例谈高考含参不等式恒成立问题的求解策略

含参不等式的恒成立问题是学生难以理解和掌握的一个难点,是高考常见的题型.教师要引导学生掌握求不等式恒成立中参数范围的常见策略与方法,根据不同的条件,选择恰当的方法,确定不等式恒成立中的参数范围,提高学生的解题能力.     

不等式恒成立问题与转化思想的统一

不等式恒成立问题是高中数学的重点,转化思想是主要的数学思想之一.为了进一步加深学生对不等式恒成立问题的全面理解,提高学生的综合能力,教师可将不等式恒成立问题与转化思想统一起来.     

一道“不等式恒成立”问题的解答探究

导数中不等式恒成立问题,对于学生而言一直都是一个难点.处理此类问题一般有两种方法:分类讨论、参数分离.学生遇到“不等式恒成立”问题,首选的方法就是“参数分离”.本文简要呈现师生应用“参数分离”解决一道“不等式恒成立”问题的思考与解答历程,尝试对这类方法进行梳理,希望能起到抛砖引玉的作用.     

不等式恒成立问题的求解方法

恒成立问题是高中数学学习中常见的问题,学生往往感到困难,摸不着头绪,不等式恒成立问题的一般形式是根据不等式恒成立求相应的参数的取值范围。解决不等式恒成立问题,主要有以下几个方法。     

数列中的不等式恒成立

不等式的恒成立问题是学生较难理解和掌握的一个难点,以敷列为载体的不等式恒成立问题的档次更高、综合性更强,是高三第二轮复习中不可多得的一个专题.     

从2010年高考数学试题中窥探二阶导数

不等式恒成立问题是高考试题考查的重点内容之一能够体现出学生的逻辑思维能力,分析问题、解决问题的能力从一个新的角度出发,浅论利用二阶导数来剖析高考试题中的不等式恒成立问题.     

浅谈“恒成立”问题的教学

众所周知,不等式恒成立问题是高中数学的一个重难点,由于它能较全面的考察一个学生的数学素养,因此,它一直是高考的热点之一。要解决好恒成立问题,首先要求学生必须具备扎实的基本功:如函数知识、不等式知识、转化与化归思想、分类讨论思想等等;其次,还要有良好的逻辑思维能力。由于这些,学生在学习过程中大多都会感到棘手。     

不等式恒成立问题的求解策略

恒成立问题是高中数学教学中的一个重点和难点.恒成立问题能够很好地考查函数、数列、不等式等知识,以及转化、化归等数学思想.因此,涉及恒成立的问题越来越受到高考命题者的青睐.针对高中数学中的不等式恒成立问题,从解题方式的角度进行分类,并通过实例探讨各类不等式恒成立问题的解法.     

浅谈"恒成立"问题的教学

众所周知,不等式恒成立问题是高中数学的一个重难点,由于它能较全面的考察一个学生的数学素养,因此,它一直是高考的热点之一.要解决好"恒成立"问题,首先要求学生必须具备扎实的基本功:如函数知识、不等式知识、转化与化归思想、分类讨论思想等等;其次,还要有良好的逻辑思维能力.     

不等式恒成立问题的求解策略

恒成立问题是高中数学教学中的一个重点和难点.恒成立问题能够很好地考查函数、数列、不等式等知识,以及转化、化归等数学思想.因此,涉及恒成立的问题越来越受到高考命题者的青睐.针对高中数学中的不等式恒成立问题,从解题方式的角度进行分类,并通过实例探讨各类不等式恒成立问题的解法.     

Social inequalities in access to higher education in Croatia: five decades of resilient findings

This article provides a panoramic view of research findings on social inequalities in access to higher education in Croatia since the 1960s, guided by the question of what has changed in the findings. Our review shows that there is stark continuity over the last five decades: students from better educated family backgrounds tend to be overrepresented in higher education; students from better educated and white-collar family backgrounds are more likely to enrol in academic as opposed to professional study courses; students at one Croatian university in particular stand out in terms of their more privileged social background; and medicine seems to be the prime academic field for observing social reproduction. We note that these persistent findings run parallel to a dramatically changing political, economic and social context in Croatia, including transformations in the 1990s resulting from social ownership of the means of production to widespread private ownership, as well as transformations from a one-party political system to the establishment of a multi-party political system. The article maps possible theoretical explanations for the resilience of social inequalities in access to higher education in the context of dynamic times. It also questions the role of educational policies in this process.     

东盟留学生教育的问题与解决对策

中国-东盟博览会落户南宁，中国-东盟自由贸易区的建立，将使广西特有的地缘区位优势与东盟国密切的人文关系，得到更大的发挥。新的机遇使广西大学在开展东盟留学生学历教育的学科优势、管理优势、地缘优势和机遇优势凸显，分析现有问题，找出解决对策，必将使这所历史悠久，学科较齐全的综合大学在东盟留学学历教育事业中越来越发挥更大的作用。     

三个积和式不等式

积和式理论在概率统计等领域有较广泛应用,该文给出三个有用的积和式不等式,并给出详细的证明.     

Absolute value inequalities: high school students’ solutions and misconceptions

Inequalities are one of the foundational subjects in high school math curricula, but there is a lack of academic research into how students learn certain types of inequalities. This article fills part of the research gap by presenting the findings of a study that examined high school students’ methods of approaching absolute value inequalities, their common mistakes, misconceptions, and the possible sources of these mistakes and misconceptions. The research study used two tools—a questionnaire and personal interviews. The questionnaire was given to 481 students in the 10th and 11th grades in Israel who studied mathematics at intermediate and advanced levels. It was administered after the students had studied inequalities. Thirty-two students were interviewed in order to find their ways of thinking and the sources of their errors. The main types of mistakes that students consistently made when solving absolute value inequalities were found. Based on the study’s findings, teachers can understand students’ thought processes and use this understanding to conduct remediation and enhance mathematics instruction.     

Students encountering race and negotiating friendships,sexuality and language on campus

By drawing on a theoretical framing based on the geography of encounters, this article examines how students give meaning to racialised encounters on campus. These encounters are mediated by long established notions of difference based on power inequalities where race remains a powerful source of difference. However, race is not simply enacted but produced as it weaves through student friendships, heterosexual partnering and through language. By focusing on the construction of race in student encounters on campus, the article uncovers the points at which students produce relations of inequalities, their contestations and the continuities in racialised power structures. The article concludes by pointing to the value in understanding the race-friendship-heterosexual-language tension, which might help work towards understanding and addressing inequalities based on locally relevant interventions on campus.     

Inequity as a Source of the Cultural Gap in an Urban School-University Collaborative

Based on a 5-year naturalistic evaluation of an urban university-school collaborative that focused on preparing teachers for urban schools, this analysis was initiated to determine to what extent inequalities between the university and school personnel mitigated the attainment of intended outcomes. Results indicated that some positive change occurred, such as professors and teachers learning to speak the same language on instructional teams, which led to improved field experiences for students. However, cultural differences with concomitant inequities between school and university personnel prevented more permanent change. Inequities of power were inadvertently written into the proposal and were exacerbated at two levels: (1) the collaborative policy board, in which districts, due to larger representation, wielded greater power over budget and hiring in the collaborative; and (2) instructional teams where professors wielded power over several teachers with resistance from teachers. By the end of 5 years, the funded portion of the urban teacher education program that included a collaborative policy board and instructional teams had fallen mostly by the wayside. Cooperation between professors and teachers reverted to precollaborative levels with only loose coupling remaining. Preservice students continue to do field experiences in the professional development schools under supervision. The university education unit recognized the benefits, but continues to struggle with how to revive the level of cooperation that began with the urban program and to create long term partnerships that go beyond mere placement of students into the field.     

Measuring cognitive achievement gaps and inequalities: The case of Brazil

This paper introduces a new measure of educational inequalities based on cognitive achievement data, and uses it to examine achievement inequalities in mathematics between groups of students enrolled in basic education in Brazil. The groups of students are defined by their race, sex, socioeconomic status (SES), and region of residence. The Brazilian system of basic education currently produces poor results with respect to both quality and equity. The paper recommends that Brazil should work, concomitantly, to improve the achievement levels of its students and to close the cognitive gaps observed among different groups of students. Placing emphasis on just one of these goals is not an adequate public policy at this time. Proposals for carrying out these reforms can be classified as input or management strategies and are briefly discussed.     

构建高等院校学生党建工作长效机制初探

高校学生党建工作是一项系统工程，建立科学有效的运行机制是做好学生党建工作的关键。本文在分析目前高校学生党建工作存在问题的基础上，提出从建立系统的学生党员培养教育体系、构建以学生党建为核心的团学工作平台、以及进一步发挥学生党员的先锋模范作用等方面形成长效有序的学生党建工作新机制。     

Reproduction and transformation of students’ technology practice: The tale of two distinctive secondary student cases

Disparities in the technology practices, skills and knowledge of school students still exist, despite widespread investment, and use in schools. In order to understand why inequalities remain, we first need a more nuanced understanding of students’ technology practice, including understanding how their backgrounds, circumstances and experiences shape their perceptions of and engagement with technology. This paper proposes that research in the field of educational technology would benefit from a sociological framing in order to highlight how and why students use technology at school and in their everyday lives. The paper reports on a qualitative embedded case study of 13–16-year-old students in two Australian secondary schools. In-depth case studies of two selected students illustrate the complex nature of students’ technology practice. Bourdieu’s concepts of field, habitus and capital are used as a lens through which to view and understand inequalities in students’ technology practice. The findings demonstrate the utility of sociological theory in educational technology research by highlighting systems and structures of reproduction and transformation. Furthermore, the findings can inform an approach to teaching and learning that considers students’ varied experiences, knowledge, perspectives and backgrounds relating to technology.     

Routes through higher education: BME students and the development of a ‘specialisation of consciousness’

With changing demographics and the advent of mass higher education, there has been a significant impact on graduate transitions which has led to greater inequalities in access to social support during the transitionary period between undergraduate study and entrance into the labour market. This article explores the experiences of students in their final year of undergraduate study by drawing on 43 interviews with Black and Minority Ethnic (BME) students. Using Bourdieu, we argue that BME students preparing to enter the labour market display a ‘specialisation of consciousness’: a set of practices framed by their prior background and experience, choice of university and the support derived from attending university. ‘Specialisation of consciousness’ is an ongoing process in which BME students identify and understand racial inequalities in higher education and accept the limiting consequences these have on transitions into the labour market or further study.