First, teach students to attend classes and develop.
The habit of positive thinking.
Every time we have a new lesson, we should first cultivate students' habit of using their brains actively and listening carefully. Teach students four skills: listening, watching, thinking and speaking.
Will listen: Listen carefully. Don't listen is don't listen. Students should remember while listening and thinking, and grasp the main points. We should not only listen carefully to the teacher's explanation, but also listen carefully to the students' speeches and listen to the problems in others' speeches. In order to examine and train students' listening ability, the following exercises can be organized: (1) Teachers dictate questions and students write numbers directly; (2) Teachers dictate application questions, and students write or say the questions they know and want. This kind of exercise can train students to concentrate, listen and think, and cultivate their agility and conscious memory ability.
Ability to read: mainly to cultivate students' observation ability and habits. First of all, we should give students the right to observe, and don't replace students' "seeing" with teachers' good words. Teachers must not talk or talk less about what students can master through their own search and thinking. To read, first of all, you are willing to pay attention. Teaching should provide sufficient observation materials to attract students to read. Teachers' blackboard writing and demonstration should be accurate and vivid, which can arouse students' interest in observation. Under the guidance of teachers, students change from semi-independent observation to completely independent observation, and only have "observation tips", so that students can gradually master the observation methods of making judgments and discovering laws through observation and comparison. In classroom practice, we should design more topics that can arouse the interest of observation and train the ability of observation. For example, after learning the Preliminary Understanding of Fractions, you can design the following exercises (see Figure 7 1): Observe, how much does the shadow part account for in the whole?
Another example is to arrange such an exercise after learning "Divisibility of Numbers":
Look at the numbers in the following groups. Please find the numbers in different categories and explain the reasons.
(2)0、 1.2、3、 13、5、27。 (1.2 is not an integer)
(3) 10、8、44、56、65、 12。 (65 is not an even number)
(4)33、39、 12、2 1、49、57。 (12 is not an odd number, and 49 is not a multiple of 3)
For example, after learning "Reciprocity of Fractions and Decimals", you can do this exercise: find the rules and fill in the blanks.
Make students learn to use the concepts they have mastered to observe and compare, make judgments, develop their intelligence through observation, and gradually develop the habit of careful observation.
Thinking: thinking, first of all, you must be willing to think. In class, students should be willing to think with their brains. In addition to the teacher's teaching inspiration, but also rely on "promotion" to urge their brains. Ask students and teachers to think immediately and be ready to answer every question they ask. If you can't answer, repeat the question and tell me what you think and what you don't think. Tell the students that this is also an answer. Insisting on doing this can improve the teaching efficiency of questioning. Because all the students in the class, without exception, should think positively, whether they like it or not. When asking questions, you can give priority to those who may not be able to answer them, and then ask those who can answer the former questions. In this way, teachers can not only know whether underachievers are thinking and what are the obstacles to thinking, but also improve the ability of ordinary students to solve problems and exercise the flexibility and profundity of thinking. After asking questions, teachers should evaluate them in time and encourage those who answer well and dare to speak.
Will say: listen, see and think, and break through by saying this. Language is the result of thinking. If you want to talk, you must think. Grasping and asking students to say this link as much as possible in class can promote students to think more; If you want to think well, think well, think well, you have to listen carefully and watch carefully. If we catch the talk, we can promote the other three meetings. Therefore, we should attach great importance to the cultivation and training of students' oral and answering ability.
According to the training of math class, we can take the following measures.
First, train students to speak loudly. In the first class, teachers and students introduce each other, and the training of speaking begins. Please stand up, loudly say my name is XXX, how many points I got in the final exam last semester, and then tell me my plan to learn math well in the new school year in one or two sentences. The teacher found that it was good, and immediately praised: "XX students have correct posture, natural attitude, complete sentences, concise language and very loud voice: very energetic!" . Set an example through praise and let students know their own requirements. Since then, every class has been trained in combination with inspection and review, basic training and other teaching links. Ask students to answer questions loudly, and everyone must pass the standard acceptance of "qualified voice"
Second, let students get used to "saying ideas". The so-called thinking is the process of thinking and thinking. In class, every student should be given the opportunity to express his ideas, such as whispering alone, practicing speaking among peers, talking to each other in groups of four and so on. Learn the way of thinking by speaking. Through this kind of training, students will get used to speaking their ideas. For example, once ask students to answer a question in the blank: "The sum of two consecutive even numbers is 82, and these two even numbers are () and () respectively. When answering, a classmate said: These two even numbers are 40 and 42. I think so, because the difference between two adjacent even numbers is 2, that is, the sum of these two even numbers is 82 and the difference is 2. 82 minus 2 divided by 2 is equal to 40, and 40 is a smaller even number; 40 plus 2 equals 42, which is a big even number. So these two consecutive even numbers are 40 and 42. The second student replied: I got it by adding two even numbers. I think both even numbers should be close to half of 82, so one even number is 40 and the other even number is 42. The third student said: I think, according to the sum of two even numbers 82, we can find that the average of these two even numbers is 4 1, and 4 1 is odd, because the difference between two adjacent natural numbers is 1, then the two even numbers adjacent to 4 1 are 4 1. Students have a good foundation and are well organized. Obviously, the process of saying ideas is the process of training logical thinking ability. Cultivate students' language organization and thinking logic by talking about ideas.
Third, train students to use mathematical language. In teaching, it is necessary to help students understand concepts, rules and other terms in textbooks, and require students to answer questions in mathematical terms completely, with concise and accurate language. After guiding students to observe, analyze, reason and judge, inspire students to summarize definitions, laws or formulas in their own words. Make perceptual knowledge rise to rational knowledge. Doing so can not only arouse students' enthusiasm, but also enable teachers to get feedback information in time and examine students' understanding, thus correcting the mistakes in other words in students' narration and deepening their understanding of knowledge. After students use their own words, they should be unified into the textbook language. If students are asked to sum up the meaning of a score, divide the unit "1" into several parts on average, and the number representing such a part or parts is called a score. Students often miss the word "average" in their narratives. At this time, they can show a small blackboard prepared in advance, with several circles drawn on it, one of which is divided into two parts equally, and the other is also divided into two parts. Guide the students to observe the similarities and differences, make them realize the difference between "divided into several parts" and "divided into several parts on average", and then let the wrong students count again. In this way, students not only understand the definition (rule) itself, but also understand the written language to express this definition (rule), and can also speak it accurately. In the process of organizing language, students' thinking is organized and accurate.
Fourth, give the underachievers the right to speak. The difficulty in cultivating students' habit of thinking and answering questions actively lies in cultivating underachievers. Underachievers generally turn a blind eye and listen but don't hear in class, because they are not good at observing, listening and thinking. Therefore, we should try our best to let underachievers learn to use their brains, that is, to give underachievers the right to speak. Underachievers are guilty and have a low voice when answering questions in class. If they make a mistake, they will be laughed at by their classmates and even more afraid to raise their hands next time. If you don't talk, you don't want to, don't use your head. Therefore, to help underachievers learn to use their brains, we must find ways to make them speak and dare to say and answer. For example, the first few classes after succession can be used as key classes for underachievers. Before class, tell the underachievers the exam review questions and teach them how to answer them in detail. Because the underachievers are one step ahead in their studies, they have clear thinking, dare to raise their hands in class and have a loud voice when answering. Seize the opportunity to praise the small progress. Underachievers gradually cultivate courage and then gradually increase the difficulty. Underachievers have tasted the sweetness, and with self-confidence, their enthusiasm for speaking is high. Underachievers can also actively use their brains to answer questions, and they can also promote intermediate students and top students. Speaking promotes thinking and keeps students' thinking active.
The above training can be carried out by oral practice, recitation, summary of definitions, answering questions, group discussion, debate and other forms.
Second, teach students to think and develop the habit of independent thinking.
To teach students to think, we must first let them "live in a world of thinking". This requires our teaching to create conditions and stimulate students' thinking. Let students master the thinking method in the process of observing and comparing, analyzing and synthesizing, abstracting and summarizing, reasoning and judging mathematical materials. The way of thinking, just listen to "talk" and not listen. The way of thinking depends on students' independent thinking to understand. Only by constantly savoring the fun of thinking can students gradually develop the habit of independent thinking.
Taking the teaching of "the least common multiple of two numbers" as an example, this paper explains how to make students learn thinking methods and develop the habit of independent thinking in the process of learning mathematical algorithms.
First of all, stimulate the desire to think and make clear the goal of thinking.
"Why should the least common multiple of two numbers at least include their common prime factor and unique prime factor?" This is the difficulty of this part of the textbook and the key for students to understand the algorithm. Doubt is the key to discovery and the driving force of thinking. I give this difficult problem to students as a self-study thinking question. Faced with this problem, many students can't help thinking: "Yes, why? Eager to find "roots" and "evidence", active in thinking. This problem not only aroused the desire to think, but also became the goal of everyone's concentrated thinking.
Second, provide a suitable thinking foundation.
Because the textbook (page 4 1 of the textbook of four provinces and cities) does not directly answer the above questions, students can't "hard" face this question, but should provide some information and give hints. For example:
Why do 18 and 30 have at least their common prime factor and their unique prime factor?
point out
What prime factors should be included in the multiple of (1) 18? How many prime factors should a multiple of 30 include?
(2) What prime factors must be included in the common multiples of18 and 30? Please try it. What did you find? )
Third, we should leave enough time for thinking.
If the thinking time is too short, most students have not "figured it out" or even the underachievers have not "wanted to go in", which will definitely dampen the enthusiasm of most students for independent thinking. In order to make every student in the class start thinking, we must set aside enough time for thinking. After five or six minutes of independent thinking and trying to practice, many students found something, excited and eager to try, which led to the requirement of "speaking out".
Fourth, organize many exchanges in time.
In order to meet the requirements of students who want to "speak", group discussions and class discussions were organized in time. During the discussion, the students gradually made it clear that finding the least common multiple of two numbers should be both "public" and "small", and studied how to ensure these two points. For example, a classmate said, "In the least common multiple of 18 and 30, if only 18 and 30 share prime factors 2 and 3, then the product of multiplication is 6, which is the greatest common multiple of 18 and 30, not the common multiple." Some students said: "The least common multiple of 18 and 30 should include not only their common prime factors 2 and 3, but also the unique prime factor 3 of 18 and the unique prime factor 5 of 30, because only in this way can it be guaranteed to be the common multiple of 18 and 30." Someone added: "There is a 2 in the prime factor of 18, a 2 in the prime factor of 30, and a 3 in the prime factor of 18, so as to ensure that it is the least common multiple of 18 and 30." The students are enthusiastic, and their speeches leap forward, complementing each other and correcting each other. Many people can also use the information provided by teachers as their own arguments. Because this arithmetic and algorithm was not told by the teacher, but came up by myself, many people showed a happy look.
After independent thinking, we should organize discussion, discussion and debate in time, so that students can express themselves, exchange ideas and experience the fun of independent thinking.
Only independent thinking can produce opinions. There is a desire to communicate when there is an opinion, and communication can stimulate new thinking. The flexibility and profundity of thinking are exercised in communication, and the thinking ability is also improved accordingly. When students are interested in thinking, they will gradually form the habit of independent thinking.
Third, teach students to read and develop.
The habit of self-study
Textbooks are silent teachers and the main source for students to acquire systematic knowledge. Therefore, it is necessary to guide students to read textbooks carefully, insist on reading before class, during class and after class, and form the habit of self-study in preview and review.
Reading before class is to preview the textbook before class. Ask students to open their textbooks after finishing their homework every day to see what they will learn the next day. Especially in each unit and the new lesson at the beginning of each class, questions should be marked when reading, so that teachers can focus on the classroom with questions when giving lectures. Sometimes teachers can ask interesting questions and guide students to find their own books to read. For example, after finishing the basic example of the application problem of "difference times", the topic "What are the expressions of difference, see who finds more" is put forward, and students are required to finish it after class. At first, students thought for themselves, then they did textbook exercises, and some even rummaged through extracurricular books and problem sets everywhere. In the discussion the next day, some students summed up six different expressions of "difference": A is greater than B, B is less than A, A is less than B, and B plus several equals A. After A gives B a certain amount, A and B are equal, A minus 15, B plus 3, and the two numbers are equal. On the basis of this preview, it is convenient for students to learn more complicated differential application problems. This kind of preview can lead students' interest to extracurricular activities, extensive reading and active learning.
Reading in class is learning textbooks in class. Reading mathematics textbooks under the guidance of teachers is the main way to teach students autonomous learning methods and cultivate their autonomous learning ability.
Mathematics textbooks, without story lines, are less attractive and less readable. If you only ask for reading in general, you will inevitably have the phenomenon of "not understanding" and "not seeing clearly", so reading textbooks must have requirements and guidance.
First of all, teachers can lead students to read, specifically guide students how to grasp the main contents and key points of each chapter in the textbook, how to understand mathematical concepts, think about problems and ask questions. For some key words, phrases and sentences, we should circle and mark them, chew the words repeatedly, correctly understand the mathematical language and master the mathematical concepts.
To guide reading, we should choose different methods according to the content of the textbook. In some textbooks, it is difficult for students to see the key points. Teachers can ask questions, and students can read books with questions, find answers, find out the reasons and master the rules. In some textbooks, students have a certain knowledge base, so they can do exploratory exercises first, and then compare them with the textbooks to deepen their understanding. Some teaching materials, students can understand independently, let them read by themselves, and then organize exchanges to further digest and understand.
Reading after class is reviewing textbooks after class. Students should be guided to form the habit of reviewing textbooks before doing homework. Ask students to read the textbooks before doing their homework every day, see what the teacher said in some books that day, think about what the teacher said and what to pay attention to when doing the questions, and then do the questions.
It is necessary to guide students to form the habit of sorting out what they have learned while reading textbooks. After learning each unit, the teacher can leave no homework, and the students can review the textbooks themselves, sort out what they have learned, classify and number them, and practice writing short review outlines or notes. Every once in a while, choose excellent notes to organize circulation and comments, so as to mobilize the enthusiasm of "self-study".
Fourth, teach students to examine questions and develop.
The habit of finishing homework carefully
Examining questions is the key to solving problems correctly. Many mistakes made by students in solving problems are often not the lack of necessary knowledge, but the lack of necessary habits and skills in examining questions. In order to improve the correct rate of homework, we must make great efforts to cultivate students' habit of carefully examining the questions and seeing the requirements of the questions before solving them. Every time a new lesson is taught, teachers should guide students to practice and examine questions in a planned, purposeful and persistent way, learn the methods of examining questions while learning new lessons, and form the habit of examining questions.