Education academic Dr Zanele Ndlovu presented her research at the International Conference on Mathematical Education (ICME) in Germany, discussing the genetic decomposition of Cramer’s rule.
This stems from her study which explores pre-service teachers’ mental constructions when learning matrix algebra.
The study was guided by the belief that understanding the mental constructions the pre-service teachers made when learning mathematical concepts, led to improved instructional methods.
‘Background knowledge and understanding of notation are important aspects for students to understand in order to conceptualise the concepts in matrix algebra,’ said Ndlovu. ‘Students who had a weak schema of basic algebra were not able to make the necessary mental constructions or vice- versa. Also, students often made non-standard notation and linguistic distinctions.’
Since difficulties with the learning of linear algebra by average students are universally acknowledged, Ndlovu’s study provided a modified itemised genetic decomposition which is anticipated to help in the teaching and learning of matrix algebra concepts.
‘The aim of providing the modified genetic decomposition is to contribute in the teaching and learning of advanced mathematics as lecturers could use the modified genetic decomposition to analyse the mental constructions of their students when learning matrix algebra concepts.’
Ndlovu believes students need to have a conceptual understanding of the concepts taught in their first major module since these concepts form the basis for other modules they will learn as future mathematics teachers.
‘As future mathematics teachers it is imperative to develop conceptual understanding of mathematical concepts so that they will teach mathematics with confidence and to have the requisite knowledge to help learners at school.
‘If we hope our secondary school learners will develop the sense of mathematical reasoning, then at the outset the same idea needs to be instilled in the teachers.
‘The better place to start is with undergraduate students, especially in their first year. Pre-service teachers need to develop a sufficient sense of dealing with more abstract concepts in order to do justice in the teaching of these concepts at school level,’ said Ndlovu.