数形结合思想及其在教学中的应用（
1.1 数形结合思想方法概述 1
1.2 数形结合思想方法历史演进 1
2 数形结合思想在初等数学教学中的应用 4
2.1 数形结合思想在小学数学教学中的应用 4
2.2 数形结合思想在初中数学教学中的应用 7
2.2.1 数形结合思想在初中数学教学中的地位 7
2.2.2 数形结合思想在初中数学教学的应用举例 8
2.3 数形结合思想在高中数学教学中的应用 10
2.3.1数形结合思想在高中数学教学中的地位 10
2.3.2 数形结合思想在高中数学教学的应用举例 11
2.3.3 数形结合思想的课堂灌输 15
3 数形结合思想在高等数学教学中的应用 17
4 结束语 22
致谢 24
参考文献 25
摘要：数、形是数学中两大基本概念，可以说全部数学大体上都是围绕这两个基本概念的提炼、演变、发展而展开的。数形结合是根据数学问题的条件与结论之间的内在联系，既分析其代数意义，又揭示其几何直观，使数量关系的精确刻划与空间形式的直观形象巧妙、和谐地结合在一起。数形结合是贯穿中小学数学教学始终的基本思想，同时在高等数学教学中它也有很大的益处。
关键词：数形结合；数学教学；数学思想
The Thinking of Combining Numbers with Shapes and It’s Application in Teaching
Tang Xinyang
（College of Mathematics and Information Engineering , Jiaxing University）
Abstract: Number and shape are two basic concepts of mathematics，it can be said that the evolving of all the mathematic are generally surrounding the abstraction, evolution and development of the two basic concepts. Combining numbers with shapes is according to the intrinsic link between conditions and conclusions of mathematical problems, it can both analyze the meaning of algebra and reveal the intuitive of geometry which make a artful and harmonious combination between accurate depiction of the number-shape relationship and intuitionistic image of spacial modality. Combining numbers with shapes is basic thinking through mathematics teaching in primary and secondary schools all along, at the same time, it has a great benefit in higher mathematics teaching.
Key words: combining numbers with shapes; mathematics education; mathematics thinking
致谢
本人的本科毕业论文是在各位老师的指导帮助下完成的。我是幸运的，在求学的路上有如许众多的良师益友，他们的支持和帮助使我顺利度过了历史性的四年大学生活。
首先我要诚挚的感谢我的论文指导老师龚淑华老师和本科指导老师李启会老师。龚老师在我写毕业论文期间热情面对我的一次又一次的打扰，帮我理清思路。其对学生认真负责的态度，在今后的教师生涯中也是值得我学习的。同时，如果没有李老师平时在我学习生活上的督促和谆谆教导，我也不会如此顺利地完成学业。
其次，我还要感谢我的母亲和其他亲人。正是他们一直的支持和鼓励，才使我能有不断学习的机会；也是他们为我的工作四处打点，才使我无后顾之忧专心完成毕业论文。
我还要感谢曾经为我授课的各位老师，您们不仅教授了我数学专业知识，更用自己的言行向我展示了为人师的高尚品德。
还要感谢我们数学052的所有亲爱的同学和我的室友，你们伴随我经历了人生中唯一的也是独一无二的四年，那些灿烂缤纷的回忆会是我今后生活的动力。
在以后的日子里，我会感谢学校的一切！谨此向所有的人表示我最诚挚的谢意！
参考文献
Angelika Bikner-Ahsbahs,Susanne Prediger. Diversity of theories in mathematics education-How can we deal with it?[J]. ZDM,Volume 38,Number 1,2006.2.
徐文龙.＂数形结合＂的认知心理[D]. 广西:广西师范大学,2005.
顾亚萍.数形结合思想方法之教学研究[D]. 南京:南京师范大学,2004.
朱家生.数学史[M]. 北京:高等教育出版社,2004.
刘加霞.“数形结合”思想及其在教学中的渗透[J].小学教学数学版.2008,5:44-46.
徐先荣.谈初中数学数形结合的教学策略[J].大教论坛. 2007.4:75.
邹良量.数、形结合法在解题中的应用[J].广西轻工业. 2008, 6:125-137.
周房安.巧用数形结合法解题[J].高中. 2006, 6:21-22.
刘会芳.浅谈数形结合思想的课堂灌输[J].安庆师范学院报.2003,3:118-119.
崔秋珍. 数形结合与高等数学问题处理[J]. 洛阳工业高等专科学校学报.1997,4:38-40.
朱殿利.数形结合法在高等数学中的应用再探析[J].岱宗学刊.1998, 4:23-25.
Ross L.Finney. 托马斯微积分（英文版）[M]. 北京: 高等教育出版社,2004.
Shuxingjiege thoughts and in teaching applications (
Directory
1 Introduction 1
1.1 an overview of one way of thinking Shuxingjiehe
1.2 Historical Evolution of a way of thinking Shuxingjiehe
2 Shuoxingjiege thought in Elementary Mathematics Teaching 4
2.1 Shuxingjiehe thought in Primary Mathematics Teaching 4
2.2 Shuxingjiehe thought in junior high school mathematics teaching 7
2.2.1 Shuoxingjiege thought in junior high school mathematics teaching position 7
2.2.2 Shuoxingjiege thought in the application of mathematics teaching junior high school for example, 8
2.3 Shuxingjiehe thought in high school mathematics teaching 10
2.3.1 Shuoxingjiege thought in high school mathematics teaching position 10
2.3.2 Shuoxingjiege thought the application of mathematics teaching in high school, for example, 11
2.3.3 Shuoxingjiege thinking classroom indoctrination 15
3 Shuoxingjiege Thought in Higher Mathematics Teaching 17
4 Conclusion 22
Thanks 24
References 25
Abstract: The number, shape are two basic concepts in mathematics can be said that all the math in general are focused on the extraction of these two basic concepts, evolution, and development started. Shuoxingjiehe is based on the conditions and conclusions of mathematical problems the intrinsic link between both analyze its algebraic sense, but also reveal the geometric intuition, so that the precise characterization of the relationship between the number of forms of visual image and space cleverly and harmony together. Shuxingjiege runs through primary and secondary mathematics teaching has always been the basic idea, while in higher mathematics teaching it also has great benefits.
Key words: Shuxingjiege; mathematics teaching; mathematical thought
The Thinking of Combining Numbers with Shapes and It''s Application in Teaching
Tang Xinyang
(College of Mathematics and Information Engineering, Jiaxing University)
Abstract: Number and shape are two basic concepts of mathematics, it can be said that the evolving of all the mathematic are generally surrounding the abstraction, evolution and development of the two basic concepts. Combining numbers with shapes is according to the intrinsic link between conditions and conclusions of mathematical problems, it can both analyze the meaning of algebra and reveal the intuitive of geometry which make a artful and harmonious combination between accurate depiction of the number-shape relationship and intuitionistic image of spacial modality. Combining numbers with shapes is basic thinking through mathematics teaching in primary and secondary schools all along, at the same time, it has a great benefit in higher mathematics teaching.
Key words: combining numbers with shapes; mathematics education; mathematics thinking
Thanks
My undergraduate thesis is the teacher''s guidance and assistance to you for completion. I was lucky, in studying the way like a large number of mentor Hsu, and their support and help me successfully through a historic four-year university life.
First of all I would like to sincerely thank my thesis instructor Gong Shuhua Qi teachers and undergraduate instructor will be a teacher. Teacher Gong warm in my face during the writing of my thesis again and again disturbed, to help me sort out ideas. Its serious and responsible attitude towards the students, the teachers in the future it is worth my life-long learning. Also, if the teacher does not normally Lee to study life in my supervision and earnest instructions, I would not be so successfully complete their studies.
Secondly, I would also like to thank my mother and other relatives. It is the support and encouragement they have been before so I can have life-long learning opportunities; is what they work for me, four RBI, it made me worry-free to concentrate on the completion of dissertation.
I would also like to thank you once taught my teacher, you have taught me not only the knowledge of mathematics, but also use their own words and actions showed me become much more noble character.
Would also like to thank our math 052 for all my dear classmates and my roommate, you have gone through life with me is unique and the only four-year, those bright colorful memories will be my future life motivation.
Over the next days, I will be grateful for all the school! All of them would like to express my most sincere thanks!
References
Angelika Bikner-Ahsbahs, Susanne Prediger. Diversity of theories in mathematics education-How can we deal with it? [J]. ZDM, Volume 38, Number 1,2006.2.
Hsu Wen-lung. "Shuoxingjiege" in cognitive psychology [D]. Guangxi: Guangxi Normal University, 2005.
Gu Yaping. Shuoxingjiehe thinking of teaching and research [D]. Nanjing: Nanjing Normal University, 2004.
Chu health. History of Mathematics [M]. Beijing: Higher Education Press, 2004.
Liu Jia-xia. "Shuoxingjiege" Thought and its penetration in teaching [J]. Primary School Teaching math version .2008,5:44-46.
Xu Rong. To talk about junior high school mathematics Shuoxingjiehe teaching strategies [J]. Great teaching forum. 2007.4:75.
Liang-volume. Number, shape combined method in solving problems [J]. Guangxi light. 2008, 6:125-137.
weeks Fusayasu. Shuxingjiege Solving Problems Using [J]. High School. 2006, 6:21-22.
Liu Hui-fang. Shuxingjiege thinking of classroom indoctrination [J]. Anqing Teachers College, reported .2003,3:118-119.
CUI Qiu-Zhen. Shuoxingjiege deal with the problem of higher mathematics [J]. Luoyang Technology College .1997,4:38-40.
Zhu Dian-Lee. Shuoxingjiege method in the application of higher mathematics and then Analysis [J]. Daizong Journal since.1998, 4:23-25.
Ross L. Finney. Thomas Calculus (English) [M]. Beijing: Higher Education Press, 2004.
