21世纪是一个知识、经济、科技高速发展的时代，这个时代最需要的资源就是人才，人才决定着国家的竞争力。人才需要具备良好的天赋，但更重要的是可以在适当的时候接受恰当的教育。作为人才培养的核心阶段，中学教育承担起了非常艰巨的责任与义务。在众多学科之中，数学学科支持着科技的发展，而科技的发展在一定程度上决定着国家的未来，因此对数学优等生的培养势在必行。现如今，我国的教育家、数学家和一线教师通过与教育发达国家的交流学习已经意识到了数学优等生培养的重要性并付出了相应的行动。 我国培养优等生的方式大致可以分为四种：①重点中学；②中学理科班；③少年班；④校外科学机构（数学竞赛培训）。但是在实际操作过程中，每个学校、每位教师所实施的选拔和教育都没有统一的标准。到底怎样的教育才能选拔、培养出数学优等生，才能将数学优等生培养成为数学人才，这也正是本文研究的问题，希望通过本文的研究能够提出较为有效的数学优等生培养建议。 本文采用个案研究法、教师访谈法、观察法和文献研究法，通过对教育、数学教育发达的国家关于数学优等生教育的相关文献的综述，以及对北京师范大学附属实验中学高一9班教师课前深入访谈、课堂实录和课后追溯式访谈的分析得出以下结论：①选拔数学优等生是一个持续性的活动，在培养的过程中选拔。选拔培养的内容以教科书中的基本知识为主；②培养目标多元化，包括兴趣、思维、能力、人格；③课堂设置为必修加选修，必修内容是教科书基础知识，而选修包括数学建模、数学竞赛等；④课堂实施以“高难度、高速度”为基本原则，采用情景教学法、问题导学法和探究小组活动法等教学方法，设置开放性、思考性问题，布置综合性、逻辑性例题、习题和作业；⑤评价方式以区分度较高的全年级统一试卷进行标准性测验为主，以数学竞赛等数学其他领域表现为辅；⑥退出机制设定于高一学年结束。除此之外，若要制定出较为有效的数学优等生培养方法更要从以下7个方面进行加强：①丰富教学内容，如高等数学和科普讲座等；②增加课外科研小组的培养方式等；③建立数学优等生培养教师的选拔机制；④建立导师制度，聘请校外机构或大学教师作为数学优等生的导师；⑤评价方式需要达到外部和内部的分层，要智力因素与非智力因素双结合；⑥奖励机制的外因对内因产生极大的影响；⑦建立法律保障制度。

The 21st century is an era of rapid development of knowledge, economy, science and technology, in which talents are the most needed resource, since talents determine a nation’s competitive power. Talents should be gifted, but something more important is that they could receive suitable education in appropriate time. As the core stage of talents cultivation, middle school education undertakes very arduous duty and obligations. Among numerous subjects, mathematics sustain the development of science and technology, which to some extent determines a nation’s future，therefore it is imperative of the cultivation of gifted and talented students in mathematics. Nowadays, through communication and mutual learning with countries of developed education, educators, mathematicians and front-line teachers in our country have realized the importance of the cultivation and have made corresponding efforts. It could be roughly divided into four modes of the cultivation of gifted and talented students: ① key middle school; ② science class in middle school; ③ special class for gifted youny; ④ by scientific research institutions outside school (math contest training). But in the actual operating process, there are no unified standards of selection and education by different schools and teachers. Which kind of education can select and cultivate gifted and talented students in mathematics and then train them into mathematic talents, are the issues this paper intend to study. It is hoped that with the research in the paper, effective proposals of cultivating gifted and talented students in mathematics could be raised. Case-study method, teacher-interview method, observational method and literature research method are adopted in this paper. Through the summarize of related articles of gifted and talented students’ cultivation in countries of developed mathematics education as well as the analysis of in-depth interviews before class, veritable records in class and tracing type interview after class to the senior one teachers in Beijing Normal University Affiliated Experimental Middle School, the following conclusions are drawn afterwards: ①it is a continuous activity of selecting gifted and talented students in mathematics, and the selection exists in the process of cultivation. The training content of selection give priority to the basic knowledge in textbooks; ②training goal are diversified including interest, thinking, ability and personality; ③the setting of class teaching content should be compulsory and optional courses, hereinto compulsory part include the basic knowledge in textbooks, whereas optional part include mathematical modeling, mathematics competition and so forth; ④the implementation of class takes a basic principle of “high-difficult, high-speed”, adopts situational teaching approach, question raising method and activity method of exploring team, etc., sets up opening and thinking problems, and assigns comprehensive and logic examples, exercises and homework; ⑤evaluation method gives priority to standard test by whole grade unified examination papers with high distinction degree and takes other behaviors such as mathematics competition in mathematics as complementary; ⑥withdrawal mechanism is set at the end of senior one. Besides, if we want to map out relatively valid methods in cultivation of gifted and talented students, the following seven aspects are strongly recommend: ①enriching the teaching content, such as advanced mathematics and science popularizing lectures; ②increasing the training modes of extracurricular scientific research teams; ③set ting up selecting mechanism of the teachers; ④setting up tutorial system, and invite college teachers and out-school institution teachers to be the tutors of gifted and talented students; ⑤evaluation method should realize layering of external and internal and should make combination of intelligence factor and non-intelligence factor; ⑥the external causes of rewarding mechanism generate great influence on internal causes; ⑦establishing the legal protection system.