|Conceptual Understanding of Dot Product of Vectors in a Dynamic Geometry Environment
Current trends in research on the impact of technologies in mathematics education emphasize their increased role in supporting students’ conceptual understanding in comparison with numerous previous studies about technology contribution in procedural understanding. This article exemplifies the role of Dynamic Geometry Systems utilizing students’ understanding of concepts in Linear algebra in the transition between upper high school and university education. Students’ conceptual understanding is identified through guiding features as: concept definitions and concept images, according to the theory of Tall and Vinner (1981); three modes of description and thinking: arithmetic, geometric and axiomatic-structural, according to the theories of Hillel (2000) and Sierpinska (2000); concepts’ properties which construct axiomatic definitions; and concepts’ applications and their connections with other concepts. Authentic video recordings serve as a collected data set for qualitative analysis of students’ interactions in the designed Dynamic Geometry Environment. The study is part of a larger design-based research undergoing seven phases in a cyclic manner, ending with evaluation and dissemination of created teaching and learning materials as visual dynamic applets and worksheets.