reasons that make linear algebra important (Harel, 1989a; Kolman & Hill, 2008). Linear algebra can be divided into two main sections, Matrix Algebra and Vector Spaces Theory. Matrix Algebra includes matrices, operations in matrices and their properties, determinants and systems of linear equations and solution methods. Due to its much more abstract structure, vector spaces theory is the part that students have the most difficulties in linear algebra
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