There is widespread agreement in education about the existence of a cohort of students with ability or potential above that of their peers. In this thesis, they will be referred to as “highly-able” students, and the focus will be on those students whose high ability is in mathematics. Contrary to popular belief, highly-able students have additional educational needs to be catered for. In Ireland, classroom differentiation remains the sole in-school measure available, despite post-primary mathematics education undergoing large-scale changes over the past decade. In the mid-2000s, research highlighted the performance of Ireland’s top students in international mathematics assessments as an area of concern, yet these have failed to improve and, in some cases, have actually disimproved. When the additional needs of highly-able students are not met, they are at risk of negative traits of perfectionism, under-achievement, behavioural problems in class, and so on. This research focussed on addressing the additional educational needs of highly-able students in Ireland by targeting an improvement in their mathematical Problem-solving Potential (PsP), a newly-designed triad construct with three influencing factors: problem-solving skills, mindset, and mathematical resilience. To facilitate the development of potential, external resources and supports are needed to act upon and encourage the abilities and traits of an individual. In order to achieve that, a mathematics intervention was designed. The intervention utilised collaborative problem-solving as the pedagogical approach, following the Collaborative Problem-solving (CoPs) model specifically designed for this research, to outline the problem-solving process in a group dynamic. Although it is sometimes presumed that highly-able students prefer to work alone, research has found that they are willing collaborators with like-minded peers. The intervention was implemented across six cohorts of students, accessed through the Centre for Talented Youth Ireland, over a three-year period, and resulted in an increased PsP for 97% of participants.