In the traditional classroom teaching, "the teacher tells the students to listen and the teacher asks the students to answer", the students may be able to get a mathematical conclusion and get a decent score "quickly and economically". However, in this single passive acceptance learning mode, students' edges and corners are smoothed, their personality is suppressed, they lack the spirit and consciousness of independent thinking, and they will become more and more mechanical and disciplined. As a challenging way of learning, inquiry learning is not only the main way of learning activities in specially designed inquiry learning courses, but also can penetrate into classroom learning activities of various disciplines. Introducing research-based learning into senior high school classroom will change students' learning from simple acceptance to positive emotional experience and deep cognition and participation, which will inevitably promote the improvement of learning methods and all-round quality including high-level thinking. At present, due to the pressure of college entrance examination, the research of inquiry learning is mostly theoretical and far from teaching practice, so it is difficult for teachers to really study and apply it in teaching. The author believes that research-based learning must move from experts to teachers, from theory to practice, and from macro to micro.
Experiential high school mathematics classroom research-based learning pays attention to process experience, that is, let students experience, feel, explore and finally understand and master in certain problem situations. In such a problem situation, students use their existing knowledge, skills and experience to make well-founded guesses and inferences, constantly change their angles and backgrounds, and re-examine and correct them. Through such repeated speculation, students can get rid of the false and retain the true in self-denial and self-affirmation, gradually explore the essence of the problem, and finally draw a reasonable conclusion. In this process, students seem to get only direct knowledge and experience, but in fact, they also get the satisfaction of their own needs, psychological balance and strong interest in mathematics. Interaction in the process of inquiry learning, teachers and students are in an equal position, and there is no difference between strength and weakness. Teachers put students in the main position, give full play to their own functions of organization, guidance, promotion and encouragement, and let students actively participate in research activities with their own knowledge, experience and thinking, so as to realize teacher-student interaction and teaching.
The key to quality reconstruction of mathematics teaching is to reconstruct the material content in the textbook to make it realistic, interesting and challenging. Therefore, teachers should take students' knowledge, direct experience and life world as important curriculum resources, and strive to explore practical problems that occur around students and imply some mathematical phenomenon or law, so as to fully mobilize students' enthusiasm, initiative and creativity in learning. The traditional view of structural reorganization focuses on the acquisition of mathematical knowledge and the training of mathematical skills, so it presents a closed-loop teaching model of "example-exercise" in teaching. In classroom teaching, teachers should reconstruct learning materials, pay attention to the reorganization and reprocessing of teaching materials from the structural aspect, focus on highlighting the logical structure of "creating problem situations-mathematizing realistic problems-problem solving and modeling-application and expansion", more embody the value orientation of "learning mathematics" and create favorable conditions for students' sustained and harmonious development.
Creating situations and asking questions with questions will cause collisions and communication. Problems are the starting point of cognitive activities and research activities. No problem can be separated from a certain situation. In teaching, the so-called problem situation is to create a kind of "disharmony" or "conflict" between the teaching content and the students' knowledge-seeking psychology, and introduce them into the situation related to the problem, thus forming the problem consciousness and stimulating the cognitive impulse. Mathematics is abstractly summarized from the quantitative relationship and spatial form of the objective world. Teachers can guide students to mobilize their existing experience to understand mathematics through the background and richness of mathematics learning content, and refine their common sense into mathematics, so as to realize the interest and functionality of mathematics.
The main task for teachers to improve their independent inquiry in time and space is to determine the form of research. The forms of inquiry learning in mathematics classroom mainly include: ① Students' independent inquiry. Every student can explore and discover freely and openly in his own way of thinking according to his own experience, and form a personalized understanding and expression of the studied problems. This can enhance the sense of autonomy and cultivate students' spirit of inquiry and innovation. (2) Group or class cooperation to explore exchanges. Students' cooperation or communication on the basis of independent inquiry can satisfy students' desire for self-expression and realize their self-worth. At the same time, they can further explore and integrate teaching resources. Through the cooperation and communication between teachers and students, students can share the results of inquiry in communication.
According to the different characteristics of high school mathematics content, the following methods can be used for teaching: experimental investigation. For the content close to life, students can be required to pass a certain data survey, and then analyze and summarize it to find a reasonable answer, such as installment payment. Observation and induction. Let students start from the existing knowledge and experience, and summarize and discover the general laws of things from specific examples through sorting, classification, observation and calculation. Through a series of activities such as exploration and discovery, observation and analysis, induction and verification, students' thinking methods of exploring laws are strengthened.