函数概念是中学数学的核心知识，是重要的数学概念，同时也是高中数学的一个教学难点。本研究主要关注高中生函数概念发展的情况，试图对高中生函数概念的发展水平、发展趋势以及影响高中生函数概念发展的原因等做初步的探讨。本研究采用文献分析法、问卷调查法、访谈法作进一步的研究。本研究的研究假设为（1）用变量、集合、定义域、值域、对应关系、解析表示、表格表示、图象表示八个方面构建函数的概念系统。（2）将高中生对函数概念的认知水平划分为三个层次。即层次1：内化阶段；层次2：符号阶段；层次3：对象阶段。以此作为理论模型，编制调查问卷，选取山东省枣庄市第八中学的高一、高二、高三学生为研究对象进行测试，回收有效问卷465份。另外，选取该高中的3名数学教师进行访谈。通过数据的整理、统计与分析，主要研究结果如下：1. 高中生函数概念发展水平量表的制定（1）基于因子分析，将函数概念的内容划分为变量与集合、函数概念的三要素、函数概念的表示方法三个维度。（2）基于聚类分析，验证函数概念发展的层次水平，确定了函数概念发展的内化、符号、对象三个层次。即：①内化阶段：通过不断熟悉两个集合中的元素按一定的法则相对应的过程，产生函数概念。②符号阶段：能够利用概念、图形、符号、关系式等将函数概念表示出来。③对象阶段：将函数概念作为一个独立的对象，能与其它概念（如方程、算式、映射等）进行区分，可研究它的一般性质，并能用函数处理有关的问题。（3）在内容维度和层次水平的基础上制定高中生函数概念发展水平二维量表。2. 高中生函数概念发展的水平和特点（1）从总体上说，高中生函数概念的发展并不是随年级的增长呈直线上升的趋势，而是在高二有所回落。（2）在年级差异上，高一与高二没有显著性差异，高三与高一、高三与高二存在显著性差异。高三的平均成绩明显高于高一和高二。（3）在性别差异上，总体来说，高中男、女生函数概念发展水平趋于一致，没有显著性差异。还有一些结论这里不作具体表述。3. 对高中各年级关于函数概念发展状况的表现给出了具体描述。4. 影响高中生函数概念发展的原因主要从课程与教材的设置、函数概念本身、教师、学生四个角度进行具体分析。

The fundition is the central knowledge of mathematics and plays an important role in Maths.as well as a hard nut in mathematics teaching in high school. This study focused on the development of the high school students’ function concept. This text is trying to discuss the development trend and cognitive level of the function concept of the high school students. Also want to find the reasons which affect the development. The methods such as lieratures, question inquiry and the talking etc are used in the study.The research hypothesis for this study are: (1) using eight aspects to construct the function systerm which are variable, collection, domain, range, the correasponding relations, pictorial representation, analytic representation and form representation. (2) There are three levels about cognitive of the function concept with students in the high school. Level one: interiorization level, level two: symbol level, level three: objectification level. According to the theoretical model we prepare the questionnaire. We select the students in the Zaozhuang No.8 high school of Shandong province as the research objects. We recycled 465 copies effective quetinnaire. In addition we choose 3 mathmatics teachers of this school as interview objects. Though data sorting, statistics and analysis, we get the following ideas: 1. Making the scale of the level and dimension of the function concept. (1) Based on factor analysis, the content of the function concept is divided into three demisions which are variable and collection, the three elements of function concept, the three representations of function concept. (2) Based on cluster analysis, we validat the cognitive level of function concept which we have made and confirm the interiorization level, symbol level, objectification level of the fundition concept. Specific conditions as follows. Level one: interiorization level, students via gradually familiar with the corresponding process of elements in two sets in certain rules and produce the function concept. Level two: symbol level, express the function concept using concept, graphics, symbols, relation, etc. level three: objectification level. Condenses the function concept into an object, it can be distinguished and studied the general properties and can be used to deal related issues. (3) Then we establish the scale of the level and dimension of the function concept.2. The cognitive level and feature of the function concept of students in the high school.(1) All in all, the development of the seniors’ function concept is not the trend of rising along with the growth of the grade in a straight line, but there was a downward slide in senior 2. (2) On the grade differences, there is no significant difference between senior 1 and senior 2. However, the perceptions of function between senior 1 and senior 3 as well as senior 2 and senior 3 are quite different. The average score of senior 3 is obviously higher than that of senior 1 and senior 2. (3) On the gender differences, in general, there is no significant different between high school boys and girls. There are some other conclusions don’t make the specific expression. 2. We give a detailed description of the performance of the seniors’ function concept. 3. The reasons affecting the development of the high school student’ function concept are analysed from four aspects which are the curriculum and the teaching material setting, the function concept itself, the students and the teachers.