Innovation in thinking has the same meaning as originality, creativity or creative thinking in thinking activities, but innovation emphasizes "novelty", that is, innovation refers to the intellectual quality of independent thinking to create achievements with social (or personal) value and novelty components. Its characteristic is that the subject carries out novel combinatorial analysis and abstract generalization of knowledge, experience and thinking materials, thus reaching the advanced form of human thinking; Its result, whether it is concept, theory, hypothesis, scheme or conclusion, contains new factors and is an innovative thinking activity. Of course, this novelty is not an absurdity divorced from reality, but a novelty with social value. It may be ignored or misunderstood by people, but its views or products will eventually be recognized by society.
In mathematics teaching, the innovation of thinking is mainly manifested in being good at independent thinking, analyzing and answering questions, advocating the spirit of exploration and innovation, and of course including small inventions and small creations. As teachers, we should consciously inspire students to ask more questions. Asking questions is the result of thinking and the beginning of innovation. Don't set many rules for students, let alone post them. That is, students often put forward many different viewpoints or new viewpoints in the process of learning, which often contain the seeds of wisdom. Even if there is only a little freshness, we should fully affirm and strongly encourage it.
In the middle school stage, the innovation of thinking is more manifested in integrating knowledge after discovering contradictions, breaking through contradictions with an offensive attitude and finally solving problems. For example:
Verification:
Analysis: This problem is considered purely from a triangle, which is more complicated. If you think of a point on the unit circle instead of a point, then you only need to prove the proposition. And series, so it is established.
(Method 2), think of points on the unit circle, and points correspond to vectors, so if you want to prove a proposition, you only need to prove it. A vector can be regarded as a force, so the resultant force of a force system with * * * points whose endpoints are distributed on the n vertices of a regular N-polygon is zero. So it is established. Proof (omitted).
It seems natural to solve physical problems by mathematical methods, but on the other hand, it is not paid much attention to. But for some problems, it is not only novel and innovative, but also strengthens the mutual connection and infiltration between disciplines.
The opposite of thinking innovation is the conservatism of thinking, which is mainly manifested in the constraints of various rules and regulations in mathematics learning, the bondage of thinking, the unwillingness to think about problems, and the desire for ready-made "regulations", resulting in the inertia of thinking. The effective way to eliminate the conservatism of thinking is to encourage students to think more and ask why. On the premise of strengthening basic knowledge and training, encourage students to think independently.
The focus of talent competition in 2 1 century is to cultivate first-class talents with innovative thinking. Only people with innovative thinking can lead and grasp the trend of scientific and technological development. As teachers, it is our unshirkable responsibility to cultivate students' innovative thinking, and it is also a subject we are constantly exploring.