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The aim of this research was to investigate the level of conceptual and procedural understanding of linear algebra concepts among first and second year university students. An initial pilot study provided enough evidence, to convince the researcher to design a theoretical framework to pursue an alternative approach for the teaching and learning of a group of linear algebra concepts. Based on the methodology a number of case studies were carried out and the outcome from the tests, interviews and concept maps were analysed. It is important to note that, it is not the intention of this study to generalise these findings for all the mathematics students of this, or any other university. However, the results indicate strong reasons for proposing further investigation in teaching and learning of linear algebra concepts.