This thesis examines the perceptions of able mathematicians to their experience of mathematics teaching and learning in post-primary schools in Ireland. Able mathematicians are defined in this study as students who have done well in assessments but also students who have displayed an interest in the subject. International research has shown that the classroom experience is fundamental in the development of students’ mathematical understanding, motivation, and identity. Despite popular myths, able mathematicians have specific needs that require differentiated instruction in the classroom. It has been suggested that giving students opportunities to experience creativity is a means of providing the challenges they need. This research aimed to investigate how able mathematicians in Ireland feel about their mathematics classroom experience, whether they feel challenged in class, and how they would respond to being given opportunities to explore creative tasks. The research design was based on the framework of Sriraman (2005), which advocated five principles to maximise creativity for students in the classroom. The first of these was engagement in the four-stage creativity process of the Gestalt psychology principle of initiation-incubation-illumination-verification. The remaining four principles recommend that students are given opportunities to experience uncertainty, the aesthetical beauty of mathematics, the freedom to think and take risks, and the scholarly aspect of mathematics. Data was gathered from 92 Transition Year students in five second level schools in Ireland. The students participated in a series of two specially designed workshops in which they were presented with unseen tasks with multiple solutions. The study design included surveys to gather data on the participants’ perceptions of their mathematics classroom experience, and to their workshop experiences. Sriraman’s Principles were used for the design of a template to analyse interviews with the students and audio recordings of the workshops. The analysis revealed that there is strong evidence to suggest that the opportunities to be creative are not being maximised in classrooms. There appears to be considerable rote learning and memorisation of algorithms, with little opportunity to have the freedom to think and explore mathematical tasks. In contrast, the workshops were shown to have given the particpants opportunities to experience Sriraman’s five principles for creativity.