1, mathematical language is abrupt in abstraction.
There are significant differences in mathematics language between junior high school and senior high school. Junior high school mathematics is mainly expressed in vivid and popular language. Mathematics in senior one involves very abstract set language, logical operation language, function language, image language and so on.
2. Transition of thinking method to rational level.
Another reason why senior one students have obstacles in mathematics learning is that the thinking method of mathematics in senior high school is very different from that in junior high school. In junior high school, many teachers have established a unified thinking mode for students to solve various problems, such as how many steps to solve the fractional equation, what to look at first and then what to look at in factorization, and so on. Therefore, junior high school students are used to this mechanical and easy-to-operate stereotype, while senior high school mathematics has undergone great changes in the form of thinking, and the abstraction of mathematical language puts forward high requirements for thinking ability. This sudden change in ability requirements has made many freshmen feel uncomfortable, leading to a decline in their grades.
3. The total amount of knowledge content has increased dramatically.
Another obvious difference between high school mathematics and junior high school mathematics is the sharp increase in knowledge content. Compared with junior high school mathematics, the amount of knowledge and information received per unit time has increased a lot, and the class hours for assisting exercises and digestion have decreased accordingly.
4. Knowledge is very independent.
The systematicness of junior high school knowledge is more rigorous, which brings great convenience to our study. Because it is easy to remember and suitable for the extraction and use of knowledge. However, high school mathematics is different. It consists of several relatively independent pieces of knowledge (such as a set, propositions, inequalities, properties of functions, exponential and logarithmic functions, exponential and logarithmic equations, trigonometric ratios, trigonometric functions, series, etc.). ). Often, as soon as a knowledge point is learned, new knowledge appears immediately. Therefore, paying attention to their internal small systems and their connections has become the focus of learning. Second, how to learn high school mathematics well
1, form a good habit of learning mathematics.
Establishing a good habit of learning mathematics will make you feel orderly and relaxed in your study. The good habits of high school mathematics should be: asking more questions, thinking hard, doing easily, summarizing again and paying 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.
2, timely understand and master the commonly used mathematical ideas and methods.
To learn high school mathematics well, we need to master it from the height of mathematical thinking methods. 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.
3. Gradually form a "self-centered" learning model.
Mathematics is not taught by teachers, but acquired through active thinking activities under the guidance of teachers. To learn mathematics, we must actively participate in the learning process, develop a scientific attitude of seeking truth from facts, and have the innovative spirit of independent thinking and bold exploration; Correctly treat difficulties and setbacks in learning, persevere in failure, be neither arrogant nor impetuous in victory, and develop good psychological qualities of initiative, perseverance and resistance to setbacks; In the process of learning, we should follow the cognitive law, be good at using our brains, actively find problems, pay attention to the internal relationship between old and new knowledge, not be satisfied with the ready-made ideas and conclusions, and often think about the problem from many aspects and angles and explore the essence of the problem. 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. We should be able to learn from textbooks and find the best learning method according to our own characteristics.
4. Take some concrete measures according to your own learning situation.
Take math notes, especially about different aspects of concept understanding and mathematical laws. The teacher is in class.
Expand extracurricular knowledge. 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 the knowledge or reasoning that is easy to make mistakes at ordinary times to prevent it from happening again.
Submit. 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 strictly.
Recite some mathematical rules and small conclusions to automate your usual operation skills.
Or semi-automated proficiency.
Knowledge structure is often combed into plate structure, and "full container" is implemented, such as tabular,
Make the knowledge structure clear 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.
Read math extracurricular books and newspapers, participate in math extracurricular activities and lectures, and take more math classes.
Foreign topics, increase self-study and expand knowledge.
Review in time, strengthen the understanding and memory of the basic concept knowledge system, and repeat it appropriately.
Solid, eliminate forgetting before school.
Learn to summarize and classify from multiple angles and levels. Such as: ① Classification from mathematical thought ② Solution.
Classification of questions and methods (3) Classification from knowledge application and other aspects. Make the knowledge learned systematic, organized, thematic and networked.
Often do some "reflection" after doing the problem, think about the basic knowledge used in this problem, mathematics.
What is the way of thinking, why do you think so, whether there are other ideas and solutions, and whether the analytical methods and solutions of this problem are used to solve other problems.
Whether it's homework or exams, we should put accuracy first, general methods first, and
Instead of blindly pursuing speed or skill, learning math well is the important issue.
To learn mathematics well, students in Grade Three should first study mathematics with strong interest, actively spread their wings of thinking, actively participate in the whole process of education, give full play to their subjective initiative, and study mathematics happily and effectively.
Secondly, we should master the correct learning methods. In order to train their ability to learn mathematics and change their learning methods, we must change the learning methods that are simply accepted, learn to learn to learn by accepting learning and inquiry learning, cooperative learning and experiential learning, and gradually learn the learning methods of "asking questions, exploring experiments, discussing, forming new knowledge and applying reflection" under the guidance of teachers. In this way, through the change of learning methods from single to diverse, our autonomy, exploration and cooperation in learning activities have been strengthened and we have become the masters of learning.