This Topical Survey deals a quick evaluate of the present kingdom of analysis on and actions for mathematically proficient scholars world wide. this can be of curiosity to a huge readership, together with academic researchers, learn mathematicians, arithmetic lecturers, instructor educators, curriculum designers, doctoral scholars, and different stakeholders. It first discusses study in regards to the nature of mathematical giftedness, together with theoretical frameworks and methodologies which are priceless in making a choice on and/or growing mathematically talented scholars, that's defined during this part. It additionally makes a speciality of study on and the advance of mathematical expertise and innovation in scholars, together with connections among cognitive, social and affective points of mathematically talented scholars. Exemplary educating and studying practices, curricula and a number of courses that give a contribution to the advance of mathematical expertise, presents, and fervour are defined in addition to the pedagogy and arithmetic content material compatible for teaching pre-service and in-service academics of mathematically talented scholars. the ultimate part presents a quick precis of the paper besides feedback for the study, actions, and assets that are meant to be to be had to help mathematically proficient scholars and their lecturers, mom and dad, and different stakeholders.

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