运用平面向量巧证不等式

平面向量引入高中课本以后,人们越来越体会到它的实用意义,它可以广泛地和其他知识联系在一起．如向量与函数;向量与三角;向量与圆锥曲线;向量与不等式等．本文仅以课本中的题目为主要实例,展示向量在不等式证明中的应用．     

三角形“四心”的向量式充要条件及其应用

2006年数学高考大纲中明确指出:要加强平面向量在平面几何中的应用.纵观近几年的高考题,我们已经体会到这种命题思想的变化.在平面向量在平面几何中的应用问题中,又以涉及三角形“四心”的试题为热点.由于三角形的“四心”与向量之间有着紧密的联系,这就为运用向量法解决这类“     

平面法向量在立体几何中的初步应用

《全日制普通高级中学教科书(试验修订本·必修)·数学》第二册(下B)中仅给出了平面法向量的定义,法向量的应用在教材中没有做进一步拓展。笔者认为,法向量是值得我们挖掘的一个问题,在求点到平面的距离,直线与平面所成角以及二面角时,如果能以平面法向量为载体,往往可以收到化难为易的效果,而且还可以使整个解题过程转化为程序化的向量运算,简捷方便,能减轻学生空间想象之困难。本文就平面法向量在立体几何中的初步应用谈一点体会。     

“平面向量”的教学体会

平面向量是中学数学中的重要内容。结合教学实践总结了平面向量教学中的三点体会。     

三角形“四心”的向量式充要条件及其应用

2006年数学高考大纲中明确指出：要加强平面向量在平面几何中的应用，纵观近几年的高考题。我们已经体会到这种命题思想的变化，在平面向量在平面几何中的应用问题中．又以涉及三角形“四心”的试题为热点．由于三角形的“四心”与向量之间有着紧密的联系．这就为运用向量法解决这类“心”题提供了可能性。预计2006年的高考还要加大对向量与三角形“心”的交汇问题的考查力度．对此，笔者给出三角形“四心”的向量式充要条件．并结合部分高考题．说明这些充要条件的应用。[编者按]     

平面向量的数量积

平面向量是高中数学的基本知识之一,而平面向量的数量积及平面向量的应用,则是其重点内容,下面我们重点讲解这部分知识,力求在该处有所突破,从而轻松拿下平面向量的数量积及平面向量的应用的有关问题.重点难点1.向量的夹角:已知两个非零向量a与b,作(?)=a,(?)=b,则∠AOB=θ(0°≤θ≤180°)叫做a与b的夹角,记作〈a,b〉.     

向量为媒一线牵

共线定理是平面向量的核心内容,初学者往往只知其表面应用,而不能深入分析其实质,导致应用上的肤浅和运算上的繁杂.本文通过几组不同背景的例子说明它们内在的联系和统一性,体会向量共线定理的作用和实质.     

平面向量基本定理的应用

作为现代数学的重要标志之一的平面向量引入中学数学后,给中学数学带来无限生机。由于向量融数、形于一体,具有几何形式与代数形式的“双重身份”,因此向量的引入大大拓宽了解题的思路与方法,平面向量基本定理是平面向量中的重要定理,是解决平面向量计算问题的重要工具．下面谈谈平面向量基本定理在几个方面的应用：     

浅谈对高中数学平面向量的认识

<正>在高中数学教学中,向量的相关知识是一项重点内容,也是江苏数学高考的主要考查内容之一.其中平面向量的数量积是C级考点;平面向量的概念,平面向量的加法、减法及数乘运算,平面向量的坐标运算,平面向量的平行与垂直都是B级考点;平面向量的应用是A级考点.近年来,高考中关于向量考查着     

平面向量、解三角形

本专题包括平面向量和解三角形两大部分,其中平面向量主要包括向量的概念与运算、平面向量基本定理及其坐标表示、向量的数量积(模与夹角问题)、向量的应用问题等;解三角形主要包括正弦定理、余弦定理及其应用.近些年来,平面向量和解三角形的高考试题难易适中,一般为基础题或中档题,常在选择题、填空题中直接考查向量的概念、性质及其几何意义以及正、余弦定理在解斜三角形中的简单应用;在解答题中考查向量工具在平面几何、三角函数、解析几何等问题中的应用以及运用正、余弦定理等知识解决数学建模问题和与测量和几何计算相关的实际问题.     

Laser-based manufacturing concepts for efficient production of tailor welded sheet metals

Laser welding is an established manufacturing technology for a large variety of automotive applications due to its attractive properties such as low heat input, high precision and fast welding speed. Especially when welding high strength steels, which are dominantly used in today＇s car body construction, the low heat input by laser welding bears significant advantages with regard to the properties of the weld seam. The exploitation of the full application potential of laser welding in mass production requires an appropriate manufacturing concept and corresponding auxiliary technologies. The present paper demonstrates the integration of laser welding into the surrounding manu- facturing concepts by a modular setup with different levels of automation. This approach offers flexible solutions for individual needs thereby optimizing investment cost, labor cost and productivity. Recently available laser sources enable exceptionally high welding speed on thin gauged sheet metals but require efficient material handling con- cepts to utilize the full speed potential. Industrial concepts are presented offering efficient material handling and high process robustness for mass production welding.     

Learning in the workplace for garage mechanics and technicians

Employees in technical firms, like garages, need more and more formations. Due to the very fast innovation in technology, lifelong learning is a real need for these labour forces. On the other hand, there are the needed formations very specialized and expensive. Another problem employers faced in these economical sectors in Western Europe is the lack of candidates. Also in secondary education schools, the wide interest for these formations is decreasing. One of the factors causes this problem is that schools don＇t have enough money for investing in new and high-tech machines. Therefore two interreg projects were submitted and approved for financing. Interreg is an initiative of the European Union meant for the permanent development of the ＂European Space＂. The third phase of interreg means enhancing the economic and social cohesion within the European Union. In this paper, we describe two successful projects, namely Autoweb and V@K, which try to help employers, employees, schools and students to keep up with the high-tech innovations with a workplace-based e-learning program.     

Accessibility in post secondary education： Application of UDL to college curriculum

The inclusion of students with disabilities at the university is a relatively new occurrence in the field of special education. Although legislation in the United States has supported the acceptance of students with disabilities at the post-secondary level, it has only provided minimal support with the emphasis on the learner rather than the curriculum. Now we are looking for multiple ways for students to access learning and demonstrate mastery. Universal Design for Learning （UDL） is currently seen as a means to reconceptionalize curriculum. This study examines the experience of four professors and their effort to use a Classroom Performance System （CPS） as part of reformatting their courses using UDL. The Center for Applied Special Technology, CAST （2001） states that the goal of Universal Design for Learning is to develop teaching methods that enable all students with diverse learning needs, including those with disabilities and cultural differences, to have equal access to classroom curriculum. This paradigm shift echoes the move in special education from a deficit model to a minority rights model put forward by Hahn （1989）, and which is the basis of inclusive educational philosophy. Together inclusion and UDL create learning environments that strive to serve all students. This research describes the implementation of clickers as part of the CPS program in college courses in a special education teacher preparation program. The case study demonstrates how technology can provide access for all learners with positive outcomes such as increased participation and application of knowledge. It also illustrates some of the difficulties in making this pedagogical paradigm shift particularly in the use of technology, and the value of overcoming the existing barriers in place.     

利用农村环境资源提高初中生物学教学质量

由于基础设施的限制,农村中学学生视野较窄,但他们所处的生活环境中生物资源丰富多彩．农村中学生物教学可利用得天独厚的自然资源,促进教学,激发学生的学习兴趣,引导学生更好地学习生物,认识生物资源与人们生活的密切关系,促进学生的资源保护意识,培养高尚的情操。     

The quantifying analysis of effectiveness of music learning through the Dalcroze musical method

Movement activities can be used to integrate with any other curriculum in childhood education. The movements can inspire the sense of rhythmic concepts for children. This study aims at investigating how children can be motivated and inspired rhythmically by body movement through Dalcroze approach. In this research, the author revealed how physical movements can motivate children＇s potential sense of rhythm and inspire children＇s interest of musical rhythmic concepts learning. The study was conducted with 1000 primary school 6th grade students from twenty primary schools in Taipei, Taiwan. These 1000 6th grade students have the same age, same music syllabus and have equally same music training at their schools. The 1000 students were divided into two equal groups, one having different activities of body movements at school, and the other without. The different activities included tapping, swinging, clapping, turning, and stamping simple rhythms. The experiments consisted two parts which were rhythm dictation and improvisational skills. All the participants were equally given the pre-test and post-test as evidences of progress of the experiment, and the researcher then compared with the differences of the two tests of the two groups before and after the experiment to see if there were any progress in their learning of musical rhythms. The study lasted 6 months and consisted of three stages： observation, comparison, and analysis. The author observed and compared the two groups of students, analyzed the results and found out that the two groups demonstrated obvious differences in their degree of progress on learning of musical rhythms.     

Same vague expression, different conceptualizations

The study was to investigate the vague words measurement across native and non-native English speakers and gender differences. Ninety-two students from the University of Oklahoma participated in this study by filling out an internet-based questionnaire on the vague words. The researchers put each of the thirty-two vague words in a context, or the same word put into different contexts. The participants were asked to rate the degree or the numerical value that they thought was the most appropriate in the context of the vague word. It was found that ten out of the thirty-two words had a significant difference across the native and non-native English speakers, and two of thirty-two words had a significant difference across genders. The word ＂fairly＂ showed the most significant difference interactions of language speaking by gender.     

How intuition contributes to high performance： An educational perspective

Intuition usually is defined as the capability to act or decide appropriately without deliberately and consciously balancing alternatives, without following a certain rule or routine, and possibly without awareness （Gigerenzer, 2007; Hogarth, 2001; Klein, 2003; Myers, 2002）. It allows action which is quick （e.g. reaction to a challenging situation） and surprising, in the sense that it is extraordinary in performance level or shape. This paper reports theories of intuition and their empirical evidence in the field of professional work. It aims at reporting the state of research on intuition, discussing the relevance of different approaches for analyzing work performance, and describing challenges for future empirical research in the domain of professional working life.     

概念图在高中生物复习总结中应用的初探

高中生物复习课教学是师生双方从新的视角对所学知识进行系统梳理、深化、拓宽及灵活应用的教与学的过程．应用概念图可以有效地组织课程内容,激发学生自主构建生物学知识体系,使知识概括化、网络化,并能灵活地迁移．     

Correlation between process parameters and primary dendrite arm spacing in laser welding of Cu and Al

A combined numerical model of thermal field and the primary dendrite arm spacing （PDAS） was proposed to correlate the process parameters and PDAS in laser welding of Cu and A1. The solidification parameters simulated by the finite volume method with commercial software ANASYS FLUENT were applied in the PDAS model to predict the dendrite arm spacing of fusion zone. Dendrite was also examined by the metallographic method to validate the model. Results indicate that the calculated PDAS agrees with metallographic measurements reasonably, especially the Hunt model. PDAS increases apparently with increasing laser power while decreases slightly with increasing welding speed. Increasing laser power increases the secondary dendrite and increasing welding speed increases the microporosity in dendrite.