Misconceptions and resulting errors displayed by in service teachers in the learning of linear independence - Mutambara, Lillias Hamufari Natsai; Bansilal, Sarah (Modestum, 2022)
The aim of this paper is to identify errors and misconceptions that student demonstrated when learning linear independence and linear dependence concepts. A case study is presented involving 73 in-service mathematics teachers at a university in Zimbabwe who were studying for a Bachelor of Science Education Honors Degree in mathematics. Data was generated from a content analysis of the written responses of the participants to two items from a structured activity sheet. Follow up interviews with five participants were used to gain a better understanding of their misconceptions. The study found that the participants had different kinds of misconceptions leading to errors which could be described as procedural, conceptual, and foundational respectively and the distribution of the errors differed across the two problems. For question 1 which was set within the vector space M2×2, students found it harder to move past the first few two steps of formulating the general vector equation and doing scalar multiplication; those who passed those two steps were mostly able to get to a correct solution. For question 2 which was set within ℝ3 most students went past the first two steps formulating the general vector equation and converting that to an augmented matrix but then made many foundational errors, most of which were related to misinterpretations of the solutions to the system of equations
Keywords: linear independence; error; misconceptions