1. Change teachers' teaching concept, strengthen communication between teachers and students, establish good teacher-student relationship and stimulate students' initiative.
Democratic teacher-student relationship and harmonious classroom atmosphere are important conditions to ensure the realization of subjective education, because creating a democratic and harmonious classroom atmosphere is the guarantee to realize subjective education and develop students' creative thinking. Once classroom teaching touches students' emotional and will fields and their spiritual needs, this method can play an efficient role. As the saying goes, "Be close to your teacher, trust your way and enjoy learning", so we should create a democratic and harmonious classroom teaching atmosphere. The democratic, harmonious, lively, pleasant and relaxed teaching atmosphere and the emotional input of teachers and students are the external conditions for students' active participation and the good soil for students' learning and personality development. In classroom teaching, teachers are faced with individuals with ideological and emotional activities. Teachers should strive to put themselves in a correct position and establish an equal and cooperative relationship between teachers and students. In classroom teaching exchange activities, teachers try to communicate with students in a consultative tone, such as: "Who has different opinions …" "Who wants to talk about …" and "Your thoughts are the same as the teacher's". Teachers should step off the platform and truly become "mentors and friends" in students' study.
American psychologist Rogers said: "Successful teaching depends on the sincere relationship of respect and trust between teachers and students, and on a harmonious and safe classroom atmosphere." From this point of view, teachers and students should strengthen communication and establish a good teacher-student relationship to create a positive, relaxed, lively and efficient teaching psychological environment.
2. Change students' learning style, guide students' independent activities and cultivate students' independence.
Student autonomy means that under certain conditions, individuals have the right and ability to dominate and control their own activities. Students' autonomy in educational activities is firstly manifested in independent subjective consciousness, clear learning objectives and positive learning attitude, and the ability to learn textbooks independently under the guidance of teachers, transform the knowledge in books into their own knowledge and apply these knowledge to practice; Secondly, students have the ability of self-regulation and self-control in learning activities, and can give full play to their potential to actively study and receive education.
At the same time, education must carry out various educational activities that are beneficial to the development of students' subjectivity according to the requirements of a certain society and the law of the development of students' subjectivity, and carry out effective standardization, scientific organization and correct guidance to provide opportunities and create conditions for the development of students' subjectivity, with breadth in time, breadth in activities and depth in content.
Elaboration of the new curriculum on the mathematics connotation of 2 1 century. It is clearly pointed out that mathematics is a process of exploring various relationships in life, and this process is a process of discovery and creation. Teachers pay attention to the research process, strategies and basic methods, not just conclusions. Traditional mathematics teaching focuses on making students recite formulas, definitions and rules for a long time, and repeating problem-solving steps over and over again, so as to speed up problem-solving with this mechanical training. The new curriculum advocates that teachers' value guidance to students is that "doing mathematics" is more important than "speaking mathematics", and "doing mathematics" is always the main theme of the classroom. In the process of exploring the classroom teaching mode independently, our school strives to make every student actively explore the formation process of knowledge or conclusion, not just accept the ready-made results. At this time, students are more the subject of learning activities than just cognitive activities. They not only actively perceive the cognitive process behind knowledge and sort out cognitive clues, but also perceive the life experience of cognitive subjects through specific learning scenes, including the confusion encountered during active exploration, the attempt to search for information, the joy when finding clues, and the happiness when solving problems. Through exploration and discovery, questioning and questioning, experience appreciation, cooperation and exchange, students are inspired and induced to try to explore, and rely on their own efforts to acquire knowledge and master skills. Under the guidance of this concept, I designed the lesson "circumference of a circle" to let students explore "what is the relationship between the circumference and diameter of a circle?" This problem develops mathematical activities. Provide students with a lot of opportunities for observation, thinking, operation, independent exploration and cooperation, and encourage students to do mathematics, thus making boring mathematics interesting and useful.
Traditional teaching overemphasizes the closure of presupposition, which is typically manifested in the implementation of planned teaching based on teaching plans, and each class must complete the prescribed teaching tasks without exception. This kind of teaching based on lesson plans is a kind of closed teaching, and the new curriculum points out that classroom teaching should not be a closed system, nor should it stick to a fixed preset procedure. Whether the teaching task of a class is completed or not does not affect the all-round development of students. The most important thing in classroom teaching is to cultivate students' autonomous learning and innovative quality. When dealing with the "circumference of a circle" class, I didn't overemphasize the integrity of the class, but put all my attention on the core issue of this class, that is, to explore the relationship between the circumference and diameter of a circle, so that students can do a lot of operations, discussions and exchanges, thus discovering the law and drawing the conclusion that the circumference is always more than three times the diameter, thus promoting pi.
In the design of this class, I pay special attention to the whole class and adopt the learning method of "cooperative research learning" in mathematics activities. Draw up a list of math activities for students.
A) ask questions. What is the relationship between the circumference and diameter of a circle?
B) Hands-on experiment: measure the circumference and diameter of a real circle and calculate the relationship between circumference and diameter (guide students to calculate the addition, subtraction, multiplication and division of circumference and diameter,)
Fill in the experimental research report form.
C) Observation and discussion: compare the characteristics of each data and find the law.
D) draw a conclusion and express a statement-(the circumference is always more than three times the diameter of the study. )
In this research process, students cooperate with each other, which is the whole process of students' autonomous learning. In this research process, teachers guide students to carry out observation, experiment, verification, reasoning, communication and other forms of activities, so that students not only acquire knowledge, but also go through the research process, learn the methods of exploration, and cultivate students' autonomous learning and cooperative communication ability.
Effective teaching under the new curriculum concept is to change students' learning style, change the single and passive learning style in the past, advocate and develop diversified learning styles, especially the learning style of autonomy, inquiry, cooperation and practice. The core of learning is "learning participation", not what teachers give students, but more importantly, how teachers guide students to learn. Teaching itself is a process of inquiry. The main purpose of teaching is to enable students to master scientific thinking methods by exploring the process of knowledge generation, so as to cultivate students' inquiry ability and creativity. Inquiry is the premise of discovery. Teachers pay more attention to the process of thinking than the result when guiding students to explore, and try to let students seek answers and discover laws through their own analysis, comparison, induction, generalization and summary.
3, contact with students' reality, effectively create life situations, and give play to students' subjective initiative,
Students' initiative in educational activities shows that students can actively participate in educational activities according to the requirements of society, consciously realize the purpose and significance of education, and actively cooperate with educators' teaching activities. Moreover, students can actively assimilate the influence of external education with their existing knowledge, experience and cognitive structure, so as to make a new combination of old and new experiences, thus realizing the construction and transformation of the main quality structure.
At the same time, students' learning mathematics is a positive and meaningful action, which requires internal motivation to motivate and promote their learning, so as to achieve their learning goals, and this internal motivation comes from learning needs. Only when students have the need and desire to learn mathematics can they have a psychological force to motivate and push themselves to learn mathematics and actively participate in learning activities. In order to meet this need and desire, in the process of mathematics teaching, we should consider the characteristics of students' physical and mental development, and combine students' existing knowledge and life experience to design interesting mathematics teaching activities, so that students have more opportunities to learn and understand mathematics from familiar things around them. Hua, a famous mathematician, said: "One of the reasons why people have a dull and mysterious impression on mathematics is that they are divorced from reality." Therefore, only by connecting with reality and learning and understanding mathematics from students' familiar life can we turn hard study into happy study and truly appreciate the fun of learning. For example, when studying volume and unit of volume's content, students can't feel "milliliter" and "liter" and understand the meaning of volume. Before class, I found that there were many kinds of beverage cans that students had drunk in the lower corner of the bookcase in the classroom. I had a brainwave and turned these "Jianlibao", "Wahaha" and "Pepsi-Cola" into the material of my study paper. I am also very excited. In the feedback session, I asked the students to estimate the volume of the beverage can and verify it through the data on the trademark. This activity pushed the class to a climax. For another example, when I was teaching the class "The Meaning of Fractions", I assigned a task before class to let students go home to collect the "scores" in life through newspapers, magazines and television, and guess the meaning of each "score". The students were very enthusiastic and collected many hot topics in the news media at that time. Starting from the case data that these students are familiar with, the students are full of interest, and they deeply understand the "meaning of scores" in life cases.
We know that mathematical knowledge is not fabricated out of thin air, it is abstracted from practical things and is the most basic reflection of the objective world. Every time students come into contact with a mathematical knowledge, they should know where this knowledge comes from and what applications it has in real life. This will help students to define their learning objectives and stimulate their interest in learning. In teaching activities, we should create an open situation so that students can think and become interested in learning activities. This situation should be based on what students can feel and understand, so that students' personal experience world can be expanded and human spiritual culture can nourish their spiritual life. On this basis, stimulate students to form a certain sense of problems and desire to learn.
For example, after the teaching of the unit "Understanding Cuboid Cube" in the next semester of the fifth grade, in order to avoid boring repetition in the review, I creatively designed the "Arrangement and Review of Cuboid Cube".
Case fragment: Teacher: Teacher Wang wants to give his grandson a birthday present: goldfish. What shape should I take for the little goldfish? Health: cuboid or cube. Teacher: We have chosen a shape, which can be made into a cuboid or a cube. Besides its shape, what should we consider? Health 1: How much material do you need to consider? How much glass do you need? Health 2: the size of the fish tank, that is, its volume; Health 3, the area of the fish tank. Teacher: The students put forward very well, and the teacher also asked several questions. Let's study them together.
1. How many square decimeters of glass does it take to make this goldfish bowl? (surface area)
2. How many square decimeters of cellophane do you need if you put anti-fog transparent cellophane around this goldfish bowl? (Surrounding area)
3. If the glass around the goldfish bowl is inlaid with aluminum alloy at the bonding place between the glasses.
The edge of the product plays a reinforcing role. How long do you think a * * * needs such a sharp edge? (Sum of sides)
Take the goldfish bowl home and put it on the table in the living room. What is the area of this table? (Floor space)
How many liters of water can this fish tank hold at most? (excluding the thickness of glass cylinder) (volume)
6. Add 5 millimeters of water to this fish tank, and then put some goldfish and coral stones in the fish tank. Now the water depth is 5.2dm, please calculate the volume of all irregular objects such as goldfish and coral stones according to the measurement results. (the volume of an irregular object)
7. As shown in the picture, I want to wrap two identical goldfish bowls in cardboard, regardless of loss. How much hard paper do I need at least (packaging problem)
In this math activity of "Setting a Suitable Home for Little Goldfish, Making a Golden Fish Tank", students related knowledge about surface area and volume, sum of side lengths, occupied area and volume, volume of irregular objects, packaging problems and so on to real life, providing students with rich perceptual knowledge and life experience, and a series of practical experience in solving problems, so that students can think with their brains and operate with their hands. Therefore, in teaching, if teachers can go beyond the textbook and create practical activities that students like, and let them collect and query information that they are interested in, then they will change from "asking me to learn" to "I want to learn", not only their "intelligence, heart and hands" will be satisfied and developed, but also their thinking space will be expanded and their thinking level will be improved.
Therefore, in all aspects of mathematics teaching, we should carefully create a learning atmosphere full of beauty and wisdom, so that students can have concrete feelings about the objective situation, stimulate their interest in learning, devote themselves to learning, and fully develop their potential abilities.
4. Pay attention to infiltrating mathematical thinking methods, inspire students' thinking and develop students' positive creativity.
Mathematical thinking method is implicit in knowledge and embodied in the process of its occurrence, development and application. In the teaching process, we should pay attention to the infiltration of mathematical methods and cultivate students' learning ability to acquire knowledge actively. Students who have mastered this ability will actively participate in mathematics classroom learning activities, thus promoting and developing students' subjectivity. Mastering basic mathematical ideas and methods can make mathematics easier to understand and more conducive to memory, which is the premise of learning to learn, develop and innovate. In mathematics classroom teaching, teachers should guide students to actively participate in the learning process. In addition to designing some situations, scientific thinking methods should be integrated into students' cognitive structure, so that students can migrate more widely, cultivate students' innovative thinking in many directions and angles, and cultivate students' ability to actively participate in learning. Once students have this ability, they can continue to succeed in their studies, enhance their self-confidence and learning motivation, and better participate in learning activities. Let students learn in activities, arouse their enthusiasm for learning mathematics, and let their thinking really "live" and "move". The following case is a successful case in which teachers have a good understanding of the growing point of teaching materials, inspired students' thinking and developed students' positive creativity.
The teacher in the teaching and research section assigned me a task to hold an open class in the whole region. The theme of the activity is "classroom teaching embodies new ideas" and the topic is "the volume of a cone". I have listened to several open classes of "The Volume of Cone" before, and the teaching design is very routine. When I was studying the textbook, I found such a problem. The average teacher can successfully draw a conclusion through experiments in this class. But according to students' cognitive rules, why suddenly compare the sizes of cylinders and cones? Why do you want to do this experiment? Unknown doing this experiment is a mathematical activity imposed on students by teachers, which does not follow students' cognitive laws at all, but is led by teachers. When I was thinking about this problem, I remembered an article I accidentally read in the magazine "Mathematics Teachers in Primary and Secondary Schools", which inspired me a lot, so I made an appropriate adaptation of the arrangement of the teaching materials and achieved very good results in teaching. I designed the teaching of cone volume in this way: students learn new knowledge by guessing. First of all, through the courseware, let the students recall that a cylinder and a cone are three-dimensional figures formed by the rotation of a rectangle and a right triangle respectively. Displays a rectangle and a triangle. The long side of a rectangle is equal to the height of a right triangle, and the short side of a rectangle is equal to the base of a right triangle. The teacher asked: What is the relationship between the area of a rectangle and the area of a right triangle? The student answers: The area of a right triangle is half that of a rectangle. Then, the courseware animation demonstration rotates the long side of the rectangle and the height of the right triangle respectively to get a cylinder and a cone. Ask the students to observe the cylinder and the cone and compare them. What is the relationship between them? After observation, the students said that the base is equal and the height is equal. The teacher then asked: Please guess, what is the relationship between a cylinder with equal base and equal height and the volume of a cone?
Due to the influence of the previous comparison area, many students thought it was 1/2, some students guessed it was 1/3 through spatial imagination, and some students guessed it was 1/4. What is the relationship between 1/2 and 1/3? Relationship or 1/4 relationship?
Teacher: What is the relationship between the volume of a cone with equal base and equal height and the volume of a cylinder?
What shall we do? (The teacher takes out a hollow cylinder and cone with equal bottom and equal height for students to observe and communicate. Some students said: You can try pouring water into the jar with a cone. I was very happy when the students said this. I guided them to do experiments to verify our conjecture. Then let the students do experiments with the materials given in their hands to verify their guesses. The design of this link really makes students realize the necessity of doing experimental verification. In this teaching process, students will be suspicious and curious by setting suspense through interest and creating contradictory cognitive conflicts.
The teaching of "the volume of a cone" I just mentioned is to fully respect students' cognitive laws and let them go through the process of guessing, verifying and summarizing. There is no shortage of guessing-verifying-inducing thinking mode, but it is difficult to use. Therefore, teachers should grasp typical lessons in teaching, let students go through such a thinking process, let students use this way of thinking and learn from it in the process of solving problems, and gradually improve their learning ability. This lesson creates a challenging problem situation. Teachers design teaching according to the process of "mathematical problem-mathematical model-mathematical method-problem solving", and guide students to experience the process of abstracting practical problems into mathematical models and exploring and applying them. It seems that teachers should make full use of the resources provided by textbooks, tap the factors contained in textbooks, scientifically adapt the contents of textbooks, creatively control textbooks, and raise challenging questions in time to promote them. And students' emotions have developed harmoniously in the process of cognition. They deepened their understanding and communication in cooperation and communication, and tasted the joy of successful exploration.
From this case, it can be seen that in mathematics teaching, teachers should use situations to guide students to conduct in-depth research and analysis of problems, so that students can innovate boldly and give full play to their main role, and teachers should strive to become catalysts and stimulants for students to acquire knowledge. Therefore, in mathematics teaching, teachers should consciously do everything possible to stimulate students' interest in learning in many ways. When students are interested in mathematics, they have the motivation to study, thus giving full play to the main role and improving their intelligence and ability.
Above, I talked about how to give full play to students' main role from four aspects. The viewpoint is not mature enough and needs further exploration and research.
I have been teaching for nearly 20 years and participated in the main education experiment of the school, and I have learned a lot. The biggest gain should be to establish your own educational ideal and form your own educational style. From this, we can explore an idea of our own education and teaching. Let me really understand that to implement subjective education in classroom practice, we must first correctly handle the relationship between teaching and learning, teachers and students, and truly realize that students are the main body of teaching activities from the ideological point of view. At the same time, our school's classroom teaching mode: create an environment to stimulate interest-independent inquiry-exchange feedback-expand the extension of teaching links, implement the guiding ideology of students' subjectivity, put students in the main position, let them take the initiative to participate, take the initiative to start, talk and think, and let students experience, feel, guess, verify, observe and think.
The real meaning of education lies in discovering people's value, tapping people's potential and exerting people's personality. And every student is not only a living subject, but also the undertaker and embodiment of quality education. Every teacher must emancipate his mind, renew his ideas, give full play to students' subjective initiative, release students' potential and talents, and establish students' dominant position in learning. As long as each of our teachers is guided by quality education, accurately understand the intention of compiling textbooks, make clear the teaching objectives, truly highlight the students' dominant position, start from bit by bit and make unremitting efforts, we will certainly cultivate high-quality talents who can "learn, survive, create and develop"