数学

Abridgement ）:Mathematics Olympiad entitled to carriers, a mathematical way of thinking on the meaning: mathematical thinking is to understand the nature of mathematical knowledge, from some of the specific content of mathematics and mathematical understanding of the excessive rise in refining a mathematical point of view, is a mathematics knowledge Structure of the essence and soul of the commander in chief and it played the dominant role of mathematical knowledge.

以数学竞赛题为载体，阐述了数学思想方法的涵义：数学思想就是对数学知识的本质认识，是从某些具体的数学内容和对数学的认识过重中提炼上升的数学观点，是数学知识结构的精髓和灵魂，它起到统帅和支配数学知识的作用。

Chapter 4, lists the teaching cases in teacher's teaching, combined the cases dissecting the teaching methods of mathematics and mathematical cerebration and methods in the point of view of psychology, then infers that to proceed the teaching of mathematical cerebration and methods is necessary. In the other hand, I compared and studied the association between the basic mathematical cerebration and methods and other mathematical knowledge, answer the questions that which mathematical cerebration and methods are more worthy to jut out. At last, infers a mode of the teaching in mathematical cerebration and methods.

第四章列举了教师在授课中的教学案例，结合案例从心理学角度对中学数学教学与数学思想方法教学进行剖析，得出进行数学思想方法教学是十分必要的；同时对中学数学教学中的数学基本思想方法与其它数学知识的关系进行了对比分析，对在中学数学教学中突出哪些数学基本思想方法为好做了解答；最后给出了数学思想方法教学的一个教学模式。

Mathematical legacy 数学遗产 Descartes' theory provided the basis for the calculus of Newton and Leibniz, by applying infinitesimal calculus to the tangent line problem, thus permitting the evolution of that branch of modern mathematics.

通过对切线问题的极限计算，笛卡尔为牛顿和莱布尼茨的微积分奠定了基础，所以使得这一近代数学分支的发展成为可能。

Therefore, in mathematics teaching, we should proceed mathematics teaching needs, students from the life experience, practical life, to dig the life meaning of mathematical knowledge, to capture the phenomenon of life in mathematics, reflect the "math from life, resides in life, with in life ", so that students understand the math on your side, and thus realized that the charm of math, feel the fun of math and realize that everyone learn valuable math, everyone can get the necessary math, different people in mathematics get different levels of development.

因此，在数学教学中，我们应从数学教学的需求出发，让学生从生活经验、生活实际中去挖掘数学知识的生活内涵、捕捉生活中的数学现象，体现"数学源于生活、寓于生活、用于生活"，使学生体会到数学就在身边，从而领悟到数学的魅力、感受到数学的乐趣，实现"人人学有价值的数学，人人都能获得必需的数学，不同的人在数学上得到不同的发展"。

The new curriculum emphasizes mathematics and the real life relation, but also proposed specially mathematics teaching is mathematics activity teaching, is also lets the student career mathematization process the activity, lets the student embark from own mathematics reality, catches mathematics question with mathematics judgment in the life, utilizes mathematics knowledge analysis life phenomenon on own initiative, thus solves the actual problem which independently in the life meets.

新课程强调数学与现实生活的联系，还特别提出了数学教学是数学活动的教学，也就是让学生经历数学化过程的活动，让学生从自己的数学现实出发，用数学的眼光在生活中捕捉数学问题，主动地运用数学知识分析生活现象，从而自主地解决生活中所遇到的实际问题。

For preparing for the researches of text digital watermarking and advantaging other researchers" development when using the Chinese mathematical expression theory, this paper designs and realizes a development platform of Chinese mathematical expression. It has been proved by experiments that the platform"s function, execution speed and stability can satisfy the requirements of conversion and operation of enormous data.This research found out that the structure information of Chinese have plenty redundant information that can be used by the Chinese mathematical expression for the digital watermarking, the data embedded can possess better robustness. Based on this finding, this paper designs a kind of text digital watermarking method of embedding watermarking by using Chinese structure, and realizes the method by using the Chinese mathematical expression platform.Considering the watermarking embedding algorithms importance to the robustness of the text digital watermarking, this paper makes fully use of the advantage of the Chinese mathematical expression theory to design a kind of layered text method, which has being realized by using the Chinese mathematical expression platform. The layered text method can handle the text as a solid structure, and the embedding data havepreferable robustness.Finally, based on the researches of the text digital watermarking method and the text layered method, this paper integrates the method of making use of the Chinese structure embedding watermarking with the robust algorithm based on text layered, and realizes a brand-new text digital watermarking method. Proved by lots of experiments, this brand-new method has good robustness and better invisibility.

为了为研究工作做准备和方便其他使用汉字数学表达式理论体系的人进行开发，本文基于汉字数学表达式理论设计实现了一个汉字数学表达式平台，实现了Unicode汉字集中的汉字、汉字数学表达式、汉字的Unicode码之间的相互转化、依据汉字数学表达式提取汉字的结构信息、由汉字数学表达式在非中文平台上不依赖字库显示汉字的图像等功能，使用复合文档技术和流压缩技术进行数据的存储，使用对汉字数学表达式进行二叉树拆分来处理汉字数学表达式中包含的信息，使用自定义哈希函数来提高运行速度，实验证明，该平台功能、速度和稳定性完全能满足大量数据的转化和运算要求；通过研究表明汉字的结构信息中存在大量可使用汉字数学表达式理论加以利用的水印加载空间，加载在该空间的数据可以具有较好的鲁棒性，基于此，本文设计了一种利用汉字结构加载水印的文本数字水印方法，并使用汉字数学表达式平台将其实现；由于水印嵌入算法对于文本数字水印的鲁棒性至关重要，本文充分利用汉字数学表达式理论的优点，设计了一种文本分层的方法，并使用汉字数学表达式平台将其实现，使文本成为一个立体的空间，使嵌入在其中的数据具有更好的鲁棒性；最后在基于汉字数学表达式的文本数字水印嵌入方法的研究和基于汉字数学表达式的文本分层方法的研究的基础上，结合利用汉字结构嵌入水印的方法和基于文本分层的抗攻击文本水印嵌入算法实现了一种全新的文本数字水印方法，经实验证明，该方法有良好的鲁棒性和较好的隐蔽性。

The study shows that generally the mathematics view of normal university students majoring in mathematics is right, they depict mathematics learning as a dynamical process. Besides some special traits belong to mathematics, estimation, measurement and decision making themselves are also in the math field; however there are still some people warp the mathematics view, believe that mathematics is an apodeictic collection. Haven't realized the power that mathematics can improve people's taste ability and perfect people's personality, they believe that math learning is a passive process during which students receive acknowledge. What is more, there are different believes existing in the understanding of mathematics essence, mathematics value and mathematics learning. These believes vary with different university students from different grades and genders.

研究数据表明，高等师范院校数学系大学生的数学观总体上来说还是比较正确的，认为数学学习是一个动态的过程，认为数学在社会生活当中有一定的作用，并且认为做数学除了有特定的内容以外，估算、测量及决定本身也为做数学；但仍有一小部分人的数学观还存在着偏差，认为数学是一堆绝对真理的总集，对数学能够培养人的审美能力以及数学能完善人的个性等较高层次的价值没有意识到，认为数学问题仅是与教材内容相关的习题和考试中的试题，并且对数学学习不感兴趣，认为数学学习是学生被动接受知识的过程，并且不同年级以及不同性别的大学生在对数学本质、数学价值以及数学学习的认识上都存在着差异。

The study shows that generally the mathematics view of normal university studentsmajoring in mathematics is right, they depict mathematics learning as a dynamical process.Besides some special traits belong to mathematics, estimation, measurement and decisionmaking themselves are also in the math field;however there are still some people warp themathematics view, believe that mathematics is an apodeictic collection. Haven\'t realized thepower that mathematics can improve people\'s taste ability and perfect people\'s personality,they believe that math learning is a passive process during which students receiveacknowledge. What is more, there are different believes existing in the understanding ofmathematics essence, mathematics value and mathematics learning.

研究数据表明，高等师范院校数学系大学生的数学观总体上来说还是比较正确的，认为数学学习是一个动态的过程，认为数学在社会生活当中有一定的作用，并且认为做数学除了有特定的内容以外，估算、测量及决定本身也为做数学；但仍有一小部分人的数学观还存在着(来源：Ad4BC论文网www.abclunwen.com)偏差，认为数学是一堆绝对真理的总集，对数学能够培养人的审美能力以及数学能完善人的个性等较高层次的价值没有意识到，认为数学问题仅是与教材内容相关的习题和考试中的试题，并且对数学学习不感兴趣，认为数学学习是学生被动接受知识的过程，并且不同年级以及不同性别的大学生在对数学本质、数学价值以及数学学习的认识上都存在着差异。

The study shows that generally the mathematics view of normal university studentsmajoring in mathematics is right, they depict mathematics learning as a dynamical process.Besides some special traits belong to mathematics, estimation, measurement and decisionmaking themselves are also in the math field;however there are still some people warp themathematics view, believe that mathematics is an apodeictic collection. Haven"t realized thepower that mathematics can improve people"s taste ability and perfect peoples personality,they believe that math learning is a passive process during which students receiveacknowledge. What is more, there are different believes existing in the understanding ofmathematics essence, mathematics value and mathematics learning. These believes vary withdifferent university students from different grades and genders.

研究数据表明，高等师范院校数学系大学生的数学观总体上来说还是比较正确的，认为数学学习是一个动态的过程，认为数学在社会生活当中有一定的作用，并且认为做数学除了有特定的内容以外，估算、测量及决定本身也为做数学；但仍有一小部分人的数学观还存在着偏差，认为数学是一堆绝对真理的总集，对数学能够培养人的审美能力以及数学能完善人的个性等较高层次的价值没有意识到，认为数学问题仅是与教材内容相关的习题和考试中的试题，并且对数学学习不感兴趣，认为数学学习是学生被动接受知识的过程，并且不同年级以及不同性别的大学生在对数学本质、数学价值以及数学学习的认识上都存在着差异。

The new mathematics curriculum yells mathematics teachers change traditional teachers" roles to nowadays teachers" roles. By analyzing the abuse of the traditional teachers roles and the requests about mathematics teachers which the new mathematics curriculum puts forward, we discover that from the lay of curriculum , mathematics teachers should actualize three facets changes as follows:from the single initiators of mathematics knowledge to the promoters of mathematics diathesis;(2)from the loyal executors of mathematics textbook to the devisers of mathematics instruction;(3)from the indoctrinators of mathematics knowledge to the organizers, guiders and participators of mathematics activity .

数学新课程呼唤数学教师由传统的教师角色向现代教师角色转变，通过分析传统数学教师角色的弊端及新课程对数学教师提出的要求，发现从课堂层面讲，数学教师角色主要要实现以下3方面的转变：(1)由单一的数学知识传授者向数学素质的促进者转变；(2)由教科书的忠实执行者向数学教学的设计者转变；(3)由数学知识的灌输者向数学活动的组织者、引导者和合作者转变。

Singer Leona Lewis and former Led Zeppelin guitarist Jimmy Page emerged as the bus transformed into a grass-covered carnival float, and the pair combined for a rendition of "Whole Lotta Love".

歌手leona刘易斯和前率领的飞艇的吉他手吉米页出现巴士转化为基层所涵盖的嘉年华花车，和一双合并为一移交&整个lotta爱&。

This is Kate, and that's Erin.

这是凯特，那个是爱朗。