Training from divergent thinking and convergent thinking.
Divergent thinking, also known as divergent thinking, is based on certain conditions or facts, thinking from many aspects and angles, resulting in a variety of possible solutions, that is, its way of thinking is outward diffusion. From primary school to middle school, there are many ways to explore and prove the "triangle internal angles and problems", and the thinking angles and methods are different. Multi-solution to one question is an excellent carrier for training divergent thinking.
Example: Talk about the use of red bricks as much as possible.
A: We can build houses, fences, pigsty, sheepfold, kennel, chicken nest, duck nest, pave roads and pave steps.
B: You can build houses, pave roads, practice qigong, lift weights, draw, write, make weapons, play chess, prevent typhoons, and put them under the wheels of cars to prevent skidding.
C: Red bricks can be used as dominoes as game equipment.
Comments: Comparatively speaking, B involves many categories, and A is limited to building materials, so B's divergent thinking flexibility is stronger than A's. C's divergent thinking is unique.
Training question: (1) Say as many things with circular patterns as possible.
(2) Try to talk about things with tetrahedral structure.
(3) Tell as many ways as possible to prove that two sides (and two angles) are equal.
(4) Tell as many ways as possible to prove that two sides are parallel (and vertical) equal.
(5) Tell as many ways as possible to add auxiliary lines.
Convergent thinking, also known as seeking common ground thinking, centralized thinking or convergent thinking, is a kind of concentration-oriented thinking and a form of thinking corresponding to divergent thinking. It refers to the way of thinking that takes a thinking object as the center, points to this center from different thinking starting points through comparison, judgment and reasoning, and finally realizes the research goal. Convergent thinking is generally used in the later creation of scheme screening and sorting, or processing or summarizing the results of divergent thinking, extracting valuable factors or forming the most suitable scheme.
For example, from the perspective of divergent thinking, the quadratic equation of one variable leads to multiple solutions; From the perspective of convergent thinking, the univariate quadratic equation is the simplest solution, which can guide the pursuit of different types of equations.
Divergent thinking is very important, you may be familiar with it. In fact, convergent thinking is equally important.
Divergent thinking for quantity, convergent thinking for quality.
Divergent thinking is "release" and convergent thinking is "convergence".
The characteristic of convergent thinking is to refine the results of divergent thinking, eliminate the false and retain the true, so as to optimize the thinking effect.
How to train convergent thinking ability? The first is to train the ability of energy classification. Tell people to classify things according to different standards, and train them to make multiple classifications according to different standards from different angles. The second is to train appreciation ability. Guide learning to identify, analyze, compare and appreciate certain things, and gradually improve their ability of identification and appreciation. The third is to train judgment ability. To cultivate subjective consciousness, we should form the good habit of independent thinking, independent judgment and drawing conclusions by ourselves. The fourth is to train the ability to choose. Convergence thinking is actually comparison, discrimination and choice. In order to learn to choose, choice is widely used in study, life and future work. The process of convergent thinking is actually the process of rejection and choice. For example, encourage people to participate in certain selection activities, encourage them to be judges, learn to strive for perfection, choose the best among the best, and learn to choose the best among various schemes, works and schemes.
Example: The theme "The application of discriminant of roots of quadratic equation in one variable"
(1) The parabola y=x2+x+c has no intersection with the axis, so we need to find the range of the real number c.
(2) The straight line and hyperbola have intersections, and the scope of seeking truth from facts.
(3) Find the real number solutions x and y of equation x2-4xy+5y2+2x-8y+5=0.
Analysis: (1) Let y=0 and get the range of real number c from △ < 0, which is the best scheme; (2) Simultaneous equation, eliminating Y, sorting into quadratic equation x2-4x+k=0 about X, and obtaining the value range of real number k by solving △≥0; (3) Arrange 5Y2-4 (x+2) y+x2+2x+5 = 0 according to y; (x-3)2≤0 is obtained by △≥0, so x=3 and y=2.
Comments: Pursuing * * *, solving multiple problems, solving multiple problems and unifying multiple problems are effective strategies for training convergent thinking. Variant training plays a role in solving a problem and understanding one kind of thing, which is an effective strategy to train convergent thinking.
Example: The reserve salt in the animal kingdom was stolen, and the judge questioned three suspects. The caterpillar said, "Bill the lizard ate it." Bill lizard: Here's the thing. Flower cat: "I didn't eat." It is known that at least one of these three guys is telling the truth and at least one of them is lying. Excuse me, who ate salt? Comments: In the process of analysis, according to the problem center, make assumptions step by step, excluding the judgment of assumptions. Finally, the only correct answer is found, and this way of thinking is aggregate thinking. In this question, suppose Bill the lizard ate it, so all three guys told the truth. This is impossible, so rule it out; Suppose the cat ate it, then all three guys lied, so they ruled it out; So only the remaining hypothesis is correct, that is, the caterpillar ate salt. During the First World War, the French 1 brigade headquarters built an underground headquarters on the front line, which was very hidden. German investigators found that 1 kitten basked in the sun on the 1 grave behind the French position every morning at around 8 or 9 o'clock. So, the Germans made the following judgment:
First, this cat is not a wildcat. Wild cats don't come out during the day, and they can't haunt positions where gunfire rumbles.
Second, the cat shelter is near the grave bag, which is probably an underground shelter, because there is no one around;
Three, careful observation, this cat is a very precious Persian breed, and it will never be an ordinary junior officer who has the conditions to play with this cat in the war, so they concluded that the shelter is a high-level command post.
As a result, the Germans concentrated the firepower of six artillery battalions and made a surprise attack there. Afterwards, it was found that their judgment was completely correct, and all the French command post personnel were killed.
Training questions:
(1) Please tell me what is glowing at home? Find out their similarities.
(2) Please write down the similarities between sea water and river water. The more, the better.
(3). "Four people, one of whom is known to have committed murder, made the following confession to the police station:
A: "B did it." B: "Ding did it." C: "I didn't do it." D: "A lies."
If one of them is a prisoner, which one should it be?
(4) "Return" thinking training:
Question form:
What else is similar? For example, vinegar residue turns into flower soil, potatoes turn into alcohol, ... Now bananas are 50 cents a catty, what should I do?
What's the use of congruence?
What's the use of similarity
What is the use of undetermined coefficient method?