First, preview habits before class
1. Analysis of the current situation: (At present, preparing for the exam before math class is not optimistic, as long as there are the following reasons)
(1) Teachers don't pay enough attention to it. .
When it comes to preview before class, many teachers and students think of Chinese preview-looking up dictionaries, dividing paragraphs, writing paragraphs and so on. Many teachers don't realize the practical significance and value of preview before math class. When arranging students to preview, teachers often say, "Go home and preview what you will learn tomorrow." Students have no idea what the teacher wants them to preview because of their limited self-study ability. When previewing, I often don't know where to start. I simply read math books and do exercises after class. For a long time, students have been perfunctory about preview. This preview has no effect at all, making it a form or slogan.
(2) Some teachers have always advocated that you can't preview.
There are also some teachers who have always argued that you can't preview. They think that after previewing, you can't go to class, and students know the result. What else does the teacher teach? Students lose their desire to explore and enthusiasm for learning in class. We often find that some teachers have finished a class and students' books have never been opened. Sometimes, after listening to a class, they finally know what he is doing in this class. They tried to create some suspense for students and arouse their curiosity. How can such a teacher be willing to let the students preview before class and let all the ideas go to waste?
(3) The requirement of preview is too high, and students' learning initiative is not mobilized.
Pupils are young and have limited self-study ability. When the teacher arranges the preview, he only arranges the preview task according to the textbook content, without considering the students' understanding ability, and requires the students according to the adult standard. For example, when teaching the "24-hour timing method", if the teacher only arranges the preview task according to the content of the textbook, qualified students can understand the 24-hour timing method under the guidance of their parents, and most students can't meet the preview requirements at all. The 24-hour timing method is actually quite abstract, because students are exposed to ordinary timing methods in their lives, so it is really difficult for students to turn around and use the 24-hour timing method. It would be much easier if the teacher asked the students to investigate how TV, radio, post and telecommunications departments express time. In this way, students not only have the ability to do it, but also can feel that mathematics is around them in the process of inquiry, so that students can truly appreciate the application value of mathematics, thus stimulating students' enthusiasm for learning mathematics.
(4) The quality of students is uneven.
Some students, because parents attach great importance to their children's learning, don't teach by themselves. As long as they arrange preview tasks, parents are explaining them. In this way, students are not interested in the process of exploring new knowledge in class. In fact, under the guidance of their parents, these students only mastered the results and did not really participate in the whole process of knowledge formation, that is to say, students only know what this part of knowledge is, but they don't know why. There are also some students who only read books and do exercises after class, so they are familiar with what they want to learn in advance and fail to really understand the connotation of preview, making preview a mere formality. Some students don't preview at all after class. For various reasons, the efficiency of preview before math class is very low.
So how to cultivate students' preview habits before class?
(1) "Guidance"-Develop a preview outline and define preview tasks.
For example, preview the understanding of cuboids and cubes.
Name ()
Preview navigation
Cuboid: ▲ research order: according to the order of face, edge and vertex;
▲ Research content: quantity, shape, size and length.
▲ Research methods: Take a look, count, cut everything, measure and compare …
Cubes: ▲ Use the experience of studying cuboids to study cubes. You can study independently or in cooperation. Look what you found. How did you find out?
What else did you find? Write it down:
In this way, students will have a clear goal, and of course they can also achieve the effect of preview.
(2) "Thinking"-let students think about the problem-solving process and methods of examples and why. What knowledge have we learned from this part of knowledge? How to answer some questions in the textbook? What else can you think of
(3) "Practice"-complete the relevant "try" and "practice" in the book to test your preview.
In fact, preview before class is one of students' learning routines and the first link in their learning process. Perhaps in our primary school stage, it still doesn't reflect its importance, but it is very important to prepare for junior high school. Some people say that pre-class preparation is like pre-war reconnaissance in a battle. Where is the bunker, where is the bunker, where is the strongest place, where is the weak link and so on. You can have a preliminary understanding through preview. In this way, when you attend class with questions, you will listen more carefully, compare your understanding of the textbook with the teacher's explanation, deepen your understanding and memory of the textbook, and correct some of your one-sided understanding. More importantly, it can also cultivate your self-study ability and enhance your sense of innovation, which is an essential ability in your future study and work.
Second, the habit of listening.
"Listen carefully to others' speeches" is not only an important source of external information, but also a manifestation of a person's civilized behavior. Unfortunately, some of our children don't know how to listen carefully to others' speeches, which shows that they can't concentrate on listening to the teacher's explanation during class and are constantly distracted; Group discussion will not listen to other students' speeches. When one person is alone, he will speak loudly, and others will not listen when they are talking. Can't chat with people, can't stare at each other, and often show an absent-minded attitude when talking with people. These are not good habits and must be corrected.
Pupils are curious and active, and their attention is unstable and not lasting. Especially when encountering novel stimuli, they are always willing to see, listen and move, which is determined by their age characteristics. Listening carefully is the basic guarantee for children to receive information, absorb knowledge and learn mathematics well. How to deal with the contradiction between the two, so that children can develop the habit of listening attentively?
1. Teachers should be infectious and attractive, attract children with vivid language and make them feel compelled to listen. Over time, they will form the good habit of loving, thinking and listening. Some teachers may be gifted at language, but I can't speak those childish languages, and I feel uncomfortable speaking them. I feel the same way. Language problems have been bothering me, but later I found that children's language can be practiced as long as you have that heart. We also found that some teachers told the same story vividly, actively mobilized children's desire for learning, and some teachers were indifferent to students after they finished speaking. For example, when teaching the understanding of 10, a teacher wrote a fairy tale: Today, the numbers of 10 from 0 to 9 are waiting in line to play games, and 9 knows that it can be the most proud. It said to the number 1~8, "You are not as big as me, especially you are -0. You are really too young to have anything. How can you talk to them? " "0" was very sad after listening, and tears flowed out of her round eyes. At this moment 1 walked up to 0, took 0 by the hand and said to 9, "We are bigger than you hand in hand!" Students are attracted by this story and naturally enter new knowledge learning. Therefore, when creating a situation, you must integrate your true feelings, so as to resonate with children.
2. Strengthen listening training. Some people say that "listening" is not easy. People listen from birth. Children attend classes every day in primary school and listen to others every day. Do they still listen? Not exactly. Some people listen to the lecture, although their eyes are wide open and they are very focused, but they don't know what to say after listening. Therefore, I said that listening needs training. First, let the students understand. No matter what teachers or students say in class, they should ask questions in time: "Did you understand what XX said just now? Can you tell us the meaning of his speech or the question he asked? " "Who knows what he just said?" Second, when listening to others, keep your eyes on them. When children speak in class, we can make such a request: "Please face everyone" and "Please listen carefully and ask questions in time". In class, when students communicate in groups, we can ask, "What's the difference between XX and XX just now?" Or "What do you have in common with his ideas?" In this way, students must concentrate on the lecture and not be distracted. In addition, students can be reminded to pay attention to the teacher's lectures through slogans, which are used more in lower grades. Teacher: "Small eyes-"Student: "Look at the teacher." Teacher: "Small ears-"Student: "Listen to the teacher." The teacher's inspiring language is also very helpful for students to concentrate on the class, such as "xx children really listen to the class, and his eyes follow wherever the teacher goes"; "XX children are really careful in class, and the teacher sees it." "XX was so absorbed in listening to other people's speeches that he heard problems that no one noticed." Wait; This can better mobilize the enthusiasm of children to listen.
3. Teachers don't repeat, don't repeat. After becoming a teacher, we gradually found ourselves more and more verbose. We repeat it again and again for fear that the students won't understand. Homework after class is written on the blackboard in case students forget it. Therefore, I suggest that students should be asked questions or assigned homework only once in the future, and don't repeat them. Make use of the teacher's good habit of "not wordy and repetitive" and develop the good habit of "being attentive, serious and not distracted" in class.
Teachers should set an example. Teachers should take the lead in what children are asked to do. Every time I talk to children, I always observe them and carefully observe every change that passes by their faces. Even when some students answered irrelevant questions, I listened attentively and waited patiently for others to finish, without interrupting. Over time, students also learned to listen to others as attentively as teachers.
Third, cultivate the habit of independent thinking.
Case: There are 80 peach trees, 20 pear trees are more than peach trees, and what percentage of pear trees are more than peach trees?
Health 1: 80-20 = 60 (tree) 60 ÷ 80 = 75% (mostly)
Health 2: 80-20 = 60 (tree) 80-60 = 20 (tree) 20 ÷ 80 = 25% (minority)
Health 3: 20 ÷ 80 = 25 (rarely)
Judging from the case, it exposes some of the current students' ideological conditions. We found that students can only "Baidu" when solving problems (he applied the idea of solving problems to the current topic when searching for similar topics), and will not seriously think about the specific situation and make specific analysis. I often hear many parents and teachers say that "my children never think independently, and they either do things blindly when they encounter problems, or ask teachers or parents". Why is this happening? It is because these children have not developed the good habit of independent thinking. The famous educator Fekov pointed out: "Teaching students to think is the most precious capital in their lives." Mathematics is the gymnastics of thinking. To learn mathematics, we should not only master its formulas, theorems, rules and concepts, but also understand the process of knowledge generation and development. We should observe, experiment, guess, verify, reason and communicate in the process of participating in mathematical activities, and this series of activities can not be separated from thinking and independent thinking of people. Only by being diligent in thinking and good at independent thinking can we deeply understand and master the essential meaning of mathematical knowledge, grasp the internal relations and laws of mathematical knowledge, and form various mathematical thinking and mathematical abilities. How to cultivate students' habit of independent thinking?
1. Teachers should create a space for children to think independently.
There is a phenomenon in many classes now. When the teacher asked questions, the middle and junior students didn't start thinking, and those students with good grades and quick thinking had blurted them out. In this way, many students are deprived of the opportunity to think by these good students. In the long run, he will be too lazy to think until things are ready. Therefore, teachers should create a good thinking space for students, let every student participate in the formation of knowledge, and let every student develop good speaking habits. Secondly, in class, our teacher should not talk too much and be too straightforward. We should give children enough time to think and give them a full understanding process. Minimize such questions: "Really?" "okay?" And some fill-in-the-blank questions, such questioning thinking is too low, and students' thinking can certainly not be trained.
2. Create opportunities for children to communicate with each other.
Let them communicate the results of their independent thinking with their partners, feel the fun of thinking in communication, learn to appreciate the results of peer thinking, and thus promote further thinking and communication. Only independent thinking can produce opinions (even if this opinion is wrong, teachers should encourage students to speak out boldly instead of following the trend and dare to insist on expressing their opinions. ), with an opinion, there is a desire to communicate. With communication, we can stimulate new thinking. Developing the profundity of thinking in communication and generating interest in thinking will gradually form the habit of independent thinking.
3. The new teaching is to strengthen variant exercises.
In mathematics learning, there will be such a word, that is "mentality". Mentality has two sides, both negative and positive. Thinking set can be understood as: always thinking in a certain habitual way, then, when this habitual thinking is inconsistent with the path to solve the problem, it will form a negative transfer, which will fix the thinking in a certain framework and make it difficult to solve the problem; But when this habitual thinking is consistent with the way of solving problems, it can promote the emergence of positive migration and help solve problems. Therefore, through variant exercises, not only can students' thinking be developed, but also their agility, flexibility, profundity and divergence in mathematical thinking can be cultivated, and their mathematical thinking ability can be improved.
4. Teach students problem-solving strategies
Now we often find that students can't start when they encounter nonstandard questions (variant questions, uncommon questions). Students don't want to think, but they don't know where to think. In other words, our students lack strategies to solve problems in their minds. What is the strategy to solve the problem? "Problem-solving strategy refers to the ways and methods to seek the answers to mathematical problems." Psychological research shows that in the process of solving problems, if you are not exposed to standard patterned problems, you need creative thinking, and you need to correctly choose a problem-solving strategy to help realize this creative process. If our students have problem-solving strategies in mind and will choose them, then no matter how difficult or complicated the problem is, they can solve it.
First, let's learn a problem-solving strategy. Problem solving strategies can be divided into general problem solving strategies and special problem solving strategies. The general problem-solving strategy is what we often call the problem-solving steps: understanding the meaning of the question, making a problem-solving plan, answering questions as planned, and answering questions. Special strategies include: example, drawing, list, finding the law, inverse deduction (column equation), transformation and so on. Below I will focus on several special strategies that we often use when solving mathematical problems.
! , sample policy
Examples are more suitable for questions that contain letters or only talk about quantitative relations but cannot be calculated, because students are used to getting answers through calculation, and using examples can turn uncountable questions into calculable questions. For example: (1) The radius of the great circle is three times that of the small circle, so the circumference of the great circle is () and the area of the great circle is (); (2) The number A is 20% of the number B, and the number B is more than the number A (); (3) There are A trees and B trees are all dead, and the survival rate is (). This kind of problem that cannot be calculated without specific data is often difficult for students to start with and can be easily solved with examples. In communication, teachers can guide students to think: "Why do some students calculate correctly and quickly, while others calculate for a long time or are wrong?" Students will soon understand that when giving examples, you should choose the calculated data according to the data in the topic, so that you can get twice the result with half the effort.
2. Drawing strategy
This strategy is suitable for solving the problem of abstraction and visualization. It is a strategy of "displaying the meaning of a problem intuitively with a simple chart, expressing the quantitative relationship in an orderly manner, and finding and determining the solution method from it". For example, when students do complex "multiple application", "percentage application" and "fraction application", they can use line charts to help us understand the meaning of the problem, clarify the quantitative relationship in the problem and find solutions. Students also want to draw pictures when solving problems, but they can't draw clearly, so they should be taught to draw line segments. For example, the percentage of application questions should be drawn as a whole "1" (not something drawn before any sentence) and then other related quantities should be drawn according to this whole "1"; Also think about whether to draw a line segment or two line segments. Only when students learn these things can painting really serve students' study.
3. Inverse strategy (column equation)
This strategy is more suitable for known results and requires the original number of questions. The reverse thinking method is relative to the forward thinking method. When analyzing and solving application problems, forward-looking thinking is based on the order in which conditions appear; Reverse thinking is a thinking method of reverse reasoning from the opposite direction (or from the result), not according to the order in which the conditions appear in the topic. Students with reverse thinking are not used to it, so equation is the best way to turn reverse thinking into positive thinking. For example, the circumference of a semicircle is 15.42 cm and the radius is ().
There is an old saying in China: "It is better to teach people to fish than to teach them to fish", which means that it is better to teach people knowledge than to teach them how to learn it. Then let's teach students to use problem-solving strategies!