Content uploaded by Lianghuo Fan

Author content

All content in this area was uploaded by Lianghuo Fan on Dec 18, 2021

Content may be subject to copyright.

Chapter 9

Textbook Use Within and Beyond Mathematics

Classrooms: A Study of 12 Secondary Schools in

Kunming and Fuzhou of China

FAN Lianghuo CHEN Jingan

ZHU Yan QIU Xiaolan HU Jiuzhong

This chapter presents a study which investigated how teachers and

students used textbooks within and beyond Chinese mathematics

classrooms. Data were collected from 36 mathematics teachers and 272

students in 12 secondary schools in Fuzhou and Kunming, two major

cities in Mainland China, through questionnaires, classroom

observations, and interviews. The study provided a general picture of

the textbook use by Chinese teachers and students of mathematics. The

results showed that textbooks were the main but not the only source for

teachers to make decisions about what to teach and how to teach. For

students, textbooks were their main learning resource for both in-class

exercise and homework. No significant differences were found between

teachers with different genders, experiences, from different regions and

schools in their use of textbooks, though some significant differences

were found between students in the two cities in their use of textbooks.

Explanations for the results are offered in the chapter.

Key words: Chinese mathematics classrooms, learning materials,

problem solving, teaching materials, textbook use

1 Introduction

Over the last two decades, the role of textbooks in both teachers’

teaching and students’ learning of mathematics has received increasing

attention from researchers (e.g., see Ball & Cohen, 1996). Many studies

have revealed that the availability of textbooks (i.e., the presence of

228

Textbook Use Within and Beyond Chinese Mathematics Classrooms 229

textbooks in class) was positively associated with student achievement,

especially in the developing countries (e.g., Fuller & Clarke, 1994;

Heyneman, Farrell, & Sepulveda-Stuardo, 1978; Schiefelbein &

Simmons, 1981). Moreover, researchers around the world have

consistently reported the extensive use of textbooks in classrooms. For

example, in Germany and Switzerland, teachers used one main textbook

for mathematics teaching for each year and overall followed the book

fairly closely (Bierhoff, 1996). In England, the majority of teaching

approaches in classroom practice were found to essentially reflect those

embodied in the textbooks (ibid.). In the US, researchers found that 75 to

90 percent of instructional time was structured around textbooks (Tyson

& Woodward, 1989; Woodward & Elliott, 1990). In Japan, Fujii (2001)

indicated that the majority of teachers taught the contents in textbooks in

a straightforward way; they usually neither went beyond the materials

nor offered less than what was included in the books, which he called “a

very honest manner”.

Studies on how teachers use textbooks in their teaching practice have

so far generated different conclusions. Relatively speaking, earlier

studies (i.e., before the mid-1980s) showed more evidence that school

teachers adhered closely to textbooks in terms of content selection and

sequencing. The teaching approaches adopted by the teachers were also

highly similar to those presented in the books (e.g., McCutcheon, 1982;

National Advisory Committee of Mathematics Education, as cited in

Kuhs & Freeman, 1979; Woodward & Elliott, 1990). However, more

recent studies revealed that there existed significant differences on the

ways in which teachers used textbooks in class. For instance, Schmidt,

Porter, Floden, Freeman, and Schwille (1987) found that there were four

patterns of textbook use by eighteen primary mathematics teachers in

Michigan, US: (1) classic textbook-follower (six teachers), (2) textbook

follower/strong student influence (six teachers), (3) follower of district

objectives (three teachers), and (4) follower of conception and past

experiences (three teachers). Similarly, Freeman and Porter (1989) also

found that there are three styles of textbook use by four primary

mathematics teachers: (1) textbook-bound (one teacher), (2) focus on the

basics (two teachers), and (3) focus on district objectives (one teacher).

How Chinese Learn Mathematics: Perspectives From Insiders

230

The inconsistency in the findings of different researches about how

teachers used textbooks in their teaching suggests that teachers’ use of

textbooks is a complex activity. Many factors could affect teachers’

behavior and decision about how textbooks are used. Textbooks

themselves could be such a factor that has direct impacts on the ways in

which teachers used them. In other words, teachers might use different

textbooks in different ways (e.g., Barr, 1988; Fan & Kaeley, 2000;

Krammer, 1985).

Another reason for the inconsistency might be related to the fact that

many of the studies on how teachers used textbooks were, as Fan and

Kaeley (2000) indicated, of small scale. As Love and Pimm (1996)

pointed out, collecting research data in this area is rather difficult.

Understandably, there could be problems concerning the external validity

of findings from such small-scale studies. In this sense, more studies,

especially those with a larger scale, are still needed.

Naturally, large-scale studies would involve more subjects. However,

the data in currently available large-scale studies were often just

collected by questionnaire surveys, as we can see from the Second

International Mathematics Study (SIMS) and the Third International

Mathematics and Science Study (TIMSS). Some researchers have

questioned about the (internal) validity of findings obtained merely from

this research method, that is, teachers’ self-reports on textbook use. In

fact, some researchers have reported a conflict between how teachers

reported their use of textbooks and how they really used textbooks in

practice (e.g., Sepulveda-Stuardo & Farrell, 1983). Sosniak and

Stodolsky (1993) pointed out that many teachers were not concerned or

self-conscious about how they used textbooks in their own teaching.

Overall, among the limited number of studies on textbook use in

teaching and learning, most were conducted in Western educational

contexts. As Zhu and Fan (2002) noted, there were few such studies

conducted in Asian countries, particularly in Chinese school settings. In

addition, most studies were from a perspective of teaching, that is, on

how teachers use mathematics textbooks in their teaching, and few were

from a perspective of learning, namely, on how students use textbooks in

their learning.

Textbook Use Within and Beyond Chinese Mathematics Classrooms 231

The main purpose of this study was to investigate how mathematics

teachers in secondary schools in two major cities, Kuming and Fuzhou,

of China used mathematics textbooks in their teaching. The study was

also partially designed to look into how students there used mathematics

textbooks in their learning of mathematics. Through investigating the

ways in which teacher and students in those two cities used mathematics

textbooks both within and beyond classrooms, we hope to provide useful

empirical evidence and shed light on what role textbooks play in the

teaching and learning of mathematics in Chinese educational

environment and how they shape the way Chinese students learn

mathematics. In addition, the study also examined some factors that

might affect the ways in which the teachers and students used the

textbooks.

2 Research Design and Procedures

2.1 Population and sample

There are several series of mathematics textbook currently being used in

Mainland China, all being approved by the Ministry of Education. In

each year, the ministry issues an approved textbook list for schools to

select. In the past, there were totally eight series of mathematics

textbooks being used at junior high school level. The majority of Chinese

students (around 70%) used the books published by People’s Education

Press (PEP) (Zeng, 1997; also see J.-H. Li, this volume). Mainly because

of its popularity, the PEP series was chosen for this study1.

However, in the latest major curriculum reform, new textbooks were

nation-widely introduced progressively from 2000 (Lian, 2000) and that

the PEP series will be finally completely phased out. As a matter of fact,

students in both Fuzhou and Kunming have stopped using the PEP series

from Junior High 1 (JH1) since 2002, though students at Junior High 2

(JH2) were still using the series. Therefore, only JH2 students in both

1 Another reason for us to select this series is that we have undertaken a study on the

textbooks and hence obtained reasonable knowledge about the textbooks, particularly on

their content, structure, and ways of representing mathematics problem solving (see Zhu,

2003).

How Chinese Learn Mathematics: Perspectives From Insiders

232

cities were involved in this study, the target population of the study.

Correspondingly, Algebra II and Geometry II of the PEP series are the

two textbooks being then used by the teachers and students.

The research subjects of this study consisted of 36 mathematics

teachers and 272 students from 12 secondary schools (6 in Fuzhou and 6

in Kunming), a stratified sample from the population. More specifically,

in each city, two schools were selected from high-performing schools

(School Cohort I), two schools were selected from average-performing

schools (School Cohort II), and the other two were selected from low-

performing schools (School Cohort III).

Table 1 presents the background information of the 36 participating

teachers, including their gender, highest education level, length of

mathematics teaching experience, and the experience of teaching with

the textbooks. All the information was gathered from the first four

questions in the teacher questionnaire used in this study (see below).

Table 1

A Profile of the 36 Participating Teachers

1 One teacher in School H did not report the year of teaching mathematics and that of

teaching with the PEP series.

As for the students, 121 were from Fuzhou and the other 151 were

from Kunming. In each city, the numbers of participating male students

and female students were nearly equal.

Textbook Use Within and Beyond Chinese Mathematics Classrooms 233

2.2 Instruments and data collection

Three instruments were designed for this study: questionnaires,

classroom observation, and interviews.

2.2.1 Questionnaire

The questionnaire survey used two questionnaires, one for teachers and

the other for students. Both questionnaires are in multiple-choice format.

The construction of the questionnaires was mainly based on the structure

of the PEP books.

There are 27 questions in the teacher questionnaire. Questions 1 to 4

are set to collect teachers’ background information, as shown in Table 1,

which is helpful to understand and analyze teachers’ responses to the

questionnaire. Questions 5 to 14 are about teachers’ general use of the

textbooks. For example, Question 7 asks teachers how often they used

textbooks (student edition) in class. Questions 15 to 24 focus on how

teachers used different groups of problems in the textbooks, such as

example problems. Questions 25 and 26 are on teachers’ understandings

of the importance of various teaching materials, including textbooks, in

teachers’ teaching and students’ learning. The last question asks teachers

whether there had been changes in their textbook use since they became

mathematics teachers.

The student questionnaire consisted of 14 questions; its design is

similar to that of the teacher one. Questions 1 to 5 are about students’

general use of the textbooks. Questions 6 to 12 focus on how students

used different parts of texts, including various groups of problems, in the

textbooks. Question 13 is about students’ understandings of the

importance of various learning materials, including textbooks, in their

mathematics learning. The last question asks students whether there had

been changes in their textbook use from year JH1 to year JH2.

A pilot test of the teacher questionnaire with 2 teachers in Fuzhou

and 3 teachers in Kunming selected from the population but not in the

sample showed that the questionnaire could be completed within 30

minutes. Moreover, none of the five teachers had difficulty in answering

the questionnaire.

How Chinese Learn Mathematics: Perspectives From Insiders

234

2.2.2 Classroom observation

Having noticed the validity issue concerning the questionnaire survey

method as raised by researchers mentioned earlier, we also employed

two other instruments: classroom observation and interview, for data

collection.

Two teachers in each sample school with different teaching

experience, that is, one teacher with less than 10-year teaching

experience and the other with no less than 10-year teaching experience,

were observed for their actual classroom teaching. All the teachers in

Fuzhou were observed for once (one class period), whereas those in

Kunming were observed twice.

The classroom observation was used to investigate what really

happened in class, with the focus being on textbook use by both teachers

and students. Instruction for classroom observation was pre-designed. All

classroom observations were documented with field notes. Those in

Kunming were also tape recorded.

2.2.3 Interview

The interviews were conducted with all the teachers who received

classroom observation. Interviews were used to ask teachers open-ended

questions which were not covered or difficult to be asked in

questionnaires; in particular, they were used to explore the underlying

reasons why teachers were using the textbooks in the ways which they

have reported in questionnaires or been observed in classroom teaching.

General instruction for interviews was also pre-designed in order to

keep the interviews focused and consistent. Understandably, in the actual

interviews, questions were posed based on what the teachers had

demonstrated in the classroom observation and other actual situations.

Each interview was scheduled to take about 30 minutes.

Textbook Use Within and Beyond Chinese Mathematics Classrooms 235

2.2.4 Data collection

Data collection from schools took place in the second quarter of 20032.

In Fuzhou, the questionnaires were distributed to about 20 JH2 students

and 2 mathematics teachers in each of the 6 sample schools with a

response rate being 100% from both the students and teachers. In

Kunming, the questionnaires were distributed to all the JH2 students and

their mathematics teachers in the 6 sample schools with a response rate

being, around 88% from the students and 80% from the teachers.

As mentioned before, in each sample school, 2 teachers with

different lengths of teaching experience were observed for their

classroom teaching. In total, 36 lessons consisting of 14 algebra lessons

and 22 geometry lessons were observed. In Fuzhou each teacher was

observed for one lesson (class period) and in Kunming each teacher was

observed for two lessons, Among the 36 lessons observed, 25 lessons

were normal lessons and 11 were review lessons.

Before the classroom observation, the information relevant to the

observed classes was gathered by the researchers, including student

background, teaching content, and the structures and characteristics of

the corresponding texts in the textbooks.

All the 12 teachers were interviewed after the classroom observation.

The interviews focused mainly on the reasons why the teachers used

textbooks in the ways that displayed in the classroom observations.

Correspondingly, the questions asked in the interviews varied from

teacher to teacher. All the interviews were documented with field notes.

Those conducted in Kunming were further tape recorded.

2.2.5 Data processing and analysis

The data in tape-recorded form obtained from classroom observations

and interviews were first transcribed verbatim. Together with the

transcriptions, all the collected data were translated from Chinese into

2 In Mainland China, a school academic year usually starts from the beginning of

September and ends around the end of next June, and when the data were collected in the

study, the two textbooks had been used by the teachers and students for close to two

semesters.

How Chinese Learn Mathematics: Perspectives From Insiders

236

English before analysis. The data from the questionnaires were then

stored, processed, and analyzed using SPSS mainly by quantitative

methods. The analysis is intended to get a general picture about how

students and teachers use textbooks in mathematics class.

The data from the other two instruments were analyzed mainly by

qualitative methods. It is used to examine how textbooks were actually

used by students and teachers in mathematics class and also the reasons

why textbooks were used in this way or that way.

In addition, to detect the factors that might affect the ways in which

textbooks were used, three criteria were respectively employed to

classify both students and teachers into different groups for comparison:

1. Region: Fuzhou vs. Kunming

2. School quality: high-performing schools, average-

performing schools, and low-performing schools (i.e.,

School Cohort I, School Cohort II, and School Cohort III)

3. Gender: Male vs. Female

For teachers, two more dichotomies were created according to their

responses to the first four questions in the teacher questionnaire:

4. Teaching experience: Novice teachers vs. Experienced

teachers;

5. Teaching experience with the PEP series: Novice users vs.

Experienced users.

In this study, “Novice teachers” refer to the teachers who had taught

mathematics for less than 10 years and the remaining teachers are

defined as “Experienced teachers”. Similarly, the time period of 10 years

was also used to distinguish “Novice users” from “Experienced users”.

We were initially also interested to know if teachers’ educational

background would affect the way in which they use the textbooks.

However, as showed in Table 1, it is quite homogenous among the 36

participating teachers in this aspect. In particular, more than four fifths of

the teachers were university graduates and all but two of them were from

normal universities. Therefore, it is difficult for this study to detect

whether teachers with different education background would use

Textbook Use Within and Beyond Chinese Mathematics Classrooms 237

textbooks differently, and “education background” was not used as a

variable for classification and hence no comparison was made against it.

3 Results and Discussions

The results of this study are reported in the following sequence: general

use of the textbooks, use of various parts of texts in the books, and some

other issues (including teachers’ understanding of the role of textbooks in

mathematics teaching and learning and their changes in textbook use

over the years), which is parallel to the sequence of the questions

arranged in the questionnaires.

3.1 General use of the textbooks

Ten questions in the teacher questionnaire and 5 questions in the student

questionnaire were specifically focused on the general use of the

textbooks.

According to teachers’ response to the questionnaire survey, about

22% teachers “always” followed the order presented in the textbooks, the

others “often” or “sometimes” did so, and no one “seldom” or “never”

followed the order. Moreover, it was found that there was significant

difference among the teachers from different school cohorts, χ2 (2, N =

36) = 8.25, p < .05. In particular, significantly more teachers from low

performing schools “always” followed the sequence in the textbooks

than those from high performing schools, χ2 (1, N = 25) = 7.68, p < .05.

The result seems understandable. As some teachers commented in the

interview, it was convenient for students to understand better and review

well what had been taught in class if teachers followed the textbooks

closely in their teaching. It appears that students from low performing

schools who were relatively slow learners could benefit more from such

a textbook use strategy.

In the questionnaire survey, the percentages of the teachers who

reported that they “always”, “often”, and “sometimes” used the

textbooks in their classroom teaching were 22%, 59%, and 19%

respectively, while no teacher claimed that he/she “seldom” or “never”

How Chinese Learn Mathematics: Perspectives From Insiders

238

used the textbooks. No significant difference was found across different

comparison groups in this aspect of textbook use.

The classroom observation confirmed the above result. In particular,

except for 5 lessons in Kunming and 1 in Fuzhou, in all the lessons

observed teachers used textbooks in their classroom teaching. The five

lessons in Kunming were review lessons taught by five teachers.

Nevertheless, all these teachers used textbooks in the other lesson

observed. Moreover, four out of the five teachers were found using

textbooks over 60% of the instructional time, with an average being

71.6%. The lesson in Fuzhou observed was a typical lesson. When being

asked why he did not use textbooks in the lesson, the teacher explained

that “it was the second lesson on Section 12.4 and the content was more

difficult so that the examples and exercises were all not from textbooks.”

In fact, in the lesson, the examples and exercises used were either taken

from past examination papers or designed by the teacher himself.

Examining the teacher’s questionnaire, we found that the teacher actually

reported that he conducted his lesson “always” following the order

suggested by the textbook and he “often” used textbooks in his class.

Different from the finding that more than 80% of the teachers

“always” or “often” used textbooks in their lessons, students’ responses

to the questionnaire showed that they used the books in classes less

frequently. According to the responses, 7% of the students “seldom” or

“never” used textbooks in mathematics classes, 29% of the students

“sometimes” did so, and the percentages of “often” or “always” using the

textbooks in classes were 41% and 23%, respectively. The difference

between teachers and students in the frequency of using textbooks in

classes, to some extent, suggests that textbooks serve more as a teaching

resource than as a learning resource in Chinese classrooms. In other

words, textbooks are indeed used more as “teaching materials” than as

“learning materials”3. By the way, no significant differences were found

among different comparison groups of students in this aspect.

The data collected from the teacher questionnaire revealed that the

percentage of instructional time being structured by textbooks in

3 In fact, “textbooks” in Chinese are usually called ke ben (课本, literally “texts for

lessons”), or simply jiao cai (教材, literally “teaching materials”).

Textbook Use Within and Beyond Chinese Mathematics Classrooms 239

mathematics classes varied from 20% to 90%, with an average being

66.7%. No significant difference was detected across comparison groups

of teachers. According to the classroom observation conducted in

Kunming, which recorded the time structure of all the lessons in detail,

we found that excluding the five review lessons without using textbooks,

there was 72.4% of the instructional time involving the use of textbooks.

The result is largely consistent with available findings from US

classrooms, where around 75 to 90 percent of instructional time was

found to be centered on textbooks (Tyson & Woodward, 1989;

Woodward & Elliott, 1990).

The TIMSS study found that in five out of 34 educational systems,

mathematics teachers relied more on the curriculum guides than

textbooks when they made decisions on “what to teach”. As to teaching

approaches, most used textbooks as their main resources (see Beaton et

al., 1996). In this study, we set two similar questions. The results showed

that the teachers used textbooks (student edition) most frequently among

all the teaching materials for both content and approach decisions (see

Figure 1).

Content Decision Approach Decision

3.33 3.68 4.24 3.74 3.80

0

1

2

3

4

5

ABCDE

3.47 3.50 4.06 3.79 3.69

0

1

2

3

4

5

ABCDE

Figure 1. Average frequency of using various teaching

materials in teachers’ content and approach decisions

Note. (1). A = National mathematics curriculum standards, B = Junior high school

mathematics syllabus, C = Textbooks (student edition), D = Textbooks (teacher edition),

E = Other materials. (2). By the ordinal scale in the figure, 5 = Always, 4 = Often, 3 =

Sometimes, 2 = Seldom, and 1 = Never.

Consistent with the results from the above analysis based on the

average frequency, an ordinal regression (PLUM) using SPSS revealed

that in both content and approach decision making procedures, the

How Chinese Learn Mathematics: Perspectives From Insiders

240

teachers used textbooks (student edition) with the highest frequency.

Table 2 shows that the order of the frequency of using the five teaching

materials for content decision is, from highest to lowest, “textbooks

(student edition)” (C), “other materials” (E), “textbooks (teacher

edition)” (D), “junior high school mathematics syllabus” (B), and

“national mathematics curriculum standards” (A). Furthermore, it can be

found that the teachers used “textbooks (student edition)” for content

decisions significantly more often than “textbooks (teacher edition)” at

the 0.01 level, whereas the frequency of using the other three materials

was at the same level as that of using “textbooks (teacher edition)”. The

order for the approach decisions is quite similar to that for the content

decisions: “textbooks (student edition)” (C), “textbooks (teacher

edition)” (D), “other materials” (E), “junior high school mathematics

syllabus” (B), and “national mathematics curriculum standards” (A).

Table 2

Log-Linear Regression Results on the Data About Content Decisions by Teachers

Parameter Estimates

-4.485 1.293 12.021 1.001 -7.020 -1.949

-2.694 1.187 5.156 1.023 -5.020 -.369

-1.164 1.173 .986 1.321 -3.463 1.134

1.294 1.170 1.224 1.269 -.998 3.586

.8005 .456 3.079 1.079 -9.370E-02 1.695

0a. . 0 . . .

4.644E-02 .455 .010 1.919 -.846 .939

0a. . 0 . . .

-1.2249 .470 6.782 1.0092 -2.147 -.303

0a. . 0 . . .

-2.41E-02 .471 .003 1.959 -.947 .899

0a. . 0 . . .

0a. . 0 . . .

0a. . 0 . . .

[FREQUENC = 1]

[FREQUENC = 2]

[FREQUENC = 3]

[FREQUENC = 4]

Threshold

[STANDARD=0]

[STANDARD=1]

[SYLLABUS=0]

[SYLLABUS=1]

[SBOOK=0]

[SBOOK=1]

[OTHERS=0]

[OTHERS=1]

[TBOOK=0]

[TBOOK=1]

Location

Estimate Std. Error Wald df Sig. Lower Bound Upper Bound

95% Confidence Interval

Link function: Logit.

This parameter is set to zero because it is redundant.

a.

Note. STANDARD = National mathematics curriculum standards, SYLLABUS = Junior

high school mathematics syllabus, SBOOK = Textbooks (student edition), TBOOK =

Textbooks (teacher edition), and OTHERS= Other materials.

In the interview, many teachers reported that they always used

textbooks in their lesson preparations. When being asked for the

purposes of using textbooks at this stage, most mentioned that to decide

teaching contents and approaches was one of the main concerns. In

Textbook Use Within and Beyond Chinese Mathematics Classrooms 241

addition, some teachers also selected example problems, in-class

exercises, and homework from the textbooks during their lesson planning.

The frequency of using various teaching materials in the two

processes across different teacher groups was more or less the same. Chi-

square tests revealed that school quality was the only factor having

significant influence on the frequency of using syllabus (χ2 [8, N = 34] =

16.83, p < .05) and textbooks (teacher edition) (χ2 [6, N = 34] = 13.94, p

< .05), when teachers decided teaching approaches. In particular,

significantly more teachers from School Cohort II at least “sometimes”

resorted to syllabus for teaching approaches than those from School

Cohort III, χ2 (1, N = 19) = 3.96, p < .05; significantly more teachers

from School Cohort II “always” or “often” used textbooks (teacher

edition) in preparing for teaching approaches than those from School

Cohort III, χ2 (1, N = 19) = 4.00, p < .05.

The questionnaire also asked teachers how often they referred to

various teaching materials to select example problems, in-class exercises,

and homework. In terms of the average frequency, the results showed

that textbooks (both student and teacher editions) were used most

frequently in the three activities (see Table 3), which is largely confirmed

from the interviews as mentioned earlier. No significant difference was

found across different comparison groups.

Table 3

Average Frequency of Using Various Teaching Materials to Select Tasks for Example,

In-class Exercise, and Homework Assignment

Example In-class exercise Homework

A 3.13 3.10 3.07

B 3.27 3.43 3.39

C 4.17 4.37 4.34

D 3.90 3.94 3.81

E 3.60 3.68 3.73

Note. (1). A = National mathematics curriculum standards, B = Junior high school

mathematics syllabus, C = Textbooks (student edition), D = Textbooks (teacher edition),

E = Other materials. (2). By the ordinal scale in the figure, 5 = always, 4 = often, 3 =

sometimes, 2 = seldom, and 1 = never.

Log-linear regression analysis again obtained consistent results. It

indicates that the five teaching materials from the most frequently used

one to the least one in all the three activities were “textbooks (student

How Chinese Learn Mathematics: Perspectives From Insiders

242

edition)” (C), “textbooks (teacher edition)” (D), “other materials” (E),

“junior high school mathematics syllabus” (B), and “national

mathematics curriculum standards” (A). Moreover, the analysis showed

that when selecting both example problems and in-class exercises, the

teachers significantly more often referred to “textbooks (student edition)”

than “other materials” at the 0.01 level, whereas the frequencies of using

the other four teaching materials were at the same significant level. For

homework assignment, the frequency of using “textbooks (student

edition)” was again significantly higher than that of using “other

materials” and the difference reached at the 0.001 level, meanwhile the

use of “national mathematics curriculum standards” was less frequently

than the use of “other materials” at the 0.05 level.

It should be pointed out that the above finding has been consistently

found by many other researchers in different educational settings. For

instance, in a survey of 28 Australian secondary mathematics teachers’

preferences in textbook characteristics and uses, Shield (1989) found that

the most important textbook use was for student exercises in class and

for homework (also see National Advisory Committee on Mathematics

Education, as cited in Nicely, 1985; Porter, Floden, Freeman, Schmidt, &

Schwille, as cited in Flanders, 1987; Zhu & Fan, 2002).

In the student questionnaire, students were asked to estimate how

much of their homework was directly from textbooks. Around 60% of

the students claimed that “almost all” or “large part” of their homework

were assigned from textbooks, while more than 20% of the students

reported that only “small part” or “very little” of the homework were

from the books. It was further found that students in Kunming received

significantly more homework from textbooks than those in Fuzhou, χ2 (4,

N = 266) = 42.52, p < .001. School quality was another factor that had

significant influence on the source of homework; students’ homework in

high performing schools was assigned from textbooks significantly more

than that in both average (χ2 [4, N = 186] = 35.02, p < .001) and low (χ2

[4, N = 169] = 15.27, p < .01) performing schools. The reason might be

that students in lower performing schools were assigned more extra

homework for reinforcement; nevertheless more evidences are needed

concerning this result.

Textbook Use Within and Beyond Chinese Mathematics Classrooms 243

The classroom observation revealed that a higher percentage of

teachers in Kunming (41.7%) assigned homework entirely from

textbooks than those in Fuzhou (25.0%). However, we did not find

teachers from different school cohorts had significant difference on

homework assigning, in terms of the source of homework. The fact that

only a limited number of lessons were observed might be one reason for

the inconsistency between the result obtained from the classroom

observation and that from the student questionnaire.

The importance of textbooks in lesson preparations was highly

evaluated by the teachers. In particular, all the teachers gave positive

evaluation and 62.9% of them rated “textbooks (student edition)” “very

important” and 54.5% gave the same evaluation to “textbooks (teacher

edition)”. Moreover, an ordinal regression (PLUM) revealed that the

importance of “other materials” was significantly lower than that of

textbooks in both student and teacher versions at the 0.01 level. It was

found that teachers from different comparison groups had no significant

differences on the evaluations of the importance of various teaching

materials in their lesson preparations.

In the teacher questionnaire, teachers were also asked how often they

required students to read textbooks before, during, and after classes.

Correspondingly, students were asked in the student questionnaire how

often they read the textbooks at the three time periods. The results were

displayed in Table 4.

Table 4

Teachers’ Requirements (TR) on Reading Textbooks and Students’ Actual Reading (S)

Before, During, and After Classes

Before the class During the class After the class

TR S TR S TR S

Always 9

(26.5%)

22

(8.1%)

8

(22.9%)

36

(13.4%)

6

(17.6%)

14

(5.3%)

Often 15

(44.1%)

66

(24.4%)

14

(40.0%)

110

(40.9%)

18

(52.9%)

72

(27.2%)

Sometimes 7

(20.6%)

115

(42.4%)

9

(25.7%)

90

(33.5%)

7

(20.6%)

112

(42.3%)

Seldom 3

(8.8%)

52

(19.2%)

4

(11.4%)

26

(9.7%)

3

(8.8%)

60

(22.6%)

Never 0

(0%)

16

(5.9%)

0

(0%)

7

(2.6%)

0

(0%)

7

(2.6%)

How Chinese Learn Mathematics: Perspectives From Insiders

244

Table 4 suggests that students read textbooks most often during the

class and least before the class. An ordinal regression (PLUM) further

revealed that students read textbooks significantly more frequently

during the class than after the class at the 0.001 level. Teachers’ direct

instruction on reading textbooks during the class might be one

motivation for students to do the in-class reading. It can be seen from the

table that more than 88% of the teachers at least “sometimes” required

their students to read textbooks in class.

The classroom observation found that the majority of teachers

(62.5%) asked students to read textbooks in class, including reading main

texts and example problems. Most lessons with reading instruction were

normal lessons (16 out of 18). The results from the follow-up interview

consistently revealed that the majority of teachers at least “sometimes”

asked their students to read textbooks in class. However, in students’

views, the main reason for them to read textbooks in class is not

teachers’ requirement on reading but their own desires (teachers’

instruction: 21.1%, self motivations: 70.5%, other reasons: 8.4%).

Table 4 also shows that teachers less frequently required students to

read the textbooks during the class than to do so during the other two

time periods. No statistically significant differences were found among

teachers from different comparison groups about this requirement. In the

interviews, many teachers also expressed their preference for students to

read textbooks before classes. In doing so, teachers expected students to

have some ideas about what they were going to learn in the next lesson

so as to achieve better learning effects. However, some teachers also

doubted whether their students would really read textbooks before and

after classes. One teacher from School Cohort II pointed out that she

required students’ parents to check students’ reading outside the

classroom. Students’ self-reports showed that nearly 25% of the students

“seldom” or “never” read textbooks before or after classes, and most of

them (68.2%) claimed that they did not read textbooks because they did

not have such a habit.

A further analysis with respect to different comparison groups of

students revealed that the students in Fuzhou read textbooks both before

classes and during classes significantly more frequently than their peers

in Kunming (Before: χ2 [4, N = 271] = 20.79, p < .001; During: χ2 [4, N =

Textbook Use Within and Beyond Chinese Mathematics Classrooms 245

269] = 12.73, p < .05]. Further study is needed to explore why there is

such a difference. Nevertheless, no significant difference was found on

teachers’ requirement on reading during the two time periods between

the two cities.

3.2 Use of various parts of texts

In the PEP textbooks, a regular chapter usually consisted of several parts:

introduction, main text (including example problems and their solutions),

various exercise problems4 (i.e., Drill, Practice, Revision, and Self-Test),

summary and revision, and enrichment materials5 (i.e., Think-it-Over,

Read-it, and Do-it6) (see more details in Zhu, 2003). To investigate how

these components of the texts are used by both students and teachers,

specific questions were designed in the questionnaires.

Mathematics textbooks, particularly Asian ones, normally devoted

much space to example problems and their solutions, including

explanations. For instance, earlier studies found that 63% of text space in

Japanese textbooks and 67% in Chinese textbooks was used for worked-

out examples and related explanations (Carter, Li, & Ferrucci, 1997;

Mayer, Sims, & Tajika, 1995;). As Love and Pimm (1996) noted,

examples were intended to offer students a model to be emulated in the

exercises which followed. In this sense, examples with their explanations

played a very important role in the process of teaching and learning.

In the present study, we found that in all but two normal lessons

(92%), teachers presented examples to students in the classes observed.

Where the examples used by the teachers in class came from was one

of our concerns. Questions 15 to 17 in the teacher questionnaire were

targeted on this issue. The results showed that the percentages of

4 According to the textbook authors, “Drill” problems (练习) are mainly for in-class use

for consolidation; “Practice” problems (习题) are mainly for in-class or after-class

assignment; “Revision” problems (复习题) are designed for chapter revision; and “Self-

Test” problems (自我测验题) are for self checking after completing learning of one

chapter (PEP, 1993a, 1993b).

5 Not all chapters have enrichment materials.

6 Only geometry books have problems entitled “Do-it”, which provide students with

“hands-on” activities.

How Chinese Learn Mathematics: Perspectives From Insiders

246

examples illustrated in class which were from textbook examples varied

from 10% to 100%, with an average being 74.4%. Nevertheless, the

teachers also reported that around 65% of in-class examples were taken

from various types of non-example problems provided in the books. It

seems to us that some teachers were not clearly aware how they selected

in-class examples.

The results from classroom observations showed that only around

35.2% of the in-class examples were textbook examples. The main texts

also contained some worked-out problems which were not designed as

examples. In the classroom observations, quite a number of teachers used

these problems as in-class examples. Including these problems, we found

that the corresponding percentage of in-class examples being worked-out

problems in the textbooks was 52.7%. In addition, no exercise problems

in the textbooks were used by the teachers as in-class examples in the

classes observed.

The questionnaire survey revealed that about 81.7% of the textbook

examples were used by teachers in their classroom teaching practices.

We also compared the examples actually used in the classes observed

and the example problems presented in the corresponding texts, and the

result showed that 80% of the textbook examples were used in class by

those teachers who were observed. When including all the non-example

problems in the main text, we found that the percentage reached 88.2%.

The classroom observations found that 75% of the teachers who

conducted normal lessons used examples which were not from textbooks

or simply designed by themselves. In the 17 normal lessons observed in

Kunming, teachers presented a total of 52 in-class examples, while there

were only 20 example problems available in the corresponding texts.

Although the teachers used nearly all of these textbook examples as in-

class examples and some of them further used the non-example worked-

out problems in the main text, 22 in-class examples were either taken

from other teaching materials or designed by the teachers themselves.

In the interview, all the teachers reported that in general they would

use textbook examples as in-class examples, meanwhile they also often

selected in-class examples from other types of problems in the textbooks

and other reference books. Although no teacher claimed that the shortage

of textbook examples was one reason for he/she used examples from

Textbook Use Within and Beyond Chinese Mathematics Classrooms 247

outside materials, most teachers indicated that the purpose for them to

resort to other resources was to deepen students’ understanding, widen

students’ views, and promote the development of students’ ability in

problem solving. It appears that the examples provided in the textbooks

were not sufficient in both quantity and quality for teachers to use in

their classrooms.

With respect to the way in which the textbooks presented the

solutions to the example problems, we found that the majority of teachers

(75.8%) “always” or “often” used the ways presented in the textbooks

but with some modifications. No one reported that he/she strictly

followed the textbooks all the time, and a minority (18.5%) of the

teachers said that they often used the ways different from the textbooks.

By the way, further analysis revealed that female teachers used the ways

presented by the textbooks without modifications significantly more

frequently than their male colleagues, χ2 (2, N = 30) = 6.47, p < .05.

Moreover, male teachers tended to use different ways from the textbooks

more often than female teachers and the difference was statistically

significant at the 0.05 level (χ2 [2, N = 27] = 8.00).

The classroom observations also showed that many teachers

illustrated the examples in the ways which were presented in the

textbooks. Moreover, the teachers in many cases added some alterative

solutions to those example problems, either demonstrated by themselves

or asked students to provide alterative solutions. In the observed classes,

we did not find any teacher who used the ways significantly different

from the textbooks.

During the interviews, teachers were asked why they in the observed

lessons used some different ways from the textbooks for presenting the

examples. Almost all the teachers told us that they would basically

follow the ways presented in the textbooks, since those ways were

usually fundamental, simple, and easy for students to understand. Using

the ways in textbooks was also convenient for students to do revision

after class. However, the ways in the textbooks might not be best ones so

that they often provided students with alterative ways to broaden

students’ minds and encourage them to think.

Various exercise problems designed for students to work through are

another important component of mathematics textbooks. As reported

How Chinese Learn Mathematics: Perspectives From Insiders

248

earlier, teachers often selected in-class exercises and homework tasks

from this component of the books. Teachers’ self-reports in the

questionnaire showed that the problems under the rubrics of “Drill” and

“Practice” had the highest rates of utilization, whereas the problems

entitled “Think-it-Over” were used least (see Figure 2).

problems problems

Used Think-it-Over

p

roblems

Used

Drill

problems

Used

Practice

problems

Used

Review

problems

39%

30%

13%

6%

3%

1%

3%

1% 1%

3%

Unused Self-Test Used Self-Test

Unused Practice

problems

Unused Drill

problems

Unused Think-it-Over

problems

Unused Review

problems

Figure 2. The use of various types of problems in the textbooks by teachers

The t-tests revealed that the teachers used the various types of

exercise problems significantly differently across the problem categories.

The results are displayed in Table 5.

It can be seen that the teachers used significantly fewer problems

under the rubric “Think-it-Over” than all the other types of problems in

class. The difficulty of these problems could be one possible reason. An

analysis on the features of the various types of problems in the textbooks

revealed that more non-routine problems were in these exercise problems

(Drill: 0.3%, Practice: 0.1%, Review: 0%, Self-Test: 0%, Think-it-Over:

9.5%; see more details in Zhu, 2003). According to the textbook authors,

the purpose of providing “Think-it-Over” problems was to enrich

students’ knowledge and inspire their interest. The contents involved in

these problems can go beyond the normal curriculum requirement (PEP,

Textbook Use Within and Beyond Chinese Mathematics Classrooms 249

1993a, 1993b). Therefore, it is reasonable that the teachers used those

problems less frequently than other problems.

Table 5

T-test Results on Teachers’ Use of Various Exercise Problems Offered in the Textbooks.

Drill Practice Review Self-Test Think-it-Over

Drill – 1.153 3.01** 2.47* 4.29***

Practice – 3.06** 1.981 4.02***

Review – 0.87 3.04*

Self-Test – 2.53*

Think-it-Over –

Note. *p < .05, ** p < .001, *** p < .001. “Drill” problems were not used significantly more

than “Self-Test” problems, but the difference approached significance, p = .056.

From the table, we can also find that the teachers used significantly

more “Drill” and “Practice” problems than “Review” and “Self-Test”

problems. The main reason appears to be the fact that “Drill” and

“Practice” problems were provided for each lesson to reinforce what

students have learned, and hence were fundamental in students’ learning,

whereas “Review” problems were provided at the end of a chapter for

chapter review purpose.

Although “Self-Test” problems were also offered at the end of a

chapter, they were not as challenging as those in “Review” and

“Practice” (Group B7), in terms of the number of steps involved in

problem solutions. As described on the book preface, “Self-Test”

problems were intentionally designed for students’ self-checking whether

they have achieved basic learning objectives (PEP, 1993a, 1993b). Since

these problems were particularly set for students’ self-learning, it was

reasonable that teachers did not use them much but left them to students

themselves.

In general, there was no much difference on the use of various types

of problems offered in the textbooks by the teachers across different

comparison groups. The only significant difference was detected on the

use of “Self-Test” problems. Experienced teachers and users used

7 The textbooks divided problems in both “Practice” and “Review” into two groups: A

and B. Problems in Group A were basic ones and meant for all the students, whereas

those in Group B were relatively challenging and meant for students of higher ability.

How Chinese Learn Mathematics: Perspectives From Insiders

250

significantly more of these problems than novices at the 0.05 level.

Being more familiar with teaching contents and the problem features

could be one possible reason for the difference. Moreover, the concern

that some students might not do these problems without teachers’

requirement so that they would possibly miss something important (e.g.,

specific problem solving skills) could also be possible motivation for the

experienced teachers/users to more often use the “Self-Test” problems.

The teacher questionnaire revealed that while teachers in Kunming

did not use significantly more “Self-Test” problems than those in Fuzhou,

the difference approached significance, t (13) = -2.14, p = .051. However,

in the classroom observations, we did not see any teacher from both

cities used these problems in actual classroom teaching. It might be

because the fact that only a limited number of lessons were observed.

Besides the frequency of using the different types of problems,

teachers were asked about the functions that these problems were used to

serve in their instruction. Five particular usages were defined in the

questionnaire. They were “in-class exercises”, “homework”, “in-class

examples”, “tests”, and “discussions”. Figure 3 displays the number of

teachers who used the various types of exercise problems for the

different purposes.

Figure 3. The usage of various types of exercise problems provided in the textbooks

Note. Three teachers did not give answers to the corresponding questions in the

questionnaire.

0

5

10

15

20

25

30

35

In-class exercises Discussions Homework In-class examples Tests

Drill Think-it-Over Practice Review Self-Test

Textbook Use Within and Beyond Chinese Mathematics Classrooms 251

It can be seen that all the teachers used “Drill” problems for in-class

exercises, while around 30% of the teachers also used these problems for

students’ homework or in-class discussions. It was quite consistent with

the book authors’ intentions, as described on the book preface (PEP,

1993a, 1993b). In the classroom observations, we also found that in the

majority of lessons (55.6%), teachers asked students to do the “Drill”

problems in class.

The figure shows that both “Practice” and “Review” problems were

more used for students’ homework. Consistently, in the observed lessons,

the majority of teachers (81.8%) assigned homework from “Exercise”

sections, although many teachers also often used other materials (45.8%)

or self-designed problems (20.8%) for homework assignment. Moreover,

only one teacher from each city selected homework from “Revision” in

our observations and both lessons were understandably review lessons.

In the interview, the teachers reported that around 65.4% of students’

homework was assigned from the textbooks.

Compared to the other types of problems, “Self-Test” problems were

more often used for in-class tests by the teachers. It was consistent with

the textbook authors’ intentions, as mentioned before. In addition, many

teachers (54.5%) reported in the questionnaire that they also assigned

these problems as students’ homework. Nevertheless, this practice was

not found in the classroom observation.

The teacher questionnaire data showed that the majority of teachers

(75.8%) used “Think-it-Over” problems for in-class discussions. As said

earlier, those problems were designed to enrich students’ knowledge and

inspire their interest, moreover a higher percentage of problems in this

section were non-routine problems (Zhu, 2003). Therefore, the result

seems understandable.

Figure 2 revealed that around 14% of all types of the problems in the

textbooks were not used by the teachers in their teaching. In the student

questionnaire, five questions were particularly designed on these

unassigned problems. Table 6 lists the number (percentage) of students

who worked on these unassigned problems under each type. The results

showed that many students did the unassigned problems.

In general, there was no significant difference among the students

from different comparison groups about the unassigned problems, except

How Chinese Learn Mathematics: Perspectives From Insiders

252

students from low performing schools did significantly more unassigned

“Self-Test” problems than those from both high (χ2 [4, N = 180] = 9.67,

p< .05) and average (χ2 [4, N = 180] = 16.92, p < .01) performing schools.

It was found that all the “Self-Test” problems were routine problems and

the majority of them (58.6%) were single-step problems (Zhu, 2003). It

appears reasonable that student in School Cohort III were relatively slow

learners so that they might need to do more elementary problems. When

answering the reason for students to do these unassigned problems, many

students indicated that it was their own choice. Only about 12.8% of the

students claimed that the reason was that their teachers required them to

do so and 7.8% of the students reported that the reason is that their

parents asked them to do so.

Table 6

Students’ Usage of Unassigned Exercise Problems Offered in the Textbooks

Drill Practice Review Self-Test

Think-it-

Over

Almost all 27 (10.0%) 21 (7.8%) 22 (8.2%) 31 (11.5%) 16 (6.0%)

Most 58 (21.6%) 51 (19.0%) 60 (22.4%) 51 (18.9%) 38 (14.3%)

About half 75 (27.9%) 84 (31.2%) 69 (25.7%) 66 (24.4%) 47 (17.7%)

Some 72 (26.8%) 73 (27.1%) 83 (31.0%) 74 (27.4%) 85 (32.1%)

Very few 37 (13.8%) 40 (14.9%) 34 (12.7%) 48 (17.8%) 79 (29.8%)

On the unassigned “Review” problems, the study found that students

in Fuzhou did significantly more than their peers in Kunming at the 0.05

level (χ2 [4, N = 268] = 11.79). Again, the motivation of doing these

problems was mainly from students themselves (69.3%).

Like many other textbooks, all but two textbooks (i.e., Geometry II

and Geometry III) in the PEP series provided answers to some non-

maintext problems at the back of the books. These answers were

prepared for students’ self-checking (PEP, 1993a). Figure 4 depicts the

usage of the answer sections by the students according to the

questionnaire data.

Textbook Use Within and Beyond Chinese Mathematics Classrooms 253

Always

14%

27%

Often

27% sometim

e

s

seldom

19%

Never

13%

Figure 4. Use of answer sections by students

The results showed that only about 40% students often or always

used the answer sections for self-checking. One reason for the low usage

of the answer sections provided in the textbooks might be that the

exercise problems were relatively easy for students, and hence they did

not feel such a need to check the answers. Another reason might be that

some students had not developed such a habit of self-checking. By the

way, it is interesting to note that students in Fuzhou used the answer

sections significantly more frequently than those in Kunming at the 0.05

level (χ2 [4, N = 266] = 13.21).

“Do-it” problems were only included in the PEP geometry textbooks.

In Geometry II there were only four problems under this category. These

problems were intended to provide students extracurricular hands-on

activities (PEP, 1993b). According to the teacher questionnaire, there

were actually more than 54% of the teachers who “always” or “often”

used these problems for in-class activities and no one claimed that he/she

“never” used such problems. Nevertheless, in the classroom observation,

there were three lessons (1 in Fuzhou and 2 in Kunming) whose

corresponding texts had “Do-it” problems, but no one used the problems

in classes observed.

As reported earlier, the majority of teachers required their students to

read texts before, during, or after class. We further asked in the

questionnaire how frequently the teachers required students to read the

various parts of texts. They included the main text, “Summary and

Review” provided at the end of each chapter, which summarized all the

key points in that chapter so as to provide a convenient source for

How Chinese Learn Mathematics: Perspectives From Insiders

254

students to do revision, and “Read-it” which was mainly for enrichment

purpose and not an essential part of the course requirement (PEP, 1993a,

1993b). The results showed that the teachers most often asked students to

read “Summary and Review”, and then the main text, but least for

“Read-it”.

The classroom observations revealed that teachers seldom discussed

the “Summary and Review” section with students in class. We believe

that teachers would more likely leave it for students’ self-learning. In

addition, as pointed out in the preface of the textbooks, the requirement

explained in “Summary and Review” was slight higher than that being

reflected in the main texts within the chapter. More reading requirements

on this part of texts from teachers were therefore understandable.

Concerning the main texts, a few teachers in the interview pointed

out that if students had understood what had been taught in class, it was

not necessary to ask them to read the corresponding texts again. In

contrast, some teachers believed that it was good for students to read

main texts before they started to do their homework. Therefore, more

diversity was found among the teachers in their requirement for students’

reading of this part compared to the part of “Summary and Review”. The

classroom observations also found that some teachers asked their

students to read the main texts in class. Moreover, the results from the

questionnaire showed that the longer the teachers used the books, the

more frequently they would asked their students to read the main texts, χ2

(3, N = 33) = 7.54, p < .05.

Similar questions were also included in the student questionnaire.

Consistently, the students reported that they read “Read-it” least

frequently and the difference between this part and the other two parts

reached statistically significant level. In particular, only 4.6% of the

students “seldom” or “never” read the main texts, and the percentage for

“Summary and Review” was 20%. In addition, it was found that students

in Fuzhou significantly more frequently read both text parts than their

peers in Kunming (Main text: χ2 [4, N = 259] = 13.14, p < .01; Summary

and Review: χ2 [4, N = 255] = 9.99, p < .05). In contrast, teachers’ self-

reports in the questionnaire showed that teachers in Kunming required

their students to read “Summary and Review” with a significantly higher

frequency than those in Fuzhou, χ2 (3, N = 33) = 8.47, p < .05. Given the

Textbook Use Within and Beyond Chinese Mathematics Classrooms 255

complexity of the teaching and learning process, the discrepancy

between teachers’ teaching and students’ leaning seems plausible.

Nevertheless, a further discussion of this discrepancy is beyond the scope

of this chapter.

Table 7 presents a summary of descriptive statistics based on the data

collected from the questionnaires. The gap between teachers’

requirement and students’ practice can be also found from the table.

Table 7

Teachers’ Requirements (TR) on Reading and Students’ Corresponding Practice (S)

Main Text Read-it Summary and Review

TR S TR S TR S

Always 5

(15.2%)

115

(44.4%)

4

(12.1%)

32

(12.5%)

11

(33.3%)

36

(14.1%)

Often 22

(66.7%)

82

(31.7%)

19

(57.6%)

60

(23.5%)

16

(48.5%)

91

(35.7%)

Sometimes 5

(15.2%)

50

(19.3%)

8

(24.2%)

110

(43.1%)

5

(15.2%)

77

(30.2%)

Seldom 1

(3.0%)

10

(3.9%)

2

(6.1%)

43

(16.9%) 1 (3.0%) 42

(16.5%)

Never 0

(0%)

2

(0.8%)

0

(0%)

10

(3.9%)

0

(0%)

9

(3.5%)

3.3 Some other issues

In the questionnaires, teachers and students were respectively requested

to evaluate the importance of various instructional materials in their

mathematics teaching and learning, with a 5-point Likert scale from the

highest “very important” to the lowest “no importance”. The majority of

teachers (90.9%) and students (91.5%) chose the highest two evaluations

(i.e., “very important” or “important”) for the textbooks (student edition).

None of the teacher and only 3 out of 259 students rated the textbooks as

“little important” or “no importance”, respectively. In addition, teachers

How Chinese Learn Mathematics: Perspectives From Insiders

256

in Kunming rated the importance of textbooks significantly higher than

those in Fuzhou, χ2 (2, N = 33) = 6.42, p < .05.

Overall, the questionnaire surveys showed that textbooks (student

edition) were the most important materials in both teachers’ teaching and

students’ learning. To students, the importance of the textbooks was

significantly higher than that of any other learning materials at the 0.001

level. Consistently, the data revealed that the majority of teachers (84.8%)

believed that the textbooks were also “very important” or “important” in

students’ learning of mathematics.

According to teachers’ responses, the next two important teaching

materials to their teaching were school mathematics syllabus and

national mathematics standards. It is somehow surprising to us that the

teachers from both cities gave a relatively low evaluation to the

importance of the textbooks of teacher edition. We think it suggests that

only the textbooks of student edition, but not teacher edition, is essential

to teachers, especially experienced teachers.

The last question in both teacher and student questionnaires asked

whether there had been changes in their textbook use since they became

mathematics teachers (for teachers) or from year JH1 to year JH2 (for

students). The results were displayed in Figure 5.

Students Teachers

Little 9%

It can be seen that teachers made more changes than their students in

textbook use. In particular, only 42% of the students, but 91% of the

teachers had some or big changes in their textbook use.

Figure 5. Changes in textbook use by teachers and students

Big

changes

Some changes

73%

18%

changes

Some

changes 35%

Big

changes

7%

22% No

changes

Little

changes

36%

Textbook Use Within and Beyond Chinese Mathematics Classrooms 257

An open-ended sub-question was included in the last question to

invite students and teachers to describe what kinds of changes they had

made in textbook use. The most frequently cited change by the students

was that they started to read the texts more (main text [1]8, Example [11],

Summary [4], Read-it [6]). Many students reported that they did more

preview (18) and review (7) this year than the last year. Moreover, quite

a number of students also mentioned that they did more unassigned

problems in the textbooks now than before, and six students particularly

cited the problems under the rubric “Think-it-Over”.

The last question in the student questionnaire further asked the

reasons for the changes in their textbook use. Several reasons were

identified by the students. One main reason was that the mathematics at

JH2 becomes more challenging than that at JH1, in terms of both the

amount of content (10) and its difficulty level (30). The second reason

was that many students (41) realized that mathematics was increasingly

important to them, although five of them just related the importance of

mathematics to school examinations. It is interesting to note that there

were four students attributed their changes in textbook use to the

textbook developers. In particular, two of them noted that since the

textbooks made changes, they made changes correspondingly. A few

students also reported that they changed the ways in which they used

textbooks in mathematics learning because of their teachers (4) or

parents (1).

The teacher questionnaire data showed that the changes made by the

teachers were more related to the ways in which they presented the topics

and structured their classroom instruction. The most obvious change was

that teachers encouraged more participation from students, including

more discussions and less repetition of what has been said in the

textbooks. Many teachers believed that learning through self-discovery

can help students to get a better and deeper understanding about what

they have learned. Four teachers claimed that their teaching was less

dependent on textbooks now and the ways in which they used textbooks

8 The number in the brackets refers to the number of students who gave the

corresponding answers.

How Chinese Learn Mathematics: Perspectives From Insiders

258

became more flexible, such as reorganizing the order of topics presented

in the textbooks.

In the interview, many teachers attributed their changes in textbook

use to the growth of their teaching experience and familiarity with the

textbooks that they had used for teaching. One teacher explained, “When

I just began to be a teacher, I was not familiar with the textbooks I used

and my teaching thus followed the textbooks very closely. Along with

the increase in teaching experience, I gained a deeper understanding of

the textbooks and hence the ways in which I dealt with the textbooks

became more flexible.” Getting to know more learning theories, such

constructivism, was another important factor that motivated teachers to

make changes in their textbook use. In addition, some teachers pointed

out that some changes they made were based on their own reflections on

the effectiveness of their teaching and correspondingly students’

performance. The change in the characteristics of students in class was

also one factor for teachers to make changes in using textbooks. Many

teachers also related their changes in textbook use to the development in

mathematics education, especially the on-going development of “Quality

Education”, a change from education for test to education for students’

overall quality.

4 Summary and Conclusions

The results presented and discussed above provided us with useful

empirical evidence and insight on what role textbooks play in the

teaching and learning of mathematics in Chinese educational settings and

how they shape the way in which Chinese students learn mathematics.

Overall, the study revealed that textbooks were the main resource for

mathematics teachers in their classroom teaching. In particular, textbooks

were the most important source for teachers to make decisions on what to

teach and how to teach, and the majority of instructional time was

structured around the textbooks. In addition, teachers largely followed

the textbooks closely in their use of various parts of the textbooks,

though noteworthily about half of the in-class examples were from other

resources due to the insufficiency in both the amount and quality of the

Textbook Use Within and Beyond Chinese Mathematics Classrooms 259

examples offered in the textbooks, and moreover many teachers also

often introduced alternative solutions to the example problems.

Textbooks were also the main resource for students’ learning of

mathematics. In particular, most problems for students’ in-class exercises

and homework were taken from textbooks, and many students also read

the textbooks and actively worked on the unassigned exercise problems

in the textbooks.

On the other hand, the study also found that many teachers have

changed the ways in which they used the textbooks for classroom

teaching over the years, and particularly they used textbooks in a more

flexible way, with the main reason being the growth of their teaching

experience and knowledge of the textbooks.

In general, the study revealed more similarities rather than

differences in the textbook use by the teachers and students within and

beyond the Chinese classroom. In particular, the study found there were

overall no significant differences between teachers with different genders,

experiences, from different regions and schools in their use of textbooks,

though there were some significant differences between students in the

two cities in their use of textbooks. Due to the design of this study, we

were not able to address this issue in a more detailed way. It would be

interesting and helpful to further study what it signals in mathematics

instruction and why there exist such differences.

References

Ball, D. L., & Cohen, D. K. (1996). Reform by the book: What is – or might be – the role

of curriculum materials in teacher learning and instructional reform? Educational

Researcher, 25(9), 6-8, 14.

Barr, R. (1988). Conditions influencing content taught in nine fourth-grade mathematics

classrooms. The Elementary School Journal, 88(4), 378-410.

How Chinese Learn Mathematics: Perspectives From Insiders

260

Beaton, A. E., Mullis, I. V. S., Martin, M. O., Gonzalez, E. J., Kelly, D. L., & Smith, T.

A. (1996). Mathematics achievement in the middle school years: IEA’s Third

International Mathematics and Science Study. Chestnut Hill, MA: TIMSS

International Study Center, Boston College.

Bierhoff, H. (1996). Laying the foundations of numeracy: A comparison of primary

school textbooks in Britain, Germany and Switzerland. Teaching Mathematics and

its Applications, 15(4), 1-157.

Carter, J., Li, Y., & Ferrucci, B. J. (1997). A comparison of how textbooks present

integer addition and subtraction in PRC and USA. The Mathematics Educator, 2(2),

197-209.

Fan, L., & Kaeley, G. S. (2000). The influence of textbook on teaching strategies: An

empirical study. Mid-Western Educational Researcher, 13(4), 2-9.

Flanders, J. R. (1987). How much of the content in mathematics textbooks is new?

Arithmetic Teacher, 35(1), 18-23.

Freeman, D. J., & Porter, A. C. (1989). Do textbooks dictate the content of mathematics

instruction in elementary schools? American Educational Research Journal, 26(3),

403-421.

Fujii, T. (2001). The changing winds in Japanese mathematics education. Mathematics

Education Dialogue, 2001(November). Retrieved June 19, 2002, from http://www.

nctm.org/dialogues/2001-11/20011105.htm.

Fuller, B., & Clarke, P. (1994). Raising school effects while ignoring culture? Local

conditions and the influence of classroom tools, rules, and pedagogy. Review of

Educational Research, 64(1), 119-157.

Heyneman, S. P., Farrell, J. P., & Sepulveda-Stuardo, M. A. (1978). Textbooks and

achievement: What we know. Washington, DC: World Bank.

Krammer, H. P. M. (1985). The textbook as classroom content variable. Teaching &

Teacher Education, 1(4), 273-278.

Kuhs, T. M., & Freeman, D. J. (1979, April). The potential influence of textbooks on

teachers’ selection of content for elementary school mathematics. Paper presented at

the annual meeting of the American Educational Research Association, San

Francisco.

Lian, Y. (2000, January 27). Some grades will change to use new textbooks [In Chinese

中小学部分年级换用新教材]. Guangming Daily [In Chinese 光明日报], A2.

China.

Love, E., & Pimm, D. (1996). ‘This is so’: A text on texts. In A. J. Bishop, K. Clements,

C. Keitel, J. Kilpatrick, & C. Laborde (Eds.), International handbook of

mathematics education (pp. 371-410). Dordrecht, The Netherlands: Kluwer.

Mayer, R. E., Sims, V., & Tajika, H. (1995). A comparison of how textbooks teach

mathematical problem solving in Japan and the United States. American

Educational Research Journal, 32(2), 443-460.

McCutcheon, G. (1982, March). Textbook use in a central Ohio elementary school. Paper

presented at the annual meeting of the American Educational Research Association,

New York. (ERIC Document Reproduction Service No. ED 216968)

Nicely, R. F., Jr. (1985). Higher-order thinking skills in mathematics textbooks.

Educational Leadership, 42(7), 26-30.

People’s Education Press. (1993a). The compulsory education three-year junior

secondary school textbooks: Algebra II [In Chinese 九年义务教育三年制初级中学

教科书: 代数,第二册]. Beijing: Author.

Textbook Use Within and Beyond Chinese Mathematics Classrooms 261

People’s Education Press. (1993b). The compulsory education three-year junior

secondary school textbooks: Geometry II [In Chinese 九年义务教育三年制初级中

学教科书: 几何,第二册]. Beijing: Author.

Schiefelbein, E., & Simmons, J. (1981). The determinants of school achievement: A

review of the research for developing countries. Ottawa: International Development

Research Center.

Schmidt, W. H., Porter, A. C., Floden, R. E., Freeman, D. J., & Schwille, J. R. (1987).

Four patterns of teacher content decision-making. Journal of Curriculum Studies,

19(5), 439-455.

Sepulveda-Stuardo, M. A., & Farrell, J. P. (1983). The use of textbooks by teachers and

students in learning and teaching. In E. Schiefelbein, J. P. Farrell, & M. A.

Sepulveda-Stuardo (Eds.), The influence of school resources in Chile: Their effect

on educational achievement and occupational attainment (pp. 72-109). Washington,

DC: International Bank Reconstruction and Development Staff Working Paper

No.530.

Shield, M. (1989). Mathematics teachers’ preferences in textbook characteristics.

Mathematics Education Research Journal, 1(1), 11-15.

Sosniak, L. A., & Stodolsky, S. S. (1993). Teachers and textbooks: materials use in four

fourth-grade classrooms. The Elementary School Journal, 93(3), 249-275.

Tyson, H., & Woodward, A. (1989). Why students aren’t learning very much from

textbooks. Educational Leadership, 47(3), 14-17.

Woodward, A., & Elliott, D. L. (1990). Textbook use and teacher professionalism. In D.

L. Elliott & A. Woodward (Eds.), Textbooks and schooling in the United States:

Eighty-ninth yearbook of the National Society for the Study of Education (Part I, pp.

178-193). Chicago, IL: University of Chicago Press.

Zeng, T. (1997). On curriculum [In Chinese 教材论]. Jiangxi, China: Jiangxi Education

Press.

Zhu, Y. (2003). Representations of problem solving in China, Singapore and US

mathematics textbooks: A comparative study. Unpublished doctoral dissertation,

National Institute of Education, Nanyang Technological University, Singapore.

Zhu, Y., & Fan, L. (2002). Textbook use by mathematics teachers at lower secondary

school level in Singapore. In D. Edge & B. H. Yeap (Eds.), Proceedings of

EARCOME-2 & SEACME-9 Conference (Vol. 2, pp. 194-201). Singapore.