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.