Eight mathematical thinking methods: 1. Transform thinking
Transforming thinking is both a method and a kind of thinking. Transformational thinking refers to changing the direction of the problem from one form to another from different angles when encountering obstacles in the process of solving problems, and seeking the best way to make the problem simpler and clearer.
Second, logical thinking.
Logic is the foundation of all thinking. Logical thinking is a thinking process in which people observe, compare, analyze, synthesize, abstract, generalize, judge and reason things with the help of concepts, judgments and reasoning in the process of cognition. Logical thinking is widely used to solve logical reasoning problems.
Third, reverse thinking.
Reverse thinking, also known as divergent thinking, is a way of thinking about common things or opinions that seem to have become conclusive. Dare to "do the opposite", let thinking develop in the opposite direction, conduct in-depth exploration from the opposite side of the problem, establish new concepts and shape new images.
Fourth, corresponding thinking.
Corresponding thinking is a way of thinking that establishes a direct connection between quantitative relations (including quantity difference, quantity times and quantity rate). General correspondence (such as the sum and difference times of two or more quantities) and ratio correspondence are more common.
Verb (abbreviation of verb) innovative thinking
Innovative thinking refers to the thinking process of solving problems with novel and original methods. Through this kind of thinking, we can break through the boundaries of conventional thinking, think about problems with unconventional or even unconventional methods and perspectives, and get unique solutions. It can be divided into four types: difference type, exploration type, optimization type and negative type.
Sixth, systematic thinking.
Systematic thinking is also called holistic thinking. Systematic thinking method refers to having a systematic understanding of the knowledge points involved in specific problems when solving problems, that is, analyzing and judging what the knowledge points belong to when getting the problems, and then recalling what types of such problems are divided into and the corresponding solutions.
Seven, analogical thinking
Analogical thinking refers to the thinking method of comparing unfamiliar and unfamiliar problems with familiar problems or other things according to some similar properties between things, discovering the essence of knowledge, finding its essence, and thus solving problems.
Eight, thinking in images
Thinking in images mainly refers to people's choice of things in the process of understanding the world, and refers to the thinking method of solving problems with intuitive images. Imagination is an advanced form of thinking in images and one of the basic methods. For more information, please click on 20 19 "Complete Mathematics Required Questions for College Entrance Examination".
Eight methods of reviewing mathematics: 1. Grasp the foundation.
Mathematical exercises are nothing more than the comprehensive application of mathematical concepts and ideas. Understanding the basic concepts, theorems and methods of mathematics is the premise of judging the type of topic and the scope of knowledge, and the basis of correctly mastering the method of solving problems.
Only when the concept is clear and the method is comprehensive, can we get a solution quickly when we encounter a problem, or when we face a new exercise, can we associate the method of the exercise we have done at ordinary times and realize a quick answer.
Second, make plans and goals.
When reviewing math, you should make a good plan, not only the big plan this semester, but also the small plan every month, week and day. The plan should be consistent with the teacher's review plan and should not conflict with each other. For example, according to the teacher's review progress, master today's knowledge points, deepen the understanding of knowledge points, and study different aspects and angles of knowledge points.
Third, beware of sea tactics and overcome the phenomenon of blindly doing questions without paying attention to induction.
Doing problems is to consolidate knowledge and improve adaptability, thinking ability and computing ability. Learning mathematics requires some exercises, but learning mathematics does not mean doing problems. In all kinds of exam questions, a considerable number of exercises can be solved through the accumulation of simple knowledge points and the deduction of axiomatic knowledge system These exercises are to expand the problem-solving methods by doing a certain amount of exercises.
However, with the reform of the college entrance examination, the college entrance examination has focused on creativity and ability-based examinations. Therefore, we should do the questions carefully and pay attention to the understanding and flexible use of knowledge.
Fourth, often do college entrance examination questions and uncover the mystery of college entrance examination questions.
College entrance examination questions are the best exercise. It is a new and good starting point when examining knowledge points, which correctly controls the difficulty of the examined knowledge points. Answering some college entrance examination questions is helpful to grasp the difficulty requirements of the college entrance examination for this knowledge point; It is helpful to judge the similarities and differences between college entrance examination questions and common questions, enhance the ability to judge the reliability of questions, and prevent digression and strange questions.
Fifth, summarize the big thinking and strategy of mathematics.
The main purpose of mathematics learning is to cultivate our creativity and our ability to deal with things and solve problems. Therefore, when dealing with mathematical problems, it is particularly important to master big strategies and big thinking, and we should pay attention to summing up in our usual study.
Sixth, do a good job in the final review to achieve a leap in mathematics learning.
The final stage of review is a special lecture. Teachers give detailed lectures and intensive training on key knowledge, key problem-solving methods and key mathematical ideas.
Accumulate certain examination experience.
There is a big exam at the beginning of each month this semester, and each unit has more than a dozen unit exams and mock exams. Seize these opportunities, accumulate certain examination experience, master certain examination skills, and give full play to their due level in the examination.
Eight, solutions to overcome the three problems
Mathematics test questions are divided into three types: multiple-choice questions, fill-in-the-blank questions and solution questions. Based on multiple-choice questions and fill-in-the-blank questions, the score is ***76. Solving problems is the key to improving scores. The solutions to these three problems, especially the multiple-choice questions, are flexible and diverse. Mastering a variety of such problem-solving methods will make the test questions fast and accurate, and at the same time win more time for solving the last six questions.
High school mathematics mind map