This article begins with a literature on characteristics of gifted students in general, explores the learning needs in mathematics of gifted students and mathematics curriculum features, and looks at the construction of gifted mathematical concept. Researches has indicated that gifted mathematical concept should consist of "cognitive", affection", and "skills" capacities based on the considerations of learning traits of gifted students and course interaction. Characteristics of gifted mathematics may include: emphasis of the systematic system, individual differences in cognition, enriched and accelerated differentiated mathematical curriculum, awareness of creativity in mathematics, insistence on challengeable non-routine high-order thinking skills in mathematics, corresponding relation to the theory of knowledge restructuring for the gifted, and inductive reasoning inter-concept proposition mathematics.
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