数学语言是数学思维的载体，学生通过数学语言表达数学思维，数学教学是数学语言的教学，而函数建模问题则是数学语言表达的良好载体。我国教育部最新颁布的《普通高中数学课程标准》中也明确指出高中生通过数学建模的学习，学生能有意识地用数学语言表达现实世界。基于以上背景本研究关注以下问题：

1、如何评价高中生的数学语言表达？

2、在函数建模问题中，高中生数学语言表达呈现的特点如何？

3、在函数建模问题中，高中生的数学语言表达存在哪些问题？出现问题的原因有哪些？

为了有效的研究上述问题，笔者以函数建模问题为内容载体，编制测试卷分别考查学生的文字语言、符号语言、图形语言的数学语言表达，并对240名高一学生进行了测试。通过文献分析，笔者确定了从表达结果的准确性、严谨性、明晰性三个维度来评价学生的数学语言表达，借助Excel软件对测试卷进行统计评分，分析测试结果及测试卷典型案例得到以下结论：

学生数学语言表达整体呈现的特点包括：（1）学生得分差距较大；（2）数学语言表达的一致性较高；（3）数学语言表达的逻辑性不足；（4）数学语言表达的明晰性不强。

从文字、符号及图形语言在各评价维度上的表现来分析测试卷结果，得到以下结论：（1）符号语言表达呈现的主要特点是准确性不足；（2）图形语言表达呈现的主要特点是严谨性不足；（3）文字语言表达呈现的主要特点是严谨性不足。

结合测试卷中的典型案例得到了测试卷呈现的不同类型语言表达的主要问题：（1）符号语言表达存在的主要问题有符号语言使用错误多和意义不了解；（2）图形语言表达存在的主要问题有作图规范欠缺及作图完整性低；（3）文字语言表达存在的主要问题有表述不规范和组织能力差；（4）多种语言表达综合运用时存在的主要问题时数学语言之间转换不灵活。

针对高中学生数学语言表达存在的问题，结合访谈，得到问题存在的两方面原因：其中学生的原因包括：（1）从学生对语言表达的态度上来看，学生的重视程度不够；（2）从学生的数学知识上看，学生的知识结构不牢固；（3）从学生的数学语言表达形成的过程看，学生操作数学语言的能力较低；（4）从学生的数学活动上看，缺乏严谨的数学表达训练。

教师的原因包括：（1）从教师对语言表达的态度来看，教师的重视程度不够；（2）从教师采取的培养策略来看，教师培养策略缺乏技巧；（3）从教师的教学行为来看，教师的语言表达示范性不足；

Mathematical language is the carrier of mathematical thinking. Students express their mathematical thinking through mathematical language. Mathematics teaching is the teaching of mathematical language, while function modeling is a good carrier of mathematical language expression. The latest Mathematics Curriculum Standard for Ordinary High Schools issued by the Ministry of Education of China also clearly points out that high school students can consciously express the real world in mathematical language by learning mathematical modeling. Based on the above background, this study focuses on the following issues:

1. How to evaluate high school students' mathematics language expression? 2. In the problem of function modeling, what are the characteristics of senior high school students' mathematical language expression? 3. What are the problems of senior high school students' language expression in function modeling? What are the reasons for the problems?

In order to study the above problems effectively, the author takes the problem of function modeling as the content carrier, compiles test papers to examine the language expression of students' written language, symbolic language and graphic language, and tests 240 senior one students. Through literature analysis, the author determines to evaluate students' written language expression from three dimensions: accuracy, rigor and clarity of expression results, scores the test papers statistically with the help of Excel software, analyzes the test results and typical cases of test papers, and gets the following conclusions:

The overall characteristics of students' mathematical language expression include: (1) Students' scores are quite different; (2) The consistency of mathematical written language expression is high; (3) Lack of logicality in mathematical written language expression; (4) The clarity of mathematical written language expression is not strong.

This paper analyzes the test results from the performance of characters, symbols and graphic languages in various evaluation dimensions, and draws the following conclusions: (1) The main characteristic of symbolic language expression is insufficient accuracy; (2) The main feature of graphic language expression is lack of rigor; (3) The main feature of written language expression is lack of rigor.