Students' innovative consciousness is not born, but cultivated purposefully and planned the day after tomorrow. On the basis of students' existing knowledge and experience, teachers purposefully create vivid and interesting problem situations to arouse students' doubts and thus stimulate their desire to explore, which not only helps students to enhance their understanding of new knowledge, but also helps to cultivate students' innovative consciousness. For example, in the teaching of "the sum of the internal angles of a triangle", the topic is briefly introduced first, so that students can cut and spell the sum of the three internal angles of an acute angle, a right angle and an obtuse angle by themselves, and make a guess to encourage students to guess and protect their enthusiasm. It doesn't matter what students guess, what matters is the process of forming this consciousness. Then let the students think further: how to prove whether the conjecture is true? To this end, first guide students to recall what they have learned before. Two straight lines l 1∑L2 are cut by the third straight line AB, and the relationship among congruent angle, inner angle and inner angle on the same side is observed. In order to form a triangle, draw a straight line from point A, and AC and L2 intersect at point C. On this basis, the teacher asks: ① What are the three internal angles of this triangle? What is the sum of these three internal angles? ② Can you prove that the sum of the internal angles of the triangle is 180 according to this diagram and previous knowledge? On the basis of their own thinking and mutual discussion, students sum up the triangle interior angle theorem. In order to deepen the study of this topic and guide students to discuss the proof methods and ideas in groups, the focus is on the practice of auxiliary lines, and students can get parallel lines that can pass through any vertex of the triangle. Further, let the students draw a triangle to see how many obtuse angles or right angles a triangle can draw at most. Why does a triangle have at most one right angle or obtuse angle? On this basis, the teacher suggested that known triangles can be classified according to different sides. Can triangles be properly classified according to their angles? Why? At this point, the teaching task of this lesson is basically completed. In this class, under the guidance of teachers creating problem situations, students do it themselves, use their brains, communicate with each other, take the initiative to demonstrate, seek knowledge and innovate independently, which not only cultivates students' innovative consciousness, but also makes them learn vividly, understand deeply and remember firmly.

Second, through variant teaching, cultivate students' innovative consciousness.

Problem-solving teaching is the core of mathematics classroom teaching and one of the effective ways to cultivate students' innovative consciousness. In problem-solving teaching, students should not only actively participate in the inquiry process of examples, but also actively participate in the review process after solving problems, giving students time and space to think, allowing students to gain new knowledge and generate new thinking in thinking and discussion, thus cultivating innovative thinking quality.

For example, it is known that the bisectors of 1 ∠ABC and ∠ACB intersect at F, and the intersection point F is DE∨BC, AB is in D and AC is in E, which proves that BD+CE = DE.

First, adjust the original problem, hide the conclusion and know the transformation. As shown in Figure 2, in the isosceles triangle ABC, the bisectors of AB = AC ∠ ABC and ∠ACB intersect at point F. If F intersects, DE∨BC intersects with AB and AC at point D and point E respectively. Please observe carefully and write the isosceles triangle in the picture. Students draw a conclusion through thinking: ① There are four isosceles triangles △ Ade, △BFD, △EFC and △BFC, and then guide students to observe what new discoveries are made. Through students' discussion and exploration, it is concluded that the distance from 2f to △ABC is equal, so AF is the bisector of △ABC. ③ BD = DF and CE = EF, then DE = BD+CE and △ADE perimeter = AB+AC. ④∠BFC=∠BAC+ 1？ 2∠ABC+ 1？ 2 ∠ACB=90 + 1？ 2∠BAC. Now the condition "AB = AC" in the original question has been removed. Is it still effective for students to learn the above findings? Through exploration and research, the students draw the following conclusions: ① Without two isosceles triangles, only △BFD and △ EFC are still valid, ③ still valid and ④ still valid. Then guide the students that point F is the bisector of the inner corner of ∠ABC and ∠ACB. What else can you think of? Some students seem to understand. What is the conclusion of thinking about the outer bisector from the inner bisector? Through this variant training, the flexibility of students' thinking is improved, and their innovative consciousness is also cultivated in thinking, discussion and exploration.

Third, encourage questioning and induce innovative consciousness.

"Learning begins with thinking, and thinking comes from doubt" and "learning is expensive in doubt". Students' doubts in learning are a manifestation of students' active learning, and it is indispensable to cultivate innovative consciousness. Einstein said, "It is often more important to ask a question than to solve it." As teachers, we should not only doubt carefully, but also understand that it is more important to encourage students to ask a question than to solve it. While affirming his bold questioning, teachers should teach students how to ask questions and encourage them to dare to ask questions, so as to cultivate students' keen observation and rich imagination, especially their ability to change and discover new problems and relationships.

Fourth, design open questions and cultivate innovative consciousness.

Open-ended questions aim to open students' thinking and tap their potential learning ability. The design of open-ended questions should be suitable for students' cognitive rules and learning level, conform to their real life, provide students with room for imagination and innovation, encourage students to apply knowledge flexibly to solve practical problems, and cultivate students' innovative consciousness.