Proving and solving problems in mathematics is a good way to cultivate innovative thinking. For example, proof in geometry, solving problems in number theory, reasoning and proof in algebra, etc. These courses need to use innovative thinking, explore the essence of problems in the learning process, and find the laws and solutions of problems.

These can help students to exercise logical thinking, analyze problems and cultivate innovative ability, so that students can have better problem-solving ability in their future study and work.

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To cultivate students' innovative thinking, we can consider the following methods:

1, stimulate curiosity: encourage students to ask questions, explore and investigate. Cultivate their curiosity and thirst for knowledge about new things, and let them take the initiative to find answers and solutions to problems.

2. Provide diverse learning experiences: create diverse learning environments and experiences, including field trips, experiments and artistic creation. Stimulate students' creativity and innovative thinking through different learning methods.

3. Encourage independent thinking: provide opportunities for students to study independently and encourage them to think independently and express their opinions. Carry out group cooperation, debate and discussion activities to promote students' critical thinking and innovative ability.

4. Cultivate the ability to solve problems: teach students the ability to analyze problems, propose solutions and implement plans. Encourage them to face challenges, keep trying and improving, and cultivate the courage and perseverance to solve problems.

5. Provide creative tasks and projects: Designing tasks and projects requires students to exert their creativity and innovative thinking to solve problems. Encourage them to try new methods and ideas and cultivate their innovative spirit and ability.

6. Provide opportunities for practice and feedback: Let students try their innovative ideas through practice and provide timely feedback and guidance. Encourage them to learn from their mistakes, and encourage them to sum up experience, reflect and improve.

7. Tutor guidance: through the guidance of tutors or teachers, guide students to think and practice in innovative projects. Tutors can provide professional knowledge, guide students to conduct in-depth research and guide the whole innovation process.

8. Promote cooperation and communication: encourage students to cooperate and communicate, and let students learn to cooperate with others, listen to their opinions and develop their creativity through team cooperation projects, sharing meetings and other activities.

Cultivating students' innovative thinking requires long-term accumulation and practice. Teachers can provide support and encouragement for students, create a positive learning environment, and guide students to develop the ability of independent thinking, problem solving and innovation.