Comparisons Between Mathematics Education in China and the United States
Liping Ma began the workshop with a general comparison of mathematics education in China and the United States. Ma taught elementary school for 7 years in China before earning a master’s degree in teacher education at East China Normal University and a doctorate from Stanford University. Drawing on her knowledge and experience in both countries, she presented her assessment of similarities and differences in the two systems. This chapter summarizes her remarks as well as selected comments from others.
THE ORGANIZATION OF EDUCATION
Education in China is divided into 6 years of elementary school, 3 years of middle school, and 3 years of high school (high school is not compulsory), with the first 9 years being compulsory education. (See Box 1-1.) Admission to high school is by competitive exam, with about 50 percent of high schools offering general education and 50 percent offering vocational education. Parents provide support for their children to attend high schools, and scholarships are available for students from poorer families. School hours are from 8:00 a.m. until 5:15 p.m. for high schools (compared to approximately 7:30 a.m. to 2:15 p.m. for many U.S. high schools). Usually, one school in each city is designated to provide special education for students with disabilities. There is no home schooling in China, unlike in the United States. There are few athletic and nonacademic extracurricular
activities. However, many students participate in after-school activities to prepare for tests, including the entrance exam to universities, which students can take just a single time (unlike the SAT Reasoning Test and ACT, which can be taken multiple times in the United States). Text messaging has become a popular way for teachers and administrators in China to communicate with parents about homework or school notices.
Many elementary school students learn mathematics from a specialized mathematics teacher, but that is not universal. In grades 1 and 2, the mathematics teacher may also teach Chinese literacy. In some places, mathematics teachers also teach science, though science is not a prominent part of the curriculum in Chinese elementary schools. In schools in rural or remote areas, an elementary teacher in China may teach all subjects, as is often the case in similar situations in the United States. Nevertheless, mathematics specialist teachers in elementary schools are common in China and less common in the United States.
Mathematics instruction in China using western notation1 did not begin until 1894, when an American missionary, Calvin W. Mateer, published the first arithmetic book in Chinese that used Arabic numbers written horizontally rather than vertically. And mandatory elementary education was not instituted in China until 1904—52 years after the first mandatory school attendance law was passed in Massachusetts. However, Chinese culture has emphasized teaching and learning for thousands of years, Ma pointed out. At about the same time that Socrates (469–399 BC) lived in the West, Confucius (552–479 BC) was writing extensively about the role of teachers in society. (See Box 1-2, Confucius’ Teachings on Education.) Confucius’ teachings have remained a constant part of Chinese education, which has not been the case with Socrates.
Even today, Ma observed, all Chinese students learn several sayings from Confucius directed specifically toward education. These sayings can be summed up in three phrases:
To silently appreciate a truth.
To learn continually.
To teach other people unceasingly.
Confucius established a tradition of deep respect for teachers in China, which forms a component of what Ma called “the invisible part” of education. “We don’t see it when we go into classrooms. But it is in teachers’ minds.” Even during the Cultural Revolution in China, when books were largely abandoned, ideas about teaching and learning were preserved in the culture.
Today, teachers in China are still highly respected. “Teachers at any level are respected by all people in society,” mentioned Shiqi Li, a professor of mathematics education at East China Normal University. “Especially they are respected by students and their parents.” The career hierarchy for Chinese K–12 teachers (described in Chapter 3) is comparable in prestige to that for higher education, and master teachers see themselves as being at the same level in the K–12 system as distinguished professors do at universities.
Confucius’ Teachings on Education
In his teaching, the superior man guides his students but does not pull them along; he urges them to go forward and does not suppress them; he opens the way, but does not take them to the place. Guiding without pulling makes the process of learning gentle; urging without suppressing makes the process of learning easy; and opening the way without leading the students to the place makes them think for themselves. Now, if the process of learning is made gentle and easy and the students are encouraged to think for themselves, we may call the man a good teacher.
Only through education does one come to be dissatisfied with his own knowledge, and only through teaching others does one come to realize the uncomfortable inadequacy of his knowledge. Being dissatisfied with his own knowledge, one then realizes that the trouble lies with himself, and realizing the uncomfortable inadequacy of his knowledge, one then feels stimulated to improve himself. Therefore it is observed, “The processes of teaching and learning stimulate one another.”
RESOURCES AND REWARDS FOR TEACHING
Ma explained that Chinese teachers have three kinds of intellectual resources for improving teaching: “wisdom of teaching passed down throughout history,” regular exchanges among colleagues, and recent research on education. In contrast, the main intellectual resource for teachers in the United States is new ideas about education generated by educational research. Most U.S. teachers do not learn the theories directly, but they learn new approaches based on the theories, which they implement in their classrooms. Also, regular exchanges among teachers, which are common in China, are less frequent in U.S. elementary schools. In addition, teachers’ self-reflection in China is an important way to improve teaching.
Ma described two kinds of rewards that motivate U.S. teachers. One is salary, and the second is personal interest in students. In her opinion, salary levels are not as important in China as in the United States: “Chinese teachers think, ‘Okay, the salary is not bad.’” The U.S. system is more professional. In contrast, Chinese teachers have the “moral satisfaction” of being a teacher.
THE CONTEXT OF TEACHING
The physical layout of Chinese classrooms differs from that of U.S. schools (Figure 1-1). Chinese teachers have much larger classes: typically around twice the size of U.S. classes. When Ma was an elementary school teacher in China, she said, she had classrooms with as many as 60 students, and she has attended classes in China that have more than that. Also, classes in China typically have all of the desks facing the teacher, whereas in the United States, desks may be clustered into groups so that students can work together (though many U.S. classrooms are still organized along traditional lines, as in China). As a Chinese teacher, I don’t feel comfortable if I don’t see all the eyes of my students. When we teach math, we all focus on math. But in U.S. classrooms, many things are going on.”
Also, in Chinese schools, students tend to stay in one room and teachers travel to that room to teach. In the United States, teachers can decorate and be creative in their homeroom, Ma explained, because they “own” the room. But in China, students own their rooms and teachers travel to them.
The home base for teachers in China is typically a teachers’ room shared by several teachers. These rooms are primarily for work rather than for relaxation. They have desks, tables, a telephone, and bookshelves (Figure 1-2). Teachers use these rooms to grade homework, prepare and analyze les-
sons, and interact with other teachers. Teachers’ rooms often are for teachers of the same grade or same subject, so that they can work together.
In contrast, Ma observed that many teachers’ rooms in the U.S. schools tend to be geared more toward relaxation than work. U.S. teachers spend less time in teachers’ rooms and more in their homerooms compared to Chinese teachers. As a result, they are less likely to see their colleagues in teachers’ rooms, reducing their opportunities to collaborate.
U.S. teachers’ rooms are organized for both work and relaxation, whereas Chinese teachers’ rooms are a base for work and collaboration throughout the school day.
Chinese teachers have fewer classes than do U.S. teachers, typically just two or three per day, whereas U.S. teachers are in their classrooms for most, if not all, of their day. (See Box 1-3, A Day in the Life of a Chinese Teacher.) Outside the classroom, Chinese teachers spend considerable time grading homework. “That way, they know what problems students are encountering in doing the homework,” described Fang Wei, a teacher at Suzhou High School in Jiangsu Province. With 40 to 50 students per class, a teacher might have 90 homework assignments to correct each day. In Wei’s school, the 28 mathematics teachers are separated into two teachers’ rooms with facing desks so they can talk with each other as they are marking homework or preparing lessons. Teachers typically use a teachers’ room to answer students’ questions and help weak students. When a student is
present, they mark his or her homework, so that the student can correct it in person. Chinese teachers may have an hour and a half for lunch, compared with 20 to 30 minutes for many teachers in the United States.
In China, teachers often sit in on lessons given by other teachers and provide the teachers with comments after the class. Master teachers also give demonstration lessons to all of the mathematics teachers in a school. Every week there is time for mathematics teachers to discuss teaching, either in a whole group or divided by grades. Common topics for discussion are reflections about lessons, getting help with trouble spots, making connections between content areas, getting across difficult points, analyzing student errors and solution methods, and sharing successful experiences. Sometimes, teachers also discuss mathematics education with mathematics teachers from other schools, education experts in universities, or master teachers from other cities. All of the mathematics teachers in the city of Suzhou, for example, have a specific time set aside on Thursday afternoons when they are not teaching so that they can meet to discuss mathematics education and see if they are progressing at the same pace. Hongyan Zhao, a master teacher in Beijing, estimated that mathematics teachers in China spend about one-third of their time while in school on lesson planning and preparation, one-third of their time teaching, and one-third of their time engaged in discussions with other teachers (including grading).
Testing in China is focused on the tests given at the end of middle school and high school that dictate entrance into high schools and colleges, respectively. In addition, at the local district or city level there is a universal final exam for mathematics given at the end of each academic year that is voluntary, though most schools participate. Testing, which has been used for thousands of years in China for government hiring, is viewed as less critical in China than in other countries such as the United States. The prevailing view is that if students work hard they all have the potential to do well on tests. An important factor in judging teachers has been the success of their students on high school and college entrance exams, but more recently and in the larger cities, other aspects of teacher performance are being assessed. For example, peer evaluations and student evaluations are becoming more important.
CHANGES IN CHINESE MATHEMATICS EDUCATION
Mathematics education in China has been undergoing important changes in recent years. Reform efforts patterned in part on the standards
A Day in the Life of a Chinese Teacher
Hongyan Zhao, a master teacher at the upper secondary school attached to Tsinghua University in Beijing, described a busy but not unusual day in her life as a teacher. She arrived at the school at 7:30 a.m. to begin work. First, she went over the lesson plan before going to class, reviewing the best way to teach her students about linear equations. She then taught a lesson to a class of grade 12 students, with the first part of the lesson being teacher-oriented, and the second part, student-oriented. “I raised the question of how many ways there were to express the linear equations, and the students would discuss it first, and then write down the result on the blackboard.”
She then taught a lesson to grade 11 students, part of which involved letting them enclose various rectangles with rope. “When the conditions were simple, they could finish the tasks by using their knowledge of arithmetic. When the conditions were complicated, they could use their knowledge of equations to get the length and width of the rectangle to finish the tasks.”
Next, she observed a class taught by a young teacher who had been teaching for 3 years. “The lesson was about geometric proof. I found that most students listened carefully, but I still found a few stu
developed by the National Council of Teachers of Mathematics (NCTM) have sought to make mathematics instruction more effective for all students. For example, Chinese classrooms traditionally have been organized in such a way that student discussion is difficult, but Chinese teachers have come to recognize that student discussions can benefit learning (for additional information on Chinese student learning, see Cai and Cifarelli, 2004). As a result, Chinese teachers have begun to encourage students to participate in discussions, even though their classrooms are not set up for such discussions.
dents had difficulties following the teacher. I exchanged opinions with the teacher after class and showed him another proof and talked with him on how to improve the effectiveness of the lecture in class.”
After that, she graded students’ homework and corrected tests from the previous day. “I found that they still had some problems understanding the knowledge of functions. I talked with those who had more difficulties with it.” She also gave three advanced students an assignment to do research on several questions that had recently appeared on the National College Entrance Exams.
Next, she attended a group activity to prepare lessons, part of which was devoted to helping one of the younger teachers learn how to give students individual help based on their level of understanding. She then attended a lesson-preparing activity in the nearby lower secondary school. “Master teachers must attend such activities, giving advice on the arrangement of the teaching program and the transition of knowledge between junior and senior high schools.”
Finally, she attended a meeting in her school, where she gave two assignments to fellow teachers. One was to ask each teacher to write a summary of the work done in the previous semester. The other was to write the work plan for the next semester.
“This is one of my workdays, busy but fruitful.”
At the same time, the focus on student achievement remains very high in Chinese mathematics classrooms. Ma expressed the opinion that in the United States, teachers want to make their students happy in the present. But in eastern countries, teachers want their students to be happy in the future, which means that they need to work hard in school.