Many studies have identified the fact that most mathematics teachers experience challenges in using technology in their teaching, and learners also find it difficult to use it in their learning. Teachers often fail to address opportunities regarding this usage to address the situation. This paper explores factors contributing to teachers' and learners' challenges and opportunities for using Information and Communication Technology (ICT), such as computers, in the teaching and learning of mathematics in the OR Tambo Education District. A case-study design was used. The sample comprised 5 teachers and 5 learners selected from 5 performing schools in the District. Individual interviews and open-ended questionnaires were used for data collection. Content analysis was used to analyse the data. The study revealed that a lack of computer tuition opportunities, school managers' attitudes and limited material resources contributed to challenges and opportunities regarding the use of computers in mathematics instruction in schools. The study concluded that a lack of teachers' access to the use of computers in schools made it difficult for them to assist learners in the use of computers for teaching and for school tasks. Recommendations have been made to help enforce and monitor the use of available computers in schools.