Inquiry learning is "a learning method and process in which students acquire knowledge, skills and attitudes through inquiry activities such as finding problems, investigation and research, hands-on operation and expression and communication". Inquiry learning of mathematics is to position teaching activities as the main body of students. The question is how to learn, which is inquiry. The most general explanation for exploring is "knowing things around you through practice". In this way, "inquiry learning" simply means "let students know and acquire their own knowledge through their own practice". Practice here mainly refers to students' conscious learning activities. The characteristics of research-based learning in mathematics are mainly embodied in openness, research and practicality. Its function is to create a good atmosphere for students to explore, debate and encourage each other to learn, and to provide students with opportunities for independent exploration, cooperative learning and independent knowledge acquisition. Mathematics inquiry learning pays more attention to the learning process. The materials of inquiry learning in mathematics are not only provided by teachers themselves, but also teachers should encourage students to sum up problems through thinking, investigating and consulting materials, and even put forward mathematical problems through daily life situations, and then refine them into inquiry learning materials. In the process of research-based learning, students are the masters of learning, the researchers and solvers of problems, and the protagonists, while teachers help students at appropriate times and play the role of organization and guidance. The evaluation of research-based learning in mathematics not only pays attention to the results of learning, but also pays attention to the degree of students' participation in learning, the depth and breadth of thinking, and pays attention to new extracurricular skills, carefully cultivates the innovative spirit beyond textbooks and self, and at the same time, dynamically pays attention to students' emotional changes to serve students' lifelong development.

Second, the basic model of mathematics inquiry learning classroom teaching

The basic way to adopt inquiry learning teaching method in mathematics classroom teaching is "exploration and research", because the idea of compiling experimental teaching materials is to ask and solve problems, and the course emphasizes the formation and development process of knowledge, not the results or conclusions. In classroom teaching, students learn relevance and knowledge through colorful subject participation, and teachers are the instructors and collaborators of teaching. Therefore, I gradually formed the inquiry learning mode of "subject participation, inquiry learning" in mathematics practice, and its basic process is:

Create a situation → independent inquiry → cooperation and exchange → display and evaluation → application expansion → reflection and innovation → preview and guidance.

1. Creating situations: The so-called mathematics inquiry teaching, in my opinion, means that teachers obtain learning materials and free and open experience space by creating problem situations; Establish equal teacher-student relationship and colorful teaching forms; Maintain a certain "self-learning" time; Take advantage of various conditions and start from the existing life experience to bring students into the situation; Let them feel the experience in this situation by asking questions, exploring and discussing problems, and actively acquire knowledge and apply it to solving practical problems; So as to comprehensively develop innovative ability, emotional attitude and values. In classroom teaching, I usually use the following three methods to set the situation:

(1) Create problem scenarios through preview detection;

(2) Creating problem situations from practical problems;

(3) Creating problem situations by reviewing old knowledge;

(4) Creating problem situations with mathematical stories;

(5) Creating problem situations with game plays;

(6) Creating problem situations with hands-on operation and practical activities;

2. Independent exploration: Under the guidance of questions, students "discover" mathematical conclusions by themselves through hands-on practice, independent exploration and independent thinking, and gain experience in mathematical activities through experiments, operations, observation, analogy, induction and speculation. Teachers should consider "adapting to students' research as much as possible and coordinating! "Teachers make full use of materials such as' do it',' try it' and' think about it' in textbooks to guide students to carry out related math activities. When students experience the essence of new problems, they should open up a new situation, let students discover new problems and boldly let them explore. The teacher's task is to open a broad exploration space for students.

3. Cooperation and communication: I adopt cooperative group production as the organizational form of cooperation and communication, actively advocate intra-group cooperation, discuss and communicate, and make students active in class; Competition between groups, let them discuss and argue; Use various means to guide students to express their feelings, so that students can express themselves boldly in class and develop their personality.

4. Presentation and evaluation: reflect and evaluate the obtained mathematical thinking methods, focusing on students' self-evaluation, emphasizing feelings, experiences, presentation and expression; Students mainly explain how knowledge is discovered and what classes are available to promote students' active development; Teachers should give affirmation and encouragement in time and evaluate students' learning attitude and ability; At the same time, evaluate related activities and pay attention to the combination of various evaluation forms. In the teaching process, teachers should pay attention to the following characteristics of students' inquiry learning evaluation:

(1) Participatory evaluation: under the guidance of teachers, participatory evaluation allows students to express their opinions boldly by creating various evaluation opportunities and activities. In the evaluation process, students have a deeper understanding of themselves and their peers, close the cooperative relationship with their peers, gain and experience happiness, success and collective honor, and learn to exchange information and actively participate in activities.

(2) Interactive evaluation: "Inquiry learning" classroom teaching is a mathematical activity, including the interaction between teachers and students, as well as the interaction between students. I don't advocate one-way evaluation of teachers, but strongly advocate multilateral interaction and multi-directional communication between teachers and students, so that students can learn to learn, cooperate and create in horizontal evaluation.

(3) Difference evaluation: There are differences among students, so I insist on hierarchical evaluation. For students with strong learning ability, it is important to evaluate their learning results and quality; It integrates artistry, ideology and imagination, and fully explores and displays students' personality characteristics. For students with weak learning ability, it is important to evaluate their learning attitude and learning process and try to find out each student's own bright spot.

(4) Multi-evaluation: The content and requirements of the test questions can be varied, providing all kinds of students with opportunities for success. I use the "open" or "practice" mode of problem group to guide students to have a meaningful expression process of designing and solving mathematical problems, so as to obtain beneficial enlightenment from scientific methods. At the same time, I also insist on the exemption system. In each class, according to students' participation attitude, classroom performance, practical ability and innovative ideas, some students are relaxed or exempted from inspection.

5. Application expansion: After students acquire relevant knowledge, teachers will help students master the application of knowledge through the analysis and explanation of typical examples, and consolidate exercises by using exercise groups. In addition to using the examples and "exercises in class" materials in the experimental textbook, I also selected some exercises as supplements according to the actual situation of students. I pay special attention to strengthen the variant training for students in this link, in order to cover all aspects and flexibly use the knowledge I have learned to solve related problems. Sometimes I use it according to what I have learned. I make full use of the materials such as "back garden", "reading" and "subject research" in the experimental teaching materials to extend and expand the relevant knowledge, so that students can apply what they have learned and explore some practical problems, thus cultivating students' mathematical scientific spirit and innovative practical ability. I also use some famous historical themes (such as the exploration of Pythagorean theorem, the problem of bisection of angles, the famous works of island calculation and Li's wine).

6. Reflection and innovation: After systematically summarizing what they have learned in the form of questions, teachers will further seek novelty and difference from their classmates, and put forward mathematical questions of thinking, exploration or sustainable development, thus stimulating students' enthusiasm for exploration, forming a thinking storm and further developing mathematics learning.

7. Preview guidance: before the end of each class activity, show the students the theme of the next class activity, constructively put forward preview requirements, and remind students to make necessary preparations; Sometimes, predicting the relevant information of the recent exam will really make the inquiry learning of mathematics go out of the classroom and into students' lives, so that "inquiry learning" is closely linked and interwoven into a continuous and gradual whirlwind, constantly cultivating the ability to solve problems in life and improving the level of activities.

Third, the effectiveness and prospect of inquiry learning in mathematics teaching

Judging from the practice of carrying out research-based learning in mathematics, all students who choose the teaching course of research-based learning in mathematics not only do not affect the learning of mathematics subject content, but also show obvious advantages over ordinary teaching courses in terms of average scores, A-level rate, non-D-level rate, innovative personality, emotion and will. Because they have studied mathematics courses related to disciplines, some have deepened their understanding and love of mathematics courses through their own personal practice. Through this inquiry learning, students' understanding of mathematics is really related to how to solve some problems in life with mathematical knowledge, from just learning knowledge from books, coping with exams and returning to real life. How to apply mathematical knowledge to real life is the biggest benefit for students in inquiry learning. Therefore, research-based learning is conducive to cultivating students' innovative spirit, practical ability and lifelong learning ability. Guiding students to actively carry out inquiry learning and take the road of scientific inquiry can also prompt teachers to update their educational concepts and improve teaching methods. In the future teaching, we should work harder to carry out inquiry learning. Modern middle school students have great creative potential and development space. If we create an environment suitable for their development, build a platform for their development and provide more opportunities to give full play to their creative potential, then our middle school students' return to society will be immeasurable. Let's provide more development opportunities for children and let them give full play to their intelligence.

Through the teaching practice of research-based learning, preliminary results have been achieved, but more scientific planning and long-term experiments are needed to obtain better results and guiding conclusions to adapt to the teaching concept of the new textbook.

In a word, the key to developing inquiry learning in junior high school mathematics teaching is to change teachers' teaching methods and students' learning methods. Carrying out inquiry learning in junior high school mathematics teaching is an important measure of mathematics reform in the new century, an urgent need of the development of the times and a strong call for students' lifelong development. With the deepening of the new round of curriculum reform, our math teachers are inevitably faced with opportunities and challenges, and there are still many problems in inquiry learning, which need us to explore and improve constantly in teaching practice.