Relation between understandings of linear algebra concepts in the embodied world and in the symbolic world

For the use of embodied notions in teaching linear algebra, some studies indicate that it is helpful, but another study indicates that it is sometimes problematic. Hence more study is needed. In this study, linear (in)dependence and basis were focused on, and the relation between understandings of them in the embodied world and in the symbolic world was investigated. The effectiveness of an instruction emphasizing geometric images of them was also investigated. The main results of the study were the following: conceptual understanding of linear dependence of four spatial vectors such that any three of them do not lie on the same plane was positively associated with understanding of basis in the symbolic world; however, understanding of linear dependence of such vectors had not been improved by a geometrical instruction.