First, inspire students to break away from convention and change their perspectives.
Interesting questions can bring children into a challenging mathematical world, especially those "interesting questions" or mathematical problems that cannot be solved by common methods according to common quantitative relations. This road is impassable, so we might as well find another way to guide students to think from another angle, which may have the effect of "a bright future"
For example, calculate the area from the convention: it is known that the area of parallelogram ABCD is 32 square centimeters, and E and F are the midpoints of AB and BC respectively, and calculate the area of quadrilateral AEFC.
This question is difficult to answer at first glance, and the teacher causes students to think outside the box:
Although it can be known that the quadrilateral AEFC is trapezoidal, the upper and lower bottoms and heights are unknown, and the area of the triangle EFB is also unknown, so it is impossible to directly calculate the area of the trapezoid, and it is also impossible to calculate the area by subtracting the whole part. We must adjust our thinking and think from different angles.
Add two line segments parallel to AB and BC in the diagram (as shown on the left). The triangle ABC is divided into four parts with equal area, and the trapezoidal AEFC accounts for three of them. As long as we know the area of triangle ABC, we can find the area of trapezoid AEFC, and the solution is:
32÷2÷4×3= 12 (square centimeter)
Second, guide students to observe problems from different angles
In the new curriculum textbooks, there are many contents in this respect, especially the "model in mathematics textbooks". Observation is the basis and source of thinking, observation is purposeful and conscious perception, and observation should fully reflect the essence of things. This requires teachers to guide students to observe from different angles and get a comprehensive and comprehensive understanding of a thing in order to carry out comprehensive and correct thinking activities. Multi-angle observation is conducive to cultivating students' ability to deal with problems flexibly and think from multiple angles. For example, the position, number pairs, views, statistics and the combination of numbers and shapes in geometry in current mathematics textbooks should guide students to observe and think from multiple angles, thus cultivating students' divergent thinking ability.
Third, encourage students to dare to question authority and doubt ready-made conclusions.
The task of teaching is not only to impart knowledge, but also to generate knowledge. If we are superstitious about authority and the ready-made conclusions of textbooks, human beings will never progress and society will never progress. Therefore, in teaching, teachers should not restrict students' thinking, but should encourage students to dare to break the rules, think further and even see if they can overturn the existing conclusions. Don't let students think in one mode of thinking, but guide them to be good at analyzing problems from different angles and cultivate their divergent thinking.
For example, fill in the numbers regularly: 2, 4, 8,,,
The reference answers given by the teacher are 16, 32, 64, 128.
Guide students to find the law in analysis: 2 1, 22, 23 ... that is, the "law" is 2n (that is, the general term formula), from which the upper solution can be obtained. If you analyze another solution:
1× 0+2, 2×1+2, 3× 2+2, ... that is, the "law" is: n(n- 1)+2 (that is, the general formula), from which we get: 2,4,8,6544.
Looking at the above comparative analysis, this question can only be written as follows: ①2, 4, 8, …, 2n, …; Or 2, 4, 8,16 …; ② 2,4,8, …, n(n- 1)+2, … or 2,4,8, 14, …
In this way, it is a definite sequence (that is, "law"). In order to have a unique solution, it changed the original problem to:
①2,4,8, 16, , , , ;
②2,4,8, 14, , , , 。
In short, to cultivate students' divergent thinking ability in classroom teaching, we should create effective thinking situations from four dimensions: reality, foundation, thinking and interest, and master the above training methods. At the same time, teachers should take "igniting effective interest" as the starting point, "activating knowledge prototype" as the fulcrum, and "stimulating mathematical thinking" as the focus, strive to tap the educational factors of textbooks and actively and steadily carry out divergent thinking training.