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Powered by跪求一篇有中英文的数学类文章2000字左右!本人要翻译一篇数学类小论文,特别是国外著名数学家的公式定理之类的翻译.要有中英文哈,只要是能用的就加给50分!
发现法与小学数学教学近年来,有些教师在小学数学课试验用发现法进行教学,这是小学数学教法改革的一项新的尝试.随着教法改革的深入,不少教师提出这样的问题：什么是发现法?在小学数学教学中如何运用发现法?作为一种教学方法,必须具有某些独有的特征,能与其他教学方法相区别.为了便于教师进行研究,现根据所了解的一些材料,对发现法的特点及其在小学数学教学中的运用做一简单介绍,以供参考. 一 发现法的特点
发现法是近二十多年来国外倡导的一种教学方法,也有人称为探究问题法.五十年代末六十年代初,根据科学技术的迅猛发展和培养人才的需要,国外在提出改革传统教材的同时,相应地要求改革传统的教学方法.有些心理学家和教育工作者倡导“发现”的学习方法,强调要让学生自己发现和创造知识.例如,瑞士心理学家皮亚杰就提出：“要引导儿童去重新发明他们能够发明的事物.”美国心理学家布鲁纳更完整地提出发现学习的理论.他强调,学习是发现知识、理解一个学科的基本认识结构、运用直观和分析推理以及依靠内在动机的过程.他认为,“发现不限于寻求人类尚未知晓的事物,确切地说,它包括用自己的头脑亲自获得知识的一切方式.”因此,他提倡在教学中广泛运用发现法.
倡导者们认为发现学习的优点主要是：1.发挥学生主动性和创造性,发展他们的智力；2.可以较深地理解知识,并且较好地保持在记忆中；3.使学生更容易迁移,并且提高学习和研究较难的教材和问题的兴趣和信心；4.学生获得探究知识的技能,从而提高学生独立学习的能力.
运用发现法的一般步骤如下：1.创设问题的情境,提出要解决的问题；2.拟出解决问题的方法和途径,收集资料；3.提出假设；4.检验假设；5.总结,做出共同的结论.
可以看出,发现法教学的过程与科学家发现新知识的过程基本上是一致的.照布鲁纳所说,两者属于同一类的活动,差别仅在程度而不在性质.
纯发现法的教学,自始至终强调儿童自己独立进行活动.这种方法,国外的学前教育工作者运用得多一些,在学校教育中也有运用.但是,纯发现法存在较大的缺点,它只适用于介绍新教材,有时儿童有困难,不能保证达到预期的目的和获得系统完整的知识.因此有人（如美国的柯尔士）提出引导发现法,即在拟定解决问题的途径或提出假设时,教师可以适当予以提示和帮助.这样,学生做起来比较容易,可以有效地控制学生的学习活动,并保证达到预期的目的.二 发现法在小学数学教学中的运用
自从倡导发现法以来,在国外的小学数学教学中有一些教师运用了发现法,但不普遍.最早在六十年代初,布鲁纳曾和美国数学家狄因斯合作,研究试用发现法教小学数学.他曾在小学三年级试用发现法引导儿童根据正方形的边长求面积,发现（x+ 1）（x＋1）=x2+2x+1.以后一些数学教学法研究人员在这方面做了不少的研究.现在从国外书籍中选几个例子来说明.
例1：一位数除两位数的教学.
给出一道题如39÷3.学生可以先拿39个物品,每3个一份,把它们分成13份.做几个这样的题目以后,可以让他们把物品组成10个一组.例如,给出这样一道题：“哈利买了4条糖果,每条有10块.他吃了1块,把剩下的每3块包成一包,分给同学,分给了几个同学?”
学生可能有以下几种解法：
1.每3个分成一堆,然后数出分得的堆数；
2.从三个10中各先拿出1个,剩下的每9个分给3个同学,再把其余的也每3个分成一堆.
3.与2.相似,但他们看出有4个9.
4.他们看出3个10正好分给10个人,剩下的每3个分成一组.
5.与4.相似,但他们看出剩下的9个正好够分给3个人.
在学生得出解法之后,全班进行讨论.教师对不同的算法不给出评价.再出一道题,许多学生会选用比他第一次用的更为简便的方法.进一步教师提出引导性问题,促使学生找出更为有效的计算方法,形成一般的竖式计算.
例2：乘法分配律的教学.
给出一道一个数乘以和的应用题,例如：“有3个男孩和4个女孩,分给每人2块饼干,一共需要多少块饼干?”让各小组研究这道题可能有几种方法.学生想出下面的解法：
每人的块数×（男孩数+女孩数）=2×（3＋4）,（每人的块数×男孩数）＋（每人的块数×女孩数）=（2×3）＋（2×4）.
还可以用长方形阵列的方法（即按照已知数画几行点子,再导出算式）.每个小组可以自己设数,排成大小不同的阵列.让学生写出积,然后在其中某两行之间或某两列之间折叠一下,把阵列分成两部分,重新写出算式,求出积来.以4×7为例,可以写成如下的形式：开始先让学生各拿一张正方形纸,沿对角线折叠,发现每个三角形的三个角是由一个直角和两个半个直角组成的.随后让学生拿一张长方形纸,沿对角线剪开,再试试能不能发现每个三角形的内角和是多少.有的学生很快发现三角形内角和等于2个直角,因为一个长方形有4个直角,而剪成的两个三角形是完全相等的.
教师还收集了一些等边三角形容器.儿童发现可以把6个这样的容器拼成一个新的图形.而且可以把三个拼在一起立在桌子上（右图）.这说明每个角（根据已学的图形的对称很快发现等边三角形的三个角相等）等于2个直角的三分之一.这再一次说明三角形的内角和等于2个直角.然后教师向学生提问,能不能发现任意三角形的内角和是多少.教师建议学生各画几个不同的三角形,给每个角标上号.有的学生折叠三个角,使它们对在一起；有的学生撕开三个角,把它们拼在一起.他们发现拼成的角的边形成一条直线.有些学生试图发现三角形的内角和是否有不等于2个直角的.
最后教师建议,在一个球面上画一个三角形.学生很高兴地发现,在球面上画的三角形有些内角和是2个直角,还有一些却大于2个直角.
从上面的几个例子可以看出,在小学数学教学中运用发现法,基本上符合前面介绍的几个步骤.几个例子突出的共同点是激发儿童动脑筋想办法发现规律.解决问题；不同的是,有的教师引导多一些,有的教师引导少一些.三 对发现法的评价
自发现法问世以来,国外对这种方法有各种各样的评价.除了象前面介绍的发现法的倡导者所指出的一些优点以外,也有不少人提出意见.
有些人对发现法持反对的态度.例如,美国心理学家加涅不相信只要使学生掌握思考方法,就可以培养起能力.他强调教学要使学生掌握大量有组织的知识,教师要给以充分指导,使学生按照规定的程序进行学习.美国另一心理学家奥苏博则认为,大多数学习应当是学生主动解决问题,但必须由教师建立一个系统的序列和方式.他认为听讲也可以是一个智力上主动的过程,而在探究的情境中学生也可能是被动的.
也有人认为发现法有它的适用范围,不能作为唯一的一种教学方法.苏联教学法专家巴班斯基曾指出,这种方法花的教学时间多,在培养一些不复杂的技能技巧时作用是不大的.美国的小学数学教学法研究工作者恩德希尔认为,在教学新概念和一般概括性知识时可以用这种方法,而关于概念的名称、符号表示法仍需要教师予以讲解,而且在发现新知识以后,还要适当地通过讲解法复述概念,指出它的属性,以及计算方法的一些细节（如进位加法要说明竖式具体怎样加,注意哪些事项）等.日本福冈大学秋山俊夫根据日本的试验,认为发现法对于具体运思阶段后期至形式运思阶段前期的学生（十岁左右——十二岁左右）比较有效,但也认为要花费时间和劳力.
结合我国具体情况如何在小学数学教学中运用发现法,还没有完整的经验,有待于进一步试验研究.Discovery method of teaching primary maths In recent years, some teachers at the primary school math class discovery method used in the experiments for teaching and learning, this is the reform of primary school maths teaching a new attempt. With the deepening of reform teaching, many teachers make such a question: What is discovery? At primary school maths teaching how to use discovery method? As a teaching method, must have certain unique characteristics, can be differentiated from other teaching methods. Teachers in order to facilitate the research, now know the basis of some materials, the characteristics of the discovery method and its application in Primary Mathematics Teaching introduce easy to do one for reference. One of the characteristics found in the Law Discovery method is advocated over the past two decades abroad as a teaching method, it was also known as the law into question. At the end of the fifties and early sixties, in accordance with the rapid development of science and technology and personnel training necessary, to propose reforms in the traditional foreign materials simultaneously, corresponding to the requirements of reform and traditional teaching methods. Some psychologists and educators to advocate for "discovery" of the study methods, emphasis should allow students to discover and create their own knowledge. For example, the Swiss psychologist Jean Piaget put forward: "To guide the children to re-invent them to be able to invent things." American psychologist Bruner put forward a more complete theoretical study found. He stressed that the study is to discover the knowledge, understanding a basic understanding of the structure of disciplines, the use of intuitive and analytical reasoning as well as to rely on intrinsic motivation process. He believes that "discovery is not limited to human beings to seek things not yet known, precisely, it includes the minds of their own personal access to knowledge, all the way." Therefore, he advocated the teaching of the extensive use of discovery method. Advocates consider the merits of the main study found are: 1. To play a student initiative and creativity, their inte 2. To understand the deeper knowledge and better
3. To enable students to more easily migrate and improve study and research materials and more difficult questions of int 4. students to explore knowledge, skills, thereby enhancing the ability of students in independent study. Discovery method to use the general steps are as follows: 1. The creation of problem situations, the
2. To be a solution to the problem and ways to 3. M 4. T 5. Summing up, to do a common conclusion. We can see that the discovery method of teaching the course with new knowledge, scientists have discovered the process is basically the same. According to Bruner said, the two activities belong to the same category, the difference is only in nature and not at the level of. Pure discovery method of teaching, emphasis throughout the child's own independent activities. In this way, the use of foreign workers than some pre-school education, in school education also have to use. However, the net found that there is a big disadvantage Act, it applies only to introduce new materials, and sometimes have difficult children, can not guarantee to achieve the desired purpose and to obtain complete knowledge of the system. So someone (such as the United States of Coles) to guide the discovery method, namely, in the preparation of a solution to the problem or make the assumption that when teachers can be prompt and appropriate help. In this way, students make up more easily, you can effectively control the learning activities of students and to ensure that the desired objective. II found in Primary Mathematics Teaching Since the discovery method advocated since the primary school math teaching abroad in some of the teachers have used the discovery method, but not universal. The earliest at the beginning of the sixties, Bruner had狄因斯American mathematician to study law trial found that primary schools teach math. He has worked in primary schools found that three-year probation law to guide the child in accordance with a square of side length for the area and found that (x + 1) (x +1) = x2 +2 x +1. After some math pedagogy researchers in this area to do a lot of research. Selected books from abroad are now a few examples to illustrate. Example 1: A two-digit number in addition to teaching. Give a problem such as 39 ÷ 3. Students can先拿39 items, each a three, put them into 13. Make several of these topics later, you can allow them to put items comprising a group of 10. For example, give this a problem: "Harry bought four candy, and each has 10. He ate one, put the remaining 3 per package into one package, distributed to the students, points to a few classmates ? " Students may have the following method: 1. Every 3 months into a pile, then the share of th 2. 10 from three out of the first one, the remaining nine points each to three classmates, and then the rest of it into a pile of every 3 months.
3. And 2. Similar to, but they have seen 4 9.
4. They could see just 10 minutes three to 10 individuals, each of the remaining three are divided into one group.
5. And 4. Similar, but they could see the remaining nine minutes just enough to give personal 3.
After students arrive at solutions, the entire class for discussion. Teachers do not give a different algorithm evaluation. Together with another title, many students choose more than he first used a more simple approach. Further questions guiding teachers to students to find more effective methods of calculation of the vertical formation of the general computing. Example 2: Multiplication分配律teaching. Together give a few times and the application of title, such as: "Have three boys and four girls, to the two cookies per person, a total number of required block cookies?" Let each group may have several这道题Ways. Students come up with the following method: Each block a few × (number of boys a few + Girl) = 2 × (3 +4), (each block a few × few boys) + (each block a few girls a few ×) = (2 × 3) + (2 × 4). Can also use a rectangular array of methods (that is, draw a few lines in accordance with the已知数ideas, and then export the formula). Each group can set the number of line array of different sizes. Allow students to write the plot, then at a certain one of two lines or between a fold between the two click, put the array into two parts, re-write a formula to derive the plot. To 4 × 7 as an example, the form can be written as follows: Started to let students get a square of paper, folded along the diagonal and found that each of the three angle triangles are from a right angle and two composed of half a right angle. Then allow students to take a rectangle of paper, cut along the diagonal, then should not try to find the angles of each triangle and how much. Some students quickly discovered the triangle equal angles and two right-angle, because a rectangle has four right angles, and cut the two triangles are completely equivalent. Teacher has collected a number of containers an equilateral triangle. Children found to put six such containers up a new graphics. But can also put the three together with legislation on the table (right). This shows that each corner (according to the study of symmetric graphics quickly discovered an equilateral triangle of three equal angle) is equal to two right angles to one-third. This shows, once again the triangle equal angles and two right angles. And teachers to students to ask questions, can be found in any triangle are the angle and how much. Teachers recommended students draw several different triangles, each corner give up its subscript. Some students folded three Kok, Some students torn three angle, put them together to fight. They found that the angular form themselves into the number of edges to form a straight line. Some students try to find angles and whether the triangle is not equal to have the two right-angle. Finally, teachers suggested that a spherical surface draw a triangle. Students are very pleased to find that in the sphere draw some angles and the triangle are two right angles, and some are larger than two right angles. From the above few examples we can see that maths teaching in primary schools found that the use of law, basically in line with the introduction of a few steps ahead. A few examples to highlight the common ground is to stimulate children's brains to find ways to discover the laws. Problem- are different, and some teachers to guide a little more, some less teacher guidance. 3 pairs of discovery method evaluation Since self-discovery method, foreign on this method has various evaluations. As described above except the discovery of law advocates have pointed out a number of benefits, also has a lot of people comment. Some people found that opposition to the attitude of law. For example, the United States do not believe that as long as Gagne psychologists help students consider ways to be able to develop a capacity. Him to emphasize teaching students to master a large number of organized knowledge, teachers should be given full guidance to students in accordance with the study procedures. Another American psychologist奥苏博that the majority of students are studying should take the initiative to solve the problem, but it must be a system set up by teachers of the sequence and manner. Attendance can also consider him an intellectual on the initiative process, while at secondary school students explore the contexts may also be passive. It was also suggested that the Law has found its scope of application, can not be used as a sole teaching method. Soviet pedagogy Babanski experts have pointed out that this method of teaching time to spend many, in the development of some skills when complex skills are modest role. The United States of maths teaching in primary schools恩德希尔research workers think, in teaching new concepts and general all-embracing knowledge can use this method, and about the concept of the name, symbols, said method is still required to be on teachers, but also in discovering new knowledge after, but also properly explain the law through the concept of repeat, pointing out that its property, as well as some details of calculation methods (such as binary adder to explain how to increase vertical specific and pay attention to what matters) and so on. University in Fukuoka, Japan, Toshio Akiyama Japanese pilot that discovered the specific delivery method for thinking at an advanced stage to form the early stages of Thinking students (aged around - around the age of twelve) are more effective, but also want to consider spending time and effort. How to combine the specific circumstances of our country at maths teaching in primary schools found that law, not yet complete experience, need to be further studied.
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电影一个勺子将于11.20日全国首映。首映前，16日将会有一个与众不同的“超前点映”。你想成为全国首批观看电影的观众吗？快去一个勺子官方贴吧发贴晒出你经历过的勺（傻）人勺（傻）事。分享精彩的朋友将会得到我们的观影名额哦！名额有限，先”勺“先得！
点亮12星座印记,
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前排！　　　——【来自跳了小苹果装用客户端～】
前排混眼熟
继续留名！　　　——【来自跳了小苹果装用客户端～】
继续插　　　——【来自跳了小苹果装用客户端～】
前排！我喵的就是不要小尾巴，有本事来咬我啊，汪汪……　　　--来自萌出一脸血客户端
求个妹子！　　　——【来自跳了小苹果装用客户端～】
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