Specifically, the differences between junior high school mathematics and senior high school mathematics mainly focus on the following points:
1, poor knowledge. There are many connected knowledge points in junior and senior high school mathematics, such as four propositions and function concepts. Therefore, when teaching new knowledge, teachers should guide students to contact with old knowledge, review and distinguish old knowledge, and pay special attention to analyzing and comparing those knowledge that are easy to make mistakes and confuse, so as to achieve the effect of reviewing old knowledge and learning new knowledge. For example, when learning the solution of quadratic inequality in one variable, teachers should guide students to review the knowledge of quadratic equations and quadratic functions they learned in junior high school, and make necessary preparations for learning the solution of quadratic inequality in one variable, such as the discriminant of roots, the formula for finding roots, the relationship between roots and coefficients (that is, "Vieta theorem"), and the images of quadratic functions. Junior high school mathematics knowledge is little, shallow, easy and narrow. 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", and there are actually 720 degrees and "negative 300 degrees". Therefore, high school will expand 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. The square root of a negative number in junior high school is meaningless, but it is stipulated in senior high school that =- 1 makes the square root of-1 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. With the opening of many courses (there are nine students studying at the same time), there are at least six classes in high school mathematics study every day, and three classes are self-study, so that the study time of each subject will be greatly reduced, and the amount of extracurricular problems assigned by teachers will be reduced compared with junior high school, so that the time for concentrated mathematics study will be less than that of junior high school, and the math teacher 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 course. (2) The difference between imitation and innovation. They imitate teachers' thinking and reasoning more, while high school students imitate doing problems and reasoning. However, knowledge is difficult and extensive, so students can't imitate it all, that is, students can't imitate training to do problems, and it is impossible to develop students' self-thinking ability. Students' math scores can only be considered 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 bring students an unfavorable mentality, while those of senior high school students bring conservative and rigid ideas, closing their rich 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.