Current location - Training Enrollment Network - Mathematics courses - What is logical thinking? How to use it well to learn mathematics?
What is logical thinking? How to use it well to learn mathematics?
1) concept

Logical thinking refers to a way of thinking that conforms to some artificial thinking rules and forms. What we call logical thinking mainly refers to the way of thinking that follows the traditional formal logic rules. It is often called "abstract thinking" or "thinking with eyes closed". Logical thinking is the rational activity of human brain. The thinking subject abstracts the information materials obtained in the perceptual knowledge stage into concepts, uses the concepts to make judgments, and makes inferences according to certain logical relations, thus generating new understandings. Logical thinking has the characteristics of standardization, rigor, certainty and repetition.

(2) Features

Characteristics of concept: connotation and extension.

The characteristics of judgment: first, judgment must judge things; Second, there are always true and false judgments.

Characteristics of reasoning: The logical characteristics of deductive reasoning are: if the premise is true, then the conclusion must be true, which is inevitable reasoning; The logical feature of non-deductive reasoning is that although the premise is true, it cannot guarantee the conclusion to be true, and it is probabilistic reasoning.

(3) Methods

Answer? definition

This is a logical way to reveal the concept connotation. It is to reveal the unique and essential attributes of the object reflected by the concept with concise words. The basic method of definition is "species difference" plus the recent concept of "genus". Rules of definition: 1. The extension of the defined concept is the same as that of the defined concept; Second, the definition cannot be negative; Third, the definition cannot be metaphorical; Fourth, you can't define it circularly.

b? divide

It is a logical method to clarify all the extensions of the concept and divide the concept of "genus" into several concepts according to certain standards. The logical rules of division are as follows: first, the sum of extensions of children is equal to the extension of parents; Second, a division process can only have one standard; Third, all the sub-items must be listed; Fourth, the division must be carried out step by step according to the relationship between genera and species, and it is not allowed to go beyond the level.

Distracted thinking

(1) concept

Divergent thinking refers to a diffuse thinking mode presented by the brain when thinking, which is relatively common. It is characterized by broad vision and multi-dimensional divergent thinking.

Divergent thinking is also called radiation thinking, radiation thinking, diffusion thinking or divergent thinking.

(2) Features

Answer? fluent

It is the free play of ideas. It means generating and expressing as many ideas as possible in the shortest time, and quickly adapting and digesting new ideas. Wit is closely related to fluency.

Fluency reflects the speed and quantity characteristics of divergent thinking.

b? flexibility

It is a process of overcoming some rigid thinking frame set in people's minds and thinking in a new direction.

Flexibility needs horizontal analogy, cross-domain transformation and analogy to make divergent thinking spread in different aspects and directions, showing extremely rich diversity and versatility.

c? Uniqueness

Refers to the ability of people to make unusual and novel reactions different from others in divergent thinking. Uniqueness is the highest goal of divergent thinking.

d? Multi-sensory (combined)

Divergent thinking not only uses visual thinking and auditory thinking, but also makes full use of other senses to receive information and process it. Divergent thinking is also closely related to emotions. If thinkers can find ways to stimulate interest, generate passion, make information emotional and give it emotional color, it will improve the speed and effect of divergent thinking.

(3) Methods

Answer? conventional process

Material divergence method-take as many "materials" as possible in an article as divergence points and imagine its multiple uses.

Function divergence method-from the function of something, conceive all kinds of possibilities to obtain this function.

Structural divergence method-take the structure of something as the divergence point and imagine the possibilities of using the structure.

Form divergence method-imagine the possibilities of using a certain form with the form of things as the divergence point.

Combination divergence method-take something as the divergence point and combine with other things as much as possible to form new things.

Method divergence method-take a certain method as the divergence point and imagine the possibilities of using this method.

Causal divergence method-take the result of the development of things as the divergence point, infer various reasons from the results, or infer various possible results from the reasons.

b? Hypothetical reasoning method

The hypothetical problem, whether it is random choice or limited choice, should be related to the opposite situation, and it is an object and state that is temporarily impossible or nonexistent in reality.

It doesn't matter, most of the ideas obtained by hypothetical speculation may be unrealistic, absurd and infeasible. It is important that some ideas can be transformed into reasonable and useful ideas.

c? Collective divergent thinking

Divergent thinking needs not only all our brains, but also the infinite resources around us to brainstorm. Collective divergent thinking can take different forms. For example, we often jokingly call it "Zhuge Lianghui".