直觉思维在中学数学解题中的应用探析中英文对照.pdf

《直觉思维在中学数学解题中的应用探析中英文对照.pdf》由会员分享，可在线阅读，更多相关《直觉思维在中学数学解题中的应用探析中英文对照.pdf（4页珍藏版）》请在淘文阁 - 分享文档赚钱的网站上搜索。

1、关于直觉思维在中学数学解题中的应用的探析中英文对照About the intuition thinking in the middle school mathematicsproblem solving application analysis contrast in both Chineseand English数学直觉思维是人们在分析解决问题时快速动用自己所有经验和知识，在对对象作过总体上的观察分析之后，直接触及事物本质，作出假设，然后再对假设作出检验或证明的一种思维方法。它主要表现在对数学对象的敏锐洞察，从而直接猜断和总体把握在我们找到解答和证明之前，直觉先已帮助我们对结论或解题思路产生

2、预见然而，在目前中学数学教学中往往偏重于演绎推理的训练，强化形式论证的逻辑的严密性，忽视了直觉思维在解题中预知导向和顿悟作用，也失去了数学思维形成过程中直观生动的一面这在一定范围上限制了学生思维素质的提高，与现代素质教育要求背道而驰，所以在中学培养学生的直觉思维是中学数学教学的目标之一。Mathematics intuition thinking is the use of analysis to solve the problem,as in all his experienceand knowledge,in observation of the object made overall a

3、nalysis,directly touch the essence,make assumptions,and then the hypothesis is tested to make or prove a kind of thinking method.Itmainly displays in discerning to the mathematical objects,thereby directly to guess and overallgrasp,before we find solution and prove that intuition first has helped us

4、 to foresee,however,conclusion or their thinking in the current middle school mathematics teaching tends to layparticular stress on training of deductive reasoning,strengthening forms demonstrate logical rigor,ignored the intuition thinking in the problem solving unpredictable guidance and insight,h

5、as lostits intuitive and vivid in the process of mathematical thinking form side that in a certain extentlimit the improvement of the students thinking quality,run counter to the modern qualityeducation requirements,so the training of the students intuitive thinking in middle school is oneof the goa

6、ls of middle school mathematics teaching.1.联想和猜想。联想是由当前感知的事物回忆起有关另一事物的心理过程。在数学思维活动中，联想可以沟通数学对象和有关知识间的联系。而联想思维是人们在认识事物的过程中，根据事物之间的某种联系，由一事物联想到另一事物的心理过程。它是一种由此及彼的思维活动。联想思维在认识活动过程中起着桥梁和纽带的作用。对于一些未知的数学知识，通过已知知识和未知知识之间的联系，从而使一些有未知知识的数学问题得以解决。在数学的具体解题过程中，通过对题设中的条件、图形特征以及求解目标分析，从而联想到有关已知的定义、定理、法则等，最终找到解题的思

7、路和方法。本文将对在数学中运用的联想思维进行研究，包括其作用以及如何培养。1.Lenovo and guess.Lenovo is recalled by the current perception of things about thepsychological process of the other things.In mathematical thinking activities,lenovo cancommunicate mathematical relation between objects and the related knowledge.And associativet

8、hinking is in the process of recognizing things people,according to a link between things,by athings associated with the psychological process of the other things.It is a kind of send a thinkingactivity.Associative thinking in the process of cognitive activities play the role of a bridge andlink.For

9、 some unknown mathematical knowledge,through the connection between the known andunknown knowledge,so that some unknown knowledge to solve mathematical problems.Inmathematical problem solving process,based on the conditions of the problem set,graphics,analysis characteristics and target,to associate

10、 with the known definition,theorem,law and so on,finally found the ideas and methods to solve problems.This article will study of associativethinking used in mathematics,including its function and how to develop.爱因斯坦认为：科学研究真正可贵的因素是直觉思维，同样，数学解题中联想灵感迸发也离不开直觉思维。对问题在作全面的思考之后，不经详尽的推理步骤，直接触及对象的本质，迅速得出预感性判

11、断。可以说联想是灵感诱发而产生的。特别地，在一些若干问题往往无从下手，着不到边。这时就需由联想来产生解题灵感。使本来困难、受阻的题目，迎刃而解。Einstein thought:scientific research intuition thinking is really valuable factors,similarly,lenovoinspiration is also inseparable from the intuitive thinking in mathematical problemsolving.Theproblem after a comprehensive think

12、ing,not the detailed steps of reasoning,touches the essence ofthe object directly,quickly concluded a hunch sexual judgment.We can say that lenovo is inducedby inspiration.In particular,several problems in some often do not know how to start,with no side.At this time we have to by lenovo to generate

13、 inspiration to solve problems.Make originallydifficult,obstruction of the topic,solved.例 1：若 a，b，c，dR，且 a2+b2=1，c2+d2=1Case 1:if a,b,c,d R,and a2+b2=1,c2+d2=1求证：-1ac+bd1，sin2+cos2=1Verification:1 ac+bd 1 or less,or less sin2 alpha+cos2 alpha=1分析：联想 a=sin，b=cos，c=sin，d=cosAnalysis:lenovo a=sine beta

14、,b=cosine beta,c=sin gamma,d=cos gamma则可以令。You can make.从而从问题很容易得到解决。From the problems easily solved.通过以上的理论和例子我们发现，联想思维在具体的解题过程中，有着非常重要的作用。其思维方式不仅可以使很多数学题目,特别是着手较难的数学题目，可以通过这种思维形式得到轻而易举的解决。而这样的联想思维是在具体的学习过程中逐步培养起来的。而数学是一门有着与现实生活密切联系的学科。在日常的生活、工作以及学习中培养这种思维是无意识，也是潜意识。联想是产生直觉的先导。猜想则是直觉的结果，所谓直觉，信息加工的原

15、理来看，就是将零散、孤立的信息快速联系和重组，从中产生新的有价值信息，联系和重组的能力依赖于每个人的联想空间，因此不时地引导学生对面临的问题进行联想。Through the above theoretical and example we found that the associative thinking in specificproblem solving process,has a very important role.Its way of thinking can not only make manymath questions,especially to the difficul

16、t math problems,can be easily solved by this kind ofthinking form.This lenovo thinking is gradually cultivated in the specific learning process.Whilemathematics is an has a closely connection with real life subject.In daily life,work and studytraining this kind of thinking is the unconscious,is unco

17、nscious.Lenovo is the intuition of theguide.Guess is the result of intuition,intuition,the principle of information processing,will bescattered,isolated information fast contact and restructuring,which provides new valuableinformation,links and restructuring ability depends on each persons space of

18、lenovo,so from timeto time to guide students to lenovo are faced with the problem.O.K.吉霍米曾说过：在心理中，思维被看作解题活动虽然思维并不是总等于解题，但可以断言，形成最有效办法是通过解题来实现。而联想灵感是创造性思维中最富有创造性特征的重要组成部分，所以联想灵感在解题中有着不可低估的作用。再者，在中学数学的教学中对联想思维的培养是很重要的，中学数学教师在授课的同时要注重对这些思维的培养。O.k.,Mr M once said:in psychology,thinking while thinking is

19、 seen as a problem solving activityis not always equal to the problem solving,but can assert that the formation of the most effectiveway is through problem solving.While lenovo inspiration is the most creative features of creativethinking is an important part of,so lenovo inspiration having the effe

20、ct that cannot underestimatein the problem solving.Moreover,in the middle school mathematics teaching in the cultivation ofassociative thinking is very important to middle school mathematics teachers in teaching must payattention to training the thinking at the same time.2.经验和规律。数学直觉思维在解题中应用较多都是利用长期

21、积累经验和掌握的规律，它是一种理性直觉，虽然有时抛弃了常规的推理和论证，但它又有迹可寻，决非空穴来风有时又不受任何模式限制,思维空间的广度和深度较大较深，它就要我们具备丰富的经验和掌握常见数学规律、大胆的预测，探索解题的方向。下面再举个例子来继续探讨。2.The experience and regularity.Widely applied in the mathematical intuition thinking in problemsolving are using long-term accumulate experience and master of law,it is a ra

22、tional intuition,although sometimes abandoned conventional reasoning and argument,but it is,it is by no meansunfounded sometimes is not restricted by any mode,greater scope and depth of the deeperthinking space,it is we have rich experience and master the common mathematical laws,boldprediction and

23、exploration direction for problem solving.Another example below to continue.例 2：过抛物线y=ax2（）的焦点F 作一直线交抛物线于 P、Q 两点，若线段PF、FQ的长度分别是 p、q。则+=（）。Example 2:a parabolic y=ax2(a 0)line intersect the focus F of parabola in two points P and Q,if the length of the line segment,FQ PF,respectively,P and Q.S+s=().本

24、题是圆锥曲线中最典型的焦点弦问题，看似很难，其实只要看下答案，四个答案都是定值。经验告诉我们一个直觉：结论与直线的位置无关，所以只要取PQ 垂直 x 轴这一特殊情况就可以啦。通过这个例子，说明在解决数学题时，有时经验也是可以帮上忙的。当然，这个经验的获得可能需要经过大量的实践才能获得The focus of the subject is the most typical conic string problems,seems difficult,in fact as longas look at the answer,four answers are constant value.Experi

25、ence has taught us an intuition:conclusion has nothing to do with the location of the straight line,so as long as take the PQvertical x this special condition is ok.Through this example,when solving math problems,sometimes experience is also can help.And,of course,the experience acquired may need to getthrough a lot of practice