The difference between junior high school mathematics and senior high school mathematics;

1, poor knowledge.

Junior high school mathematics knowledge is less, shallow, easy and comprehensive. High school mathematics knowledge is extensive, which will promote and extend junior high school mathematics knowledge and improve junior high school mathematics knowledge. For example, the concept of angle in junior high school is only within the range of "0- 1800", and there are actually 7200 and "-300" angles. Therefore, high school will extend the concept of angle to any angle, which can represent all angles, including positive and negative angles. Another example is: when studying solid geometry in high school, you will find the volume and surface area of some geometric entities in three-dimensional space; In order to solve the problems such as the number of queuing methods, we will also learn the knowledge of "permutation and combination". For example: ① There are several queuing methods for three people in a line (=6); ② Four people play table tennis doubles. How many games are there? (A: =3 kinds) Senior high schools will learn mathematical methods to count these arrangements. It is meaningless to square a negative number in junior high school, but it is stipulated in senior high school that i2=- 1, so the square root of-1 is I, that is to say, the concept of number can be extended to the range of complex numbers. These knowledge students will learn step by step in the future study.

2. Differences in learning methods.

(1) The classroom teaching in junior high school is small and the knowledge is simple. Through slow-paced classroom teaching, we strive to make all-round students understand knowledge points and problem-solving methods. After class, the teacher assigns homework, and then repeatedly understands the knowledge through a lot of in-class and out-of-class exercises and out-of-class guidance until the students master it. In senior high school, math learning is the same as the curriculum (there are nine students studying at the same time). Every day, there are at least six classes and three classes for self-study, so that the learning time of each subject will be greatly reduced, while the amount of extracurricular questions assigned by junior high school teachers will be relatively reduced, so that the time for concentrated math learning is relatively less than that of junior high school, and math teachers will supervise each student's homework and extracurricular exercises like junior high school, so that they can master knowledge for each student before starting a new class.

(2) The difference between imitation and innovation.

Junior high school students imitate doing problems, they imitate the teacher's thinking and reasoning, and senior high school students imitate doing problems and thinking. However, with the difficulty of knowledge and the wide range of knowledge, students can't imitate it all, that is to say, students can't imitate training to do problems, and they can't develop their self-thinking ability, and their math scores can only be average. At present, the purpose of mathematical investigation in college entrance examination is to examine students' ability, avoid students' high scores and low energy, avoid thinking stereotypes, advocate innovative thinking and cultivate students' creative ability. A large number of imitations of junior high school students have brought unfavorable mentality to senior high school students, and their conservative and rigid concepts have closed their rich anti-creative spirit. For example, when students compare the sizes of A and 2a, they are either wrong or have incomplete answers. Most students don't discuss in groups.

3. Differences in students' self-study ability.

Junior high school students have low self-study ability. The problem-solving methods and mathematical ideas used in general exams have been repeatedly trained by junior high school teachers. The teacher focuses on his patient explanation and a lot of training. Students can do problems by memorizing (not all) the conclusions in class, and students don't need to learn by themselves. But high school has a wide range of knowledge, so it is impossible for teachers to train all the questions in the college entrance examination. Only by explaining one or two typical examples can this type of exercises be integrated. If students don't learn by themselves and don't rely on a lot of reading comprehension, they will lose the answers to a class of exercises. In addition, science is constantly developing, exams are constantly reforming, college entrance examination is also deepening with the comprehensive reform, and the development of mathematics questions is also constantly diversifying. In recent years, applied questions, exploratory questions and open questions have been constantly raised. Only when students study independently can they deeply understand and innovate and adapt to the development of modern science.

In fact, the improvement of self-study ability is also the need of a person's life. It also represents a person's accomplishment from one aspect. A person's life is only 18-24 years of study with a tutor. In the second half of his life, the most wonderful life is that he has been studying all his life and finally achieved self-improvement through self-study.

4. Differences in thinking habits

Junior high school students have a small range of learning mathematics knowledge, a low level of knowledge and a wide range of knowledge, which limits their thinking on practical problems. As far as geometry is concerned, we are all exposed to the three-dimensional space in real life, but junior high school students only learn plane geometry and cannot think and judge the three-dimensional space strictly. The range of numbers in algebra is limited to real number thinking, and it is impossible to solve the type of equation roots in depth. The diversity and extensiveness of senior high school mathematics knowledge will enable students to analyze and solve problems comprehensively, meticulously, profoundly and rigorously. It will also cultivate students' high-quality thinking. Improve students' progressive thinking.

5, the difference between quantitative and variable

In junior high school mathematics, questions, known and conclusions are all given by constants. Generally speaking, the answers are constant and quantization. When students analyze problems, most of them are quantitative. Such a process of thinking and solving problems can only solve problems unilaterally and restrictively. In high school mathematics learning, we will widely use the variability of algebra to discuss the universality and particularity of problems. For example, when solving a quadratic equation with one variable, we use the solution of equation ax2+bx+c=0 (a≠0) to discuss whether it has roots and all the roots when it has roots, so that students can quickly master the solutions of all quadratic equations with one variable. In addition, in the high school stage, we will explore the ideas of analyzing and solving problems and the mathematical ideas used in solving problems through the analysis of variables.

Mathematical differences between junior high school and senior high school;

1, the mathematical language has a sudden change in abstraction.

Many students reflect that the concepts of set and mapping are difficult to understand, and they feel far away from life and seem to be "mysterious". Indeed, 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 abstract set language, logical operation language, functional language, space solid geometry and so on.

2. Transition of thinking mode 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 to solve the fractional equation in several steps, what to look at first and then what to look at with factorization. Even for plane geometry problems with flexible thinking, they have determined their own thinking routines for equal line segments, equal angles,,, and. Therefore, junior high school students are used to the stereotype that machinery is easy to operate, while senior high school mathematics has undergone great changes in its thinking form. As mentioned in the last section, the abstraction of mathematical language puts forward high requirements for thinking ability. Of course, the cultivation of ability is gradual, not overnight. This sudden change in ability requirements has made many freshmen feel uncomfortable, leading to a decline in their grades. Freshmen in senior high school must be able to transition from empirical abstract thinking to theoretical abstract thinking, and finally need to initially form dialectical thinking.

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. This requires, first, to review after class and remember a lot of knowledge; Second, we should understand and master the internal relationship between old and new knowledge, so that the new knowledge can be assimilated into the original knowledge structure smoothly; Thirdly, because knowledge teaching is mostly carried out in a piecemeal way, when the amount of knowledge information is too large, its memory effect will not be very good. Therefore, we should learn to sort out the knowledge structure, form a plate structure, and implement "full container", such as tabulation, so that the knowledge structure can be seen at a glance; Classification, from one case to one class, from one class to many classes, from many classes to unity; Make several kinds of problems isomorphic to the same knowledge method; Fourth, it is necessary to summarize and classify more and establish a knowledge structure network of disciplines.

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