解题策略讲座

(十四)转化法将一些复杂的问题,通过适当的变换,转变成简单的问题,这种变换在数学上称为转化。转化法就是改变思维的角度,变化思维方式,将问题从一种形式转     

小学数学奥林匹克试题解题思路种种

十五、用转化法解题对于一些复杂的问题,通过适当的变换,往往能变成你熟悉的简单的基本题,这种变换在数学上称为“转化”,就是改变思维角度,变化思维方式,将问题从一种形式转化为另一种形式的方法,这种方法叫作“转化法”。     

学术性期刊编辑思维方法的探讨

探讨学术性期刊编辑思维方法,旨在让凌乱、无序的编辑思维相对条理化、清晰化,实现编辑质量和效率的双赢。文章从作者研究问题的思路和文稿行文的普遍走势,采取先考察文稿的"干",再考察文稿的"支",最后考察文稿的"叶"的移步换景方式,变换思维方法,运用最具代表性的编辑思维方法解决文稿中的某个问题。即用收敛性思维法考察文稿的主题,用发散性思维法考察文稿的结构,用质疑性思维法考察文稿的模型和观点,用探究性思维法求证文稿的疑点和难点。     

变换思维 化繁为简

追求简捷是数学思维的特征,化繁为简是数学解题的正确方向。对于一个较复杂的数学问题,当从正面思考难以奏效或用直接法不能解决时,应及时突破思维定势,变换思维角度,让灵活多样的数学思维方法登堂入室。具体来讲,主要有以下策略:     

变位思维例析

变位思维是指在常规思维受阻时,变换思维方式或者变换角度来分析处理问题的一种思想方法。当我们遇到难题时,如果按照常规思维模式来分析,无从人手,或者头绪纷繁,一时半会理不清思路。这时若能变换一个思维角度,或者变换一种思维方式来分析,问题往往会变得十分简单。在教学过程中注意多向思维训练,对学生分析能力、应变能力的培养,必将产生积极作用。     

正弦量的P变换与P-1变换

从教学角度,利用构造思维,提出一种P变换与p-1变换,从而将正弦电路分析中正弦量与相量的抽象的“对应”关系转换为一种数学变换关系,并证明了这种变换的基本性质.进而利用这些性质建立起基尔霍夫定律,以及线性元件方程的相量形式.使得初学者能深刻理解相量法,降低学习难度.     

用‘纵横变换法’复习应用题

用“纵横变换法”复习应用题,能起到以一当百、触类旁通的作用。“纵横变换法”是以一道基本应用题为基点,按照思维发展的不同层次,利用纵、横变换得到一组题,从而达到系统复习知识、提高解题能力这一目的的一种较好的复习方法。纵变换包括扩缩变换、复合变换等;横变换包括互逆变换、情节变换等。复习刚开始,教师先编一组题,让学生解答并分析各题之间的内在联系,接着,指导学生编题、解答,并提出     

构造法在解题中的应用

在数学解题过程中,对已有知识和方法采取分解、组合、变换、类比、限定、推广等手段进行思维的再创造,构造新的式子或图形来帮助解题的方法称之为构造法．构造法作为一种数学方法,属于非常规思维,带有试探性、不规则性和创造性．构造法解题过程的模式可用下列框图表示：     

谈谈“变换法”在阅读教学中的作用

所谓“变换法”,是指教师在语文阅读教学中,根据学生的知识基础、能力水平,以及在写作中存在的问题,把握阅读课文的中心,明确阅读目标,抓住阅读重点和难点,有针对性地变换课文中的某些内容,设计一些能激发学生创新思维的思辨题的一种导读方法。“变换法”内容丰富,形式多样,包括变换课文的标题、词语、句子、语段、情节顺序、人称、文章的结构、主旨和体裁等等。限于篇幅,这里仅以变换课文题目、词语为例,谈谈“变换法”在阅读教学中的作用。     

以变式教学拓展学生思维

数学变式教学可以让学生在“变”的过程中感悟知识真谛,扩充思维结构,增强对知识相互联系的再认识,达到举一反三、融会贯通,不断提高分析问题和解决问题的能力,不断提升思维水平。具体而言,可以变换思考的方向,打破思维的定向性;变换思考的角度,引导思维的灵活性;变换思考的对象,拓展思维的广阔性;变换思考的思想方法,培养思维的精细性。     

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.     

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.     

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.     

Use of Reference in the Narratives of Kurdish-Persian Bilingual Children

This study investigates some of the differences and similarities between Kurdish-Persian bilinguals and Persian monolinguals with respect to the use of referring expressions in spoken narratives. The narratives were elicited from 36 participants, consisting of 24 bilinguals （Groups l and 2） and 12 monolinguals （Group 3） in the first four grades of primary school using picture narrative book. The results have revealed that Group 1 （bilinguals told the story in Kurdish） used definite noun phrases most frequently followed by zero anaphors, indefinite noun phrases, and pronouns. Group 2 who narrated the story in Persian produced definite nouns most frequently followed by pronouns, zero anaphors, and indefinite noun phrases. Group 3 （Persian monolinguals） employed definite noun phrases most frequently followed by zero anaphors, pronouns, and indefinite noun phrases. The significant difference between Groups 1 and 2 and Groups 2 and 3 has been in indefinite noun phrases and between Groups 1 and 3 in the use of pronouns. One reason is that children universally apply similar strategies regardless of their first language （L l）. The conclusion is that some of the differences are due to the difference in the structure between Persian and the dialects of Kurdish.     

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.     

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.     

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.     

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．     

Assessing graduate attributes for employability in the context of lifelong learning： The holistic approach

To promote economic and personal growth, higher education students＇ employability, ensuring their preparedness for the workforce, is emphasized. From the employer＇s perspective, judging whether a graduate is employable depends upon whether the graduate exhibits the attributes which employers value. Yet, with the growing emphasis on lifelong learning, it is important for higher education to re-consider and reframe the development and assessment of attributes of graduates in the context of lifelong learning. In this paper, these attributes will be explored in that context, and the issue of how assessment helps the development of graduate attributes is to be considered. Student engagement is proposed in this paper as the holistic, useful approach for the development of employability and lifelong learning. The holistic approach reflects the fact that what is required in a workforce is not the acquisition of knowledge, skills and dispositions per se, but the capability to make an engagement through which knowledge, skills and dispositions are connected as a whole. The lack of emphasis on students＇ engagement could lead to mistakenly selecting as important for the focus of assessment simply the acquisition of skills, knowledge or dispositions, rather than the holistic connection of these to their application in the workforce.     

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.