A case study of in-service teachers' errors and misconceptions in linear combinations

Many mathematics education researchers agree that students struggle to understand the key concepts in linear algebra courses. The purpose of this study was to examine in-service teachers' errors and misconceptions in the area of linear combinations. The participants were 73 Zimbabwean mathematics teachers who were enrolled in an in-service programme that was delivered under tight time frames. Data were generated from the teachers' written responses to two tasks based on linear combinations and semi-structured interviews. The study distinguished between errors that were conceptual (deeply seated misunderstandings), procedural (related to using related procedures) or foundational in nature (calculation errors or those arising from interpretation of previously learnt concepts). The results showed that errors were mainly of the foundational type, relating to misinterpretations of solutions to systems of equations as well as computational errors related to row reduction processes. It is recommended that the stakeholders of the programme should consider extending the time frames for the teaching to allow more time for the participants to engage more deeply with the materials.