First, stimulate interest, guide topics, independent learning, inquiry
The topic of arousing interest refers to the teacher's classroom introduction, and self-study inquiry refers to the students' activities after the teacher prompts. This link plays an important role in influencing the overall situation and radiating the whole class. Teachers are required to be like an invisible "magnet" at the beginning of a class. Although it only lasts for a minute or two, it can attract students' attention, arouse their emotions and form a good classroom atmosphere. The teacher's brief introduction is to pave the way for students' autonomous learning and inquiry. With a strong interest, students will take the initiative to enter the stage of self-study and inquiry, tap their own potential, give play to their autonomy, and cultivate their self-study habits and abilities. Students' autonomous inquiry consists of four interrelated learning elements: learning, thinking, doubt and questioning. Students can combine learning, thinking, doubt and questioning in self-study and inquiry, which will add infinite fun and motivation to self-study. The enthusiasm and initiative of students' inquiry learning often comes from a situation full of doubts and problems for learners. Creating problem situations allows students to find and put forward "problems" hidden in problem situations, which is closer to their thinking reality and can trigger their inquiry. Finding problems is often more important than solving them.
Second, correct guidance and independent inquiry.
The so-called independent inquiry is to let each student explore, discover and recreate relevant mathematical knowledge freely and openly according to his own experience and his own way of thinking. Because students should be active in learning knowledge, not passive. Teachers can't replace students' own thinking, let alone the thinking of dozens of students with differences. By doing mathematics, students can experience the joy of acquiring knowledge. The purpose of independent inquiry is not only to acquire mathematical knowledge, but more importantly, to enable students to learn scientific inquiry methods in the process, so as to enhance students' independent consciousness and cultivate students' exploration spirit and innovation ability. For example, in the teaching of "application problems in proportional distribution", the author did not rush to standardize students' problem-solving behavior after leading out the questions to be explored, but guided students to explore the problem-solving methods independently. Finally, the students came up with a variety of correct methods from different ideas, which fully reflected their rich creativity.
Thirdly, study and inquiry should be combined to explore cooperatively.
Students' self-study and inquiry means that there is exploration in learning and learning in exploration. General problems can be explored while learning and solved by yourself. Problems that cannot be understood or solved can be solved at this stage. In the face of students' questions, teachers don't have to explain too early. They just need to synthesize everyone's problems, put forward one or two key questions, and organize students to cooperate and explore. For example, when teaching the calculation of rectangular area, the author asked each student to prepare 24 pieces of square paper 1 cm before class, and asked each member of the group to spell out a rectangle with these 24 pieces of paper in class. Everyone spells differently. After spelling, explore: How long and wide are these figures? What is the area of these figures in square centimeters? What is the relationship between the length, width and area of each figure? Through hands-on operation, brain thinking and cooperative communication, students find that the area of each rectangle is equal to the product of length and width, thus obtaining an accurate calculation formula.
Fourth, strengthen understanding and practical exploration.
This link is not only the consolidation of inquiry results, but also the test of inquiry effect, and its role is to help students learn methods. First of all, according to the requirements of the textbook, teachers should cooperate with students to explore the situation, briefly summarize and discuss the main points and difficulties of what they have learned, make the finishing point and give students a clear explanation. After that, students are required to use the knowledge gained from self-study and discussion to learn to draw inferences from others and solve similar or related problems. Mathematics Curriculum Standard for Full-time Compulsory Education (Experimental Draft) emphasizes that students' problem-solving is a process of exploration, not a process of simply solving problems with ready-made models. It is of great significance for students to learn to ask questions, understand problems from the perspective of mathematics, solve problems comprehensively by using the knowledge and skills they have learned, form some basic strategies, experience the diversity of solving strategies, and cultivate students' practical ability and innovative spirit. This requires that the exercises designed by us should not only help students to consolidate and master knowledge, but also help to cultivate students' awareness of mathematical application and practical ability.
Fifth, encourage evaluation and extend exploration.
The main purpose of evaluation experience is to promote the development of students' subjectivity. The main task of experience evaluation is to enhance students' initiative development motivation and improve their initiative development ability. To this end, the author believes that the following two points should be paid attention to in classroom teaching: first, to evaluate the subjective spirit and quality of students' autonomy, initiative and originality in independent inquiry, cooperative discovery and practical application, so that students can gain emotional experience of actively exploring and acquiring knowledge and enhance their confidence and motivation in learning; The second is to guide students to reflect in the process of inquiry learning, focusing on refining mathematical thinking methods and effective strategies to solve problems, so that students can understand mathematical thinking methods and learning strategies, and consciously point their thinking to these aspects, so as to improve their ability to solve problems and actively acquire new knowledge.
Whether inquiry-based classroom teaching can achieve practical results depends on whether students participate, how to participate and the degree of participation. At the same time, only when students actively participate in teaching can we change the boring situation of classroom teaching and make the classroom full of vitality. The so-called students' active participation, that is, giving students the right to explore independently, does not require students to run according to a set designed by the teacher in advance, but to let students try every step of exploration first, push them to the active position and let them learn by themselves. Teaching tasks are mainly completed by students themselves.