Shedding Light on the East Asian Learner Paradox: Reconstructing student-centredness in a Shanghai classroom

Abstract

The East Asian learner paradox refers to the apparent contradiction between the teacher-dominated learning environment in East Asia, which is generally perceived to be non-conducive to learning, and the outstanding performance of East Asian students in comparative studies. This study attempts to explain this phenomenon based on the perspectives of a Chinese teacher from Shanghai, his group of students, and the author's own observations as a researcher. The analysis was based on the theory of variation and it showed how the teacher handled the relationship between the procedural and conceptual aspects of the mathematics. This analysis also shows that the teacher in this study had a strong pedagogical belief and highly valued his students' thinking and participation. At the same time, his students also expressed a consistent concern for learning the mathematical content. Therefore, this author argues that what seems to be a teacher-dominated lesson may actually be interpreted as an alternative form of student-centredness, which is accepted in the teacher's culture.

Introduction: Where is the paradox?

In recent years, the phenomenon referred to as the East Asian learner paradox has been discussed by a number of authors (e.g. see Biggs, 1996; Leung, 2001; Mok et al., 2001). Stated briefly, this is the apparent contradiction between the teaching methods and environment in East Asian schools (i.e. large classes, whole-class teaching, examination-driven teaching, focus on content rather than process, emphasis on memorisation, etc.) and the fact that East Asian students have regularly performed better than their Western counterparts in comparative studies—such as those carried out by the International Association for the Evaluation of Educational Achievement (IEA) (Mullis et al., 2000). The mismatch between an “unfavourable classroom image” and outstanding achievement has generated much discussion on this so-called “paradox”. It has also led to many studies on the psychological and pedagogical perspectives of Chinese teaching and learning (e.g. see Leung, 2001; Paine, 1990; Stigler & Hiebert, 1999; Watkins & Biggs, 2001). Findings from these studies have gradually revealed a more comprehensive picture of Asian classrooms.

Following the IEA studies, Stigler and Hiebert (1999) carried out a video study which aimed to investigate teaching styles and methodology across different cultures. One of their claims was the identification of teacher scripts that can be seen in the practices of teachers in the United States, Japan, and Germany.

Although Stigler and Hiebert's (1999) study had a powerful argument, many continued to doubt whether a national teaching script really does exist. Lopez-Real and Mok (2002) commented that the Japanese lessons described in the video study certainly did not “fit” the Asian stereotype. At the same time, Clarke and Mesiti (2003) reported that the proposed U.S. lesson pattern did not correspond to any of the 25 U.S. lessons analysed as part of the Learner's Perspective Study project. Another study by Jablonka (2003) showed that the German model reported by Stigler and Hiebert (1999) was in poor correspondence with a sample of 30 German mathematics lessons as well. One research study even claimed it was unlikely that a uniform script could be found among five lessons by the same teacher (Lopez, Mok, Leung, & Marton, 2004)! Overall, there was little evidence to support the existence of national teaching scripts.

Other studies on the East Asian paradox focused on teachers themselves and how they taught in the classroom. Paine (1990) described Chinese language teachers in terms of the virtuoso model, where the role of the teacher is mainly to demonstrate, and students are expected to follow. On the other hand, An, Kulm, and Wu (2004) described Chinese teachers in terms of their emphasis on the development of procedural and conceptual knowledge by relying on rigid, traditional practices. In the case of mathematics, this meant more value on teaching content. This is in line with Ma's studies (1999) where mathematics teachers in Chinese elementary schools showed better understanding of subject matter compared to teachers in the United States.

In contrast, teachers in the United States develop their students' understanding of mathematical concepts through activities that promote creativity and inquiry (An et al., 2004). This difference in teachers' knowledge and goals is definitely an important factor in explaining how students perform in the classroom.

Research findings seem to suggest that a teacher-dominated lesson may not be necessarily bad for learning, just as a student-centred lesson may not always be positive. It is obvious that simple social interaction labels such as, “teacher-dominated” or “student-centred” have not explained the heart of the matter. In fact, patterns of interaction in East Asian classrooms today actually indicate a pluralistic picture. In particular, Mok and Morris (2001) state that although teacher-centred features continue to persist, curriculum reforms now have group work activities in typical classroom scenarios in Hong Kong. Therefore, it is possible that the East Asian classroom is a more subtle learning environment than crude observation suggests.

To have a fair understanding of a particular lesson, we need to understand it based on the perspective of relevant stakeholders such as teachers and students. The data discussed in this paper were taken from the Learner's Perspective Study, an international project where researchers videotaped a continuous sequence of lessons from different countries all over the world (Clarke, Emanuelsson, Jablonka, & Mok, 2006). This paper takes advantage of this rich data set, to present a micro-study of mathematics teaching and learning in a Shanghai school.

The Learner's Perspective Study

The Learner's Perspective Study (LPS) is led by Professor David Clarke from the University of Melbourne, Australia. It involves a number of international partners from Africa, Australia, China (Hong Kong, Macau, and Shanghai), the Czech Republic, Germany, Israel, Japan, Korea, Philippines, Singapore, South Sweden, the United Kingdom, and the United States.

One of the project's important features is its documentation of sequences of lessons, rather than recording of individual classes in the 1998–2000 Third International Mathematics and Science Study Video Study (TIMSS 1999 Video Study). Each participating class was videotaped for a minimum of 10 consecutive lessons after a familiarisation period of recording. Researchers then used these lesson videos in video-stimulated recall interviews with students after each lesson. This was in order to learn how they reconstructed the lesson and what meaning particular events held for them. Two students were interviewed in depth about what they had experienced after each lesson while teachers were interviewed three times during the whole period of recording. They were allowed to refer to particular lesson videos during their interviews.

Contextual Data

The lesson discussed in this paper took place in a school in Shanghai, one of the fastest developing cities in China. The teacher in the study was awarded a Lecturer in Secondary School by the Shanghai Academic Title Appraisal Committee in 1992 and had been teaching for more than 20 years.

LPS researchers videotaped a sequence of 15 mathematics lessons of this teacher and his Grade 7 class (age 13–14). The videos of the lessons were coded according to class organisation using the V-prism software. Based on the calculation of real time over 15 lessons, 67.1% of the lesson period was spent on whole-class instruction, 21.6% was spent on individual work, and 11.3% spent on small group or pair work.

The teacher often used two kinds of arrangements in teaching his lessons: a simple teacher-led whole-class interaction and a short period of individual or group work followed by whole-class interaction.

Whole-class interaction consisted of the teacher frequently asking questions and the students answering them. There were hardly any instances of students raising their own questions. On the other hand, all individual and group work began with a clear task displayed on a PowerPoint slide and instructions from the teacher. These intervals were all very short (about 1 to 3 minutes), but frequent, with the teacher continuously walking along the aisles to look at students' work. After these periods of individual and group work, the teacher always resumed a whole-class discussion of the work they had done. As seen in the lesson video, the students were consistently attentive and followed the teacher's instruction. There were no instances of either inattentiveness or off-task behaviour.

For this study, I chose to analyse the teacher's 40-minute lesson on the topic of simultaneous equations. This was also one of the lessons which the teacher referred to during the LPS interviews.

The Enacted Object of Learning through the Lens of Variation

According to Marton, Runesson, and Tsui (2003), the process of learning always involves something called the object of learning. Every teacher has an intended object of learning that they want to teach their students. Since this object begins as a part of the teacher's awareness, lessons must be structured in a way that this intended object of learning will come to the fore of their students' awareness as well.

The enacted object of learning is a researcher's description of the lesson from the perspective of a specific research interest. It describes how an object of learning is manifested in the teacher's lessons.

According to Marton et al. (2003), learners must be given the opportunity to discern aspects of an object in terms of its dimensions of variation and how its parts relate to the whole. The delineation of the dimensions of variation in a lesson represents a researcher's perspective of the enacted object of learning, that is, a potential space of learning. Therefore, it is important to pay attention to what varies and what does not in a learning situation and give empirical examples of particular patterns of variation (see Table 1).

Table 1. Dimensions of variation

Variation	Description
Contrast	A comparison between what the object is and is not. For example: “three” and “not three”, “two” and “four”.
Generalisation	An experience of various appearances of the object. For example: grasping the concept of “three” in three apples, three monkeys, etc.
Separation	A separation of one aspect of the object from the other aspects. To experience this, one aspect must vary while other aspects remain invariant.
Fusion	An experience of taking several critical aspects into account.

Variation is also a component of Gu's theory (1991, 2004), which is based on a longitudinal empirical study on the reforms of mathematics education from 1977 to 1987. Here, he introduces the concept of variation in practice, where teachers arrange a sequence of good-practice exercises based on the variation of concepts, backgrounds, and the complexity of the situation. In designing these exercises, the teacher is advised to avoid mechanical repetition and to create an appropriate path for practising the thinking process with increasing creativity (Gu, 1991).

Although the teacher in this study did not explicitly mention the use of variation to enhance his teaching, lesson videos show that he did use it as a strategy.

To explain the enacted objects of learning found in the teacher's practice, I will describe the forms of variation seen in three different tasks that the teacher used in his lesson. During his interview, the teacher referred to these tasks as: the situational question (wen ti qing jing), the trial activity (chang shi huo dong), and learning to summarise (gui na). The lesson's intended object of learning was the “method of elimination by adding or subtracting equations”.

Task 1: The situational question

The teacher began the first task by asking students to solve the following problem:

Xiu-min and his family are planning a trip to Beijing for a holiday. They book three adult tickets and one student ticket, costing a total of 560 dollars. Suddenly, Xiu-wang, Xiu-min's classmate, learns about the trip and wants to join them as well. So, they buy three adult tickets and two student tickets, costing a total of 640 dollars. Please calculate the cost of one adult ticket and the cost of one student ticket.

A student named Dora (all students' names in this paper are pseudonyms) solved the task mentally and was asked to describe her method to the whole class. Her answer is translated below:

Three adult tickets and one student ticket cost 560 dollars. If you add one more student ticket, it becomes 640 dollars. Six hundred forty dollars minus 560 dollars equals the price for one student ticket.

Dora had obviously thought of this method using her knowledge of basic arithmetic. The teacher immediately complemented her answer by repeating her description in his own words and emphasising the concept of subtraction.

The class is then asked to do the problem again, this time using the method of equations. This directed the students' attention to the method instead of the answers to the problem. The teacher guided the students in writing the Equations 3x + y = 560 and 3x + 2y = 640, and obtaining the answer by subtracting one equation from the other. He then compared this method with Dora's and explained how the two were actually equivalent.

This task shows how the teacher created dimensions of variation by skilfully making use of contrast. The contrast between Dora's and the teacher's description of the arithmetic method is a variation between two oral representations of the same method. I call this a Level 1 contrast. The contrast between the arithmetic method and the equation method is more subtle and can be therefore considered a Level 2 contrast. At this level, students may need the teacher's help in seeing how the two different methods are fundamentally the same. However, how well students learn the equation method depends on their own comprehension of the lesson.

After introducing these two levels of contrasts, the teacher then discussed a method of subtracting equations in parallel with the elimination-by-substitution method, which they had learned in an earlier lesson. In this case, the students must compare the new lesson with a previous one. Given the more abstract nature of this task, I call this a Level 3 contrast.

Task 2: The trial activity

After discussing Task 1, the teacher asked the class to solve Task 2 (3x + 2y = 8 and 3x - 2y = 4) using the method of subtracting one equation from the other. He allowed students to discuss among themselves and think about what they should do. After a few minutes, two students, Dorris and Felix, presented their methods to the class. Dorris suggested subtracting the equations while Felix suggested adding them instead.

In this task, the teacher presented the coefficients in such a way that students could either subtract one equation from the other to eliminate “x”, or add the equations to eliminate “y”. This was meant to help them learn about “separating” the coefficients of the equations—an important aspect of applying the method. At the same time, the teacher directed students to focus on how they can solve the problem rather than just getting the final answer. This is seen in the way the teacher continued to bring the conceptual aspect of the method to the attention of the class. A few of the questions he asked the class are translated below:

T: So I have some questions, why can you use the method of deduction for the two equations? Why can you use the method of addition for the two equations? What is the reasoning behind it? How do you account for the use of such steps?

The teacher's questions invited students to justify the validity of adding or subtracting equations. On the teacher's request, the students explained their answers by referring to properties of equations and equalities. This discussion brought the conceptual aspect of the method (the properties of equations) into the foreground, forming a contrast to the procedural aspect discussed earlier.

Task 3: Learning to summarise

In this task, the teacher asked students to determine whether to add or subtract the following pairs of equations:

In this problem no two pairs of equations were the same yet they shared certain similarities. The teacher guided his students by showing them different cases of the coefficients and leading them to a possible generalisation. He then discussed the criteria for deciding when to add or subtract the equations. This way, the teacher ensured that the students took note of what he wanted them to observe and arrived at the same conclusion.

Seeing Parts in the Whole and the Whole in the Parts

The analysis of the teacher's three tasks indicates an enacted object of learning within the framework of variation. Some dimensions were obviously prescribed in the design of the tasks while more pertinent ones were embedded in the teacher's verbal questions. For example, his question on why the elimination method can be applied (in Task 2) solicited a number of answers concerning the property of equations. This helped focus attention on the method's conceptual aspect and worked well with the earlier discussion on its procedural aspect. The teacher taught the class to see both aspects as a coherent whole by asking the students to reflect upon their experiences. Such reflection is important for bringing about critical discernment.

The teacher appeared to be very experienced at reminding his students of the activity's important points. He drew attention to the key features of the lesson and made sure students were able to achieve skills such as: seeing the equation method as an equivalent of their classmate's arithmetic method, comparing this method with what they had learned in a previous lesson, applying what they learned in Task 1 to Task 2, and justifying the use a particular procedure.

The Teacher's Perspective: Putting a theory into practice

Throughout the three interviews with LPS researchers, the teacher showed that he was very aware of his personal teaching style. He explicitly mentioned the application of Gu's pedagogical theory (Experimenting Group of Teaching Reform, 1991; Gu et al., 2004), indicating that it was the same theory emphasised by the school as well. Gu's theory includes a component where the concept of variation can be applied in deciding on examples and exercises. As mentioned earlier in this paper, the teacher did not mention the term “variation” in his interview but features of variation were quite explicit in his practice.

According to the teacher, Task 1 (the situational question) had the following functions: to engage students quickly, to increase their interest in the lesson, and to build a good foundation for future activity. The teacher knew that the question was simple enough for the students to calculate mentally (kou suan) and would quickly draw them into the lesson. True enough, this was what happened in class. However, engaging students alone does not guarantee a good foundation of knowledge so the teacher devised a special exercise where the class solves the question once more, this time by setting equations. This, in the teacher's words, “translates the students' thinking into systems of equations”—creating a foundation for understanding the method of elimination by addition or subtraction. The teacher believed that the question he designed for Task 1 served this function much better than questions provided in the textbook. More importantly, his students liked it.

The teacher conceptualised Task 2 (trial activity) in line with Gu's emphasis on providing an exploratory experience for students. He explains his design below:

[The trial activity] demonstrated what I actually wanted to say about the elimination method by addition or subtraction. It also allowed the students to explore knowledge on their own. This type of activities is emphasised by our school. We should throw out the old ideal that a teacher should only feed knowledge in class and nothing else.... The main aim is to teach them the methods, not just computations.

While learning the methods was definitely the main objective of this task, room for exploration was very limited and carefully controlled in the classroom. Most students followed the teacher's steps of subtracting the equations while a few tried adding the equations as an alternative method. All of this was also completely within the teacher's expectations.

If Task 1 was meant to engage students and Task 2 was to help students understand the methods, Task 3 was designed to help students summarise (gui na) the lesson. This is an important aspect in Gu's theory (1991), where the teacher is expected to summarise or help students develop the ability to summarise the main features of what they have learned.

On the surface, Task 3 looked like a simple practice activity where students apply the concepts they've learned. Actually, the teacher's main objective was to provide an opportunity for students to make their own observations. He describes this process below:

At that time, I asked such questions so that the students could discuss it and reach a conclusion... after the students had their discussion, we exchanged ideas. If the student's summary was not comprehensive enough, I would give some hints and we would then work out the conclusion together. Since they are only Form one students, they still need the teacher's help.

Providing students the chance to form their own summaries can be an end in itself and also a means to another end. In this task, the teacher obviously wanted the class to arrive at what he saw as the proper conclusion.

Teacher-centredness and Student-centredness from the Perspective of the West

An analysis of the teacher's lesson shows that all the events—including the questions he asked and the students' answers—closely followed his careful planning and expectations. Based on this observation, one may conclude that the teacher was “dominating”, given that he controlled what happened in class and what the students were supposed to understand from the lesson.

However, from the teacher's perspective, his lesson was definitely not teacher dominated. Given that his lesson was planned with a pedagogical theory in mind, he considers his teaching very different from the traditional Chinese way of knowledge transmission. As his comments show, each part of his lesson was supported by a student-oriented rationale which emphasised objectives such as: helping students develop a certain capability, motivating them to work on a certain task, letting students try out their skills, and providing a foundation for further work. In fact, the teacher highly valued his students' participation and mentioned this frequently in his interviews. In explaining his actions during the lessons, he often said, “I let the students investigate”, “I let them try”, and “I give them questions to think about”. He also gave serious consideration to the students' abilities, thinking, and participation. In this sense, the teacher's design of the lesson is “student centred”, or at least a transition from traditional practice to a more student-centred model. Still, his practice remains different from Western models, where the teacher's role is that of a facilitator and students are encouraged to express a diversity of meanings during lessons.

The teacher's actions were also based on his intended object of learning, “the method of elimination by subtraction and addition”. The format of the lesson was a means to help the students see the object of learning in ways the teacher wanted them to see it. In other words, the teacher's model can be framed as an experience of exploring an intended object of learning.

Students' Views

Analysis of LPS data showed that the 30 students in class liked the lesson because of the content and the way it was taught. Frank and Tom, two students who were interviewed after the lesson featured in this paper, pointed out important parts of the lesson which were consistent with their teacher's perspective.

Frank's comments showed that he was an active and critical thinker. He first pointed out the part where the teacher had transformed Task 1 into equations. The next two parts of the lesson which he considered important occurred when the methods of addition and subtraction were being compared and when the principle of the method was explained. Both referred to the conceptual aspect of the method and the relationship between different methods or concepts.

Tom's interview showed that he was an attentive student who highly valued his teacher's knowledge. His comments often began with the phrase, “the teacher was saying”, when referring to the explanation of the method, the elaboration of a concept, or the conclusion of one part of the lesson. He showed concern during occasions when he noticed his own weakness—such as one instance where he was unable to answer the question in Task 2. From Tom's perspective, almost all parts of the lesson were important.

Interviews with Frank and Tom show that although they appeared to be obediently following the teacher's direction, they were also actively reflecting on what was happening in the lesson. This kind of mental activity is implicit, and would have been hard to see if the students themselves had not pointed it out in the post-lesson interviews.

Conclusion

The East Asian learner paradox has generated great interest in the nature of teaching and learning mathematics in the Asian region. While research studies such as the TIMSS videos introduced the idea of a national script to explain the different outcomes among various countries, other studies doubt the existence of a uniform national script and emphasise that labels such as “teacher-dominating” do not accurately describe reality.

Obviously, one will always encounter diverse teaching paradigms in different classrooms around the world. However, there is still more to discover. In this paper, I have attempted to incorporate the views of a teacher and his students with those of a researcher in order to have a better understanding of the East Asian paradox.

The lesson presented in this paper shows how the teacher made an effort to understand Gu's theory (1991, 2004), a pedagogical framework that is well recognised and implemented in his local region. So while the teacher planned his lesson according to his own design, he also valued his students' participation and believed that knowledge should not be acquired by transmission alone.

The content-oriented and teacher-dominated image of the lesson could be due to the teacher's own interpretation of student-centredness—which is different from what is defined by Western education. While student-centredness is often seen as a process of learning where exploration is valued and students initiate the pursuit of knowledge, the teacher developed a framed experience to explore the intended object of learning based on his understanding of how his students think. Consequently, unexpected responses and departures from the lesson plan were considerably rare. In this sense, the lesson is teacher dominated but not necessarily detrimental to learning.

Interviews also show evidence of keenness, active thinking, and a consistent concern for learning the lesson among the teacher's students. While this could be due to other factors such as examinations and societal expectations, it is also likely that the students welcome their teacher's practice of providing them with a framed exploratory experience in the classroom. This includes the teacher's skilful use of variation to illustrate important aspects of the lessons, such as: the coefficients of the equations, the contrast between methods, and the relationship between procedural and conceptual aspects. This helps meet the students' expectations in terms of how the content is explained.

In fact, the use of variation is by no means new in Chinese ways of teaching. In two other independent studies by Gu et al. (2004) and Huang and Leung (2004), variation is considered an important feature of the Chinese way of teaching. Whether or not this is pertinent to the students' appreciation of their teacher's method may be worthy of further investigation. There is much more to discover in understanding the East Asian learner paradox. Does a paradox really exist or is it simply a puzzle with a few missing pieces? The Shanghai teacher's alternative form of student-centredness may well be a missing piece to the paradox jigsaw.

Acknowledgement

The work described in this paper was fully supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. HKU 7192/02H). The author would like to thank Professor Derek Hodson, Professor David Clarke, Mr Ivor Johnson, and the reviewers for their advice in the manuscript.