(1) Create situations to guide students to obtain information.
Creating rich situations and relaxed learning atmosphere can relax students' emotions, facilitate students to enter the learning state independently, publicize their personality, cultivate their beliefs and release their potential.
There are many ways to create situations. For example: activate the teaching situation map into math games, math manual classes, multimedia teaching, outdoor classes, demonstration classes and so on.
① Math games.
For example, the fifth grade statistics and possibilities, Volume I, page 10 1.
I created a lively game situation for students-passing parcels. While the students were in high spirits, I thoughtfully put forward the practical problems that need to be solved urgently-hey! Why are there more boys than girls performing programs? Soon, the students will be related to what they learned yesterday. Because there are more boys than girls, it is more likely to be spent by boys. After the teacher fully affirms the students' answers, he will further doubt in time-so how likely is it for boys to perform the program? Teachers guide students to observe, discover and collect mathematical information from situations, and screen and extract all information. There are 28 boys in the class, 16 girls. The possibility of boys performing programs is, then the possibility of girls performing programs is. At this time, you can ask further questions to deepen students' understanding of new knowledge, such as: How likely is it for a girl with a braid to perform a program? How likely are the students in blue to perform the program? Even let the students ask questions, and then he will call the roll.
This not only makes students have a strong interest in mathematical knowledge, but also cultivates the habit of thinking about problems from the perspective of mathematics and cultivating the habit of solving problems actively.
Another example: when the first volume of the sixth grade talks about location, the content involved is several pairs.
This game was designed by me. I randomly called the roll, and the students who arrived stood up. The students in the class answered in turn according to their seats. Stand up. Students can use number pairs to represent it. Choose the fastest and most accurate students to answer. Then change the rules of the game. Students in the class randomly name a number pair in turn, and the number pair indicates who stands up. It depends on who responds the fastest.
A math class passed quickly, and all the students showed their expressions of wanting more. Students learn while playing, and play while learning. I participated, I studied, and I am happy!
② Handicraft course
For example: cuboids and cubes in the fifth grade.
The day before I talked about cuboids and cubes, I left an assignment to observe which objects around us are cuboids. What are cubes? Get the materials you need ready. We will make a rectangular box and a cubic box in class to see who can do it quickly and well. The next day, the students brought the materials they needed, including iron wire, battens, plasticine, plastic foam, chopsticks and building blocks. The students began to work hard in groups. Although some students didn't do very well, they independently obtained many features of cuboids and cubes by hand. For example, to make a cuboid, you need three groups of sticks with different lengths, and each group has the same length. Take the opportunity to tell them that these three groups are called the length, width and height of a cuboid. Every three articles will be given a point, and we will tell them that this point is called the vertex and so on, so that the knowledge obtained is very vivid. Our mathematics involves a lot of geometric knowledge, such as circles, rectangles and squares, triangles and so on. And we can make abstract things more intuitive by hands-on operation.
③ Multimedia teaching.
Using multimedia teaching, the teachers in our school are all high-level, and our school organizes teaching skill competitions every year. Teachers deeply understand the contrast between teaching in the multimedia classroom and teaching students in the classroom. Obviously, they are more involved in multimedia teaching. And multimedia teaching is suitable for almost every math class. However, multimedia teaching needs to spend a lot of time making courseware, which is the main reason why teachers seldom use multimedia teaching. In fact, this problem can be improved. For example, I find that the courseware made by our teacher is exquisite. I think this is a misunderstanding, as long as our courseware is complete and clear. Isn't there a saying that simplicity is beauty? When we were in Yichuan Primary School, the courseware of those teachers was very simple, which made us feel "simple but not simple!" And there are many free courseware online, which we can use completely! In a word, we should make effective use of multimedia to make classroom teaching more vivid.
④ Outdoor class
For example, the position and direction of the second volume of the third grade.
We can take students to the campus, find the right direction, observe carefully, and see what is in the southeast and northwest of the school. Which direction is the gate? What about the water room? Through observation and questioning, students can clearly understand the distribution of various buildings on campus, and then draw a plan of the school, so that students can grasp the position and direction well. There are also classes such as campus design, which can be conducted outdoors.
Usually teaching is in the classroom, and students will feel very fresh when they suddenly go outdoors. We should grasp the freshness of students and make our teaching achieve the best results.
⑤ Demonstration class.
For example, the volume of the cylinder in the sixth grade.
In this class, I adopted a demonstration class. Since the volume of cuboids and cubes we have learned can be calculated by the bottom area × height, can the volume of cylinders also be calculated by the bottom area × height? The students' answers are either yes or no, so I ask students to demonstrate their views. Why? Why not? At this time, students seem to have no way to start, so I use multimedia demonstration to guide students by demonstrating the formula of circle area in time. To calculate the volume of a cylinder, we must first transform it into the shape we have learned. At this time, the students suddenly realized and quickly demonstrated with learning tools. Beyond my imagination, all the groups got the correct conclusion, each student explained the truth clearly, and several students expressed it perfectly. The students reached a conclusion through demonstration. Now some students still mention this lesson, saying that they have a deep memory. After class, I lost no time in asking, so can all three-dimensional figures be calculated by bottom area × height? , which ones can? What can't? What can and can't be done? Please carefully observe the similarities and differences among cuboids, cubes and cylinders, and the answer will be obvious. Tomorrow, we will award the Star of Wisdom Award to students who have good reasons to get the correct answer.
In fact, as long as we are bold and innovative, our math class will be wonderful! With a wonderful class, are you afraid that there will be no wonderful performance from students?
(2) Pay attention to the examination of problems and cultivate students' analytical ability.
Ask students not to make random calculations without thinking before solving problems. But first, we should read the question carefully, find out the key sentences in the question, find out the necessary known conditions and quantitative relations to solve the problem, and find out the conditions given in the question. What's the question to answer? In this way, the relevance to the questions raised will be developed in a targeted manner. For example, Mr. Wang bought five boxes of pens, each box 10, each 8 yuan. How much is a * * *? The teacher prompted the students to think backwards according to the problem. What do you need to know about these pens? That is to say, the total price is needed. To know the total price, you have to know the quantity and unit price. The known conditions only tell us the unit price per 8 yuan, not the quantity. But there are two known conditions for buying 5 boxes per box 10. According to these two known conditions, multiply the number of pens per box by the number of boxes. If 10×5=50 (pens), we have to find the total number of pens, that is, the number. Then calculate 8× 50 = 400 (yuan) according to total price = unit price × quantity. This method is based on the association of students after reading the questions, which leads to thinking, thus cultivating students' thinking in images and solving practical problems, which is conducive to the development of thinking ability and mastering the steps and skills of solving problems. Teachers should use positive thinking and reverse thinking to cultivate students' thinking ability.
Paying attention to the examination of questions has also been fully reflected in the formula calculation. Before making it, we should sort out the trunk of the sentence, write the framework according to the trunk, and then fill in the decorative graphics, and our graphics will be completed. For example: column calculation
What's the difference between 25 times the sum of 4 and 3.2 and 18?
Many students easily worked out the formula of 25× 4+3.2- 18. If the trunk of the problem is found first, the accuracy will reach at least 95%. What's the difference according to the question? We know that the last step should be subtraction, so we look for subtraction or subtraction, and then find the trunk, subtract what? (Sum minus 18) Once the trunk of the problem is found, the framework of the problem can be listed ()-18 =, so it is necessary to find modifiers. In Chinese, the word ×× is generally used as an attribute to modify nouns or pronouns, and so is mathematics. Problems 4 and 3.2 were used to modify the sum, so they could not be opened. So we can put it in brackets ((4+3.2))- 18 = At this time, we find a bracket in the bracket, so how about changing the outer bracket into a bracket [(4+3.2)]-18 = 25,25? 25×, ok, put it in [25× (4+3.2)]- 18 = our formula is listed. Just check it again at last. It will be very troublesome at first, but the method is skilled, fast and accurate.
(3) Analyze the quantity and cultivate students' comprehensive ability.
Analytical ability is the basic ability to solve problems, and the core of analytical ability is thinking ability. Solving practical problems in mathematics is inseparable from thinking ability. There are great differences in terms of human physiological factors. In education and teaching, we should pay attention to process analysis and give hints on the basis of what students know, so that students can better master analytical and comprehensive learning methods, find the necessary and correct conditions for solving problems, correctly solve practical mathematical problems, and cultivate students' logical thinking ability.
For example, teaching: the school bought four basketballs and one spent 100. According to this calculation, how much does it cost to buy eight basketballs? The teacher guided the analysis and asked how much it would cost to buy eight basketballs. Is the condition mentioned in the question directly used to calculate: what is the relationship between the condition of four basketballs, 100 yuan and buying eight? This is a question about the relationship between unit price, total price and quantity. The first step is to calculate the unit price from a sentence that costs 100 yuan (100 ÷ 4 = 25 yuan). Step 2 Calculate the total price: It can be calculated according to the formula (25× 8 = 200 yuan). So it costs 100× 2 = 200 yuan to buy eight basketballs.
(d) By analogy, cultivate students' knowledge transfer ability.
Some students pay too much attention to the isolation, mechanical memory and understanding of individual knowledge, and tell the facts, which separates the relationship between knowledge points and the comprehensive understanding and application of the relationship between knowledge points, and stifles the ability to solve problems. Modern learning attaches great importance to the transfer of learning, and the goal of learning is to form students' ability and methods to use what they have learned flexibly to solve similar problems. Some even put forward the slogan of "learning for migration". At present, examinations at all levels pay special attention to the examination of students' learning quality, in which the ability of students to transfer and use what they have learned to solve practical problems is the core of learning quality. However, in the actual operation and application process, a large number of students can't transfer knowledge effectively, and they are often at a loss when faced with new problems and situations, or copy knowledge mechanically or make it up at will, which directly affects the problem-solving effect. This requires us to attach importance to the cultivation of knowledge transfer ability in our usual study. The effective way and method to cultivate knowledge transfer ability is to train knowledge in variant form, and then summarize, classify and summarize it.
For example, I thought of such a problem when I was learning to solve the problem of fractional multiplication and division.
There are 24 boys and 24 girls in our class. How many girls are there?
24×
How many people are there in the class if the known conditions remain the same?
If the first known condition becomes that there are 24 girls in our class, what about other conditions and problems?
If there are 24 boys and 2 girls in our class, how many girls are there?
How else can I change it?
After finishing, we classified these questions according to the algorithm, and the students quickly divided them into two categories, and summarized the calculation methods of each category. In each category, find out the differences and connections between each question.
In fact, knowledge transfer is not only used in practice, but also in the knowledge of new professors. For example, in the second volume of the third grade, students are required to master three digits multiplied by two digits, but after we finish the class, should students add the phrase "three digits multiplied by two digits" and then four digits multiplied by three digits? What about three digits times three digits? At this time, the teacher asked the students to try to calculate "Who is the smartest teacher?" "At this time, you will be surprised to find that so many students can do it.
There is a connection between knowledge. We always pay attention to the cultivation of students' knowledge transfer ability in our usual teaching, which not only makes students' thinking more flexible, but also makes our classes easier. Taking a new lesson is like reviewing old knowledge.
In addition, when we do excellent courses or other exercises, we will find that some exercises are beyond the cognitive structure that students should have, that is, beyond the scope. Most teachers choose to give up talking and not doing. I will talk about every topic. If the teachers carefully observe, they will find that these problems are beyond the scope, but with our previous knowledge, we can solve them with a little migration.
(5) Open exercises to stimulate students' thinking development.
Problem-solving skills should be formed through certain exercises. In the exercises of teaching materials, most of them are closed exercises with clear conditions and rigorous forms, which are basically designed for students to consolidate their knowledge and assimilate their cognitive structure, and it is easy for students to have a tendency to memorize. If we design some open exercises while consolidating what we have learned, it will be beneficial to give full play to students' potential. Open exercises include open conditions (insufficient or redundant conditions) and open conclusions (.
For example, after teaching a percentage of knowledge, a question is designed. Forty-eight students from a certain class visited the park, and the ticket office said, 5 yuan and 50 yuan have a 20% discount per person. How can we buy an economy? After careful consideration and calculation, the students came up with the following ways to buy tickets:
1. Buy all one 5 yuan: * * You need to pay 5×48=240 yuan.
2. Buy two more: 5×80%×50=200 (RMB).
3. Buy two more tickets and get a 20% discount: 5× 80 %× 50-2× 5× 80% = 192 (RMB).
4. Buy two more tickets and sell at the original price: 5× 80 %× 50-2× 5 = 190 (RMB).
The fourth method has the lowest cost, but it is speculative and cannot be adopted. This kind of open practice enables students to develop their thinking in the process of conceiving problems, solving problems and even making mistakes.
(6) Develop students' mathematical language ability and let language help students learn effectively!
Thinking ability is the core of analyzing and solving problems, and mathematical language is closely related to mathematical thinking: mathematical language is not only the carrier of mathematical thinking, but also the concrete embodiment of mathematical thinking; It is not only a tool of expression but also a tool of communication. The development of students' mathematical language and mathematical thinking is the premise of complementing each other, and it is also the guarantee to improve the effectiveness of mathematics classroom. However, in mathematics teaching, I found that students often can't express their thinking process clearly in words, and some problems can be done, but they can't reason. Language is the shell of thinking, and the lack of language often exposes thinking problems. Only when a student can correctly express related concepts in accurate, clear and concise language can he reflect the correctness of his thinking process and show that he understands what he has learned. Therefore, in a sense, "talking about the topic" is more difficult and important than "doing the topic". It is necessary to cultivate students' mathematical language ability and let language help them learn effectively!
(7) Learn to "take advantage of opportunism", seek a shortcut to skillfully solve problems, and achieve twice the result with half the effort.
"opportunism" is explained in modern Chinese as follows: using opportunities and clever means to seek personal gain, that is, not wanting to work hard, relying on cleverness to get lucky. This is a derogatory term used to describe a person who plays tricks for personal gain. However, in my years of mathematics teaching, I found that sometimes when thinking about mathematics problems, we might as well take some "opportunistic" ways and use our own intelligence to find a shortcut to skillfully solve problems, so as to achieve twice the result with half the effort.
For example, in the general review of the first volume of senior one, there is such a problem:
Counting from the left, it is the () th bead. Colour 14 beads.
When doing the first small question, most students worked it out one by one 18. But I am not satisfied with this, but once again inspired "Is there any other number method?" At this time, some students will think of the method of "two twos or five fives, or count 10 first, then eight, and then add up". When doing the second small question, most students still count to 1 1 from the left. At this time, I am not limited to this, but encourage students to actively think "Is there a faster and better way?" At this time, some students suggested that you can start from the right and count backwards: 18, 17, 16, 15, 14. Some people even say, with the method of 18-4 = 14, 18 counts four squares backwards, and the fourth one is the one to be colored.
Another example is the title:-=+= Its characteristic is that the numerator is 1 and the denominator is adjacent. When calculating, you only need to multiply the denominator to be the denominator, add the denominator to be the numerator, and subtract the denominator to be the numerator.
Another example: number A is greater than number B, and number B is less than number A.. Our solution is to regard the number B as the unit "1", that is, 1 share, then the number A is 1+= share. If the number B is less than the number A, we must use their difference to impose the number A, that is, ÷ =
This kind of problem is a teaching difficulty, and nearly half of the students can't understand it. At this time, the method of "opportunism" can be adopted, with the numerator unchanged and the numerator and denominator added. That is =
In addition to variant exercises and open exercises, we can also use analogy exercises and other training methods, which not only increase the interest in practice, but also better cultivate students' ability to analyze and solve problems.
In short, in problem-solving teaching, teachers can stimulate students' interest in positive thinking and gradually understand and digest problems according to the extension of teaching content and examples. In the long-term thinking training process, we should increase students' wisdom and ability, correctly guide students to actively explore new knowledge by using existing knowledge, think about problems from different angles, correctly use thinking methods, and analyze problems with practice. Further breaking through the difficult contents in primary school mathematics teaching, improving the efficiency and effect of classroom teaching, and combining learning knowledge with using knowledge will certainly further improve students' awareness and ability to solve problems and promote the development of students' thinking ability.