初中数学教学情境创设案例开发与教学研究

摘要

新课程改革以来，情境教学几乎在各个学科的教学中都得到了体现，成为知识点呈现的载体．创设情境成为初中数学课堂中一道亮丽的风景．然而许多教师在教学中为了情境创设而设置的许多图片和视频犹如电视广告般铺天盖地而来，如此的情境创设在数学课堂中的有效性是很值得质疑的，笔者尝试用一支粉笔、一本课本的“裸课”教学，却迎来了学生的掌声一片.所以如何寻找情境创设与数学学习的结合点，是我们数学教师应该领会的教学内涵.

梳理比较国内外文献发现，数学教学中情境创设的研究有如下特点：①“情境创设”研究是当前教育研究的热点之一；②从宏观的理论论述和教学实践研究都有一定的积淀，但在案例开发研究上尚少；③引课创设情境较多，而数学迁移方面较少且深度不够.特别是二次课改以来，情境创设更趋于理性，原来存在“五花八门、热热闹闹”的展示渐渐回归到数学教学的本质上来，教学中更加注重数学的核心知识，让我们对数学情境创设有了更进一步的认识，并吸引着我们投入到数学教学的情境创设研究中去.

根据目前中小学教育改革的实际情况，本研究另辟思路，以《浙教版》的初中数学教科书内容为载体，以初中生学习阶段为对象，以“文化情境—迁移情境—问题情境”为主线，分别从文献研究、案例开发、教学实践三方面着手，根据具体情境以现实课堂教学实践为实验室，探索“如何进行数学情境创设、以怎样的载体进行数学情境创设、创设什么样的情境对数学学习的核心最有效”，进行了初中数学教学情境创设的案例开发与教学研究．讨论了在数学教学中情境创设的误区，总结了在情境创设中应遵循的原则．并进一步反思与探索，谨慎地决定如何恰当地使用信息技术，定位在“促进学生数学思考的工具”上，用动画情境来激活情感经验、以动态直观去诱发理性思考、注重情境素材的全程性和发展性、注视情境活动的自然性和融合性，以数学文化的背景、问题设置的核心、学习迁移的思路去组合各种信息，以各式的情境创设表达，让头脑中的“数学实验”变成现实，使得数学教学中的情境创设的研究更具有全面性和参考性．

关键词： 数学迁移；数学文化；问题解决；数学情境

A CASE STUDY OF THE DEVELOPMENT AND PROMOTION OF MATHEMATICS TEACHING SITUATION IN JUNIOR HIGH SCHOOL AND TEACHING RESEARCH

ABSTRACT

Since the implement of the New course, the situation of teaching has been embodying in almost every subject .It has become the carrier of the knowledge. The creation of the situation has become  a picturesque sceneries in the math class in junior high school.However, a lot of teachers set up many pictures and videos in the context teaching .Such a context creation in the math class is well worth the effectiveness of the question .I attempted to use a piece of chalk, a textbook to give a "naked" class. Of course, it ushered in the applause to another.  So how to find the bonding point of the situation creation and math learning is very important. It’s also the teaching connotation that we math teachers should grasp.

Compared with the document and literature in China and abroad ,we will find out the following special features in the situation creation of math teaching. "Created" the current situation is one of the education study of ；From macroscopic theory and teaching research has a definite, but on developing research on cases are still less ；To the promotion of the class situation more than math migration. Especially the situation to create more to reason, "variety and hilarious" show gradually return to the essence of mathematics, The more important core knowledge of mathematics, so we have created a situation in the further understanding, and attracts us into the study of the development and promotion of mathematics teaching situation.

According to the Primary and secondary educational reform under the current realities, the research has some new perspectives to the zhejiang math textbook in order to improve the contents for vehicles, the learning stage, the object，to the " Cultural contexts――The context of migration,――Problem situations"for one in charge，in which case studies, research and teaching three aspects, According to the specific situation in real classroom practice as a laboratory. Explore“how to make math situation created. What is the carrier to mathematics in the context of creating，What kind of situation created is the most effective to study maths . A junior high school math education development and promotion of the context of the teaching and research ．Discussed the major traps in  promotion of the situation.  Summed up in the promotion of the situation  we should follow the principle．And further reflection and the exploration  in deciding how to correctly using information technology, In “Promoting student in mathematics thinking tool”， With animation situation to activate emotional experience. For dynamic visual to induce uses reason and on the context of material for the race, sex and development. At the context of activities, and blending nature in mathematics and cultural background. The question of the core is to study migration way of combined all kinds of information to various situation. let's set up in mathematics "into reality experiment is the mathematics of creating more comprehensive research and reference to sexual ．

KEY WORDS：

Mathematics migration；Mathematics culture；To solve problems；Mathematics situation

目      录

摘要…………………………………………………………………………………Ⅰ

ABSTRACT…………………………………………………………………………Ⅱ

目录……………………………………………………………………………………Ⅲ

一、引言………………………………………………………………………………1

（一）研究背景……………………………………………………………………1

（二）研究问题……………………………………………………………………2

（三）研究意义……………………………………………………………………4

二、文献综述…………………………………………………………………………6

（一）国外有关情境创设的研究综述………………………………………………6

（二）国内相关研究综述……………………………………………………………7

（三）概念界定………………………………………………………………………7

三、案例素材开发……………………………………………………………………11

（一）文化情境——以数学文化为背景的情境创设……………………………11

1．为什么要在初中数学教学中渗透数学文化？……………………………11

2．创设怎样的文化情境对学生数学学习是有效的？ ………………………12

3．《黄金分割》案例设计分析…………………………………………………14

4．《勾股定理》案例设计分析…………………………………………………18

（二）迁移情境——以学习迁移为目的的情境创设……………………………24

1.什么是数学学习迁移 ………………………………………………………25

2．情境创设在学习迁移中的作用是什么……………………………………26

3．《反比例函数》教学中的情境创设与学习迁移 …………………………27

4．《认识不等式》教学中的情境创设与学习迁移 …………………………33

（三）问题情境——以问题解决为核心的情境创设 …………………………36

1．“问题解决”的涵义 ………………………………………………………36

2．以问题解决为核心的情境创设的有效性…………………………………36

3．《一元二次方程》教学中的情境创设 ……………………………………38

4．《二元一次方程》教学中的情境创设 ……………………………………40

5.习题教学和试题编制中的情境创设 ………………………………………43

四、教学实践研究 …………………………………………………………………50

（一）情境创设的误区 …………………………………………………………50

（二）数学情境创设应该遵循的原则 …………………………………………52

五、结语与反思 ……………………………………………………………………57

参考文献 ……………………………………………………………………………………59

攻读学位期间取得的研究成果 ……………………………………………………………61

致谢……………………………………………………………………………………………62

浙江师范大学学位论文独创性声明 ………………………………………………………63

学位论文使用授权声明 ……………………………………………………………………63

浙江师范大学学位论文诚信承诺书 ………………………………………………………64