First, based on life, stimulate students' interest in learning mathematics.
Einstein said, "Interest is the best teacher." Learning inspired by students' inner needs and interests is naturally autonomous learning. The teacher's job is to turn the goal to be achieved into students' internal needs and the teaching content into students' interest points. On this basis, teaching activities will be carried out smoothly in the state of students' thirst for knowledge, and students will understand learning as their own business, not imposed by the outside world (teachers or parents). In the process of learning, students will actively explore and solve problems in learning through various channels. Students' body and mind are in a state of pleasure and stretching, and their autonomy is easy to be brought into play and reflected.
Taking the familiar life situations and interesting things as the starting point of teaching activities, students can quickly enter the "nearest zone" of thinking development and master the initiative of learning. The strategy of creating life situation should give more consideration to students' life foundation, and strive to establish similar or similar connections between students' life and math problems, so that students can have more construction foundation and exploration motivation. For example, when talking about the triangle exterior angle sum theorem, the introduction of the theorem was adapted as: "Xiaoming walked around the periphery of a triangular flower bed (as shown in the figure) and turned an angle at each corner (∠ 1, ∠2, ∠3), so when he returned to his original position, it was a * *. Do you want to know the sum of the outer angles of a triangle? " ..... This problem comes from life. After it was put forward, the students felt a sense of deja vu. I have a great interest in this problem, which has stimulated students' learning motivation and laid a good foundation for solving this problem. Second, set targeted questions and cultivate good thinking habits. Targeted problem design is a problem that focuses on teaching objectives, highlights key points and difficulties, and has clear design intentions. Not only in the design of classroom questioning, but also in the problems existing in the learning process. Teachers should aim at designing problems and teaching objectives, and strengthen students' complete thinking habits. In the teaching of plane geometry, there are several exercises for discussion. Question 1: In the same plane, how many parallelograms can be spelled by putting two congruent triangles (three sides are not equal) together and making a set of corresponding sides overlap? Question 2: If the distances between point A and point B on the plane and the straight line CD are m and n(m￠n) respectively, what is the distance between the midpoint of the straight line AB and the CD? For the above problems, students are often not comprehensive enough when considering them, that is, they do not fully consider the placement of graphics. Practice has proved that this kind of problems have strong pertinence and clear goals, which can reflect the problems existing in students' learning in time, deepen students' understanding of knowledge and achieve good results. In classroom teaching, students should also design some questions that are easy to be confused and fooled, so as to make their thinking more comprehensive and mature. For another example, after learning the "trilateral relationship of triangle", I designed such a question: Xiaoming's home is 2 kilometers away from school, Xiaohong's home is 3 kilometers away from school, and Xiaohong's home is how many kilometers away from Xiaoming's home? Many students see this problem and think it is very simple, 5 km or 1 km. Obviously, students are fixed by thinking. They think that Xiaoming's family, Xiaohong's family and school are in a straight line. Once they are found not in a straight line, they feel cheated. Through such questions, students feel that they should consider the problem comprehensively and thoroughly, so as to gradually cultivate students' complete mathematical thinking habits and lay a solid foundation for solving problems. Third, set up acceptability questions to stimulate students to actively participate in problem design. Acceptability is to design some questions with moderate difficulty according to students' cognitive rules, so that students can easily understand and master mathematical knowledge. According to the teaching principle of "jumping up and picking peaches", the problem design should be moderate. The so-called "degree" means that the difficulty is moderate and just right. Students can accept it, which is too easy to stimulate students' interest in thinking. If it is too difficult, it will dampen students' enthusiasm for thinking.
Second, through the careful design of setting questions, stimulate students' thinking.
With the implementation of new curriculum standards, problem design is becoming more and more important in classroom teaching, which is of great significance to improve teaching quality and cultivate students' thinking and problem-solving ability. Teaching should be based on problems. The so-called question-based teaching is to let students walk into the classroom with questions and walk out of the classroom with questions. Therefore, the problem is the key to the success or failure of a class. It can not only enliven the classroom atmosphere, stimulate students' interest, understand students' knowledge, but also penetrate students' hearts, induce students to think, develop students' intelligence, adjust students' thinking, and realize emotional communication between teachers and students. For example, in the teaching of complete square formula, the author created such a problem scenario. There is an experimental field in a forest area. Now divide it into four pieces and plant different plants on it: Question 1: How many ways can you represent the total area of the experimental field? Question 2: Please calculate (a+b)2 and a2+ab+ab+b2 Question 3: Observe the results of the two formulas. What did you find? Through the introduction of this problem scenario, students unconsciously stimulated their enthusiasm for learning and actively explored new knowledge. In the process of experience, exploration and communication, students feel that everything is so natural and easy to accept. Therefore, the author believes that teachers should carefully arrange and ask questions properly, so that students can master knowledge and jump up to pick peaches, which is neither readily available nor hard to jump up to catch. Only in this way can we learn more easily and naturally, and can we inspire students to actively explore new knowledge. Setting up hierarchical problems and activating the hierarchical design of students' thinking problems are of great significance for solving "general problems" and reducing the difficulty of thinking. That is, lay a ladder, gradually deepen, and design some "sub-problems" around a "general problem". When designing questions, teachers should follow the students' thinking characteristics, from easy to difficult, from simple to complicated, from shallow to deep, step by step, hierarchical, rhythmic, coherent, echoing and gradually deepening, so that students can carry out exploration activities step by step around "general problems". For example, we are discussing how to divide a known line segment into 2: 3: 4. The following questions can be designed and then advanced layer by layer. Question 1: which knowledge point is emphasized in this picture? Question 2: What do you associate with dividing line segments according to this ratio? Question 3: How to draw with the bisection theorem of parallel lines? Question 4: If the question is changed to divide the line segment into 3: 5: 7, how to draw it? Question 5: What have you learned by reflecting on the drawing process of this question? For another example, when calculating (n is an integer other than 0), you can design the following "question" chain: Question 1: What do you think of when calculating and observing features? Question 2: How to split articles by the article splitting method? Question 3: What did you get by reflecting on the calculation process just now? Question 4: Observing the above question, what will you do with the above formula to keep the previous equation unchanged? Question 5: What did you learn from it? These two problems have a common feature. By setting up "sub-problems", the difficulty of thinking about problems is reduced. Students actively think about in-depth problems and find corresponding countermeasures, which enriches the experience of mathematics activities, improves the level of thinking, and enables students to feel the joy of success in active thinking activities.
3. Carefully organize activities to reveal the essence of mathematics by asking questions.
Activity teaching is a basic teaching paradigm, which is carefully designed and guided by teachers, and promotes the reorganization, reconstruction and development of students' emotional state, cognitive structure and function through their active and conscious participation, exploration and practice. The purpose of the activity is not the activity itself, but to establish or reorganize various contacts and relationships through experience, so as to realize the optimization of students' all-round quality development. For example, I designed an activity like this:
Teacher: Please draw a square with the fastest speed. then
(1) Think about it, can the painting method you choose stand up to scrutiny?
(2) Compare and see if the students around you have a better way than you.
Teachers patrol, students draw pictures and then communicate with each other.
The teacher asked the student representatives to explain their painting methods.
Sheng: Draw two equal, vertical and equal line segments and connect these four endpoints in turn.
Teacher: Please think about whether your painting can stand scrutiny.
A student (1) bisects the other party diagonally to get a parallelogram; (2) Equal diagonal lines indicate that it is a rectangle; (3) Diagonal lines are perpendicular to each other, indicating a diamond shape; (4) It is both rectangular and rhombic, that is, square.
Teacher: A student's answer is very good, which shows that this method can withstand scrutiny and has scientific basis.
B: Draw two equal parallel lines first, and then draw a vertical line.
The teacher asks questions while operating, and gradually makes the language more rigorous in the questioning. In practice, draw a line segment first, and then make both ends into vertical lines. Take the length of two vertical lines as the length of vertical lines and connect four points to form a square.
C: First draw an isosceles right triangle, and then draw two right parallel lines at both ends of the triangle to form a square.
Teacher Wang asked students to draw squares by themselves, guided students to think about exams and communicate and cooperate in mathematics with "thinking" and "comparison", and asked students to reflect on whether their operation process meets the requirements with "whether it can stand scrutiny" to sublimate their thinking.
4. Use group discussion wisely to improve the efficiency of classroom structure.
How to effectively enhance the effectiveness of "group cooperative learning"? The author believes that under the premise of correctly understanding and grasping the basic theoretical connotation and characteristics of "group cooperative learning", teachers can adopt the following strategies:
(1) Scientifically set up cooperative learning groups. The formation of study groups is the premise of cooperative learning activities. To form a study group, teachers should carefully study and design the grouping of students, so that the overall level of each group is basically the same, so as to ensure fair competition among each group. The group generally follows the principle of "heterogeneity within the group and homogeneity between groups" and consists of 4 ~ 6 people; Grouping should not only consider the age characteristics and thinking characteristics of students, but also consider the reasonable differences in gender, personality characteristics, sexual orientation, learning level and family background, so as to give full play to their respective strengths and advantages in learning. After the establishment of the group, the members of each group must be required to be friendly, frank, democratic and equal, which embodies the group strength and spirit of the group.
(2) Clarify the goal and division of responsibilities of "group cooperative learning". Clear learning objectives and division of responsibilities are the key elements of "group cooperative learning". In the process of "group cooperative learning", each member should have a clear cooperative learning goal and a specific division of responsibilities. Only when the division of labor is clear and the responsibility lies with people, can team members fully participate, understand their respective responsibilities and master the assigned tasks, and cooperative learning can be carried out in an orderly and effective manner. It is worth reminding that the goal of "group cooperative learning" is the learning goal established by the group members and the direction of their efforts. This requires that group members not only strive to achieve their personal goals, but also work together to help other members of the group achieve the expected cooperative learning goals.
(3) Cultivate the team consciousness and cooperation ability of team members. Cultivating the team consciousness and cooperation skills of group members is the key to the smooth development of "group cooperative learning" activities. Cooperative learning is not an individual learning behavior, but a collective behavior. In order to achieve the same learning goal, each member needs to have enough team consciousness and cooperation ability. That is, team members must know each other, trust each other, and often communicate effectively; Members should be responsible not only for their own learning, but also for the learning of other students in the group. They should help and support each other, form a strong sense of collective responsibility, properly resolve possible contradictions and establish a harmonious and friendly close partnership. Cultivating team members' team awareness and cooperation skills mainly includes: the awareness and skills of mutual trust, unity and mutual assistance; Consciousness and skills of actively expressing opinions; Learn the awareness and skills of group discussion; Respect others' consciousness and speaking skills; Awareness and skills to handle disputes in a friendly way.
(4) Establish a reasonable evaluation mechanism of "group cooperative learning". Reasonable evaluation mechanism is an important way to improve the effect of group cooperative learning. In the process of cooperative learning, it is necessary to establish a reasonable evaluation mechanism in order to give full play to the maximum potential of each member and realize the dialectical unity of * * * with goals and personal goals. Reasonable evaluation mechanism can combine the evaluation of learning process with the evaluation of learning results, and the evaluation of group members with the evaluation of individual members, so that students can realize the value and significance of cooperative learning and pay more attention to the process of cooperative learning.
The above four strategies reflect the characteristics of junior high school mathematics. The author thinks that only by improving teachers' quality, changing educational concepts, making teaching contents lively, adopting scientific teaching methods, actively implementing "two-base" teaching under the careful organization of teachers and effective learning methods of students, rationally using diversified teaching methods, stimulating students' interest in learning, and rationally developing students' abilities can we optimize mathematics classroom teaching and achieve remarkable teaching results.
References:
[1] Mathematics Curriculum Standard (experimental draft), Beijing Normal University Press, June 2004
[2] Ma Fu, Zhang Fei, editor-in-chief of "New Curriculum Teaching Method of Junior Middle School Mathematics". Northeast Normal University Press, 2004.5.
The optimization of junior high school mathematics classroom teaching process refers to the ideal effect of teaching quality on the basis of comprehensive consideration of the purpose of teaching materials, teaching rules, principles, teaching forms and methods, in-depth study of teaching materials and consideration of students' characteristics.
First, establish a democratic and equal teacher-student relationship.
Let students be inspired and encouraged in an atmosphere of equality, respect, trust, understanding and tolerance, and get guidance and suggestions. Teachers are important partners of students and equal leaders in their learning process. Teaching behaviors respect each other, teaching resources are searched and learning activities are interactive. Teachers should not prevaricate about students' questions. They should cherish the achievements of students' learning, their understanding of mathematical knowledge and their thinking on mathematical problems. Teachers should not deny or ignore even wrong conclusions and inferences. They should guide and guide students in an equal and communicative way, and affirm their "bright spots" in their guidance. In particular, it gives timely affirmation and appreciation to students' creative and innovative conclusions in learning, so that students can feel the "tolerance" and "charm" of teachers.
Second, fully prepare before class.
Students are the main body of learning. Teachers should provide rich learning contents for students' learning, including analyzing teaching materials and handling teaching materials flexibly. Starting from students' life experience and existing experience, starting from intuitive and imaginary problems, let mathematics background be included in specific scenes of things that students are familiar with, let students' common sense and empirical knowledge be used, and make mathematics courses more realistic, contemporary and more closely linked with the world that belongs to students. At the same time, teachers should train students to actively participate in preparing lessons before class, such as preparing learning tools, previewing teaching materials, doing small experiments in group activities before class, and collecting information outside the classroom. , so as to give full play to students' exploration ability and develop in exploration, discovery and acquisition.
Third, advocate independent exploration and perceive the mystery of the problem.
Junior high school mathematics learning is one's own activity process. It is a mathematical activity with students as the main body. Therefore, in mathematics classroom, teachers should guide students to acquire some concepts and knowledge through modern teaching technology, and encourage students to boldly use epiphany perception to find strategies to solve problems; Encourage students to cultivate perseverance and perseverance in the process of independent research, and create time and space for students themselves; Highly activate students' thinking from concepts and methods, and help students choose thinking strategies and modes to solve problems.
Fourthly, highlighting key points and resolving difficulties are the key to improve the efficiency of mathematics classroom teaching.
Generally speaking, the teaching content of each class has its own unique teaching points that students need to master. In order for students to master the teaching content of a class, they must highlight the key points. In the teaching process, there are often some knowledge points that students are difficult to understand and master in every class. As teachers, we must proceed from the reality of students, grasp the key points, find out the difficulties and solve them, in order to achieve the expected teaching purpose. In order to make students clear about the key points and difficulties of this class, teachers should come up with certain methods to attract students' attention to the key contents in class. The key content of the lecture is the climax of the whole class. Teachers should leave a deep impression on students by changing intonation, gestures, blackboard writing, application models, projectors and other visual teaching AIDS, stimulate students' interest in learning and improve their ability to accept new knowledge.
5. Choosing appropriate teaching methods is the key to improve the efficiency of mathematics classroom teaching.
Teaching methods are the collective name of teachers' teaching methods and students' learning methods. Teaching is for learning. If the teaching methods are not appropriate, students will not be able to better understand and master the content of classroom teaching, let alone improve the efficiency of classroom teaching. Each class has corresponding teaching tasks and objectives. In teaching, teachers should flexibly choose teaching methods according to the changes of teaching content and the actual situation of students. There are many teaching methods for new teaching. We use this teaching method to impart knowledge to students. In geometry class, we often insert demonstration methods to show students geometric models or verify geometric conclusions. Other methods can also be used flexibly in combination with the classroom content, so that students can give full play to their subjective initiative and develop their ability to acquire knowledge independently through their own observation, exploration and hands-on operation. Sometimes, in a class, multiple teaching methods should be used at the same time. Generally speaking, such teaching efficiency is effective only when most students have mastered as much knowledge as possible. As the saying goes, "There is no fixed method in teaching, but the proper method is the most important thing." As long as it helps to cultivate students' thinking ability, it is a good teaching method. We should explore hard and communicate with each other to ensure the continuous improvement of classroom teaching efficiency.
Sixth, create a learning situation.
Students' learning junior high school mathematics is the systematization of students' common sense of life, which is inseparable from students' real life experience. Mathematics learning in class is the summary and sublimation of related phenomena and experiences in their lives. Therefore, teachers should create realistic and attractive learning background according to students' specific situation, teaching content and teaching environment, stimulate students' learning interest and motivation, break through the boundaries of textbook world, life world and network world, and find the best "combination point". For example, students are very interested in cartoon cards, projections, physical objects or vivid language descriptions, and their thinking is easily inspired, developed and activated. This intuition is a kind of catalyst, which generates sustainable power for the created problem situation and brings certain life color to students' learning activities. It not only creates the appearance of creating situations, but also enhances the cultivation of students' awareness of learning strategies, which will certainly promote students' positive thinking; Create a life situation, mathematics comes from life, and let students feel that mathematics is around.
Seven, stimulate students' interest in learning.
"Interest is the best teacher." The organic combination of information technology and mathematics teaching is conducive to stimulating interest and mobilizing students' enthusiasm for learning mathematics. In any fruitful study, students must have a strong interest in learning materials. Interest in learning is the main motivation for students to acquire knowledge, broaden their horizons and enrich their psychological activities. Interest in learning comes from curiosity, which is the nature of students. They are interested in new things they know but have never seen. However, traditional teaching can't meet their requirements and stimulate their enthusiasm for learning. Integrating multimedia technology into mathematics classroom and using the characteristics of multimedia information technology to create various situations for students, such as illustrations, synchronized audio and video, dynamic and intuitive images, can mobilize the participation of students' various senses, stimulate their strong desire for learning, stimulate their learning motivation and interest, and thus achieve the purpose of improving their learning enthusiasm. The application of computer in teaching not only completely lightens the burden, but also helps teachers and students to devote their energy and attention to higher-level teaching and learning, and also helps teachers and students to better understand and be familiar with information technology, thus significantly improving the teaching effect.
Efficiency is the premise to ensure the quality of junior high school mathematics teaching. Improving the efficiency of classroom teaching is one of the main goals pursued by our teachers. Only when teachers study hard, carefully choose teaching contents, skillfully design teaching methods, create a relaxed learning environment and guide students to learn in various forms can they achieve the best optimization of classroom teaching.
"How to Optimize Junior High School Mathematics Classroom Teaching" by: Teacher Fan Wen.