期

：

2010

年

9

月

18

日

毕业论文写作日期：

2010

年

9

月

18

日至

2011

年

4

月

20

日

学生签字：

指导教师签字：

摘

要

数形结合思想即借助数的精确性阐 明图形的某种属性。

利用图形的直观性阐

明数与数之间的关系< /p>

,

这是沟通数形之间的联系、并通过这种联系产生感知或认

知、

形成数学概念或寻找解决数学问题途径的思维方式。

数形结合是解决数学问

题的一个有力工具，

也是中学 数学中极为重要的基本方法之一，

通过数形结合可

将抽象的数学 语言与直观图形相结合，

使抽象思维与形象思维相结合，

缩短了 思

维链，

简化了思维过程。

数形结合中 的数应广义地理解为解析式、

函数、

复数等

;

其中的形，可以是点集空间图形，进而使数形结合的思想方法焕发生机和活力，< /p>

使应用的范围不断拓宽和深化。因此

,

由 此可见，数形结合对发展学生由抽象到

直观

,

< br>再由直观到抽象的思维是非常重要。本文重点阐述了如何在具体的问题中

进行形与 数、

数与形的转化

,

以及在数学例题中 去培养学生数形结合的解题能力。

从而达到锻炼学生思维的灵活性与广泛性，提高学生解 决问题的能力。

关键词

：

数形结合；

参数方程；

复数；

不等式

Abstract

The Combination of thinking that help to clarify the accuracy of a few graphics

as an attribute. Clarify the use of intuitive graphical relationship between the number

and

the

number,

which

is

the

number

of

communication

links

between

form

and

produced

through

this

link

or

cognitive

perception,

the

formation

of

mathematical

concepts

to

solve

mathematical

problems

or

to

find

ways

of

thinking.

The

Combination

of

mathematical

problems

to

solve

a

powerful

tool,

is

also

extremely

important

in

middle

school

mathematics

one

of

the

basic

methods,

by

The

Combination of mathematical language can be abstract and intuitive graphics combine

to

make

the

abstract

thinking

and

thinking

in

images

combine

to

shorten

the

the

thought chain, simplifying the process of thinking. The Combination of the number

should

be

broadly

understood

as

analytic,

functions,

complex

numbers, etc.;

one

of

the

form,

can

be

a

point

of

space

graphics,

and

then

radiate

the

way

of

thinking

Shuxingjiege vigor and vitality, so that applications continue to broaden the scope and

deepened. Therefore, we can see, The Combination of students

from the abstract to

the

development

of

intuitive,

then

to

the

abstract

visual

thinking

is

very

important.

This

article

focuses

on

how

specific

issues

in

the

shape

and

number,

number

and

shape

of

the

transformation,

and

examples

in

mathematics

to

students

in

problem-solving ability Shuxingjiege. Training students to achieve the flexibility and

breadth of thinking to improve their ability to solve problems.

Keywords

: the Combination of Math-image;

parameter-equation;

complex number;

inequality;

目

录

第一章

绪论

„„„„„„„„„„„„ „„„„„„„„„„„„„„„

6

第二章

浅析数形结合在中学数学解题中的应用

„„„„„„„„„„„„„

8

2.1

以形助数

„„„„„„„„„„„„„„„„„„„„„„

8

2.2

以数助形

„„„„„„„„„„„„„„„„„„„„„„

9

2.3

“数”

、

“形”结合

„„„„„„„„„„„„„„„„„„

11

总结及进一步工作

„„„„„ „„„„„„„„„„„„„„„„„„

13

参考文献

„„„„„„„„„„„„ „„„„„„„„„„„„„„„„„

15

致谢

„„„„„„„„„„„„„„ „„„„„„„„„„„„„„„„„

16

第一章

绪

论

随着社会的发展

< br>,

教学研究的重心已由过去的偏重内容

,

转向于传授知识和

能力并重的研究。强调人的潜能开发

,

心理品质培养和社会文化素质的训练。在

全面提高全体学生的 基本素质的基础上

,

使各种能力在学生身上得到不同程度的

协调发展。

作为教育者必须自觉地、

科学地 、

有针对地培养出适合新时代需求的

人才

[3]

。就数学而言

,

我们又应该如 何做到实现素质教育呢

?

数学是研究现实世界中的数量关系和 空间形式的科学。

“数”和“形”是数

学中最基本的两个概念。 数量关系借用了图形的性质

,

可以使许多抽象的概念