Teachers should first make students understand the importance and feasibility of self-study through a large number of facts and reasons. Let students know that lifelong learning has become the basic means of human survival, and self-study is the main form of lifelong learning. At the same time, it is also the need of mathematics learning and the only way to success. Let students realize the importance of self-study ideologically, and let them know that many successful people are self-taught. Only when students understand the meaning of self-study, will they be willing to learn by themselves, and will they take the initiative to learn by themselves, not because of the teacher's request. At the beginning, we should set some related questions, arrange specific tasks and guide students to learn independently. After students successfully try to teach themselves, they will naturally be full of confidence in teaching mathematics by themselves.
Second, to stimulate students' interest in self-study
Interest is the first element of success. Teachers should not only pay attention to students' interest in learning mathematics, but also pay attention to students' interest in "teaching mathematics by themselves". Only by stimulating their interest can students be willing to carry out self-study activities under the guidance of teachers. First of all, teachers should carefully design their study plans. At the beginning, the preview content in the study plan should not be too much, and the goal should be low, so that students can achieve it with a little effort and give them a sense of accomplishment. Then, students should be given time to show their self-study results. The way of presentation can be oral presentation, blackboard writing performance or group evaluation that students like, and stimulate students' interest in self-study through their favorite forms. Teachers should give affirmation and praise to students' progress in time. For some practical problems, such as origami, cutting, measurement and so on. , you can arrange for students to complete independently or in groups, and then compete between groups. Over time, students will find it interesting to learn mathematics by themselves, which will naturally form the habit of self-study and gradually improve their self-study ability.
Third, teach students specific self-study methods.
Cultivating students' self-study ability is a systematic and complicated process. In order to cultivate students' self-study ability, students must be required to preview before class, listen to lectures with questions, communicate and explore with classmates in class, review examples consciously after class, learn to do induction and summary by themselves, and then finish homework. These are all self-study classes. As a teacher, we should have a concrete and feasible plan and determine where to start. Only after long-term training can students' self-study ability be enhanced. I think we should start from the following aspects:
1, let students learn to teach themselves in reading textbooks.
For a long time, when it comes to reading, people naturally think of Chinese or English. Many students have no habit of reading math books. Even if you read a book according to the teacher's requirements, you just look at the theorems and examples in the book. Therefore, teachers should give timely guidance so that students can develop reading habits and master reading methods. The content of mathematics reading is mathematical language such as mathematical symbols, mathematical charts and mathematical terms. From years of teaching practice and investigation and analysis, it is found that students find it difficult to learn mathematics mainly because of improper understanding of the meaning of the question, disorder of language expression and difficulty in language conversion, in fact, poor mathematics reading ability. Therefore, we must attach importance to mathematics reading training in mathematics teaching. First of all, let students attach importance to mathematics reading ideologically and understand the importance of reading, thus stimulating reading desire. Secondly, teachers should guide students to "read" in a planned way. It can take many forms. Before class, students can teach themselves to read the guidance materials, read according to the outline, and set a few small questions for the reading content; You can also do inductive reading after class. In the process of reading, we should spread, analogize and associate knowledge, so as to achieve this and that, from less to more, from fragmented structure to forming a whole.
2. Let students learn to teach themselves in questioning.
Einstein once said, "It is more important to ask a question than to solve it ..." As the saying goes, only thinking can make you doubt, only doubt can ask questions, and only doubt can inspire students to think, doubt, ask questions, argue and answer questions in the process of "self-study". To cultivate students' self-study ability, we must first cultivate students' questioning ability. The key to cultivating students' questioning ability lies in how to make students ask questions and have the ability to ask questions, so that students can constantly have questions such as "what", "why" and "how to do it" about the knowledge points we have learned and all kinds of things we have encountered. While encouraging students to question boldly, teachers should strengthen the training of students' questioning ability and demonstrate some questioning methods in their usual education and teaching work. You can also ask questions about the teaching content in the study plan, let students think for themselves, and then bring questions to the classroom to discuss and discuss with students and teachers. Let students learn independently in questioning, and learn independently in questioning.
3. Let students learn to teach themselves in cooperation and communication.
As a way of learning, cooperation and communication have attracted more and more attention from all countries. Many developed countries in the west have taken the cultivation of mathematical communication ability as one of the new mathematics teaching goals.
When preparing lessons, teachers should carefully design some questions that students can exchange and discuss, and think out in advance which questions need necessary inspiration and guidance, and which questions need students to cooperate and communicate. In the lesson plan before class, some problem situations can be given for students to think about on the basis of reading. Then, in classroom teaching, teachers should give full play to the activity function of the group, provide students with more opportunities for discussion and analysis, and let students complement each other in knowledge, learn from each other's strengths in learning methods, gather wisdom and learn from each other's strengths, and collaborate and innovate.
The form of communication can be between students or between teachers and students. The communication between students can be in class or after class. The communication above class can take many forms, such as deskmate communication, group communication, group communication, class communication and so on. Above the classroom, students should be given ample opportunities to show their self-study results. Because the class time is limited, teachers can also assign some tasks that need to be communicated after class. The content of after-class communication can be aimed at the problems encountered in preview or homework. The communication between students can not only improve their understanding and application of mathematics knowledge, but also cultivate their self-study ability and team spirit.
For example, when I was teaching the center line of a triangle, a question came up in the preview class: What quadrilateral is obtained by connecting the midpoints of various quadrilaterals in turn? Please do it, record your findings and communicate with your classmates in class. In class, let them communicate with each other first, and then send representatives, which shows that the students' enthusiasm is very high, and the students summarize the content of this class clearly without the teacher's explanation.
In fact, organizing cooperative exchange learning is not a simple matter, which requires teachers to do a lot of preparatory work before class, understand the characteristics of students, thoroughly understand the teaching materials, and preset certain questions. Let them gain enlightenment and inspiration in communication and argument, and experience the collective strength and the fun of self-study.
4. Let students learn to teach themselves by induction.
It is also one of the important means to cultivate students' self-study ability to guide students to sort out and summarize their knowledge and make them discover and understand some mathematical thinking methods. Teachers should guide students to sort out, classify and integrate their knowledge, understand its context, communicate its vertical and horizontal relations and grasp the knowledge structure as a whole according to the key points of knowledge, the difficulties of learning and the weak links of students. Finishing can not be limited to the simple low-level repetition of existing knowledge, but should be good at drawing inferences from others, guiding migration and discovery in the nearest development area of students' cognition, and constantly expanding students' cognitive structure.
For example, after the first chapter of the ninth grade "Graphics and Proof", students are required to sort out and summarize the relationships among parallelogram, rectangle and rhombic square in a certain way, and form a knowledge network by comparing and discriminating the relationships between knowledge, so as to cultivate students' sorting consciousness and develop their sorting ability.
In the process of knowledge arrangement, teachers should consciously cultivate students' awareness of independent arrangement and develop students' ability of independent learning.
Fourth, the cultivation and persistence of self-study habits.
From primary school, teachers let students go home to preview what they will learn the next day. However, even in middle school, how many students can preview consciously? They always give priority to the homework that needs to be written, and then forget the preview content assigned by the teacher. Most students have no habit of self-study. If you want to develop the habit of self-study, it must be a concrete and long-term process, and you can't rush for success. At the beginning, every day the teacher carefully designed a "tutoring plan". The so-called tutoring plan is a plan to guide students to learn independently. Because students don't have the habit of self-study, they can't generally say which unit and which section to preview, so they must be given specific self-study tasks. For example, teach yourself how many pages of the textbook, think about the "practice and exploration" in the book, think about the three questions raised in the book, record your own thoughts, and so on; Or 3 cases and 4 cases on one page of the self-study textbook. Is there anything you don't understand? Write it in a book, discuss it with group members in class and so on. Teachers should give students time in class, first communicate what they don't understand in self-study, and then show their thinking results in various ways. In the process of specific training, we should not be impatient, but step by step and stick to it for a long time. Let students get the joy and fun of success from self-study and let them have confidence in self-study.