初中数学解题题典

初中数学解题题典（精选5篇）

初中数学解题题典 第1篇

There are three separate sources of danger in supplying energy by nuclear power(原子能).First, the radioactive material must travel from its place of production to thc power station.Ahhough the power statkms themselves are strongly built, the containers used for the transport of the materials are not.Normally, only two methods of transport are itl use, namely road or rail.Unfortunately, both of these may have an effect on the general public, since they are sure to pass near, or even through, heavily populated areas.Second, there is the problem of waste.All nuclear power stations produce wastes that in most eases will remain radioactive for thousands of years.It is impossible to make these wastes nonradioaclive, and so they must be stored iii one of the inconvenient ways that scientists have invented.For example, they may be hurled under the ground, or dropped into deserted mines, or sunk in the sea.However, these methods do not solve lhe problem, since an earthquake could easily break the containers.Third.there may occur the danger of a leak(泄漏)or an explosion at the power station.As with the other two dangers, this is nm very likely, so it does not provide a serious objection to the nuclear program.Itowever, it can happen.Separately, these three types of dangers are not a great cause for worry, l‟akcn to gethcr, though, the probability of disaster(灾难)is exrrtmtly high.1.Which of the following is FALSE?

A.It is possible that a leak or explosion occurs at a power station.B.It is unusual for radioactive materials to be transported across land.C.The containers are likely to be broken by an earthquake.D.Nuclear wastes remain dangerous in most cases for many years.2.The author thinks that the ways to store nuclear wastes are ______.A.easyB.impossible

C.reasonableD.ineffective

3.What do we learn from the last paragraph?

A.The power station is a safe place.B.The dangers of nuclear energy can be prevented.C.The general public are strongly against the nuclear program.D.By itself, none of the three dangers is very likely to cause much worry.4.What is this passage about?

A.Uses of nuclear power.B.Dangers from nuclear power.C.Public anger at nuclear power.D.Accidents caused by nuclear power.答：1.B 2.D 3.D 4.B

解析：

2．由第三段最后一句可知，那些储存核污染的方法解决不了问题，由此可判断出选项。3．最后一段大意是三种危险分开以后没有危户，符合题意。4，从全文中看，文中列举了三种危险，故选B项。

The Fourth “21st Century Cup” National English Speaking Competition is to be held in Shanghai.Organizers;China Daily and Shanghai Broadcasting Network

China University English Speaking Association(协会)(CUESA)

Co-sponsors(联合主办单位): English-speaking Union(ESU);Lotus Software(Chi-na)Co, Ltd.;Times Publishing Group of Singapore;Hilton Shanghai;Pearson Educa-tion;Foreign Language Teaching & Research Press-1-

Date: March 26(Friday), 1999

Place: Hilton Shanghai

Competition Format(形式): Each student will present a prepared speech on the given topic, followed by a

three-minute offhand speech and a three-minute question and answer period with the judges.Prepared speech period: six minutes Offhand speech peri-od: three minutes Q & A period: three

minutes

Speech Topic: People and Nature: In search of harmony(和谐)in a new age—your per-sonal opinion(Topics for the

offhand speech will be given on the day ofcompetition.)

Prizes: Besides books and certificates(证书), the top two winners will be offered schol arship(奖学金)to travel to

the annual international English-speaking competi-tion, which will be held by the English-speaking Union in London in May, 1099.The third and fourth place winners will be offered a study trip to Singapore, sponsored by the Times Publishing Group.The fifth through the i0th place win-ners will be offered cash prizes.All the competitors will receive certificates from the English-speaking Union and book prizes provided by Pearson Education and the Foreign Language Teaching & Research Press.The teachers of the top two winners will also receive a one-year membership to the International Association of Teachers of English as a Foreign Language(IATEFL).1.The main purpose of this passage is ______.A.to invite you to take part in the competition

B.to help to improve your spoken English

C.to tell you some information of the competition

D.to show you how to win the competition

2.Suppose you get the sixth place, you‟ll ______.A.travel to London for free

B.become a one-year member of IATEFL

C.get some money, some books and a certificate

D.get a chance to study in Singapore

3.All “offhand speech” is ______.A.a speech not longer than three minutes

B.a speech without preparation

C.a speech with a piece of paper in hand

D.a speech which is well prepared hefore

4.Which of the following statements is wrong?

A.The competitors won‟t know what they will speak about until March 26, 1999.B.The time-limit for each student is 12 minutes.C.Each student must speak on at least two topics.D.Only two students can have the chance for the international competition.答：l.C 2.C 3.A 4.C

解析：

1．考查作者的写作意图。2．考查猜测词义。3．由Competition Format一段分析可知。4．考查推理判断。由Competition Format一段可以看出本句错误。

Xin Hua tn 1999, President Jiang Zemin examined five state owned enterprises and delivered speeches about existing problems and possible solutions.His speeches gave rise to many questions.What roles should enterprise leaders play? Since economic reform and open policies were started in the early 1980s, what changes have taken

place in state owned enterprises? Readers will find answers to these questions and more in “Liaoning in Transition of Reform” a series of articles by Louise Cadieux.Louise Cadieux has done much research on China‟s state-owned enterprises.After visiting representative enterprises in l.iaoning Province, she wrote the articles with her u-nique, western view.We hope her views will help our readers better understand China‟s state-owned enrerprises.l.A state-owned enterprise is one that _____.A.belongs to one person or a group of persons

B.belongs to a country

C.a country runs

D.one or a group of persons run

2.From the passage we know it‟s true that _____.A.Louise Cadieux only answered President Jiang‟s questions

B.Louise Cadieux had more questions than President Jiang did

C.Louise Cadieux answered some of President Jiang‟s questions by her researches

D.President Jiang‟s questions are too many and too hard for Louise Cadieux to answer

3.This passage suggests that _____.A.some problems are really existing in state-owned enterprises

B.ways should be and can be found to solve the existing problems

C.it‟s time for the leaders to look back and find proper ways of management

D.all the above three

答：1.B 2.C 3.D

解析：

1．此题属事实理解题，从state-owned一词可知选项。2．从结尾一段可判断出C项。Louise Cadieux对中国的国企进行了研究。3．文中提到了国企存在的问题、解决办法及领导者应思考的管理办法，故选D项。

A branch of computer science cailled artifical intelligence uses programs that help solve problems by using human knowledge and experience.Artificial intelligence systems are al-so called expert systems, which enable computers programmed with great amounts of in formation to think about many possibilities such as diseases that certain symptoms(症状)could indicate and make a dccision for tile treatment.Computers are used in teaching as well.Programs that perform computer-aided in-struction(CAI计算机辅助教学)are designed to help students at all levels, from ele-mentary school to the university level.The student sits at a computer terminal(终端).The terminaI‟s screen displays a question for the student to answer.If the answer is wrong or incumplete, tile computer may ask the student to try again.It then may supply the correct answer and an explanation.CAf is also used in some adult education programs and as part of the employee training programs of some business companies.One of the most important uses of computers is to communicate information over long distances.They can send information to each other over telephone lines.As a result, computers keep banks, newspapers, and other institutions supplied with hnformation.A computer network consists of many computers in separate rooms, build-ings, cities, or countries, all connected together.Computer networks allow people to communicate by using electronic mail a document typed into one computer and sent to an-other.Such document generally travel in only a few minutes, even if they are being sent over a long distance.The computer‟s ability to share information with other computers over a network linked by telephone lines is a major revolution in telecommunieatitms.The Internet, an international network of computer networks, has spread out since the early 1990‟s.The Internet began as.a US network of scientific and military computers in the 1960‟s.Now it

is an international system for sending and receiving electronic mail, software, and elec-tronic documents and picture files all over the world.The Internet has already cut the cost of long-distance communicaions for many people.In the future it will completely change the way people work.With the lnternet, increasing numbers of people can work at home instead of in their office.Computers and their programs are the most complex devices in human history, and probably the most useful.Modern industrial societies now depend on them.As comput-ers become more powerful and widespread, computer education must continue to increase also.1.From the first paragraph we get to know that artificial intelligence systents _____.A.are beyond scientists‟ control

B.will take the place of doctors

C.will take the place of scientists

D.are under scientists‟ control

2.If you use E-mail to communicate with your friends, you can______.A.exchange information without paper

B.talk with your friends freely

C.talk with your friends face to face

D.exchange information without computers

3.The phrase “up-to-the-minute” in the third paragraph means ______.A.shortestB.latest

C.longestD.easiest

4.What is the main idea of this text? ______.A.Computers Are Dangerous

B.Computers Are Clever

C.Computers Are Useful

D.Computers Are lntercsting

答：1.D 2.A 3.B 4.C

解析：

1．从第一段可知人工智能系统是在科学家的控制下。2．和朋友网上交流不用纸。3．up-to-the-minute跟上时代的，最新的。4．文章主要介绍电脑的用途。故选C项。

Some doctors use magic, some use needles and others use pills.Who are they?

Among the Indians of North America the „medicine man‟ was a very important per son.He could cure illnesses, and he could speak to the spirits—the supernatural forces that controlled the world.The Indians believed that bad spirits made people ill.So, when people were ill, the medicine man tried to help them by using magic—he spoke to the good spirits and asked for their help.Many people were cured because they thought that the spirits were helping them.But really these people cured themselves.Sometimes your own mind is the best doctor for you.The medicine men were often successful for another reason, too.They knew about plants that really can eure illnesses A lot of modern medicines are made from plants that were used by medicine men hundreds of years ago.For more than five thousand years Chinese doctors have used needles to fight illnes-ses.This method is called aeupnneture(针灸).The doctor studies the sick person care fully.Then he puts needles into that person‟s body at the right places for his illness.Chi-nese doctors believe that they can control the body‟s natural forces in this way.At first, doctors in the West thought that this was just another kind of magic.Recently, however, they have found out that it is possible to cure many illnesses like this because the needles help the body to produce its own „medicines‟.In this way

the body cures itself.1.The Indians of North America enjoy_____.A.a modern medical treatment

B.an old medical treatment

C.an advanced medical treatment

D.a secret medical treatment

2.If one is iii, it is important for hint to _____.A.believe in god

B.worry about his illness

C.use magic

D.have a light heart

3.According to this passage modern medicines_____.A.have nothing to do with the old traditional medicines

B.have nothing to do with the supernatural forces

C.have nothing to do with plants

D.have nothing to do with the Indians

4.Using needles to fight illnesses_____.A.used to be popular over the world

B.is used as another kind of magic

C.is easy to learn by anyone

D.was first used by the Chinese

5.Acupuncture, in fact, ______.A.is the only way to cure many dangerous illnesses

B.can be used to cure all kinds of illnesses

C.is effective to cure many illnesses

D.is popular among the western people

答：1.B 2.D 3.B 4.D 5.C

解析：

1．美洲北部印第安人倾向药物治疗。2.从第三段Sometimes your own mind is the best doctor for you可推断出D项。3.现代的药和超自然力无关。4.针灸最早始于中国。5.文中最后一段可知。

浅析初中数学解题误区 第2篇

一、对待初中学生解题错误的态度

在初中数学教学中, 教师害怕学生出现解题错误, 对错误采取严厉禁止的态度是司空见惯的。在这种惧怕心理支配下, 教师只注重教给学生正确的结论, 而不注重揭示知识形成的过程, 害怕启发学生进行讨论会得出错误的结论。长此以往, 学生只接受了正确的知识, 但对错误的出现缺乏心理准备, 看不出错误或看出错误但改不对。持这种态度的教师, 只关心学生用对知识, 而忽视学生会用知识。例如, 在讲有理数运算时, 由于只注重得出正确的结果, 强调运算法则、运算顺序, 而对运用运算律简化运算注意不够, 但后者对发展学生运算能力却更为重要。总之, 这种对待错误的态度会对教学带来一些消极的影响。

事实上, 错误是正确的先导, 成功的开始。学生所犯错误及其对错误的认识, 是学生知识宝库的重要组成部分。因为, 数学学习实际上是不断地提出假设、修正假设, 使学生对数学的认知水平不断复杂化, 并逐渐接近成熟的过程。所以, 揭示错误是为了最后消灭错误。在教学中给学生展示的这一尝试、修正的过程, 是与学生独立解题的过程相吻合的。因而, 学生在教师教学过程中学到的不仅仅是正确的结论, 而且领略了探索、调试的过程。这对学生的解题过程会产生有益的影响, 使学生学会分析, 自己发现错误、改正错误, 提高分析问题解决问题的能力。

二、减少学生解题错误的方法

减少学生解题错误的方法是预防和排除干扰。为此, 作为教师必须要抓好课前、课内、课后三个环节。

(一) 课前准备要有预见性

预防错误的发生, 是减少初中学生解题错误的主要方法。讲课之前, 教师如果能预见到学生学习本课内容可能产生的错误, 就能够在课内讲解时, 有意识地指出并加以强调, 从而有效地控制错误的发生。老师备课时, 要仔细研究教科书正文中的防错文字, 例题后的注意、小结与复习中的应该注意的几个问题等, 同时还要揣摸学生在学习授课内容时的心理过程, 授业解惑, 让学生预先明了容易出错之处, 防患于未然。如果学生出现问题而未查觉, 错误没有得到及时的纠正, 则遗患无穷, 不仅影响当时的学习, 还会影响以后的学习。因此, 预见错误并有效防范能够为揭示错误、消灭错误打下基础。

(二) 课内讲解要有针对性

在课内讲解时, 要对学生可能出现的问题进行针对性的讲解。对于容易混淆的概念, 要引导学生用对比的方法, 弄清它们的区别和联系。对于规律, 应当引导学生搞清它们的来源, 分清它们的条件和结论, 了解它们的用途和适用范围, 以及应用时应注意的问题。教师要给学生展示揭示错误、排除错误的手段, 使学生会识别错误、改正错误。要通过课堂提问及时了解学生情况, 对学生的错误回答, 要分析其原因, 进行针对性讲解, 利用反面知识巩固正面知识。课堂练习是发现学生错误的另一条途径, 出现问题, 及时解决。总之, 要通过课堂教学, 不仅教会学生知识, 而且要使学生学会识别对错, 知错能改。

(三) 课后讲评要有总结性

批改作业时要认真分析学生作业中的问题, 总结出典型错误, 加以评述。通过对作业中学生出现的错误的讲评, 进行适当的复习与总结, 也是学生再经历一次调试与修正的过程, 增强识别、改正错误的能力。

初中学生数学解题误区 第3篇

首先，我们对错误要有充分的认识与分析：教师可以通过错误来发现学生的不足，也从某个角度揭示了学生分析问题的过程，这也是对于学生来说不可或缺的，是学生在学习过程中对所学知识不断尝试的结果。其次，在了解学生错误的原因后 ，就可对征下药，帮学生避免错误，提高解题正确性。

一、 老师应有教学态度 ：对错误的承受与宽容

事实上，错误是正确的先导，成功的开始。学生所犯错误及其对错误的认识，是学生知识宝库的重要组成部分. 利用学生典型错误并进行正确诱导会收到良好的教学效果。 如老师讲过a2-b2=（a+b）（a-b）后，让学生去分解m4-n4。很快大家就做完了。老师一边巡视一边督促检查。但在最后教师宣布只有几个人人做对时，其他同学都感到非常吃惊 。大家把m4-n4分解为（m2+n2）（m2-n2）错在哪里呢？做对同学的答案是（m2+n2）（m+n）（m-n），两相对照，大家发现原来m2-n2还可以继续分解。于是，分解因式要进行到每个因式都不能再分解为止给每个同学都留下了深刻的印象。由此可见，教师对待错误的惧怕心理和严厉态度转变为承受心理和宽容态度是十分有意义的。

二、 解题错误的原因

学生顺利正确地完成解题，表明其在分析问题，提取、运用相应知识的环节上没有受到干扰或者说克服了干扰。在上述环节上不 能排除干扰，就会出现解题错误。就初中学生解题错误而言，造成错误的干扰来自以下两方面：

1. 小学阶段知识的干扰 如小 学数学中形成的一些结论都只是在没有学负数的情况下成立的。在小学，学生对数之和不小于其中任何一个加数，但是，学了负数后，这就不是唯一结果了。也就是说，习惯于在非负数范围内讨论问题，容易忽视字母取负数的情况，导致解题 错誤。另外，“+”、“-”号长期作为加、减号使用，学生对于1-7+4-3，习惯上看作1减7加4减3，而初中更需要把上式看成正1负7正4负3之和。对习惯看法的印象越牢固，新的看法就越难牢固树立。

2.初中阶段知识的干扰 例如，在学有理数的减法时，教师反复强调减去一个数等于加上它的相反数，因而4-8中8前面的符号“-”是减号给学生留下了深刻的印象。紧接着学习代数和，又要强调把4-8看成正 4与负8之和，“-”又成了负号。学生不禁产生到底要把“-”看成减号还是负号的困惑。这个困惑不能很好地消除，学生就会产生运算错误。

三、 数学解题错误降低的有效方法

备课时，要仔细研究教科书正文中的防错文字、例题后的注意、小结与复习 中的应该注意的几个问题等，同时还要揣摸学生学习本课内容的心理过程，授业解惑，使学生预先明了容易出错之处，防患于未然。如果学生出现问题而未察觉，错误没有得到及时的纠正，则遗患无穷，不仅影响当时的学习，还会影响以后的学习。因此，预见错误并有效防范能够为揭示错误、消灭错误打下基础。讲课之前，教师如果能预见到学生学习本课内容可能产生的错误，就能够在课内讲解时有意识地指出并加以强调，从而有效地控制错误的发生。例如，讲解方程m/0.1-（0.21-0.2m）/0.01=1之前，要预见到本题要用分式的基本性质与等式的性质，两者有可能混淆，因而要在复习提 问时准备一些分数的基本性质与等式的性质的练习，帮助学生弄清两者的不同，避免产生混乱与错误。

浅析初中数学解题误区 第4篇

一、对待初中学生解题错误的态度

在初中数学教学中,教师害怕学生出现解题错误,对错误很难容忍的态度是司空见惯的。在这种心理支配下,教师只注重教给学生正确的结论,而不注重揭示知识形成的过程,害怕启发学生进行讨论会得出错误的结论。长此以往,学生只接受了正确的知识,但对错误的出现缺乏心理准备,看不出错误或看出错误但改不对。持这种态度的教师只关心学生用对知识而忽视学生会用知识。例如,在讲有理数运算时,由于只注重得出正确的结果,强调运算法则、运算顺序,而对运用运算律简化运算注意不够,但后者对发展学生运算能力却更为重要。总之,这种对待错误的态度会对教学带来一些消极的影响。

二、初中学生解题错误的原因

学生顺利正确地完成解题,表明其在分析问题,提取、运用相应知识的环节上没有受到干扰或者说克服了干扰。在上述环节上不能排除干扰,就会出现解题错误。就初中学生解题错误而言,造成错误的干扰来自以下两方面:一是小学数学的干扰,二是初中数学前后知识的干扰。

(一)小学数学的干扰

在初中一开始,学生学习小学数学形成的某些认识会妨碍他们学习代数初步知识,使其产生解题错误。例如,在小学数学中,解题结果常常是一个确定的数。受此影响,学生在解答下述问题时出现混乱与错误。原题是这样的:礼堂第一排有a个座位,后面每排都比前1排多1个座位,第2排有几个座位?第3排呢?设m为第n排的座位数,那么m是多少?求a=20,n=19时,m的值。学生在解答上述问题时,受结果是确定的数的影响,把用n表示m与求m的值混为一谈,暴露出其思考过程受到上述干扰的痕迹。

又如,小学数学中形成的一些结论都只是在没有学负数的情况下成立的。在小学,学生对数之和不小于其中任何一个加数,即a+b≥a(或b)是坚信不疑的,但是,学了负数后,a+b

所以,初中开始阶段,学生解题错误的原因常可追溯到小学数学知识对其新学知识的影响。讲清新学知识的意义(如用字母表示数)、范围(正数、0、负数)、方法(代数和、代数方法)与旧有知识(具体数字、非负数、算术方法)的不同,有助于克服干扰,减少初始阶段的错误。

(二)初中数学前后知识的干扰

随着初中知识的展开,初中数学知识本身也会前后相互干扰。

例如,在学有理数的减法时,教师反复强调减去一个数等于加上它的相反数,因而3-7中7前面的符号“-”是减号给学生留下了深刻的印象。紧接着学习代数和,又要强调把3-7看成正3与负7之和,“-”又成了负号。学生不禁产生到底要把“-”看成减号还是负号的困惑。这个困惑不能很好地消除,学生就会产生理解错误。

学生在解决单一问题与综合问题时的表现也可以说明这个问题。学生在解答单一问题时,需要提取、运用的知识少,因而受到知识间的干扰小,产生错误的可能性小;而遇到综合问题,在知识的选取、运用上受到的干扰大,容易出错。

这种知识的前后干扰,常常使学生在学习新知识时出现困惑,在解题时选错或用错知识,导致错误的发生。

由上所述,学生不能顺利正确地完成解题,产生解题错误,表明其在解题过程中受到干扰。因此,减少初中解题错误的方法是预防和排除干扰。为此,要抓好课前、课内、课后三个环节。

预防错误的发生,是减少初中学生解题错误的主要方法。讲课之前,教师如果能预见到学生学习本课内容可能产生的错误,就能够在课内讲解时有意识地指出并加以强调,从而有效地控制错误的发生。例如,讲解方程x/0.7-(0.17-0.2x)/0.03=1之前,虽然这不是分式方程,但要预见到本题要用分式的基本性质与等式的性质,两者有可能混淆,因而要在复习提问时准备一些分数的基本性质与等式的性质的练习,帮助学生弄清两者的不同,避免产生混乱与错误。因此备课时,要仔细研究教科书正文中的防错文字、例题后的注意、小结与复习中的应该注意的几个问题等,同时还要揣摩学生学习本课内容的心理过程,授业解惑,使学生预先明了容易出错之处,防患于未然。如果学生出现问题而未查觉,错误没有得到及时的纠正,则遗患无穷,不仅影响当时的学习,还会影响以后的学习。因此,预见错误并有效防范能够为揭示错误、消灭错误打下基础。

在课内讲解时,要对学生可能出现的问题进行针对性的讲解。对于容易混淆的概念,要引导学生用对比的方法,弄清它们的区别和联系。对于规律,应当引导学生搞清它们的来源,分清它们的条件和结论,了解它们的用途和适用范围,以及应用时应注意的问题。教师要给学生展示揭示错误、排除错误的手段,使学生会识别错误、改正错误。要通过课堂提问及时了解学生情况,对学生的错误回答,要分析其原因,进行针对性讲解,利用反面知识巩固正面知识。课堂练习是发现学生错误的另一条途径,出现问题,及时解决。总之,要通过课堂教学,不仅教会学生知识,而且要使学生学会识别对错,知错能改。

要认真分析学生作业中的问题,总结出典型错误,加以评述。通过讲评,进行适当的复习与总结,也使学生再经历一次调试与修正的过程,增强识别、改正错误的能力。

初中数学解题的“良方” 第5篇

关键词：解题良方初中数学

中图分类号：G633.6 文献标识码：A 文章编号：1002-7661（2015）09-0042-02

改革出创新，改革结硕果。新的一年，党中央的四个“全面”之一就是坚定不移地全面走深化改革之路。同样，在我们这僻远、美丽的荔波风景区的中学里，教改也在如火如荼地进行着。学校的“51035教学模式”让学生学习由被动变为主动，由不爱发言到滔滔不绝，真真正正成为了课堂的主人。但在数学教学中，解题是教学的一个重要环节，通过教师的解题训练和剖析，能培养学生分析、解决问题的能力。本人通过二十余年的数学课堂教学，结合学校课改和学生实际，现提出几点初中数学解题“良方”。

一、分析解题错误的原因，并提出有效措施

1.思维意识和思维能力受到限制

很多初中生因为受到小学数学教学过程中定势思维的影响和制约，就会导致出现解题错误的现象。比如，小学数学问题的答案，一般只有一个确定答案，但是初中数学习题中的答案不一定只有一个。所以，教师在初中数学教学中，要积极培养学生的思维意识，通过各种典型习题来锻炼学生的思维能力。

2.对基础知识的掌握和理解

数学基础知识是学生灵活运用能力和深入解题能力的前提，与学生的解题能力有很大的关系。所以，教师在课堂教学中，要让学生把握概念的本质，正确理解基本知识内容，在掌握牢固基础知识的前提下，再对深层次的知识进行提升，展开拓宽联想。例如，教师在讲“绝对值”这一知识内容时，先让学生理解和掌握绝对值的定义，让学生明白正数、负数、零的绝对值是什么，并知道其原因，在学生掌握这些基础知识内容的基础上，让学生进行更深入的学习。

二、教师要加强数学学法指导，让学生养成良好的解题习惯

在数学课堂教学中，教师要加强对学生学法的指导，培养学生正确的学习习惯。良好的学习习惯能提高学生的数学素质，使学生受益终生。所以，教师要注重学法教学，并采取以下指导方法。

1.加强预习指导

在课堂前，教师可布置预习提纲，先让学生自己学习课本内容，将课本知识通读一遍，然后细读加深理解，把课本上的定义、概念、定理、重点词和关键句等划出来，养成边算、边划、边读的良好习惯。通过预习指导，不仅能培养学生的阅读能力，还能培养学生的自学能力。

2.加强听课指导

教师要重视学生的听课指导，要求学生专心听课，认真听取教师所讲的解题思路和解题技巧，听例题解法，听重难点剖析等。在课堂上，让学生积极发言，勤于思考，勇于表达自己的见解和观点。此外，学生还要做好课堂练习，听取教师的讲评后，积极动手、动脑，以积极、热情的态度参与到教学过程中。

3.加强归纳总结与复习指导

教师要积极引导学生对每章节知识点的复习，养成归纳总结的良好习惯，注意新旧知识的联系，使所学知识更加条理化和系统化。针对各种类型的专题，教师要教会各类型习题的解题方法和规律，掌握解题技巧和步骤，对解题思路相似的习题，要进行总结归纳，以便更好地巩固所学知识。

三、初中数学中有效的解题方法

1.教会学生正确的思维，掌握解题基本方法

教师在课堂教学中，不仅要让学生掌握单一问题的解题方法，还要针对不同类型的问题掌握各种解题思路和技巧，学会如何解题。教师应强化思想方法教育，理解解题技巧的知识本源，让学生掌握解题规律，从而提高学生分析问题、解决问题的能力。

2.掌握转难为易的解题方法

在解决难点问题时，教师要让学生学会转难为易的解题方法，从特殊问题分散到普通问题中，将一个难点问题分为几个小问题，然后通过这些简单的小问题让学生理解和思考，再讲解几个小问题间的相互关系，该问题的解题思路为“先整体化部分，部分再组成整体”，这样能有效地解决数学难题，此外，教师在解题教学中，还应让学生掌握“先易后难，循序渐进”的解题步骤，加强学生对基础知识的联系和反思，并及时总结，不断提升。

3.巧妙地实现“数”与“形”的转化

比如，一方面通过画图的方法，利用图形解决抽象的数量关系；另一方面，利用直角坐标系能使学生具体、形象地理解问题，把几何问题转化为代数问题加以解决，这种解题方法能更好地避免出现解题错误，让学生轻松地解决难题。

4.鼓励学生进行反思，提高解题能力

学生在解题后进行反思，提出问题，既能形成师生互动的良好教学情境，又能发挥学生的主体地位，培养学生积极探索的精神，促进学生创新能力的提高。例如，学生在解题过程中出现错误后，就要制定一个错题本，认真思考出现错误的原因，并用数学语言或自己的语言对错题进行重新论述，促进知识的正向迁移，有利于思维的深刻性，提高解题能力。

5.采用一题多变法，深化学生的思路

在课堂教学中，教师可通过典型例题，调动学生学习的积极性，开阔视野，加强知识横向沟通和纵向联系。利用变式教学，把问题的结论或假设条件作相应的变化，依据一定的梯度设计变式题。比如，学生在练习深化题、迁移题和铺设题时，可采用变式方法，将所学知识连成一体，串成一线，让学生感受到学习数学的魅力，发现数学学习的乐趣所在。除此之外，教师还要引导学生区分相似概念，避免概念混淆；提醒学生一些解题误区，明确问题解答方向。

总之，初中数学解题教学，就要提高学生的思维能力，理清解题思路，掌握各种有效的、典型的、有规律的解题方法，培养学生的思维创新能力，提高学生数学学习的兴趣和主动性。教师要对学生进行耐心帮助和严格训练，对问题进行发散、引申和开拓，让学生及时归纳和总结，不断反思，进而提高学生的数学素养。