The Further Education of Gifted Mathematicians: A Vygotskian Perspective on Perceptions and Pedagogy.

Gifted mathematicians often experience challenges developing as mathematicians for the first time during their further education, an educational phase in which national policy prioritises the study of mathematics for lower-attaining students. Institutions do not therefore routinely provide the specialised support gifted mathematicians require to overcome the challenges associated with this phase. To investigate the nature of their challenges and develop a pedagogical model to support their advanced mathematical-development, this study invited three Year 12 gifted mathematicians from an English 16-19 free school to participate in advanced problem-solving interventions. They kept digital-diaries for four weeks, and participated in interviews to reflect on their experiences. Interpretative phenomenological analysis was refined to facilitate a chronological analysis of their data, which established a detailed picture of their respective successes and challenges. Their views were then critically evaluated collectively, to create a joint understanding of their support needs. The Vygotskian theoretical perspective was honed for application as a theoretical framework to explore the nuances of their perceptions. This facilitated an improved understanding of: adjustment to the abstract nature of problem-solving required throughout advanced mathematical-development; the process through which gifted mathematicians can utilise their feelings of frustration to fuel their motivation to nonetheless continue developing; the strategies through which practitioners can effectively scaffold this development; and, subsequently, how gifted mathematicians might situate themselves within the social context of advanced mathematical-development to facilitate their own success. An effective balance between a gifted mathematician’s need to make tangible progress and their competing need to perceive the role of their own independence as a significant factor when making that progress was found to be a core consideration which evolved as they developed. The study establishes a first pedagogical model of advanced mathematical-development for supporting a gifted mathematician to make progress with a growing sense of independent capability.