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辽宁师范大学硕士学位论文
I
摘 要
近几年来,现代信息技术快速发展,使得教育发生了巨大的改变。学生可以
通过更多的方式去学习知识,教师也可以使用更多的现代信息技术来丰富教学手
段。使用现代信息技术,一来可以帮助教师更好的组织教学活动,二是可以更好
的教授知识,三可以为学生提供更好的教学环境。我国是十分重视在数学课堂中
使用信息技术的,在新教材中增加了许多有关使用现代信息技术应用的部分。
在《普通高中数学课程标准(2017 版)》中,要求教师合理的运用现代信息
技术手段在教学活动中。同时,要求在函数这一章的教学中,要重视图形在数学
学习中的作用,使用数形结合的思想,解决函数抽象性的问题
[1]
。本文主要研究
MATLAB 在高中函数教学中的应用,通过查找文献了解目前的研究进展,然后在
实习学校进行实例研究。
本文研究首先是通过查找相关资料,研究函数部分哪些知识可以使用
MATLAB,然后进行整理。通过在某高中实习,对目前高中函数教学现状进行调
查,并调查目前函数教学中存在的问题。对师生发放调查问卷,了解目前高中教
师与学生对于 MATLAB 的了解情况和使用情况。将 MATLAB 与函数教学有效结
合,在建构主义学习理论下提出教师直观演示课型,进行实例分析。本文研究以
对数函数的图像与性质为例,利用 MATLAB 进行高中函数的可视化教学。
在教学评价主要包含学生满意度调查、测试题成绩、教师评价三部分,在教
学评价后,及时的完善教学设计。通过对实验班与普通班进行对数函数题目的测
试,对成绩进行汇总,验证结论。通过对结果分析,发现新的教学设计能够使学
生更好的掌握函数知识,提高学生的动手操作能力。在教学设计中使用 MATLAB,
可以激发学生的学习兴趣以及对于函数的探索精神,比传统的函数教学模式更具
有优势。
关键词:MATLAB;现代信息技术;高中函数
MATLAB 在高中数学中的应用研究-以高中函数为例
II
The application of MATLAB in high school mathematics
---Take high school function as an example
Abstract
In recent years, the rapid development of modern information technology has
greatly influenced the field of education and promoted the development of education.
Students can learn knowledge in more ways, and teachers can use more modern
information technology to enrich teaching methods. Using modern information
technology can help teachers organize teaching activities better, teach knowledge better,
and provide students with a better teaching environment. Our country attaches great
importance to the use of information technology in mathematics classroom, and many
parts about the application of modern information technology have been added in the
new textbooks.
In the general high school mathematics curriculum standard (2017 Edition),
teachers are required to reasonably use modern educational technology in teaching
activities. At the same time, in the teaching of function chapter, we should pay attention
to the role of graphics in mathematics learning, and use the idea of combination of
number and shape to solve the problem of function abstraction
[1]
. This paper mainly
studies the application of MATLAB in senior high school function teaching, through
searching the literature to understand the current research progress, and then carries on
the case study in the practice school.
In this paper, first of all, by looking up the relevant information, we study which
knowledge of the function part can use MATLAB, and then sort it out. Through the
practice in a senior high school, this paper investigates the current situation of function
teaching in senior high school, and summarizes the existing problems in function
teaching. The questionnaire is distributed to the teachers and students to understand the
current understanding and use of MATLAB by high school teachers and students.
Combining MATLAB with function teaching effectively, this paper puts forward the
teacher's intuitionistic demonstration course type under the constructivism learning
theory, and makes an example analysis. This paper takes the image and property of
logarithmic function as an example, and uses MATLAB to carry out the visual teaching
of high school function.
The teaching evaluation mainly includes three parts: student satisfaction survey,
test scores and teacher evaluation. After the teaching evaluation, we should improve
the teaching design in time. Through the test of logarithm function in the experimental
class and the ordinary class, the results are summarized and the conclusion is verified.
Through the analysis of the results, it is found that the new teaching design can make
the students master the function knowledge better and improve the students' practical
operation ability. The use of MATLAB in teaching design can stimulate students'
辽宁师范大学硕士学位论文
III
interest in learning. For the spirit of exploring function, it has more advantages than the
traditional function teaching mode.
Key words: MATLAB; Modern information technology; High school function
MATLAB 在高中数学中的应用研究-以高中函数为例
IV
目 录
摘 要 ................................................................................................................................ I
Abstract .................................................................................................................................II
1 绪论 ................................................................................................................................... 1
1.1 研究目的及意义 ............................................................................................... 1
1.1.1 研究目的................................................................................................. 1
1.1.2 研究意义................................................................................................. 1
1.2 研究的背景 ........................................................................................................ 2
1.3 研究的内容 ........................................................................................................ 3
1.4 研究的方法 ........................................................................................................ 3
1.5 主要术语界定 .................................................................................................... 3
1.6 文献综述 ............................................................................................................. 4
2 相关理论基础 ................................................................................................................ 5
2.1 MATLAB 简介 ..................................................................................................... 5
2.2 使用 MATLAB 原因 .......................................................................................... 5
2.3 建构主义学习理论 ........................................................................................... 6
2.4 史密斯-瑞根教学设计模式 ........................................................................... 7
3 MATLAB 在高中函数教学应用情况的问卷调查 .................................................. 9
3.1 高中数学教师使用 MATLAB 在高中函数教学情况的调查 ................. 9
3.2 高中学生对于 MATLAB 的了解情况的调查 ........................................... 13
3.3 问卷调查的结论与建议 ................................................................................ 17
4 MATLAB 在高中函数教学的实例分析 .................................................................. 19
4.1 高中函数相关的应用示例 ........................................................................... 19
4.1.1 高中函数知识 ..................................................................................... 19
4.2.2 MATLAB 在函数教学的应用实例 .................................................. 20
4.2 MATLAB 在高中函数教学应用的实例分析 ............................................. 26
4.3 MATLAB 应用于高中函数教学的教学设计 ............................................. 27
4.4 教学过程设计 .................................................................................................. 30
5 MATLAB 应用于高中函数教学的教学评价 ......................................................... 41
5.1 对数函数测试成绩 ......................................................................................... 41
5.2 学生满意度的调查 ......................................................................................... 43
5.3 教师的评价 ...................................................................................................... 45
辽宁师范大学硕士学位论文
V
6 修改后的教学设计 ..................................................................................................... 48
结论与建议 ........................................................................................................................ 56
不足与反思 ........................................................................................................................ 58
参考文献 ............................................................................................................................ 59
附录 A 高中教师对 MATLAB 使用情况的调查问卷 .......................................... 61
附录 B 高中学生对于函数教学使用 MATLAB 的情况调查问卷 .................... 62
附录 C “高中函数教学现状”访谈提纲 ................................................................... 63
附录 D 对数函数测试题 ............................................................................................. 64
附录 E MATLAB 应用于函数课堂的满意度调查问卷 ....................................... 67
附录 F “MATLAB 应用于函数教学的教学评价”访谈提纲 ................................ 68
附录 G 对数函数的教案 ............................................................................................. 69
附录 H MATLAB 绘制对数函数的程序 .................................................................. 82
致谢 ..................................................................................................................................... 85
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