The research of educational psychology shows that students' cerebral cortex is easy to form an exciting center, with the most active thinking, the highest degree of active participation and the strongest practical ability under the environment of no mental motivation, no psychological burden, comfortable mood and full emotions.
(A) to establish a new relationship between teachers and students
Students are active subjects with thoughts and feelings, and the relationship between teachers and students is the basic relationship in educational activities. Teachers are the organizers, instructors and participants of teaching activities, while students are the masters of learning, only with the division of roles and equal personality. Teachers should serve students. Teachers should step down from the high platform, go deep into the students and turn the teacher-student relationship into a friend relationship. Face every student with full enthusiasm, good mood and sincere smile, care, respect, trust, understand and care for every student, so that students can feel the approachable teacher. In teaching, teachers should always communicate with students in the tone of "Who wants to talk about …", "Who wants to add …" and "Please talk about …", so as to truly become a member of the students, form ideological exchange, emotional exchange and personality collision between teachers and students, and stimulate students' desire for autonomous learning.
(B) to create a democratic and harmonious classroom atmosphere
The process of primary school mathematics teaching is not only the process of guiding students' cognition, but also the process of emotional communication between teachers and students. Create a democratic, relaxed, friendly and equal teaching environment, so that students can form unrestrained thinking space under the condition of psychological relaxation, and promote students' positive thinking and imagination. In teaching, everyone has the opportunity to talk about doubts or key issues and carry out activities such as self-evaluation and mutual evaluation. Rogers pointed out: "The general conditions of creative activities are psychological safety and psychological freedom. Only psychological security can lead to psychological freedom and students' creativity. "Only by establishing a harmonious relationship between teachers and students can teachers and students work closely together to create a pleasant atmosphere and become the driving force for students to learn independently.
Second, the creation of autonomous learning situation
Suhomlinski pointed out: "In people's hearts, there is a deep-rooted need to become discoverers and researchers, and in children's spiritual world, this requirement is the strongest." Therefore, teachers should go deep into students, reasonably choose learning strategies, mobilize students' learning enthusiasm to the maximum extent, encourage students to think, ask questions, say and do problems, seek happiness from discovery, actively acquire knowledge, and realize the use value of mathematics and the pleasure of "doing" mathematics.
(A) "interest"-to stimulate autonomous learning
Interest is a positive tendency for people to understand the objective position, and it is a great motive force for a person to acquire knowledge and develop, which pushes people to explore new knowledge and develop new abilities. In teaching, teachers should use the charm of mathematical knowledge to create situations and activate thinking according to students' curious psychological characteristics. For example, when teaching "Year, Month and Day", create an introduction, "Do students like birthdays?" After the student answered, he then asked, "How old are you and how many birthdays have you had?" In this way, I asked several students in succession to make them realize how old they are and how many birthdays they have. Finally, I became suspicious: "Xiaoya is 12 years old and has only had three birthdays. Why? Do you want to know the secret? " Hearing this, the students felt a strong thirst for knowledge, and they were all in high spirits. At this time, the teacher seized the opportunity to guide them into the new class in time.
Once students are interested in what they have learned, they will have great internal drive, full of self-confidence, actively explore and consciously learn. In teaching, teachers should pay attention to create an "imbalance" between teaching content and students' internal needs, stimulate students' interest in autonomous learning, and make students change from passive to active and actively participate in learning.
(B) "Questioning"-inducing autonomous learning
The ancients said: learning comes from thinking, and thinking comes from doubt. Doubt can stimulate students' desire for knowledge, make students' thinking in an active, positive and happy state of acquiring knowledge and stimulate students' interest in learning. Teachers should adopt appropriate methods to create situations according to students' psychological characteristics and mathematical knowledge characteristics, so as to stimulate students' thirst for knowledge and actively explore and learn new knowledge.
For example, after learning "area calculation of rectangle", first demonstrate: "How many pieces of rectangular paper with a length of 20 cm and a width of 10 cm can be cut into square paper with a side length of 5 cm?" Ask the students to try to answer, and then organize the students to discuss: (1) 20×10 ÷ (5× 5) = 8 (2) (20 ÷ 5) × (10 ÷ 5) = 8. What does the remainder mean? What's wrong? What should I do? ..... to stimulate students' thinking sparks and make them feel the need for further exploration. Then after full discussion, operation and reflection, combined with multimedia dynamic demonstration, students can truly understand the basic methods of solving problems, and at the same time, according to the characteristics of the topic, choose flexible methods to answer, further improve students' cognitive structure, achieve forward-looking teaching purposes, and improve students' ability to solve practical problems.
Einstein said, "It is often more important to ask a question than to solve it." Teachers carefully cultivate the spark of students' autonomous learning, encourage students to question and ask difficult questions, guide students to dare to ask questions, be willing to ask questions, be good at asking questions, stimulate students' thirst for knowledge, make students become active explorers, and drive students to learn mathematics actively.
It can be seen that the creation of autonomous learning situation is the catalyst for students' autonomous learning and the internal motivation for students to engage in learning activities. It can make students sprout a strong thirst for knowledge, produce a heartfelt self-pursuit, and make students change from passive to active, from self-confidence to initiative, consciously study, climb hard, and truly become the masters of learning.
Third, provide opportunities for autonomous learning.
Bruno, a famous American psychologist, said: "Learners should not be passive recipients of information, but active participants in the process of knowledge acquisition." Only through students' active participation and independent exploration can mathematical knowledge be transformed into students' own knowledge and students' autonomous learning ability be cultivated.
(A) to guide the study of law, autonomous learning
How to make students learn to "discover" knowledge by themselves is the key to improve their learning ability. Therefore, students should be guided to understand and discuss with each other through their own learning, so that they can gradually have the learning ability of reading, operating, thinking, discussing, summarizing and analogy. Teachers should be good at setting exploratory questions and encourage students to express their wishes and abilities to prove themselves.
Then guide students to observe and compare, so that students can understand the meaning of "multiplication and division" and stimulate students' desire to further explore new knowledge. Then, let the students give their own examples and communicate at the same table to provide enough material for summarizing the law of multiplication and distribution. Then, organize students to observe, think, analyze and compare, discuss and communicate, and ask them to summarize in one sentence. Students put forward "laws" in the process of mutual exploration, mutual supplement and mutual correction. Finally, guide reading textbooks and understand the key words in the law, such as "can be used", "used separately" and "used again". This can guide observation and discussion, strengthen group interaction, guide oneself to explore, and complete the process from understanding the appearance of things to summarizing the essential attributes of things. This kind of self-study and mutual exploration is based on reading and studying textbooks. Students should discuss and explore each other in various forms around textbooks, so that students' learning activities will always have a core and teaching activities will become reading activities.
(B) cooperation and exchanges, independent research.
In classroom teaching, cooperative learning is conducive to the emotional exchange and information exchange between teachers and students, to the collision of thinking and the cremation of wisdom, to strengthening students' subjective consciousness, and to students becoming active participants in learning activities.
Primary school students are easy to look at problems in isolation and one-sidedly because of their poor knowledge and association ability, and there are few opportunities for cooperation. Therefore, teachers should create more atmosphere for students to participate in the teaching process and give students more opportunities for cooperation and communication. For example, when teaching "Calculation of Rectangle Perimeter", students will show a rectangle with a length of 6 cm and a width of 3 cm on the basis of mastering the characteristics and concept of rectangle perimeter. First, let the students study in groups and calculate the circumference of this rectangle according to the existing knowledge and skills. Then let the students express their opinions on how to find the perimeter of a rectangle: ① 6+3+6+3 = 18cm, ② 6+6+3+3 = 18cm, ③ 6 × 2+3x2 = 18cm, ④ (6+3 )× 2. Finally, organize students to discuss and communicate, learn from each other's strengths and reflect on themselves. Students can not only sum up the formula for calculating the circumference of a rectangle: the circumference of a rectangle = (length+width) ×2. Moreover, in the process of seeking knowledge, students' understanding of knowledge has deepened, their thinking has been trained and inspired, and their language expression ability, self-study ability, analytical ability, problem-solving ability and unity and cooperation ability have been improved.
Carrying out cooperative learning in teaching inspires students from different viewpoints and methods, and has a richer and more comprehensive understanding of the problems, which not only cultivates students' cooperative spirit, but also strengthens their self-analysis and self-improvement consciousness of inquiry and improves their ability of independent learning.
(3) Hands-on operation and independent practice
Educator Tao Xingzhi said: "There are two treasures in life, the hand and the brain." Primary school students' thinking is mainly based on concrete images. In the process of knowledge construction, teachers consciously set up students' hands-on operation situations according to students' active and curious psychological characteristics and the characteristics of mathematics knowledge itself. Through hands-on operation and the participation of various senses, students' interest in learning is stimulated, and the classroom is in an orderly state of active exploration.
For example, when teaching the derivation method of "trapezoid area formula", first guide the students to review the derivation methods of triangle and parallelogram area formulas, and then tell the students in a kind and gentle tone: In this class today, let everyone be a small teacher and use the learned methods to derive the calculation formula of trapezoid area to see who has the most novel, unique and creative method. Then, ask the students: (1) What figure can the trapezoid be transformed into? (2) What is the relationship between the converted new figure and the area, upper bottom, lower bottom and height of this trapezoid? Think about operation, practice boldly, and explore the method of deducing trapezoidal area formula.
Finally, under the guidance of the teacher, let the students exchange and summarize, and draw the conclusion that no matter which deduction method is used, the area of the trapezoid = (upper bottom+lower bottom) × height ÷2. At this time, students' divergent thinking and concentrated thinking are unified, which greatly improves students' initiative and enthusiasm for learning.
Skilled practice and independent research.
Through the practice in teaching, students can gradually internalize the acquired knowledge into sports skills and psychological skills. In design exercises, teachers should not only make students interested in learning materials, but also make the materials consistent with the content, so that students can develop positive thinking, and at the same time discover laws and master knowledge in the process of multi-faceted participation.
When calculating the area as shown in the figure, let the students, on the basis of their existing knowledge and experience, encourage them to try boldly, let go of practice and explore independently, and find out the areas of different division combinations. Then, through observation, collaborative learning and summarization, it is confirmed that the essence of the problem is to find the area of combined graphics.
Students design, try and summarize by themselves, and they collide with different ideas, showing students' potential and experiencing the diversity, flexibility and rationality of problem-solving strategies. Meet every student's learning needs, enlighten thinking, learn to cooperate and communicate, and let students truly become the masters of learning.
When designing exercises, teachers should be clear in thinking, focused, practical, rigorous in structure, standardized in form and properly arranged.
Games, competitions, opening-up and other exercises can stimulate students at different levels.
Actively participate in learning from different angles, explore, acquire, consolidate and deepen knowledge in the whole process of actively participating in learning, meet students' psychological requirements, realize the happiness of "I can do it" and promote students' independent development.
In short, in teaching, teachers should be good at giving students the initiative to learn, so that students can read books, talk about ideas, ask questions, find rules and practice in class. It is necessary to give students more opportunities for thinking, more space for activities, more opportunities for performances, more creative confidence and more successful experiences. Let students go through the process of mathematical activities such as asking a question, collecting and sorting out data, observing experiments, guessing and proving, and give full play to students' enthusiasm, autonomy and creativity in learning, so as to realize independent development in independent learning activities.
Fourthly, it catalyzes the emotion of autonomous learning.
Suhomlinski said: "If a child has not tasted the joy of studying and working, he has not experienced the pride of overcoming difficulties-this is his misfortune." Teachers should let every student get care and encouragement, let them learn in prosperity and experience happiness; Explore in adversity and experience success. Make learning truly become an important emotional experience in students' learning activities, and make students have the emotional experience of active learning.
(a) Experience success and enhance confidence.
Psychology tells us: "As long as a person experiences the joy of success once, it will arouse the endless pursuit of ideas and strength." Every student is eager for success, which is the psychological nature of students. Therefore, in classroom teaching, teachers should consciously create various scenarios, provide opportunities for all kinds of students to express themselves, and seize opportunities to pave the way for students' success, so that they can succeed. Teachers should try their best to meet the needs of students, meet the needs of students' sense of accomplishment, be kind to students' thinking achievements and be willing to listen to students' different opinions. Teachers should give priority to praise and positive guidance in the expression, operation and performance of students, and allow students to make mistakes, especially for students with learning difficulties. Be patient and help them analyze the causes of their mistakes and correct them. They should also encourage and praise the success of correction and let different students experience the hardships of exploration and the joy of success. In this way, the self-confidence of students' active participation is encouraged, and the enthusiasm of students' active participation runs through.
(B) encourage evaluation, enhance courage
Mathematical evaluation is to evaluate students' achievements and level through learning, and at the same time guide students to improve their learning and self-improvement; It is also an important link in implementing teaching feedback, evaluation and decision-making. In the atmosphere of autonomous learning, students have the opportunity to express their personal views and problems freely. They are active in thinking and have cognitive differences, which greatly increases the randomness and contingency of mathematics classroom teaching. Therefore, teachers should evaluate students in time and promote the development of each student. Such as calculating the surface area (unit; Cm): There are student formulas: (5× 5+5× 10+5× 10) × 2, 5× 10× 4+5× 2, etc. Get positive affirmation from teachers. If a student's formula is 5×5× 10, the teacher should say: this formula is innovative! Can you share your thoughts with everyone? Let the students share their ideas of solving problems. If students really think they are wrong, or don't understand the reasons, teachers should guide them in time and organize students to discuss. Oh, it turns out that the cuboid is divided into two cubes to find the surface area. How creative!
To stimulate students' evaluation, teachers need to "squat down", appreciate mathematics with children's eyes and accept students' different opinions. Teachers should be good at grasping the bright spots of students and use "you have made great progress!" "Your thinking is right", "The teacher believes you can answer it" and "I agree with you" ... This inspiring language activates students' thinking in time, arouses their enthusiasm for autonomous learning, and enhances their confidence and courage in autonomous learning.
(C) pay attention to emotional infection and motivation
As the saying goes: only understanding can make sense, emotion is the foundation and reason is the purpose. Teachers should be willing to devote themselves to emotion, regard the teaching process as the main channel to pour love into students, and be good at conveying love information to students with kind eyes, subtle movements, cordial attitudes and enthusiastic praise, so that students can feel the respect and loveliness of teachers and the kindness of their mothers. When teachers shine the sunshine of knowledge and wisdom on every child like the sun, they will show positive enthusiasm, produce an emotional sound and an action vibration, and produce an independent spark of will. Love is the soil and sunshine of independent learning.
Zankov said: "Whatever children can understand and feel by themselves should be understood and felt by themselves." In mathematics classroom teaching, it is a long-term and arduous task in quality education to realize autonomous learning and let students actively participate in learning. Only by allowing students to be the main body, practice with their own hands, think, discover and innovate actively with their own brains, and let them realize that they are discoverers, researchers and explorers of learning activities, can they actively mobilize their initiative and enthusiasm in learning, and can they really play their main role and become the masters of learning.