In fact, the math level of American students is uneven, which is much higher than that of China high school students. It is difficult to generalize the mathematics level of American students, and it is also difficult to evaluate the mathematics level of American ninth grade and 10.
In the United States, mathematics knowledge is not taught much in junior middle schools and primary schools, and high schools begin to study hard, especially private high schools that train students to enter universities in the future. They generally call themselves pre-university schools. Senior high school students in grade nine often have to take the math placement test, so that the school can be placed in classes. Students will be placed in different classes according to their own level, and the difficulty can range from very simple geometry to increasingly difficult algebra 1, algebra 2, pre-calculus and even calculus.
There are usually two math requirements for graduating from private high schools in the United States: first, at least take calculus first; Second, you must take math classes for two years.
Judging from these two requirements, if a student has a poor foundation in mathematics when he enters the ninth grade, he may study mathematics from geometry in the next four years of high school until he finishes the calculus preparatory course in 12 grade. If a student has learned a lot of mathematics in junior high school (American public primary schools and junior high schools often have "genius plans", and mathematics and English are taught faster), he may only need two years of mathematics. Even students who can take pre-school calculus as soon as they enter the ninth grade can take courses such as calculus or statistics, or even take credits in a nearby university in advance to meet the graduation requirements. If students are not interested in math classes, they can take more courses in other subjects that they are more interested in after completing math classes that meet graduation requirements.
Students of the same grade in the same American high school rarely have the same schedule. Each student attends classes in the teacher's classroom on time according to his own schedule. In the class of Algebra 2, it is not surprising to see the students of Grade 9, 10, 1 1 in class together.
Compared with China, American high school students are very flexible and personalized in choosing courses, and there are also great differences in the learning order of knowledge points. Mathematics classes in China schools often focus on one knowledge point for in-depth study, and then proceed to the next one after thorough study. Mathematics in America is a bit like machine gun sweeping. There are many simple but extensive contents in pre-algebra in junior high school. The following algebra 1 and algebra 2 are scanned again before calculus, and the difficulty is getting deeper and deeper. Once, an American teacher gave a math placement test to students studying in American high schools after China's second year of junior high school, and told me with difficulty, "This student knows a little algebra 2 and can do it with his eyes closed. But there is nothing in algebra 1 at all, so it is not clear which class he should be in. "
Algebra 2, a textbook used in mathematics classes in American schools, is 1000 pages thick and divided into 14 chapters. The content of each chapter is:
Chapter 1: Functional basis.
Chapter 2: Linear Functions
Chapter 3: Linear Equation
Chapter 4: Matrix
Chapter 5: Quadratic function
Chapter 6: Polynomial Functions
Chapter 7: Exponential Function and Logarithmic Function
Chapter 8: Rational Function and Root Function
Chapter 9: Characteristics and attributes of functions
Chapter 10: Conical Section
Chapter 11: Probability and Statistics
Chapter 12: Sequences and Series
Chapter 13: Trigonometric Functions
Chapter 14: trigonometric function drawing and its characteristics
Judging from this catalogue, Algebra 2 covers a wide range of contents, and many of them seem difficult. However, don't be intimidated by these titles. Some content is not difficult. As long as you understand the basic concepts, you can do the problem. American math problems focus on conceptual understanding and won't give you a detour.
Learn math and physics well, and you are not afraid to travel all over the world! This sentence applies not only to China students, but also to American students, especially young students in China.