数学

Chapter Five shows the case study of the beauty of math in high school teaching. Conic section is taken as an example to unearth the beauty of mathematics in from the following three aspects: 1. the language beauty of conic section reveals the external formal beauty; 2. the methodological beauty and the logical beauty of conic section reflect the internal rational beauty; 3. the beauty of mathematics in conic section reveals the new value in internal knowledge structure of textbooks. Moreover, the application of the beauty of mathematics in high school math teaching is also discussed from the following four points of view: the pursuit of conciseness, the construction of symmetry, the utilization of unity and the discovery of uniqueness.

首先，以圆锥曲线教学为案例来挖掘中学数学教学中的数学美，具体从三个层次探讨①圆锥曲线语言之美，是数学美的外在形式美具体展现；②圆锥曲线方法美、逻辑美，是深层次数学美的内在理性美的反映；③在圆锥曲线的教学过程中，利用其数学美处理教材，揭示内在知识结构的新价值；其次，提出数学美在中学数学学习中的具体案例运用，并具体从追求简洁性、构造对称性、利用统一性和发现奇异性四个方面来举例探讨。

This thesis is based on understanding and analysis of educational theory of Freudenthal's thought of mathematics education. It does analytical and Practical research on mathematics teaching in kindergarten in an effort to provide the thought and approach for reference. The intention is to Promote the kids to study mathematics efficiently,to master it comprehensively and to use it properly. At the same time,it also offers some constructive suggestions to the present mathematics teaching reformation.

本文基于对弗赖登塔尔数学教育思想的认识和分析，对幼儿园数学教学开展分析和操作性研究，旨在为促进幼儿有效地学习数学、理解地掌握数学、恰当地运用数学的数学教学提供一个可借鉴的思路和途径，为当前数学教育改革提供一些建议性对策。

The article shows the importance of mathematics and has probed some reform for the mathematics teaching in high profession, and also elaborated the principle of "necessity and ede- quncy" for the teaching in education, which is to join up with the professional courses;paying at- tention to the ability of students for mathematical accomplishement and enduring study; empha- sizing the adaptability of fundament, interesting, ability and major with students; and also em- phasizing to merge the mathematical mod...

本文揭示了数学的重要性，对高职高专数学教学改革做了一些探讨，阐述了高职教育中，数学教学应以"必需、够用"为原则，与专业课紧密衔接；要注重培养学生的数学素养和可持续学习的能力；要注重学生的类比推理能力的培养；强调教学要与学生的基础相应，与学生的兴趣、能力、专业相适应；强调把数学建模的思想融入到教学中，以提高学生运用数学工具解决实际问题的能力。

This paper has proposed the following explanation for this topic based on Social Couplings by Maturana, a cognitive biology scholar, organic view by Cooley, a symbolic interactionist , and model of a system in equilibrium by Argyle, a social psychologist:(1) the interaction is an act sequence of "hint-choice";(2) All the teacher and students in mathematics classroom have contributed to the formation and modification of consensual domain;(3) consensual domain in mathematics classroom is not an independent reality;(4) teacher and students' perception to consensual domain in mathematics classroom shall guide their behavior;(5) The coupling standard of consensual domain is not fixed for all observers;(6) the effect of mathematics enculturation should be reinterpreted.

本文整合认知生物学学者Maturana的社会耦合理论、符号互动论学者Cooley的有机观，以及社会心理学者Argyle的均衡系统模型，对共识域之本质与功能提出下列解释作为回应：(1)数学教室内的互动是一「暗示—选择」的行为序列；(2)师生皆对数学教室系统共识域之成型与改变有所贡献；(3)数学教室系统内的共识域并非独立於观察者之客观实在；(4)师生个体对数学教室系统共识域的知觉会指引师生的个体行为；(5)观察者描述数学教室共识域的耦合标准有狭义与广义之分；(6)数学文化传承的必然性应予重新解读。

Based on these results, we bring forward some suggestions about mathematics teaching and mathematics learning. The teacher should treat the representation as an important activity when they teach the students how to solve the problems, encourage the students to use intuitionist graphic representation and teach the students to transfer among the different representations.

最后，基于上述研究结论，在数学教学和数学学习上提出以下建议：应将数学表征作为解题的一种重要活动，应该鼓励学生在解决问题乃至数学学习中运用图形表征，在数学教学中应该注重不同数学表征之间的相互转化，这是形成数学深度理解的一种有效途径。

Maths language is a kind of language formed by maths Symbol,maths terms and improved natural language proper use of artistic langrage in teaching can make the lesson move actire ,and can sublimate the teaching while we should observe the three sourles of teaching and teaching proless ,science,technique and art,and renew the way of study leading students into the holy palace of maths,let them catch the way of thinking about maths maturally, and frnally nurtured by the beauty of maths.

数学语言是一种由数学符号、数学术语和经过改进的自然语言组成的科学语言，在教学是恰当的运用艺术语言可以活跃课堂、升华教学。但是我们一定遵守教学和教育过程的三个源泉：科学，技巧，艺术，适当地用口诀法更新学习方法。把学生领进华美的数学殿堂，使学生自然而然地达到对数学思想方法的领悟，受到数学美的熏陶。

To reason with mathematical symbol language advances the innovative thinking.

通过数学符号语言展开联想，有利于数学形象思维的发展；正确运用数学符号语言，有利于数学抽象思维的发展；熟练运用数学符号语言推理，有利于数学创新思维的发展。

China has implemented new courses in a few years, the study of middle school teachers teaching and students studying math on the investigation at this stage Instructional Design Research expounded on the need from classroom teaching and learning theories analysis, to find guidance in the design of classroom teaching under the new curriculum theory and classroom teaching on the design analysis of the whole process; From the typical class (class mathematical concepts and mathematical theory classes and study complicated math classes, the study of mathematics learning courses, open learning mathematics classes, cooperative learning math lessons) teaching the practice of design study, initial design, this is my classroom teaching design in recent years the practice of summary, the results of this study reflect.

新课程在我国已实施好几年了，本研究通过对初中教师与学生数学教学情况的调查，阐述研究现阶段课堂教学设计的必要性；从课堂教学理论、学习理论的分析中，寻找指导新课程下课堂教学设计的理论，并就课堂教学设计的全过程进行剖析；从几种典型课(数学概念课、数学原理课、数学复习课、数学研究性学习课、数学开放探究课、数学合作学习课)的课堂教学设计的实践研究中，提出初步的设计思路，这既是本人近年来课堂教学设计的实践总结，也是本研究的成果体现。

How to improve self-controlling ability?The research findings show that it is especially important for students to enhance their subjective consciousness, and to have a right math idea, and to have opportunities of experiencing the real math activity process, and to master methods of math thinking, and improve the communication among members in"math learning community". It is the point of break-through to train students to have the consciousness and skills of self-testing, if we want to improve students'self-controlling ability.

本论文的研究结果显示，培养中学生的自主意识、使学生树立正确的数学观念、让他们有机会经历数学活动的真实过程、掌握数学思想方法、加强"数学学习共同体"成员间的相互交流是培养中学生数学学科自我监控能力的关键，培养学生对数学学习过程的自我检验意识和技能是培养中学生数学学科自我监控能力的突破口。

Moreover the thesis analyse specificness of the new system in details:The process of Mathematics learning strategies.The colony of Mathematics learning strategies.The activities of Mathematics learning strategies.The individuality of Mathematics learning strategies.The modernnization of Mathematics learning strategies.The new system of mathematics learning cant apart from the firm theory foundation.

本文在对《标准》的总体目标及学习目标进行分析的基础上，构建了《标准》指导下的新的数学学习策略的体系，并分析了新的数学学习策略所呈现出的新的特点：——数学学习策略的过程性；——数学学习策略的群体性；——数学学习策略的活动性；——数学学习策略的个体性；——数学学习策略的现代化；构建新的数学学习策略体系离不开坚实的理论基础。

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。