Relation between understandings of linear algebra concepts in the embodied world and in the symbolic world - Archive ouverte HAL
Pré-Publication, Document De Travail Année : 2022

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

Résumé

For the use of embodied notions in teaching linear algebra, some studies indicate that it is helpful, whereas other studies indicate that it could be problematic or becomes an obstacle. Hence, additional research is needed. This study is focused on linear (in)dependence and basis, and investigates the relation between their understandings in the embodied and symbolic worlds. Moreover, we investigated the effectiveness of a teaching method that emphasized geometric images. The main results of the study were as follows: the 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 the understanding of basis in the symbolic world; however, the understanding of linear dependence of such vectors was not been improved by a geometrical instruction. Although a furthur study is needed to examine whether the geometric instruction in this study can be improved, the result imply that a space spanned by three linearly independent spatial vectors, which is an object in the embodied world, becomes a learning object for students.
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Dates et versions

hal-03330580 , version 1 (01-09-2021)
hal-03330580 , version 2 (17-02-2022)
hal-03330580 , version 3 (23-02-2022)
hal-03330580 , version 4 (12-07-2022)
hal-03330580 , version 5 (17-02-2023)

Identifiants

  • HAL Id : hal-03330580 , version 2

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Mitsuru Kawazoe. Relation between understandings of linear algebra concepts in the embodied world and in the symbolic world. 2022. ⟨hal-03330580v2⟩
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