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- 180 degrees", but there are actually 720 degrees and "-300 degrees", so senior high school will extend the concept of angle to any angle, which can represent all angles, including positive and negative. 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 find the square of a negative number in junior high school, but it is stipulated in senior high school that I 2 =-1+0, so the square root of-1is I, that is to say, the concept of number can be extended to the range of complex numbers, and these knowledge students will learn gradually in the future.
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. Moreover, there are more courses in high school mathematics learning (for example, there are eight courses in high school at the same time), and there are at least eight classes every day, so that the study time of each subject will be greatly reduced, and the amount of extracurricular questions assigned by teachers will be reduced compared with junior high school, so that the time for concentrated mathematics learning is less than that of junior high school. Senior high school math teachers will not be able to supervise every student's homework and extracurricular exercises like junior high school, nor will they be able to let every student master knowledge before taking a new lesson like junior high school.
(2) the difference between imitation and innovation
Junior high school students imitate doing problems. They imitate teachers' thinking and reasoning more, while senior high school students imitate doing problems and thinking. But the knowledge is difficult and extensive, so it is impossible for students to imitate them all. Even if students imitate training to do problems, 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 autonomous learning 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 only need to memorize the conclusion to do the problem (not all), and students don't need to teach 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 we master this type of exercise. If you don't teach yourself and read a lot, students 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. He also represents a person's accomplishment from one aspect. A person has a mentor for only 18-24 years in his life. In the second half of his life, the most wonderful life is that people have been studying all their lives, and self-study has finally achieved self-improvement.
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.