Learner performance in South Africa is poor in comparison with other countries as a result of poor teaching. At the core of the concern about learners' performance in mathematics in South Africa lies a controversy regarding how mathematics should be taught. The purpose of this study was to explore Grade 8 mathematics teachers' creation and utilisation of opportunities for learners to develop mathematical understanding in their classrooms. To accomplish this, an explorative case study was conducted to explore three mathematics teachers' instructional practices by using Schoenfeld et al.'s (2014) five dimensions of Teaching for the Robust Understanding of Mathematics (TRU Math) scheme, namely, the mathematics, cognitive demand, access to mathematical content, mathematical agency, authority and identity and uses of assessment. The three participants were conveniently selected from three private schools in Mpumalanga. The data collected consist of a document analysis, two lessons observations and a post-observation interview per teacher. This study revealed that only one of the three teachers applied all Schoenfeld et al.'s (2014) TRU Math dimensions. The dimension identified which the teachers applied most in their classrooms was the mathematics. The dimensions identified where teachers still lack skills were cognitive demand, access to mathematical content, agency, authority and identity, and uses of assessment. This study revealed that the content of most tasks and lessons was focused and coherent, and built meaningful connections. However, the content did not engage learners in important mathematical content or provided opportunities for learners to apply the content to solve real-life problems. Due to the small sample used, the results from this study cannot be generalised. However, I hope that the findings will contribute to student-teacher training and in-service teacher training in both government and private schools. Future research could possibly build on this study by examining the learners and how they learn with understanding by using the TRU Math dimensions. / Dissertation (MEd)--University of Pretoria, 2016. / Science, Mathematics and Technology Education / MEd / Unrestricted