“数学基本活动经验”的提出，是为了培养创新型人才。其作为“四基”之一在义务教育课程标准中提出，得到众多专家学者的肯定，随之而来的相关研究与日俱增，人们对数学基本活动经验的认识正不断深入。那么，数学基本活动经验的内涵是什么？其与数学基础知识、数学基本思想、数学能力有什么区别和联系？数学基本活动经验包含哪几个成分？每个成分上学生有哪些不同的表现？如何在内涵界定的基础上研究数学基本活动经验的主成分和层次水平划分？本文在界定数学基本活动经验的概念、明确其与数学基础知识、基本思想、数学能力的区别和联系的基础上结合统计分析的方法研究数学基本活动经验的主成分和层次水平划分，进而构建数学基本活动经验的量表。本研究选题创新，结论具有一定的现实意义。本研究界定的数学基本活动经验为：个体经历数学思维活动所积累的思考问题的方式或思考问题的习惯。在此基础上，有针对性地进行理论分析和实践调查，给出了数学基本活动经验的维度划分假设，包括8个方面：直观感知、分类、比较、归纳、类比、联想、证明、数学表达。根据维度划分假设，自行编制测试卷，选取高三学生进行测试，因素分析提取数学基本活动经验的主成分，聚类分析给出数学基本活动经验的水平划分。研究得到的主要结论如下：1.数学基本活动经验包含四个主成分。笔者借助因素分析，得到了数学基本活动经验的四个主成分：归纳概括、类比推广、符号表达、证明；2.学生在每个成分上的表现可以划分为三类。笔者借助聚类分析将学生在每个成分上的表现划分为3类。成分1划分为三个水平：水平1：能够找到等式的特点；能够模仿等式写出其它的等式；能够归纳一般式；水平2：能够找到等式的特点并且能够模仿等式写出其它的等式；不能归纳出一般式；水平3：能够找出等式的特点；不能模仿等式写出其它的等式；不能归纳出一般式。成分2划分为三个水平：水平1：能够找到合适的类比对象；能够调整类比后得出的结论；水平2：能够找到合适的类比对象；不能得出类比的结论，不知道对结论进行调整；水平3：能解决常见的类比的题目，不常见的则无从下手。成分3划分为3个水平：水平1：能用符号语言准确地表达；水平2：能够将文字语言转化成符号语言，但是不能够做到准确无误；水平3：不能够将文字语言转化成符号语言。成分4划分为3个水平：水平1：证明思路清晰，能根据题目选择合适的方法；水平2：能够选择证明方法，但是思路不够清晰；水平3：无法根据题目选择合适的证明方法，没有证明思路。结合主成分划分和层次水平划分，构建了数学基本活动经验的二维量表。

In order to cultivate student’s innovation ability，we put forward "Mathematical basic activity experience" . As one of the "four bases", many experts and scholars agree with it, the corresponding research also increase rapidly, people’s understanding of Mathematical basic activity experience is deepening. But what's the meaning of Mathematical basic activity experience? What's the difference and contact between Mathematical basic activity experience and mathematical basic knowledge, basic ideas, mathematical ability. What are the components of Mathematical basic activity experience? In every component, what's the difference between student’s performance. How to research the principal component and levels of the mathematical basic activity experience on the basis of the defined connotation. This paper define concept, clear the differences and relationship between mathematical fundamental activity experience with the mathematical basic knowledge, basic ideas，mathematical ability，then on the basis of these, research the principal components and level of mathematical fundamental activity experience, then build mathematical fundamental activity experience scale. The topic is innovative, research conclusion is meaningful.The definition of mathematical basic activity experience is: the individuals’ thinking habit or thinking way accumulated by mathematical thinking activity. On the basis of this definition, theoretical analysis and practical investigation to give the dimensions assumption of mathematical basic activity experience which include eight aspects: visual perception, classification, comparison, induction, analogy, imagine, prove, mathematical expression. According to the dimensions assumption, I prepare the test and choose high three students to take. Based on factor analysis to give the main components, cluster analysis to give the levels of mathematical basic activity experience.The main conclusions of this study are as follows:1. Mathematical basic activity experience have four main components. They are inductive summary, analogy promotion, prove, symbols expression; 2. The students' performance on each component is divided into three levels. Component 1 is divided into three levels: Level 1: they can find the characteristics of the equation; they can imitate equation to write other equation; they can conclude the general type; Level 2: they can find the characteristics of the equation; they can imitate equation to write other equation; they can’t conclude the general type; Level 3: they can find the characteristics of the equation; they can't imitate equation to write other equation; they can’t conclude the general type. Component 2 is divided into three levels: Level 1: they can find appropriate analogy object; They can adjust the conclusion after analogy; Level 2: they can find appropriate analogy object; They can’t adjust the conclusion; Level 3: they can’t find appropriate analogy object except some common problems. Component 3 are divided into three levels: Level 1: they can use express accurately by sign language ; Level 2: they can turn text language into symbolic language, but can't be accurate; Level 3: they can’t turn text language into a symbolic language. Component 4 are divided into three levels: Level 1: the prove logic is clear, they can according to the subject to choose the appropriate method; Level 2: they can choose the proof method, but the logic is not clear; Level 3:they can’t choose the suitable method according to the topic.Combined with the four main components and the levels to build the scale of mathematical basic activity experience.