数学思想方法是对数学及其研究方法的再度抽象，是数学的灵魂和精髓，是知识转化为能力的依托，对数学学习、数学研究、数学问题解决等方面均具有重要指导意义。数学资优生作为数学综合能力较强的一个群体，其数学思想方法水平可以很好地反映出他们在数学学习上的卓越特质。初高中衔接阶段是学生数学思维转变的关键时期，也是数学思想方法形成的关键时期。因此，对初高中衔接阶段数学资优生的数学思想方法水平进行研究，一方面通过数学思想方法水平可以具体分析资优生稳定的能力特征，加强了研究的可靠性；另一方面，对初高中衔接这一特殊阶段进行研究，可以探寻学生“原生态”的数学思想方法特质，对教学实践中数学思想方法的培养具有一定启示作用。 本研究以80名初高中衔接阶段的数学资优生为研究对象，对其在数学思想方法上的表现进行调查分析。笔者通过对文献的梳理，界定了本研究中数学资优生、数学思想方法等核心概念的内涵，用SOLO分类理论对数学思想方法水平进行划分研究，并针对中学数学中的四种基本数学思想方法——函数与方程思想、数形结合思想、转化与化归思想、分类讨论思想，进行具体的水平划分，以此为研究框架，命制了测量数学思想方法的测试工具并编码和对学生进行测试。依照该框架进行数学思想方法水平的量化赋分，获得研究数据，再利用Excel表格工具及SPSS20.0软件进行数据处理，得到以下结论： 1. 初高中衔接阶段数学资优生数学思想方法总体水平较高； 2. 初高中衔接阶段数学资优生数学思想方法发展较为均衡，每种数学思想方法的水平差异不大，相比之下该群体对函数与方程思想掌握得较好，对转化与化归思想掌握较差，数形结合思想和分类讨论思想的掌握情况相对居中； 3. 学生数学学业成就与数学思想方法水平间存在双向交互影响，即：学生先前数学学业成就作为其数学知识储备和数学基础的反映，可形成并影响数学思想方法的水平；反过来，学生数学思想方法水平的高低也可以在一定程度上影响其后续的学习进程乃至数学学业成就。 本研究创新之处在于： 1. 以初高中衔接阶段的数学资优生为研究对象，而此阶段正是数学思想方法形成的关键时期，因此所得结果具有重要意义； 2. 利用SOLO分类理论对数学思想方法水平进行划分，并建立了数学思想方法水平的测试框架； 3. 利用bootstrap程序中介作用检验法，将数学思想方法水平与学生学业水平的关联做了考量，以期对教学具有更多参考价值。

Mathematical thought and methodology is the re-abstraction of mathematics and research method. It is the soul and essence of mathematics, which can help transform knowledge into ability. Mathematical thought and methodology has important guiding significance to mathematics study, mathematics research, mathematics problem solving and so on. As a group with strong comprehensive ability in mathematics, the level of gifted students in mathematical thought and methodology can well reflect their outstanding characteristics in mathematics learning. The connecting stage of middle and high school is the key period of the change of students' mathematical thinking. This is also one key period of the formation of mathematical thought and methodology. Therefore, this paper investigates and analyzed 80 students’ performance in mathematical thought and methodology, who are mathematical gifted students in connecting stage of middle and high school. Through sorting out the literature, this paper defines the connotation of mathematical gifted students, mathematical thought and methodology and the other core concepts. In addition, this paper uses SOLO classification theory to divide the levels of four basic mathematical thoughts and methodologies of middle school, which are function and equation thought, combination of number and form thought, transformation thought, classification and discussion thought. This paper uses the above classification of four basic mathematical thoughts and methodologies as research framework and then make and encode testing tools. Then, this paper tests these students, scores students’ performance and obtains research data. This paper processes the data by using the Excel and SPSS20.0 software, and the following conclusions were obtained: 1. The overall level of mathematical thought and methodology of mathematics gifted students, who are in the connection stage of middle and senior high school, is high. 2. The development of mathematical thought and methodology of mathematics gifted students, who are in the connection stage of middle and senior high school, is balanced and has very little difference, although this group has a better understanding of function and equation thought and has a worse understanding of transformation thought. 3. There are two-way interactions between students' achievements in mathematics and the levels of mathematical thought and methodology. Students' previous achievements in mathematics, which reflect their mathematical knowledge reserve and mathematics foundation, can influence the level of mathematical thought methodology. On the other hand, the level of students' mathematical thought methodology can also affect learning process and mathematical achievements to a certain extent. The innovations of this study are as follows: 1. This paper investigates and analyzed mathematical gifted students who are in connecting stage of middle and high school. This stage is the key period of the formation of mathematical thought and methodology, so this paper’s result has significant meanings. 2. Based on SOLO classification theory, this paper divides the levels of four basic mathematical thoughts and methodologies and build testing framework. 3.In order to have more reference value for teaching, this paper calculates the correlation between the level of mathematical thought and methodology and the students' academic level by using the method of bootstrap program intermediary function test.