Understand and master commonly used mathematical ideas and methods in time.
The mathematical ideas that should be mastered in middle school mathematics learning are: set and correspondence, classified discussion, combination of numbers and shapes, movement, transformation and transformation.
With mathematical thinking, we should master specific methods, such as method of substitution, undetermined coefficient method, mathematical induction, analysis, synthesis and induction. In concrete methods, there are observation and experiment, association and analogy, comparison and classification, analysis and synthesis, induction and deduction, generality and particularity, finiteness and infinity, abstraction and generalization.
When solving mathematical problems, we should also pay attention to the problem of problem-solving thinking strategies, and often think about what angle to choose and what principles to follow. The commonly used mathematical thinking strategies in senior high school mathematics are: controlling complexity with simplicity, combining numbers with shapes, advancing and retreating with each other, turning life into familiarity, turning difficulty into progress, turning retreat into progress, turning static into movement, and turning into integration.
Gradually form a "self-centered" learning model.
Mathematics is not taught by teachers, but acquired through active thinking activities under the guidance of teachers. When learning mathematics, we must pay attention to "living". We can't just read books without doing problems, and we can't bury our heads in doing problems without summarizing and accumulating.
Take some concrete measures according to your own learning situation.
Take math notes, especially the different aspects of concept understanding and mathematical laws, and the extracurricular knowledge developed by teachers in class. Record the most valuable thinking methods or examples in this chapter, as well as your unsolved problems, so as to make up for them in the future.
Establish a mathematical error correction book. Record the knowledge or reasoning that is easy to make mistakes in order to prevent it from happening again. Try to find, analyze, correct and prevent mistakes. Achieve the purpose of understanding the right things from the opposite side; Guo Shuo can get to the root of the error, so as to prescribe the right medicine; Answer questions completely and reason closely.
Often organize the knowledge structure into plate structure and implement "full container", such as tabulation, so that the knowledge structure can be seen at a glance; Often classify exercises, from a case to a class, from a class to multiple classes, from multiple classes to unity; Summarize several kinds of problems into the same knowledge method.
Review in time, strengthen the understanding and memory of the basic concept knowledge system, carry out appropriate repeated consolidation, and eliminate learning without forgetting.
Learn to classify from multiple angles and levels, such as: ① classification from mathematical ideas, ② classification from problem-solving methods, ③ classification from knowledge application, etc. , so that the knowledge learned is systematic, organized, thematic and networked.
I often do some "reflection" after doing the problem, thinking about the basic knowledge used in this problem, what is the mathematical thinking method, why I think so, whether there are other ideas and solutions, and whether the analytical methods and solutions of this problem have been used in solving other problems.