求复合最值问题的5种策略

在竞赛中，常常会遇到一类在一些最大值中求最小值或在最小值中求最大值的问题，这类问题称为复合最值问题．这类问题通常构思新颖，题目抽象，解题有一定的困难，笔者对此类问题的解法作一初步探讨，供读者参考研究．     

例析最值问题解法策略

在解决函数问题时,常常会碰到求某个变量的最大值或最小值．求函数最值的方法很多,下面就结合例题归纳一下最值的几种求法．     

例析中考试卷中的最值问题

在一定范围内求最大值或最小值的问题,我们称之为“最值问题”．现结合2009年全国各地中考数学试卷中的一些最值问题来谈谈求最值问题的方法．     

复合最值问题的十大解题策略

在竞赛数学中，经常会遇到复合最值问题．所谓复合最值问题，即最大值与最小值相互嵌人求解的问题，具体地讲也就是在最大值中求最小值或最小值中求最大值的问题．这类问题比较抽象，难度较大，颇受竞赛命题者的青睐．本文拟通过典例归纳复合最值问题的十大解题策略．     

直角三角形中的最值问题

求最大值或最小值问题是初中数学中最常见的题型之一,由于其形式灵活多变,解决此类问题的方法也各不相同．直角三角形中的最值问题有其独特之处,本文举例探讨这类问题的解法,供大家参考．     

例析中考试卷中的最值问题

在一定范围内求最大值或最小值的问题,我们称之为最值问题.现结合2009年全国各地中考数学试卷中的一些最值问题来谈谈求最值问题的方法.     

函数的最大值与最小值

函数的最大值与最小值是指函数在整个定义域范围内函数值的最大值与最小值．我们遇到的求最大值和最小值的问题．绝大部分可以归结为求函数的最大、最小值．这一部分内容是学习函数时需要掌握的重要知识点．本讲将分别讨论一次函数、二次函数、简单的分式函数和无理函数的最值问题．     

例析函数最值常用解法策略

在解决函数问题,常常会碰到求某个变量的最大值或最小值,求函数最值的方法很多,下面就结合例题归纳一下求最值几种常用的方法.     

双层最值问题的解法探秘

双层最值问题是指在一个最值问题中又包含一个最值问题.它大致可分为四大类:求最大值中的最小值;求最小值中的最大值;求最大值中的最大值;求最小值中的最小值.尤以前面两类问题居多.这类问题在高考模拟卷和竞赛卷中会经常出现,常以选择题或填空题的方式呈现.最值问题,历来就是高中数学的热点和难点问题,而双层最值更加大了最值问题的理解难度.因此,大部分学生见到此类问题都是望风披靡,视为若猛虎.其实,只要认真归纳总结,还是可以找出此类问题的一般解题规律的.     

开区间上最值问题的探讨及应对策路

人教B版教材在“利用导数研究函数的最值”这一章节中谈到了“最值定理”,即“闭区间上的连续函数在该区间上一定有最大值和最小值”,关于这个定理教材中是这样表述的“假设函数y=f（x）在闭区间[a,b]上的图象是一条连续不间断的曲线,则该函数在[0,b]上一定能够取到最大值和最小值”．在实际解题中我们往往会碰到在开区间上求最值的情况,那么,最值定理在开区间上是否还成立呢？显然是不成立．对此,就有了一些需要我们特别注意的问题．     

Having a Whale of a Time

A classroom practical exercise exploring the reliability of a basic capture‐mark‐recapture method of population estimation is described using great whale conservation as a starting point. Various teaching resources are made available.     

对公推直选乡镇长与乡镇党委书记的比较

公推直选乡镇长与乡镇党委书记出现的时间、发展现状与趋势、制度依据、选举成本,以及乡镇长与乡镇党委书记在乡镇政权中的作用有明显的不同。在我们看来,直接选举乡镇党委书记,发展的空间更广阔,对乡镇民主建设与乡镇政府职能转型所起的作用更大。     

一道联赛题的推广

题1 已知实数a、b、c、d互不相等，且n＋1/b=b＋1/c=c＋1/d=d＋1/a=x．     

关于循环矩阵求逆的一种算法

给出了利用多项式的欧几里德算法判断循环矩阵的可逆性和求逆的方法     

向量与数的乘法

Vectors may also be multiplied by a number. The productof the vector a by the number λ is defined as the vector a λ=λa, the absolute value of which is obtained by multiplying theabsolute value of the vector a by the absolute value of thenumber λ, i. e. |λa|=|λ||a|, the direction coinciding withthe direction of the vector a or being in the opposite sensedepending on whether λ>0 or λ<0. If λ=0 or a=0, then λ a     

三角形的一个性质的推广

本对[1]给出的三角形的一个性质进行推广．     

向量与数的乘法

（参考译文）。 向量也可和数做乘法．向量a与数字A的乘积定义为向量aλ—λa,它的绝对值是向量a的绝对值和数字A的绝对值的乘积,     

Paving a clear path in a thick forest: a conceptual analysis of a metacognitive component

The concept of metacognition refers to one’s knowledge and control of one’s own cognitive system. However, despite being widely used, this concept is confusing because of several reasons. First, sometimes it is not at all clear what is cognitive and what is metacognitive. Second, researchers often use the same term, namely, “metacognition” even when they refer to very different aspects of this complex concept. Alternatively, researchers may use different terms to indicate the same metacognitive elements. Another foggy matter is the interrelationships among the various components of metacognition discussed in the literature. This conceptual confusion regarding the concept of metacognition and its sub-components calls for in-depth theoretical and conceptual clarifications. The goal of this article is to portray a detailed example of a conceptual analysis of meta-strategic knowledge (MSK) which is one specific component of metacognition. This specific example is used to draw a general model for conceptual analyses of additional metacognitive components. The approach suggested here is to begin with a clear definition of the target sub component of metacognition, followed by a systematic examination of this sub component according to several dimensions that are relevant to metacognition in general and to that sub component in particular. The examination should include an analysis of how the details of the definition of the target sub-component refer to: (a) general theoretical metacognitive issues raised by prominent scholars; (b) definitions formulated and issues raised by other researchers who have investigated the same (or a similar) sub-component and, (c) empirical findings pertaining to that sub-component. Finally, it should be noted that since metacognition is a relational rather than a definite concept it is important to situate the context within which the conceptual analysis takes place.     

Rate of a maintained operant as a function of temporal position within a session

McSweeney and her colleagues (e.g., McSweeney, Hatfield, & Allen, 1990) have demonstrated reliable, large magnitude rate changes in maintained operants within daily sessions under a wide variety of reinforcement schedules. The present paper examined the role of schedule of reinforcement, reinforcement rate, and total amount of food access in determining those within-session rate changes. When median rates across birds were considered, all procedures resulted in a brief period of an increasing rate, followed by a modest rate loss across the major portion of the session. However, not all individuals exhibited that pattern. When the amount of food access per session was limited by lower reinforcement rates, shorter sessions, or shorter reinforcement durations, the magnitude of the withinsession rate change was reduced from that occurring without those constraints. Additionally, under the conditions that produced strong within-session rate changes, the magnitude of the within-session rate loss was correlated with the bird’s body weight. These effects are consistent with what is typically labeledsatiation.     

Developing a professional vision of classroom practices of a mathematics teacher: views from a researcher and a teacher

The term professional vision points to the many nuanced ways professionals see. This paper traces the development of a professional vision of a researcher and a teacher looking at classroom practices. The researcher’s interest was to capture and study notable aspects of the teacher’s practice. Through a coding scheme, disparate classroom events were organized and analyzed to yield a researcher’s professional vision of the teacher’s practices. For the teacher, through reviewing the video records of his own classroom practices, his professional vision provided a basis for him to reflect and develop professionally. Leveraging on the work of the researcher, he initiated and transformed his own practices. Their collaboration yielded a mutually informed development of professional vision of classroom practices. In juxtaposing the two developments, the researcher and the teacher’s views can be contrasted, their distinctive interests highlighted and common grounds explored. Some implications for developing professional vision are drawn, and it is in the common grounds of the teacher’s professional development and seeing with a goal of enhancing of student learning that hold some promise of a mutual interest in developing a professional vision of classroom practices.