Ask more questions, think hard, be practical, summarize again, and pay attention to application. In the process of learning mathematics, students should translate the knowledge taught by teachers into their own unique language and keep it in their minds forever. Good habits of learning mathematics include self-study before class, paying attention to class, reviewing in time, working independently, solving problems, systematically summarizing and studying after class.
Understand and master commonly used mathematical ideas and methods in time.
Mathematics thoughts that should be mastered in middle school mathematics learning include: set and correspondence thoughts, classified discussion thoughts, combination of numbers and shapes, movement thoughts, transformation thoughts and transformation thoughts.
With mathematical ideas, we should master specific methods, such as method of substitution, undetermined coefficient method, mathematical induction, analysis, synthesis and induction. In terms of specific methods, commonly used are: observation and experiment, association and analogy, comparison and classification, analysis and synthesis, induction and deduction, general and special, finite and infinite, abstraction and generalization.
When solving mathematical problems, we should also pay attention to solving the problem of thinking strategy, and often think about what angle to choose and what principles to follow. The commonly used mathematical thinking strategies in senior high school mathematics include: controlling complexity with simplicity, combining numbers with shapes, advancing forward and backward with each other, turning life into familiarity, turning difficulties into difficulties, turning retreat into progress, turning static into dynamic, and separating and combining.
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". You can't just read books without doing problems, and you can't just bury your head in doing problems without summing up the accumulation.
Take some concrete measures according to your own learning situation.
Take math notes, especially the different aspects of concept understanding and mathematical laws, as well as the extracurricular knowledge that teachers expand in class. Write down 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. Write down error-prone knowledge or reasoning to prevent it from happening again. Strive to find wrong mistakes, analyze them, correct them and prevent them. Understanding: being able to deeply understand 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; Several kinds of problems boil down to 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 summarize and classify from multiple angles and levels. Such as: ① classification from mathematical thoughts, ② classification from problem-solving methods, ③ classification from knowledge application, etc. , so that the knowledge learned is systematic, organized, thematic and networked.
Often do some "reflection" after doing the problem, think about the basic knowledge used in this problem, what is the mathematical thinking method, why do you 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.