中美中小学教育粗浅比较

看到很多父母们想了解中美教育的相同和不同，老友强烈建议我分享这篇两三年前所写的分析论文。其中可能有不少错误，大家凑和看哈！表格和图像贴不上，如果你有兴趣，和我联系，会发给你。（版权要求，如果您要转发，请先告诉我一声。谢谢！）
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Abstract

 

Introduction

Comparing Singapore to the U.S. isn’t a fair comparison. Singapore has a total population of 4.48 million ¹. That is much smaller than New York City and fairly close to Los Angeles.

Comparing Japan to the U.S. is not a good comparison either. In Japan, private upper-secondary schools (equivalent to the U.S. high schools) account for about 55% of all upper-secondary schools in the entire country, and neither public nor private schools are free ².

In this paper, China is chosen to be compared with the U.S. because of two reasons. First, both countries have large and diverse populations. Second, the majority of the student populations in both countries receive secondary education in the public schools.

Comparison of the Secondary Public School Systems

Compulsory Education - Twelve Years vs. Nine Years

In the United States, the public educational system normally comprises 12 grades of study over 12 calendar years of primary and secondary education. High school is an upper secondary school which educates kids from grade nine or ten through grade twelve.

In China, the Law on Nine – Year Compulsory Education guarantees school-age children the rights to receive at least nine years of education which include six years of primary education and three years of junior secondary school (middle school) education. However, it is not compulsory for the senior secondary education (high school). The middle school graduates who have proven to be high achievers are encouraged to choose to continue a three-year academic high school education which will eventually lead to university, while the rest of the children switch to a vocational course in vocational high schools ³.

Comprehensive High Schools vs. Different Schools for Different Populations

⁶.

Just like the "detracking" reform trend in the United States, many school officials and parents in China started questioning the fairness of the "key" school system. In the year of 2010, the "key" schools have been eliminated in several cities including Shanghai to "ensure a fair and an overall level of education" ⁵.

 

Comparison of the High School Math Curriculum and Learning Standards

 

Curriculum Structures

The table below compares the high school curriculum structures of the New York State (Math A and Math B) ⁷, the China academic high schools ⁸, and the China vocational high schools ⁹.

 

	U.S. - Math A and Math B 7	China academic high school 8	China vocational high school 9
Data Sets	X	X	X
Linear Algebra	X	X	X
Algebra II	X	X	Fundamental Functions (Exponential function, Logarithmic function, Power function)
Three-dimensional Geometry	Optional	X	X
Plane Analytic Geometry	No	X	X
Trigonometry	X	X	X
Plane vector	Optional	X	X
Triangle identity transformation	X	X	Optional
Calculus	X	X	Optional
Number Series	X	X	X
Inequalities	X	X	X

　

Learning Standards

Both the education systems in the United States and China consider problem solving as one of the key skills, and the learning standards of problem solving in the curriculums are pretty much the same.

The major difference between the U.S. and China academic high school learning standards is the reasoning and proof. The China education system in the academic high schools requires the students to know the origin of the concepts and be able to prove the major theorems and formulas.

Comparing with the learning standards of the U.S. and the China academic high schools, the standards of the China vocational high schools where the majority of the China student populations receive the senior secondary math education shows surprisingly significantly lower expectations.

The following table compares the learning standards of the Trigonometric Functions in the New York high schools, the China academic high schools, and the China vocational high schools:

U.S. – Algebra 2 and Trigonometry 7	China academic high school Curriculum – Trigonometry 8	China vocational high school Curriculum – Trigonometry 9
Express and apply the six trigonometric functions as ratios of the sides of a right triangle	Express and apply the six trigonometric functions as ratios of the sides of a right triangle. Use the functions’ definitions in the unit circle to prove the given formulas and theorems.	Same as the U.S. Learning Requirement
Know the exact and approximate values of the sine, cosine, and tangent of 0, 30, 45, 90, 180, and 270 angles.	Find the values of sine, cosine, and tangent of 0, 30, 45, 90, 180, and 270 angles by using functions’ definitions in Unit Circle and proven theorems in Two Dimensional Geometry.	Be able to use calculators to find the values of the sine, cosine, and tangent of 0, 30, 45, 90, 180, and 270 angles.
Sketch and use the reference angle for angles in standard position	Apply the reference angle in problem solving and proof.	Same as the U.S. Learning Standard
Know and apply the co-functional and reciprocal relationships between trigonometric ratios	Be able to prove the co-functional and reciprocal relationships between trigonometric ratios by using the unit circle.	Know the co-functional and reciprocal relationships between trigonometric ratios
Use the reciprocal and co-function relationships to find the value of the secant, cosecant, and cotangent of 0, 30, 45, 60, 90, 180, and 270 angles.	Use the reciprocal and co-function relationships to find the value of the secant, cosecant, and cotangent of 0, 30, 45, 60, 90, 180, and 270 angles. Use the unit circle to prove the findings.	Be able to use calculators to find the value of the secant, cosecant, and cotangent of 0, 30, 45, 60, 90, 180, and 270 angles.
Sketch the unit circle and represent angles in standard position	Same as the U.S. Learning Requirement	Same as the U.S. Learning Requirement
Determine the length of an arc of a circle, given its radius and the measure of its central angle.	Determine the length of an arc of a circle, given its radius and the measure of its central angle. Determine the measure of the central angle, given the length of the arc and the radius. Determine the radius of a circle, given the length of an arc of the circle and its central angle.	Not required
Find the value of trigonometric functions, if given a point on the terminal side of angle q	Use the value of special angles (0, 30, 45, 60, 90, etc.), proven formulas and the functions’ definitions in Unit Circle, find the exact or estimated value of trigonometric functions, if given a point on the terminal side of angle q .	Know how to use the calculator to find the value of trigonometric functions, if given a point on the terminal side of angle q .
Restrict the domain of the sine, cosine, and tangent functions to ensure the existence of an inverse function	Restrict the domain of the sine, cosine, and tangent functions to ensure the existence of an inverse function. Use the unit circle to prove the existence.	Know the features of the inverse functions of sine, cosine, and tangent.
Use inverse functions to find the measure of an angle, given its sine, cosine, or tangent.	Same as the U.S. Learning Standard	Not required
Sketch the graph of the inverses of the sine cosine, and tangent functions	Same as the U.S. Learning Standard	Not required
Determine the trigonometric functions of any angle, using technology	Determine the trigonometric functions of any angle by using the definitions of the functions in the Unit Circle.	Same as the U.S. Learning Standard
Justify the Pythagorean identities	Same as the U.S. Learning Standard	Not required
Solve trigonometric equations for all values of the variable from 0 to 360	Same as the U.S. Learning Standard	Not required
Determine amplitude, period, frequency, and phase shift, given the graph or equation of a periodic function	Same as the U.S. Learning Standard	Know the definitions and features of the trigonometric functions’ amplitude, period, frequency, and phase shift.
Sketch and recognize one cycle of a function of the form y = A sin Bx or y = A cos Bx	Sketch and recognize cycles of a function of the form y = A sin Bx or y = A cos Bx. Be able to prove the findings by using the function’s definition in the Unit Circle. Be able to give real life example of such functions (in science, i.e. physics, or in real life)	Not required
Sketch and recognize the graphs of the functions y = sec(x), y = csc(x), y = tan(x), y = cot(x)	Same as the U.S. Learning Standard	Not required
Write the trigonometric function that is represented by a given periodic graph	Same as the U.S. Learning Standard	Not required
Solve for an unknown side or angle, using the Law of Sines or the Law of Cosines	Same as the U.S. Learning Standard	Same as the U.S. Learning Standard
Determine the area of a triangle or a parallelogram, given the measure of two sides and the included angle	Same as the U.S. Learning Standard	Not required
Determine the solution from the SSA situation (ambiguous case)	Same as the U.S. Learning Standard	Not required
Apply the angle sum and difference formulas for trigonometric functions	Use the functions’ definitions in Unit Circle to prove the angle sum and difference formulas.	Not required
Apply the double – angle and half – angle formulas for trigonometric functions	Use the functions’ definitions in Unit Circle to find and prove the double – angle and half – angle formulas.	Know the double – angle and half – angle formulas for trigonometric functions

Comparison of the Learning Climates

 

"No Child Left Behind" vs. "Survival For the Fittest"

In the United States, the teachers are expected to respect the students’ equity and civil rights in education. Regardless of the children’s race, ethnicity, class, gender, or language proficiency, the education system tries to ensure that all students will learn and use math ¹⁰.

In China, because of the fierce of the competition in the academic high school entrance and the university entrance, the teachers and the schools normally would focus on the best students, because "only the bests (students) will have the chance to survive (continue with their academic education)" ¹¹.

Most of the middle schools and high academic high schools in China use a practice to "sort" their students after the semi – annual and annual examinations. All of the students are "ranked" based on their academic achievements for the year and the results are often posted to all parents and all teachers. The sorting practice certainly increased the already fierce competition among the students and also creates tremendous pressure on the teachers. Often the student’s name and the class are also posted as a part of the published ranking report.

The children who are in the middle would receive warnings, and would be asked to work harder in order to catch up. The parents of the students on the bottom normally would be informed by the schools and teachers that if they "do not take actions to improve fast enough", their children would "have no chance to survive", and therefore they soon would be "not worth teaching" ¹².

Homework and Parental Involvement

In the United States, many math teachers at the secondary schools complain that many kids in their classes do not do the homework. Many parents do not want to see their kid struggle and are not supportive to the homework either. According to a survey in 2009, the average time an American secondary school student spent on homework is around two hours per week.

In China, it’s on the other extreme. According to a survey in Beijing academic high schools in 2010, the average hours an 8^th grade student spent on homework is 20 hours per week.

The newspapers in China calls the academic competitions in middle schools and high schools "the battlefield", and a common description of the Senior High School Entrance Exam and the College Entrance Exam is "Millions of kids trying to pass a single-plank bridge at the same time".

Unlike the American parents, the Chinese parents strongly believe that only the hard work and practice will lead their child to a key academic high school and eventually a university. Therefore, it’s extremely rare to hear any parents complain about the long hours their children spent on homework.

Most of the parents know their kids’ ranking at school in every subject area, especially in Mathematics because of its importance in both the High School Entrance Examination and the College Entrance Examination. The teachers often are contacted by the parents for "additional homework" which would "help the child to improve the ranking" ¹². It’s common for the top tier "key" schools to publish books of "Collections of Advanced Math Problems" for each grade, or make copies of those books for the students and their parents who seek additional homework after school.

As a direct result of the long hours of homework and self-study at home, the math teachers in the China middle schools and academic high schools, especially in the "key" schools often find themselves to be pushed by the students to increase the difficulty levels of the courses.

Teachers’ Qualifications and Developments

Teachers’ Qualifications

In most of the states and school districts in the United States, the secondary school math teacher’s qualifications are similar – the teacher needs to have a bachelor’s degree in a math or math - related field, pass a certification test, and obtained certain classroom teaching experience.

In China, the secondary school math teachers’ qualifications vary substantially among the regions and schools.

On the middle school level, most schools in the cities require the teachers to have a Bachelor’s degree in math – related area. However, the schools in the rural area often have a hard time to hire teachers, and many rural schools have no other choice but to hire high school graduates with two or three years of relevant training to be the math teachers.

On the high school level, in the large cities, most of the math teachers in the "key" schools have Bachelor’s degree in math or math education from the top tier universities in China. Some of the teachers even have master degrees in math. The salary level of the "key" school math teachers is significantly higher than that of their peers in the other schools.

The teachers in the normal academic high schools and in the "key" schools in rural areas also need to have Bachelor degree in math, pass a teacher’s certification test and a standard Mandarin language test for teaching.

The vocational high schools in China often only require their math teachers to have attended a two-year college, or have taken certain college level math courses.

Teachers’ Professional Development

　

In the United States, the secondary school math teachers’ professional development opportunities vary by states and school districts, but normally the professional training and certain support to the teachers’ developments are guaranteed.

In China, the "key" schools often are able to provide generous support to their math teachers’ professional development. Also, the "key" school math teachers normally are assigned additional responsibilities other than teaching. In major cities like Beijing and Shanghai, the secondary school math textbooks, teacher’s reference books, and books for homework assignments are all authored by the senior math teachers from the top "key" schools. Also, the "key" school math teachers’ are also responsible for providing training and training guideline to teachers in the other schools.

Comparing with the "key" schools, the normal academic high school math teachers receive less support, but they are provided the opportunities to observe the classes in the "key" schools and also to take training classes from the senior "key" school math teachers.

The teachers in technical and vocational high schools rarely receive any kind of support in terms of their professional development. In the recent years, many technical and vocational high schools start hiring contract teachers to teach the math and computer courses. Those teachers are paid based on the hours worked and can be dismissed at any time.

 

Conclusion - The Strengths and Weaknesses of Both Systems

The comparison study shows that the education system in the United States targets the majority of the student population, while the secondary school education system in China target only the top 40% of the students and especially favors the talented and gifted ones.

　

The comparison study of the curriculums, learning standards, learning climates and teacher’s qualifications lead to the following findings:

 

　

• Structure of the curriculum – the United States curriculum contains more topics than the China vocational high schools and less contents than the China academic high schools.

• Learning Standards – the difficulty level of the math courses and the expectations for the students’ math achievements in the United States are significantly higher than the China vocational schools, but lower than the China academic schools.

• Math achievements of the entire student population – the big picture shows that the overall high school math education level of the students in the United States is higher than the majority of the students in China of the same age. The students who are on and below the average level normally receive better math education in the United States than in China.

• Math achievements of the best students – the top students in China middle schools and academic high schools receive more academic supports from the education system than the high achievers in the United States. The best students in China are exposed to more advanced curriculums, teachers with more math content knowledge and better training, and also are often motivated by parents and communities to obtain high math achievement. On the other hand, the gifted and talented students in the United States receive less support than the high achievers in China, and it’s identified as a weakness of the education system.

.

References:

1. Wikipedia (2005), Demographics of Singapore

2. Wikipedia (2010), Education in Japan

3. Wikipedia (2004), Education in People’s Republic of China

4. China Youth News (2006), Reports on "Zhong Kao" (High School Entrance Examination)

5. Shanghai Daily (Jan. 20, 2010), Interviewing With the Department of Education

6. China Educational Journal (2009), Survey on Academic High Schools

7. The State Education Department of New York (2005), Mathematics Core Curriculum

8. China Education Department (2006), Mathematics Curriculum and Learning Standards for Full-time Academic High Schools

9. China Education Department (2006), Mathematics Curriculum and Learning Standards for Vocational and Technical High Schools

10. Allexsaht-Snider, M. &Hart (2001), Mathematics for All

11. China Youth News (2006), Interviewing with the Teachers post "Zhong Kao" (High School Entrance Examination)

12. Beijing Youth Daily (2005), Interviewing with the Parents Before "Gao Kao" (University Entrance Examination)

　

　

In the United States, most public high schools are meant to serve the needs of all students. While China, is like many other Asian countries, adopts the practice in which examinations are used to "sort" students into different types of high schools based on academic achievement.

In China, all of the middle school graduates are required to take the Senior Secondary Education Entrance Examination ("Zhong Kao"). The exam is designed to distinguish the middle school graduates on academic achievements. Students will be tested in Mathematics, Chinese, English, Physics, Chemistry, Biology, and Politics. The grading of the exams often adopts a Weighted Scoring Model so that Mathematics and Chinese are "weighted" about 30% more than the other subject areas.

In the year of 2005, only 43.8% of the middle school graduates were able to continue with the academic high school education ⁴. The rest of the students attend vocational high schools with completely different curriculums and learning standards. Graduates from the vocational high schools normally do not qualify for the college preparation. In the year of 2008, only 19.7% of the academic high school graduates were able to pursue college education ⁵.

Within the academic high schools, there are "key" schools and "normal" schools. The "key" schools usually are those with records of past educational accomplishments, and were given priorities in the assignment of the elite teachers, equipment and funds. The "key" school system selects the best middle school graduates into the best high schools. The "key" schools normally have much more advanced curriculums and efficient teachers’ practice than the "normal" schools.

In the year of 2009, there are 16,092 academic high schools in China, and among them, only 5% are the "key" schools

The National Council of Teachers of Mathematics (NCTM) suggested that students from Asian countries often demonstrate higher achievement in mathematics. Results of the Third International Mathematics and Science Study (TIMSS) and the National Assessment of Educational Progress (NAEP) also indicate that the U.S. secondary schools math education is declining. Does it mean the U.S. secondary schools mathematics education is truly falling behind the Asian countries such as Singapore, Japan, and China?

This paper presents findings from a comparison study of the U.S. and Chinese Secondary Public Schools mathematics education from a different perspective. The comparison study seeks the whole picture of the U.S. and China Secondary Schools Math education statuses by looking into the two countries’ public school systems, curriculums and learning standards, learning climates, and teachers’ qualifications and professional development. The comparison study focuses on the comparisons of the entire student population instead of the high achievers. The paper also explores the strengths and weaknesses of both systems.