Psychologists' investigation shows that happy and excited mood and mild and relaxed learning environment have the functions of spreading and strengthening cognitive and innovative thinking activities. An equal and relaxed learning environment is conducive to mobilizing students' enthusiasm for inquiry learning, mobilizing students' initiative to participate in inquiry, stimulating students' desire for inquiry, making students dare to think, ask, do and show, and ensuring the development of inquiry activities.

Second, refine the materials to be explored.

Inquiry learning mainly organizes students' activities around asking questions and solving problems. Therefore, the key to inquiry learning is to turn knowledge learning into "inquiry" into mathematical problems. This requires teachers to choose and design teaching content that is beneficial to students' inquiry according to the content of teaching materials and students' intelligence level, creatively turn knowledge conclusions in teaching materials into inquiry questions, put students in question situations, make students clear their inquiry goals, have a strong desire to explore, and actively participate in inquiry activities to explore and discover scientific knowledge.

Third, constantly create opportunities.

In teaching, through the interaction between students and between teachers and students, mathematics classroom has become a stage with rich connotations. In mathematics learning activities, students' ways of thinking and intellectual activities are different, so students must be allowed to experience cooperation and communication as much as possible. Feel different ways and processes of thinking. Cooperation and exchange enable students to participate in it, brainstorm, complement each other's thinking, broaden their thinking, enable students to obtain clearer concepts and more accurate conclusions, enable students to learn from each other's strengths in mutual evaluation, and enhance their learning confidence.

Fourth, reappear grace in expansion and extension.

The process of inquiry learning is, in the final analysis, the process of feeling, experiencing and training learning strategies and methods. It is its natural requirement and higher pursuit to cultivate students' innovative consciousness, guide students to turn the unknown into the known, and infer the unknown according to the known. Therefore, it is necessary to expand and extend the learning content as appropriate as possible, guide students' interest from in-class inquiry to extracurricular inquiry, and stimulate them to enter a higher level of inquiry learning.