A Qualitative Method Research on the Representations of Preservice Teachers in Linear Algebra

This study was conducted to determine the algebraic and geometric representations of some linear algebra concepts exhibited by pre-service teachers and to reveal the misconceptions about these representations. The study participants consisted of 6 pre-service teachers selected among the 3rd-grade students enrolled in the department of elementary mathematics teaching at a university in the Central Anatolia region in the 2021-2022 academic year. The data were collected through the "Form" developed by the researchers. As a result of the study, it was determined that the associations of pre-service teachers were mostly correct or partially correct in the context of algebraic representation and mostly partially correct or incorrect in the context of geometric representation. It was concluded that pre-service teachers with high and medium-level linear algebra performance were more successful in showing the algebraic representation of the concepts than the geometric representation. A source of pre-service teachers' difficulties in learning linear algebra is their misconceptions about points, vectors, lines, linear sum, and vector sum etc. This study is thought to contribute to mathematics education as it points out the necessity of eliminating errors and misconceptions about some concepts related to linear algebra and geometry.