首先需要自我的主观控制,如正确的大方向,循序渐进的各个步骤,然后步步为营。其次客观的条件也是不可缺少。人类生存的基础是物质资料的\'生存方式。只有做到像革命的本钱——身体也是为以后打下坚实的基础。同时,在这个奋斗过程中,傲气不可有,傲骨却必须有。身体只是一份躯壳,内在的精神气骨才是可贵的。最后,在主客观条件都已具备的同时,要把握机遇,促成量变变向质变的一个飞跃。然后才可以实现人生梦想。
初中数学总复习并不是对以前所教的知识进行简单的回忆和再现。最主要的是要通过对知识系统复习,使每一章节中的各个知识点联系起来,找出其变化规律、性质相似之处及不同点等从而形成完整的知识体系,达到以点成线,以线成面,以面成体的目的,只有这样学生才能把所学的知识融会贯通。
一、章节复习——善于转化
我在复习概念时,采用章节知识归类编码法,即先列出所要复习的知识要点,然后归类排队,再用数字编码,这样做可增加学生复习的兴趣,增强学生的记忆和理解,最主要的是起点了把章节知识由量到质的飞跃,实现厚薄间的转化。
例如,复习“直线、线段、射线”这一节内容,我把主要知识编码成(1(2(3(4。(1——一个基础;(2——两个要点;(3——三种延伸;(4——四个异同点。这种复习提纲一提出,学生思维立即活跃,有的在思维,有的在议论,有的在阅读课本,设法寻找提纲的答案,我趁势把知识进行必要的讲解和点拨,其答案如下:(1——一个基础。是指以直线为基本图形,线段和射线是直线上的一部分。(2——两个要点。①两点确定一条直线;②两条直线相交只有1个交点。(3——三种延伸。三种图形的延伸。直线可以向两方无限延伸;线段不能延伸;射线可以向一方无限延伸。(4四个异同点。①端点个数不同;②图形特征不同;③表示方法不同;④描述的定义不同;事实证明,这种善于转化的复习确实能提高复习效率。
二、例题讲解——善于变化
复习课例题的选择,应是最有代表性和最能说明问题的典型习题。应能突出重点,反映大纲最主要、最基本的内容和要求。对例题进行分析和解答,发挥例题以点带面的作用,有意识有目的地在例题的基础上作系列的变化,达到能挖掘问题的内涵和外延、在变化中巩固知识、在运动中寻找规律的目的,实现复习的知识从量到质的转变。
例如,在复习二次函数的内容时,我举了这样一个例题:二次函数的图象经过点(0,0与(-1,-1,开口向上,且在x轴上截得的线段长为2。求它的解析式。因为二次函数的图像抛物线是轴对称图形,由题意画图后,不难看出(-1,-1是顶点,所以可用二次函数的顶点式y=-a(x+m2+n,再求得它的解析式(解法略。在数学中我对例题作了变化,把题例中的条件“抛物线在x轴上截得的线段2改成4”,求解析式。变化后,由题意画图可知(-1,-1不再是抛物线的顶点,但从图中看出,图像除了经过已知条件的两个点外,还经过一点(-4,0,所以可用y=a(x-x1(x-x2的形式求出它的解析式。再对例题进行变化,把题目中的“开口向上”这一条件去掉,求解析式。再次变化后,此题可有两种情况(i开口向上;(ii开口向下;所以有两个结论。
由于条件的不断变化,使学生不能再套用原题的解题思路,从而改变了学生机械的模仿性,学会分析问题,寻找解决问题的途径,达到了在变化中巩固知识,在运动中寻找规律的目的。从而在知识的纵横联系中,提高了学生灵活解题的能力。
三、解题思路——善于优化
一题多解有利于引导学生沿着不同的途径去思考问题,可以优化学生思维,因此要将一题多解作为一种解题的方法去训练学生。一题多解可以产生多种解题思路,但在量的基础上还需要考虑质的提高,要对多解比较,找出新颖、独特的最佳解才能成为名副其实的优解思路。在数学复习时,我不仅注意解题的多样性,还重视引导学生分析比较各种解题思路和方法,提炼出最佳解法,从而达到优化复习过程,优化解题思路的目的。如:已知2斤苹果,1斤桔子,4斤梨共价6元,又知4斤苹果,2斤梨,2斤桔子共价4元,现买4斤苹果,2斤桔子,5斤梨应付多少钱?(解题略本题妙在不具体求出每种水果的单价,而是使用整体解题的思路直接求出答案为8元。又如计算(6x+y/2(3x-y/4这是一题多项式的乘法运算,本题从表面上看无规律可找,学生也习惯按多项式系数,发现第一个因式提出公因数2后,恰能构成平方差公式的模型,显然后一种解题思路优于第一种解题的思路。再如,计算若此题把各因式计算后再相乘,很繁琐,若能把各因式逆用平方差公式,再计算、约分,可以迅速地求出结果。
在复习的过程中加强对解题思路优化的分析和比较,有利于培养学生良好的数学品质和思维发展,能为学生培养严谨、创新的学风打下良好的基础。
四、习题归类——善于类化
考查同一知识点,可以从不同的角度,采用不同的数学模型,作出多种不同的命题,教师在复习时要善于引导学生将习题归类,集中精力解决同类问题中的本质问题,总结出解这一类问题的方法和规律。例如在复习应用题时,我选下列4个题目作为例题。
题目1:甲乙两人同时从相距10000米的两地相对而行,甲骑自行车每分钟行80米,乙骑摩托车每分钟行200米,问经过几分钟,甲乙两人相遇?题目2:从东城到西城,汽车需8小时,拖拉机需12小时,两车同时从两地相向而行,几小时可以相遇?题目3:一项工程,甲队单独做需8天,乙队单独做需10天,两队合作需几天完成?题目4:一池水单开甲管8小时可以注满,单开乙管12小时可以完成,两管同时开放,几小时可以注满?
上述四道复习应用题,题目表达方式不同,有的看似行程问题,有的看似工程问题,但本质基本相同,数量关系,解答方法基本一样。通过这样的归类训练,学生便能在平时的学习中,做个有心人,加强方法的积累和归纳,并能分析异同,把知识从一个角度迁移到另一个角度,最终达到常规图形能熟悉、常规结论要记忆、类同方法全套用、独创解法受启发的层次,提高举一反三、触类旁通的能力。
为使学生轻负担的复习,从题海战术中解脱出来,学得灵活,学得扎实,优化复习过程,提高复习效率,是一个行之有效的重要途径。希同仁们不断思考,不断探索,为实施素质教育做出努力和贡献。
Nowadays, many famous university campuses have become one of the popular tourist attractions. It has been shown on TV and on the radio that every year thousands and thousands of middle school students visit Tsing Hua University and Peking University and other famous universities in China. In the place far away from the capital city, the local students also visit the universities famous in their own province.
So far as the present situation is concerned, is it a good or bad thing to open the university campus for tourists? Different people have different opinions. On one hand, some people argued that it is a good thing for the students to visit the famous university campus in that it can enable the middle students to get more information about the university and they can have enough time and opportunity to prepare themselves with the chance to get into the university. On the other hand, some people hold a negative view about this phenomenon. In their opinion, the public tourism will have negative effect on the universities because it will not only do harm to the environment but also to the intellectual atmosphere.
In my opinion, the tourism to the universities is not a good thing. The campus is mainly a place for study. With the increasing tourism on the campus, it will ruin the spiritual atmosphere in this learning field.
首先,提纯范文 “谋篇布局”及结构模板。
第一段:提出问题或现象。Nowadays, … … have become one of the popular … …. It has been shown on TV and on the radio that … ….
第二段:正反列举人们的看法。So far as the present situation is concerned, is it a good or bad thing to … …? Different people have different opinions. On one hand, some people argued that it is a good thing for … … in that … …. On the other hand, some people hold a negative view about this phenomenon. In their opinion, … … will have negative effect on … … because it will not only do harm to … … but also to … ….
第三段:摆明自己观点。In my opinion, … … is not a good thing. … … With the increasing … …, it will ruin … ….
其次,提纯范文“段落写作”。
段落写作分为统一性,连贯性和完整性三方面。
统一性(unity:段落开头的主题句应该做到不可太宽泛,也不可太具体,做到有较强的概括性才能使下文做到有的放矢的展开。范文第二段首句以设问的方式提出一个问题is it a good or bad thing就有很强的概况性。下文自然会一方面从好的方面说明,另一方面从坏的方面说明。
连贯性(coherence:关联词是使文章段落之间相互连贯的必要条件。范文中nowadays, on one hand, on the other hand, in one’s opinion即以“启承转合”递进的顺序是文章条理清晰,层层展开。
完整性(completeness:以设问句“So far as the present situation is concerned, is it a good or bad thing to open the university campus for tourists?”开头,这是平时较少运用的段落写作方式——设问法。“On one hand … …. On the other hand, … ….”是段落写作分类列举法的典型用法。
再次,提纯范文“句子写作”。
1. It has been shown that … …
类似句型:It is known to us that … …
It is said that … …
It is reported that … …
It is controversial that … …
2. “… … Tsing Hua University and Peking University and other famous universities … …。”——并列句。并列句是简单的复杂句。但其运用方法并不简单,注意练习并接句的使用,会使句子显的更加饱满。
3. enable v. 使…能够
I gave him full directions to enable him to find the house.
4. in that = because
表“因为”的连词还有since, for, as,如:
The boy was absent because he was ill. = The boy was absent since he was ill.
此句以我们常用的人称开头,句式简单,我们可以通过把since提前改变句式,如:
Since the boy was ill, he was absent. 句式多样化。
最后,提纯范文“措辞”。
1. attraction n. 具有吸引力的事情。
2. thousands and thousands 成千上万的
形容“多”的表达方法:millions and millions
a multitude of
a great deal of
a large amount of
plenty of
many a
3. “some people argued that … …”中的“argue”并不是“讨论,辩论”的意思,而是“认为”。
I argue that … …
I maintain that … …
I claim that … …
I insist that … … = I think that … …
I hold that … …
I assert that … …
I assume that … …
4. negative adj. 否定的.,相反的
hold negative view = hold opposite opinions
5. phenomenon n. 现象
social phenomenon 社会现象
natural phenomenon 自然现象
6. intellectual adj. 聪明的= intelligent, bright, clever
(选词策略:使用最近所学的单词,如intellectual > intelligent > bright > clever
在分析并掌握范文之后,我们需要运用范文知识练习仿写。笔者运用2005年12月范文中的模板结构仿写了2006年12月的四级作文,以供参考:
1. 许多人喜欢在除夕夜看春节晚会
2. 但有些人提出取消春节晚会
3. 我的看法
Nowadays, the Spring Festival Evening has become one of the popular topic and attractions during every traditional New Year’s Eve. It has been shown on TV and on the radio that every year thousands and thousands of Chinese people appear to be accustomed to enjoying the sights and sounds of a brilliant feast, while gathering with their beloved family.
However, an increasing number of people have voiced different opinions towards it. So far as the present situation is concerned, is it a good or bad thing to cancel the Spring Festival Evening? Different people have different opinions. On one hand, some people argued that it is a good thing to amuse the audience in that it is composed by a numerous adequate programs, such as the emotional song, the graceful dance, the funny short sketch, the amusing comic dialogue, the delightful magic, and the marvelous acrobatics and so on. On the other hand, some people hold a negative view about this phenomenon. In their opinion, the Spring Festival Evening will have negative effect on the family harmony because it will not only do harm to having the talks between family members on the Spring Festival Eve but also to enjoying the gourmet meal in a fancy restaurant.
In my opinion, the Spring Festival Evening is a good thing. It may not remain a must for all people, but it can bring us a strong sense of festivity and serve as an alternative among the variety of holiday activities. With the increasing audience of the Spring Festival Evening, it will ruin a distinctive culture during the Spring Festival vacation.
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