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linear algebra matrix and determinant understanding

Exploring Zimbabwean A-Level Mathematics Learners’ Understanding of the Determinant Concept

Conilius Chagwiza , Lillias Hamufari Natsai Mutambara , Gladys Sunzuma

Learners bring prior knowledge to their learning environments. This prior knowledge is said to have an effect on how they encode and later retrieve ne.

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Learners bring prior knowledge to their learning environments. This prior knowledge is said to have an effect on how they encode and later retrieve new information learned. This research aimed at exploring ‘A’ level mathematics learners’ understanding of the determinant concept of 3×3 matrices. A problem-solving approach was used to determine learners' conceptions and errors made in calculating the determinant. To identify the conceptions; a paper and pencil test, learner interviews, and learner questionnaires were used. Ten learners participated in the research and purposive sampling was used to select learners who are doing the syllabus 6042/2 Zimbabwe School Examination Council (ZIMSEC). Data was analyzed qualitatively through an analysis of each learners' problem-solving performance where common themes were identified amongst the learners’ work. Results from the themes showed that Advanced level learners faced some challenges in calculating the determinant of 3×3 matrices. Learners were having challenges with the place signs used in 3×3 matrices, especially when using the method of cofactors. The findings reveal that learners had low levels of engagement with the concepts and the abstract nature of the concepts was the major source of these challenges. The study recommends that; teachers should engage learners for lifelong learning and apply some mathematical definitions in real-world problems. Teachers should address the issues raised in this research during the teaching and learning process. In addition, teachers should engage learners more through seminars where learners get to mingle with others from other schools.

Keywords: Linear algebra, matrix, and determinant, understanding.

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