Pay attention to these points in the training of rigorous thinking.

The rigor of thinking means that we should strictly abide by logical rules when studying problems, so as to achieve clear concepts, correct judgments and well-founded reasoning, which embodies the rigor and meticulousness in thinking activities. Next, I will talk about how to cultivate the rigor of students' thinking, paying attention to the following aspects:

1, training accurate expression

Whether we can accurately understand the meaning of mathematical concepts, formulas, rules and theorems is an important sign of rigorous thinking, and the degree of students' understanding is often reflected in their language expression. In addition to the teacher's language demonstration, students should be guided to pay attention to some key words in definitions, formulas, rules and theorems to make them accurate and learn to express them correctly in symbolic language.

2. Train strict reasoning.

Reasoned reasoning is the core requirement of rigorous thinking. It means that every step of reasoning should be reasonable and logical. The completion of proof depends on strict reasoning, and the reasoning process is also included in calculation and drawing. Therefore, on the one hand, we should cultivate students' habit of rigorous reasoning, on the other hand, we should often help students correct logical errors in reasoning in time.

3. Comprehensive consideration of training

It is common for students to solve problems incompletely or even make mistakes because of their incomplete consideration of problems. In order to help students learn to think comprehensively and carefully and overcome carelessness, we should pay attention to selecting some suitable contents and exercises for training in the teaching process.

Quick thinking training

The agility of thinking means that the thinking subject can make a sharp and rapid response to objective things when thinking about a problem, which reflects the reaction speed and proficiency of thinking activities. Only by mastering the basic knowledge accurately and forming skilled basic skills can we have real agility.

1, thinking orientation training

Thinking-oriented training is to train students to be good at "returning" to a certain mathematical model when encountering new problems, and to form a clear problem-solving idea as soon as possible through the analysis of known conditions and conclusions. Therefore, we should pay attention to the accumulation of mathematical ideas, methods and experiences in teaching, and pay attention to the hints of general laws.

2, thinking skills training

Our training of students' thinking ability can't be limited to mechanical operations, such as solving binary linear equations. After students have mastered the basic ideas and methods, we should focus on training students how to quickly choose the appropriate method through observation and judgment, and find out its solution, rather than using a certain method mechanically. I think this is very important. Many students pay insufficient attention to solving problems. They always start writing after they get the topic, lacking the process of analysis and observation, and are prone to detours and even detours.

Thinking flexibility training

The flexibility of thinking refers to being able to adjust and change the original thinking process and direction in time according to the changes of the situation, without being negatively affected by the mindset, being good at self-adjustment and getting rid of the old model or the usual bondage. It reflects the flexibility of thinking activities. The training of overcoming the mindset is the individual embodiment of cultivating the flexibility of thinking.

1, multi-party perception observation training

Feeling and perception are the primary forms of understanding things, while observation is the advanced state of perception and the most basic way of understanding things. Perception and observation of objective things in many aspects is helpful to change the original procedures and models and adjust ideas in time.

2. Strengthen the training of knowledge reverse application.

Changing from positive thinking to reverse thinking is a manifestation of thinking flexibility. Many problems have been revived by positive thinking, but they can also be turned into reverse thinking. Knowledge reverse application training includes the reverse application of definitions, formulas, laws and theorems.

The application of unconventional methods is also a kind of reverse thinking training. Unconventional methods, such as seeking advance and retreat, simplifying complexity, turning the customer first and facing difficulties, can broaden students' thinking, overcome the influence of fixed thinking and improve their flexibility.

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Articles on the training of thinking rigor;

1. 500 questions of logical thinking training

2. Reverse thinking training

3. 500 questions of logical thinking training

4. 500 questions of logical thinking training

5. Logical thinking training questions and answers