Perceptions of pre-service and in-service mathematics teachers on the mathematical link between matrices and vectors

Abstract

Mathematical concepts emerge from a hierarchical network of interrelated structures. Matrices and vectors are two separate topics in the Indonesian high school mathematics curriculum (ages 16-18). Meanwhile, matrices and vectors are conceptual entities linked in linear algebra. This qualitative interpretive research aims to gain an understanding of the perception of pre-service and in-service mathematics teachers on the mathematical link between matrices and vectors. We did two rounds of data collection. The first round of data collection used the written open question technique and included 60 pre-service mathematics teachers (PMT) and 24 in.service mathematics teachers (IMT). The second round used in-depth interviews on samples of PMT and IMT. Our findings show that both PMT and IMT have a perception of the mathematical link between matrices and vectors in three categories: on representation, on operation, and no link at all. Furthermore, our investigation shows that the PMT have perceptions that are established by the previous learning experiences in high school. Meanwhile, curriculum tasks considerably influence IMT's perception of the mathematical link between matrices and vectors. More study is needed to build a model of teachers’ professional development that is thoroughly aligned with school mathematics and university mathematics from both a didactic and pedagogy standpoint.