摘要数形结合就是把问题的数量关系和空间形式结合起来考察,根据解决问题的需要,可以把数量关系的问题转化为图形的性质问题去讨论,或者把图形的性质问题转化为数量关系的问题来研究。 数形结合作为一种常见的数学方法, 沟通了代数、三角与几何的内在联系。一方面,借助于图形的性质可以将许多抽象的数学概念和数量关系形象化、简单化,给人以直觉的启示。另一方面,将图形问题转化为代数问题,以获得精确的结论。因此,数形结合不应仅仅作为一种解题方法,而应作为一种十分重要的数学思想方法, 它可以拓宽学生的解题思路, 提高他们的解题能力,将它作为知识转化为能力的“桥”。以往的“数形结合”大多出现在教师的习题课中,以灌输为主,这并不完全符合新课程理念。应寻找一种办法,能使学生在上“数形结合”的习题课之前就自主地发现数形结合的存在,并自然地使用数形结合的方法解题,从而引发了对于数形结合在教学中的应用思考。58273
毕业论文关键词: 数形结合; 解题; 发展
ABSTRACT
Counts the shape union is unifying the question stoichiometric relation and the space form to inspect, according to solving the question need, we can transform the stoichiometric relation question for the graph nature question discusses, or transform the graph nature question for the stoichiometric relation question studies, “the number shape makes up for one's deficiency by learning from others strong points mutually in short”. Counts the shape union as one common mathematical method, has communicated the algebra, the triangle and the geometry inner link. On one hand, with the aid in the graph nature may make many abstract mathematics concepts and the stoichiometric relation visualization and simplification, for the human by the intuition enlightenment. On the other hand, transforming the graph question as the algebra question, obtains the precise conclusion. Therefore, counts the shape union not to take one problem solving method merely, but should take one very important mathematics thinking method, it may expand students' problem solving mentality, sharpens their problem solving ability, takes the knowledge it to transform as ability “the bridge”目录
1.摘要 2
2.正文 2
2.1数形结合思想 2
2.1.1 “数形结合”思想的内涵 2
2.1.2“数形结合”思想的历史演进 3
2.2数形结合在教学中的应用 4
2.2.1解决集合问题 4
2.2.2解决函数问题 5
2.2.3解决方程与不等式的问题 7
2.2.4解决三角函数问题 10
2.2.5解决线性规划问题 11
2.2.6解决数列问题 12
2.2.7解决解析几何问题 13
2.3数形结合运用原则 14
2.3.1等价性原则 14
2.3.2双向性原则 14
2.3.3简单性原则 14
3.结束语 142.正文
2.1数形结合思想
2.1.1 “数形结合”思想的内涵
“数形结合”一词是在华罗庚先生于1964年1月撰写的科普小册子《谈谈与蜂房结构有关数学问题》中首次正式出现,书中有一首关于包含了“数形结合”的小词:“数与形,本是相倚依,焉能分作两边飞。数无形时少直觉,形少数时难入微。数形结合百般好,隔离分家万事非;切莫忘,几何代数统一体,永远联系,切莫分离!”