Many improvements have been made in the content arrangement of the new curriculum reform textbooks. However, due to the influence of traditional textbooks and teaching models, teachers are often unable to get rid of the shackles in teaching. There is a lot less to say, that is, the essence of the lecture is not particular, and the content is neither focused nor concentrated, which makes students feel at a loss and causes low efficiency in the classroom. In fact, as long as we analyze it, the new curriculum reform textbooks are nothing more than rearranging and selecting on the basis of the original textbooks to make them more scientific and reasonable. Many contents increase the link of students' independent exploration and thinking, and pay attention to cultivating students' self-study ability and independent problem-solving ability. In teaching, teachers should pay attention to digging up teaching materials and deeply understand their contents. On this basis, according to the content of each class, the teaching time is reasonably allocated, combined and decomposed, the places that should be taught are highlighted, and the places that should not be taught are returned to students, so that students can find and solve problems, making "hands-on practice, independent exploration and cooperative communication" become the main learning methods of mathematics.
Second, focus on mobilizing students' thinking participation
Participation is the basic guarantee for students to achieve active development. Mathematics teaching is a process of mutual communication between teachers' thinking and students' thinking. From the perspective of information theory, this kind of communication refers to the dynamic process of receiving, processing and transmitting mathematical information. This process is full of mathematical communication and information conversion between teachers and students. Without the participation of students, the whole process will be difficult to flow smoothly. Therefore, improving students' participation in mathematics classroom teaching can not only improve the quality of mathematics teaching, but also improve students' quality.
So, how to mobilize students' "thinking participation"? First of all, it is necessary to create situations and skillfully ask questions, which will trigger students' psychological cognitive conflicts, and make students in a state of "thinking through their hearts but not getting them, but speaking with words and expressing their abilities". At the same time, teachers should delegate power to students, give them opportunities to think, do and speak, let students speak freely and let as many students as possible. When the conditions are met, students will naturally get excited, and their enthusiasm for participation will be high, and their participation will be greatly improved. Only by actively, actively and excitedly participating in the learning process can individuals develop. In mathematics teaching activities, the effect of teachers' leading role should be measured by whether students' main role is fully exerted. Without the active participation of students, the leading role of teachers is meaningless. Teachers' "guidance" should be scientific, enlightening and artistic, which can fully stimulate students' thinking activities. Because the establishment of important concepts in mathematics, the revelation of formula theorems and the application of knowledge all run through the spirit of human being's courage to explore and innovate, and are full of "sparks" of human creative thinking, teachers should inspire and guide students to participate in these creative activities personally, so as to achieve the purpose of developing intelligence and ability, improving the quality of creative thinking and enhancing creativity. Teachers should design teaching links that are conducive to students' participation in combination with teaching content, improve students' participation, and then cultivate students' participation.
1. Participate in the process of establishing mathematical concepts. The formation of mathematical concepts generally comes from the need to solve practical problems or the development of mathematics itself. The definition in textbooks often hides the thinking process of concept formation. Teachers should actively guide students to participate in the process of establishing mathematical concepts, which can not only make students understand the ins and outs of concepts, deepen their understanding of concepts, but also help to cultivate students' awareness of participation.
2. Participate in the formula discovery process. There are two situations in the formation of mathematical formula theorem: first, after observation and analysis, a conjecture is put forward by incomplete induction and analogy, and then logical proof is sought; The second is to draw a conclusion through theoretical deduction. Every formula and theorem in teaching is the crystallization of mathematicians' hard work, and their research contains profound mathematical thinking process. At present, the teaching materials only have the conclusion and derivation process of formula theorem, but lack the discovery process of formula theorem, and students are also very interested in this kind of problem. Therefore, guiding students to participate in the discovery process of formulas and theorems is conducive to cultivating students' sense of participation.
3. Participate in exploring different solutions to the same problem. The problem is the core of mathematics. To solve mathematical problems, students should be guided to follow four steps: defining problems, making plans, realizing plans and reviewing. Example teaching gives students some time to think. Teachers should inspire students to associate, think and explore a mathematical problem from all angles, which not only strengthens the horizontal connection between knowledge, but also improves students' thinking ability and interest in learning mathematics, which is conducive to cultivating students' sense of participation. Although it will take students a lot of time to get the above results, it is more valuable to do such a problem than to do five. At the same time, students participate freely, their sense of participation is enhanced, and their thinking is more active. Therefore, it is necessary and worthwhile to spend some time.
If students are defined in a certain way of thinking, that is, they are not really given the right to participate and autonomy, which will also lead to students' inactive thinking and lack of openness. The main way of mathematics teaching is classroom teaching, which is the place where teachers and students, learning and students, teaching materials and students interact. In the classroom, we should greatly mobilize the enthusiasm of students' thinking, give play to their subjective initiative in learning, stimulate their enthusiasm for mathematics, let them study under urgent needs, let them study mathematics consciously, and let students really become the main body of classroom teaching. Practice has proved that the enthusiasm, depth and breadth of students' participation in classroom teaching directly affect the effect of classroom teaching. Without the active participation of students, there will be no successful classroom teaching.
Third, the use of questions to stimulate the enthusiasm of students thinking
1. Carefully create problem situations to arouse the enthusiasm of students' thinking. Interest in learning and thirst for knowledge are the motivation for students to think positively. An effective way to stimulate students' interest and curiosity in learning mathematics is to create appropriate problem situations. In the situation of mathematical problems, there is a cognitive conflict between new demands and students' original mathematical level, which can induce students' enthusiasm for mathematical thinking. When teachers create problems, there are two criteria to measure the design of problem situations, that is, it is conducive to stimulating the enthusiasm of students' thinking and directly conducive to teaching purposes.
2. Enlighten and guide, and keep the continuity of thinking. In appropriate problem situations, the enthusiasm of students' thinking is fully mobilized, but how to maintain this enthusiasm and make it continue uninterrupted?
(1) Give students time to think. Mathematics learning is carried out through thinking. Without students' thinking, there is no real mathematics learning, and it takes some time to think about problems. It is worth studying how much time teachers should give students to think after asking questions. Experiments show that if the thinking time is short, students' answers are usually short, but if the thinking time is prolonged a little, students will answer questions more comprehensively, so that the qualified and correct answer rate will be improved. Of course, the length of thinking time is closely related to the difficulty of the problem and the actual level of the students. At present, in classroom learning, after teachers ask questions, they don't give time to think and ask students to answer immediately. When the student can't answer immediately, he will repeat his questions or ask some other questions to make up for the "silence". In fact, it interferes with students' thinking. And "silence" is often students thinking, seemingly calm, but in fact thinking activities are very active.
(2) Inspiration should be synchronized with students' thinking. After teachers ask questions, students should generally think about it first, and teachers can give appropriate inspiration and guidance when necessary. Teachers' inspiration should follow the students' thinking rules, make the best use of the situation, step by step, and don't force students to think according to the methods and ways put forward by teachers.
(3) We should constantly ask students new teaching questions. Problems are the core of teaching, the motive force of teaching thinking and the direction of thinking. The process of mathematical thinking is also the process of constantly asking and solving problems. Therefore, in mathematics classroom learning, teachers should constantly ask students new mathematical questions, provide motivation and direction for deeper mathematical thinking activities, and make mathematical thinking activities develop continuously. Appropriate mathematical problems must meet the following conditions: ① Problems should be directional. This means that questions should have a clear purpose and make students' thinking tend to the teaching goal. ② The difficulty of the question should be moderate. This means that the problem should not be too difficult or too easy, and there should be a certain slope between difficulty and difficulty. ③ The questions should be enlightening. Some teachers often mistake heuristic for asking questions, thinking that the more questions, the better. In fact, the question is not how much, but whether it is enlightening, whether it is a key issue, whether it can touch the essence of the problem and guide students to think deeply. For example, a piece of triangular glass broken into three pieces was introduced into congruent triangles's judgment, and the teacher asked, "If I was taken away, how many elements of the triangle were taken away? If I take II, how many elements of the triangle will I take? If you take III, how many triangular elements will you take? " This is a very critical and enlightening question, which causes students to think deeply and lays the foundation for students to learn to use "Angle Axiom".
3. Pay attention to the questions raised by students. In parallelogram class, the whole class is in the form of teachers asking questions and students answering them. The atmosphere was warm and the students' answers were good. But after class, the author found that none of these questions were put forward by students, which limited the development of students' thinking. Therefore, the author realizes the importance of cultivating students' "problem consciousness" and gradually changes the habit of throwing questions at students and letting them answer them into asking questions and solving problems by themselves. In short, in classroom teaching, carefully creating problem situations can stimulate and guide students' thinking, mobilize students' learning enthusiasm and improve their academic performance.
Four, the usual teaching should be good at connecting with the content of the senior high school entrance examination and competition.
Experienced teachers are always good at integrating learning content with the content of senior high school entrance examination or competition in the teaching process. In the process of listening to the class, students can deepen their understanding and knowledge in the process of learning the new curriculum, and unconsciously accept the influence of the mid-term exam questions or competition questions. In the usual teaching, the author pays great attention to doing problems, especially all kinds of mid-term exam questions or competition questions. After finishing, he is good at summing up, breaking down various problems into various sections, and letting similar problems run through students' training.
If you want to get good grades in the senior high school entrance examination or competition, you can't get results after a month or two of cramming. First of all, the teacher should do more questions, know fairly well, give the students a glass of water, and the teacher should have a bucket of water. The second is to infiltrate more in the classroom. Usually, in order to pay attention to the improvement of students' ability and enhance their interest in learning mathematics, the author will leave one or two math problems with certain thinking value on the blackboard in each class, or contest questions or mid-term exam questions, so that students of different levels can discuss them in their spare time, thus improving their ability to analyze and solve problems and cultivating their interest in learning mathematics.
Fifth, teach students mathematical ideas and methods
In the usual teaching, many teachers go into a misunderstanding that students can improve their academic performance by doing more questions, so the sea tactics have become a magic weapon for many teachers. As everyone knows, this not only stifles students' interest in learning, but also seriously dampens their enthusiasm for learning, not to mention activating their thinking.
We all have an experience that many people who study mathematics can still solve some very complicated mathematical problems without contact after 20 or even 30 years. Why? It is very important here that they have mastered the ideas and methods to solve mathematical problems. Basic mathematical ideas are permeated in middle school mathematics. If it can be implemented in students' thinking activities of learning and using mathematics, it will play a methodological role in developing students' mathematical ability. Therefore, only by letting students master the ideas and methods of mathematics will they be able to follow suit with ease. In fact, as long as we analyze the test questions in the senior high school entrance examination or competition less, we will find that each item contains certain mathematical ideas and methods. In the final analysis, it is not advisable to improve your grades by touching familiar questions during the examination. Teachers' energy should be used to cultivate students' mathematical thoughts and methods at ordinary times.
Sixth, give students legal guidance while giving lectures.
Guiding and teaching students to learn is an important embodiment of teachers' quality in the 2 1 century. It is a traditional teaching view to regard teaching as imparting knowledge, which also lags behind the requirements of the times. Learning method guidance, referred to as mathematics learning method guidance, is an important part of "learning to learn". The role of teachers in the teaching process is only to provide various favorable conditions for the development of students' understanding, that is, to help and guide students to learn and cultivate students' ability and habit of self-study. What teachers should do is to be good at "teaching people to fish" and teach students to learn to learn, which is also one of the requirements of the new curriculum reform. While imparting knowledge, teachers should give students more guidance on learning methods, and guide students' learning habits, learning methods, thinking and solving problems, and even doing homework, so as to make them more scientific and reasonable. Students are required to concentrate on their studies without external interference; Patience and meticulous, independent thinking, not copying other people's homework; Learn to analyze the difficulties in learning and overcome inferiority and pride.
In short, the guidance of students' mathematics learning methods should strive to change ideas and teaching methods, in-class and out-of-class, learning methods and teaching methods, teachers' guidance and students' exploration, unified guidance and individual guidance, and establish a crisscross learning guidance network to promote students to master the correct learning methods.
Seven, the language of mathematics classroom teaching should pay attention to art.
Language is the direct embodiment of teaching ideas and the most widely used and basic information carrier for teachers. The process of mathematics classroom teaching is the process of transferring mathematics knowledge. In the whole classroom teaching process, the transfer of mathematical knowledge, the feedback of students' acceptance of knowledge and the emotional communication between teachers and students must rely on mathematical language. Teachers' language expression and quality directly affect students' acceptance of knowledge, and teachers' language emotion triggers students' emotion, so teachers' language art is the core of classroom teaching art, and the teaching language should be not only accurate, standardized, rigorous and simple, but also interesting and easy to understand, and the metaphor should be humorous and appropriate.
In fact, teachers' classroom language art is varied, which not only reflects teachers' teaching ability, but also is closely related to teaching quality. Mathematics teachers should explore, summarize and improve their own teaching language in teaching practice according to the requirements of quality education, so as to achieve the dialectical unity of scientific and artistic mathematics teaching language. In this way, the teaching level will naturally improve.
Eight, good at communicating with students
As the saying goes, "Learn from your teacher and believe in it." Only by realizing the zero distance between teachers and students can students open the window of their hearts and accept everything taught by teachers.
Harmonious teacher-student relationship is the key to improve teaching quality. First, the relationship between teachers and students should be relaxed, so that students can live and study freely and happily, and their intelligence can be stimulated to the maximum extent; Second, there must be a teacher-student relationship of mutual trust. Only by mutual trust can all kinds of information output by teachers be unimpeded in students' minds, thus achieving the best teaching effect; Third, there must be expectations. Teachers are full of trust and expectation for every student, which will give students a potential inspiration and strength. Practice has proved that students like enthusiastic, kind, respectful, patient and tireless teachers. Although some teachers have profound professional knowledge and strong ability to analyze and teach textbooks, they are not good at establishing sincere and cooperative relations with students. There is an emotional gap between teachers and students, and teaching and learning cannot be coordinated, which leads to half the effort. Therefore, a good teacher-student relationship is the guarantee to improve the quality of education.
Generally speaking, to improve the quality of mathematics teaching, teachers' good self-quality is the foundation, the correct view of students is the premise, students' interest in learning mathematics is the key, excellent teaching methods are the means, and good teacher-student relationship is the guarantee.