In-service teachers mental construction of linear algebra concepts. An undergraduate case study

Abstract

This study investigated how undergraduate in-service mathematics teachers understand linear algebra concepts. The significance of the study is to reveal the difficulties and type of mental constructions they make when they are solving linear independence concepts by using inspection. The action, process, object, schema (APOS) theory was used to analyse the data collected. A descriptive qualitative case study design was used. The participants were 73 in-service teachers studying a Bachelor of Science Education Honours Degree in mathematics. Data was collected through a structured activity sheet and semi-structured interviews. The results showed that the teachers had an inadequate understanding of linear independence concepts. Many of the students developed the action conceptions of linear algebra as they were engrossed in step-by-step procedures trying to show that given vectors are linearly independent. The findings indicated that the schemata for determinants and the various theorems for determining linear independence promote learning. The modified genetic decomposition proposed has implications for teaching the concept and students should be given different kinds of sets to manipulate so that they can develop their mental constructions at the process level.