Philosophiae Doctor - PhD / In this study a mixed methods approach was employed to investigate how exposure to a teaching strategy based on spiral revision, productive practice and a mainly direct expository instructional method would influence the mathematical competencies of procedural fluency and conceptual understanding of pre-service mathematics teachers at a South African university. A secondary concern of the study was how retention and transfer abilities of participants would be influenced if they experience mathematics through a teaching strategy underpinned by spiral revision and productive practice. A revised version of the taxonomy table of Anderson et al (2001) was utilized to classify learning and instructional activities in the study in terms of mathematical reasoning and knowledge requirements. In this revised taxonomy the cognitive processes are understood to operate on knowledge structures during the process of cognition (i.e. reasoning categories based on knowledge categories.). The categories of the revised taxonomy table were the main measuring instrument for the study. The findings of the study indicate that the competencies of procedural fluency and conceptual understanding were positively enhanced by the teaching strategy. Some categories however did not show the same level of positive enhancement. Arguments are presented as to why this might be the case and possible solutions are mooted. Findings also indicate that retention and near transfer abilities of participants were positively enhanced. Far transfer abilities were unchanged post intervention. Explanations are offered for this finding and possible resolutions are suggested.