This kind of thinking breaks away from the limitation of logic and is an indispensable part of creative thinking.
For many complex mathematical problems, we can predict and judge whether they have solutions as long as we observe them on the surface with existing knowledge, which is closely related to intuition.
In teaching activities, teachers should provide background information for the development of course content, design teaching situations reasonably, encourage students to think independently, let students know how to analyze problem situations and carry out overall leap-forward thinking activities.
Teachers should be good at guiding students to find internal relations from difficult problems, comprehensively analyze various information and conditions, and make intuitive judgments.
Therefore, teachers should carefully arrange the contents of teaching materials, scientifically use diversified teaching methods and means, guide students to actively put forward personal predictions and conjectures, and carry out various induction, analogy and imagination activities.
(2) Cultivating students' analogical thinking ability In mathematics teaching, many important conclusions can be drawn by means of analogical thinking, such as Leibniz formula in advanced mathematics and many conclusions and propositions related to natural number n in linear algebra.
Therefore, teachers should attach importance to the means of letting students master scientific thinking while imparting mathematical knowledge.
Through careful analysis of the course content, students can master the key points and essence of analogy thinking method, and carry out practical application activities to improve the efficiency of learning activities.
(3) Cultivate students' reverse thinking ability. Reverse thinking refers to analyzing and solving problems from the opposite angle of habitual thinking.
With the help of reverse thinking method, we can get rid of fixed thinking, break through the obstacles of old ideas, produce ideological sparks and make innovative achievements.
In college mathematics teaching, teachers should actively guide and encourage students to use reverse thinking methods.
Specifically, teachers should design specific problem situations for teaching activities. If students only use positive thinking, they will encounter difficulties, but with reverse thinking, they can be suddenly enlightened and solve problems efficiently.
Through teachers' conscious guidance, students know how to use reverse thinking method, which can not only promote them to form a clearer understanding of mathematical problems, but also cultivate their innovative ability.
Source: No.8 issue of Jinxiu in mid-2020