Furthermore, it can find a strong method: Therefore, we started from the definition, an experience: definition and other process, finally it can find out the effective method. (3)to further apply
Furthermore, it can find a strong method:
Therefore, we started from the definition, an experience: definition
and other process, finally it can find out the effective method.
(3)to further apply and explore the method
If,thenhas nothing to do with route in G,it only has something to do with the starting point and the ending point. Presume the starting point ofas M0(x0,y0), the ending point as M(x,y),then:
When the starting point M0(x0,y0)is fixed,then the value of this integration is decided by the ending point M(x,y),therefore, it is the function of x,y,toregard this function asu(x,y),therefore
u(x,y)=
function u(x,y)of the characteristic makes us think about that the definite integration of the function thathas integration upper limit:
Again due to the definition of the whole differential , we can know that: ……②
①Expression and ② expression form of the analogy further support our thought, further guess:
Below we conduct exploring to this guess:
Because
then
as to picture 3,because curve integration has nothing to do with the route, it can adopt the integration route as:
. Therefore, we has :
again on the line section MN,y is the constant . the above expression turns into:
Therefore
Therefore
the same is :
therefore, we can gain a new conclusion:
in G it is the certain function of the whole differentialu(x,y). and :
To apply the three principles of the mathematics to guide the developing of the exploring teaching, it requires the macro-thinking and design of the teaching content and try hard to explore the interior connection between different knowledge content and the mathematics realist of the students.Through review and reflect, observation abstract and guess the exploring, the students go along with the road of “problem—exploring –discovering” to study mathematics. From the culture view, it is also a mathematics aesthetics process as to the guiding of three principles of educational mathematics of the mathematics teaching, and the discovering journey of the way of the winding path leads to a secluded quiet place[6], the reason beauty, harmony beautyand the uniform beauty of the mathematicscan gain a deep digging and showing.
4. References
[1]Wangaiyun, xunyan.The higher mathematic curriculum construction and the teaching reformation research practice[J].Mathematic Educational Journal,2002,11(2):84—85
[2]Wangyuan, luobi. The discovering of the big law[J] Mathematics Education Journal,1995,4(2):55
[3]Zhangjingzhong.What is Educational Mathematics[J].Mathematics Teachers, 1989,2
[4]Jingzhong, Peisheng,From mathematic education to educational mathematics[M].SichuanEducationalPress,1989,7:202
[5]Kangwu. .to make mathematics become easier.[J]. Mathematic Educational Journal,1998,7(3):3
[6]Luer. Talking about the method of discovering teaching [J]. Mathematic Educational Journal,1996,5(4):96—98
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