Students are energetic, subjective and cognitive people. As teachers, we must change the concept of education, reform classroom teaching, break through the teacher-centered framework, take students' development as the foundation, activate students' subjectivity, give students an opportunity to explore their own learning time and space, let students actively participate in the process of learning and research, let students live in classroom teaching, and let them study happily and develop actively. Over the past few years, I have focused on inquiry and actively carried out the practice of subjective teaching in mathematics classroom-cultivating students' independent inquiry learning.
1. Set up problem scenarios and guide students to explore independently.
Students are the main body of learning, and this subjectivity is an irreplaceable independent behavior, which must be personally participated and directly experienced by them. Teachers' responsibility lies in providing various learning conditions, giving guidance and encouragement, stimulating their heartfelt desire to learn, making them change from the passive state of "I want to learn" to the active state of "I want to learn", attracting them to "play" and letting them acquire knowledge and seek happiness with the best learning psychology. The introduction of classroom teaching directly affects students' interest in learning and thirst for knowledge. Interest is a tendentious psychological feature and the starting point of research-based learning activities. Teachers should design problem situations according to students' existing knowledge base, cognitive level and recent development fields, aiming at the problems or contents to be mastered in this class, and effectively guide students to actively participate in inquiry learning activities. For example, when I was teaching the concept of index, I held a piece of paper in my hand and asked the students: I folded it in half, infinitely. Can you guess how high it will be? When students hear that Mount Everest, the highest peak in the world, will be surpassed, they will be surprised, their interest will be greatly increased, and their emotional and cognitive needs for learning will be stimulated. For example, when introducing triangle knowledge, let students design and measure the height of TV tower by themselves. When talking about "the intersection of two circles bisects the chord vertically", let the students draw and guess, and then let them sum up the "conclusion", talk about and prove it. In this way, every time I teach a knowledge point, I always carefully design the problem scenario, concentrate the students' attention completely on the classroom, make the students' brains in the most exciting state, make the students have an impulse to try, ignite the students' thinking sparks, and have a desire to explore the text content.
2. Give students free space and encourage students to explore independently.
Classroom teaching is a bilateral activity between teachers and students, students are the main body of learning, and teachers only play a leading role. Many educators believe that "students can learn independently and are active learners"; "What attitude to students' free activities is a watershed to distinguish between good and bad education." He also sharply criticized the practice of traditional schools to suppress students' spontaneous impulses, arguing that "discipline comes from freedom." If students really want to explore independently, they should "give back" the freedom of learning in the classroom. Let students think independently, discuss and communicate enthusiastically. My attempt is to give students enough thinking space and time. In mathematics classroom teaching, I actively create conditions and opportunities for students to show their thinking, give students full space to show their thinking, and encourage them to actively explore problems. At the same time, it also gives students enough time for creative thinking activities. I show the true or false question: the heights of two sides and the third side correspond to the congruence of two triangles. I first give each student time to think and judge independently, and then make a judgment through gestures. I don't directly analyze or simply announce the answers, but let the students with different answers in the group argue and persuade each other, then make a judgment through gestures, and finally let the students explain their ideas. In this way, students have sufficient free space, can experience the whole process of solving problems in thinking activities, and really improve their ability to analyze problems.
Guide students to think in many directions. For example, in Rt△ABC and Rt△ADC, ∠ b = ∠ DAC = 90. What conditions can be added to make △ABC similar to △DAC? This topic provides a great space for students' creative thinking. In the discussion, competition and induction of students, more than 20 kinds of addition schemes have emerged, which have stimulated the peak of students' thinking and creative interest.
3. Cultivate practical operation and promote students' independent inquiry.
The learning process of students is a special cognitive process, and the main body is students. The effect of teaching should be reflected in students, and only through their own operation and practice can it be the most effective. As our teachers, we should design inspiring, exploratory and open questions, and mobilize students' initiative and enthusiasm in learning and thinking through various forms such as actual operation, answer and performance. In the preparation and implementation of classroom teaching, teachers are sometimes screenwriters, sometimes directors and sometimes audiences, while students are not only actors and audiences, but also screenwriters who modify and supplement scripts. Ask questions for students to think, design questions for students to do, tell the reasons for mistakes, and summarize methods and laws. The role of teachers lies in organizing, guiding and guiding, promoting students' independent exploration, positive thinking, bold imagination and concise opinions, cultivating students' innovative consciousness and personality consciousness of daring to think, dare to say, dare to do and dare to take risks, so that students can truly become the masters of classroom teaching, acquire knowledge, develop intelligence and cultivate ability in the activities of thinking, speaking and doing.
4. Skillfully set up layered exercises to deepen students' independent inquiry.
Hierarchical practice is an important link in the process of classroom teaching, which enables students to further consolidate and master new knowledge, form skills acquisition ability training and deepen students' independent inquiry. A mathematician once said: Mathematical exercises are like sharpening stones, sharpening students' thinking. It is true that stratified classroom practice can deepen students' understanding of new knowledge, and also expose students' problems in understanding and applying new knowledge. Grasping this link well can improve the efficiency of classroom teaching and help students achieve the purpose of knowledge transfer. Therefore, when organizing exercises, teachers must set up several groups of intensive exercises, including extended exercises, around knowledge, skills, methods, thinking and ability according to the main problems existing in students and the important contents of this lesson, so as to cultivate students' thinking habits and develop their thinking of seeking differences. The starting point is low, and there are many solutions. The exercises can reflect different levels of thinking, and every student can think successfully in the process of solving problems. It also includes thinking exercises to cultivate students' research spirit and flexible application of knowledge, and to cultivate students' creativity and flexibility in thinking. So that the spirit of independent inquiry can be further developed in application.
After several years of practice, students' inquiry ability has been improved obviously. Students have changed from simply learning cultural knowledge in the past to being able to learn independently, which broadens the field of study. Try to dig math problems from life and around you. And initially mastered some inquiry skills, learned to solve problems with scientific methods, especially those students who are not attentive enough in class and are not good at asking questions, can also change their learning attitude and become fond of asking questions.