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How Chinese learn mathematics. Perspectives from insiders

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
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
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
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,
How Chinese Learn Mathematics: Perspectives From Insiders
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
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
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
How Chinese Learn Mathematics: Perspectives From Insiders
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
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
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
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
3.47 3.50 4.06 3.79 3.69
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
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 . . .
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.
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
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
Always 9
Often 15
Sometimes 7
Seldom 3
Never 0
How Chinese Learn Mathematics: Perspectives From Insiders
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
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
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
1% 1%
Unused Self-Test Used Self-Test
Unused Practice
Unused Drill
Unused Think-it-Over
Unused Review
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*
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
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
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
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
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
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
27% sometim
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
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
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
Always 5
Often 22
Sometimes 5
Seldom 1
(16.9%) 1 (3.0%) 42
Never 0
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
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
Some changes
changes 35%
22% No
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
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.
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... A book Growing Up the Chinese Way (Lau 1996) was released in 1996 and in the field of mathematics, Chinese scholars saw the need of publishing a book by Chinese scholars who could introduce the Chinese learner phenomenon to the world, instead of just having non-Chinese discussing this Chinese issue. As a result, two books, How Chinese Learn Mathematics (Fan et al. 2004) and How Chinese Teach Mathematics in 2015 (Fan et al. 2015) were published. ...
... From a practical point of view, teaching through variation as a Chinese way of promoting mathematics teaching has been proved to be effective, as the Chinese students have outstanding performance in large scale international comparisons, such as those conducted in the International Assessment of Educational Progress (IAEP) 3 , the Trends International Mathematics and Science Study (TIMSS) 4 , and the Programme for International Student Assessment (PISA) 5 ; Chinese education has then attracted much attention all over the world (Fan, Wong, Cai & Li, 2004). ...
Teaching mathematics through variation appears an important topic as soon as we study task design, many teachers teaching consciously or unconsciously in varying these tasks. This thesis is situated in between China and France, crossing two traditions and cultural contexts, aiming to think fruitful interactions between them and improve the effectiveness of mathematics teaching by understanding the role and evolution of teaching through variation. Variation appears in two traditions of research, BIANSHI jiaoxue (teaching through variation) in China and didactical variables in France. We propose a preliminary model of “teaching mathematics through variation” by combining these two theoretical approaches with the Documentational Approach to Didactics. Our preliminary model distinguishes potential variation (the changes explicitly proposed by a given task, or series of tasks), actual variation (the possible changes made explicit by a teacher when integrating a task as a resource) and practical variation (the changes occurring when implementing the resource in class). Three research questions are explored: 1) What are the potential variations in the upper secondary school mathematics textbooks and other curriculum resources in China and France? 2) What are the actual variations in the Chinese and French cases to achieve the teaching goal? 3) What are the practical variations in Chinese and French cases? How does the case teachers take into account these practical variations? For addressing these issues, an analytical framework based on our initial model is proposed for studying different types of variations (contextual, representational, conceptual and procedural) in each stage (potential, actual, and practical) through teacher’s documentation work. As a critical element of our analytical framework, we propose the concept of variation path. This study allows to enlighten our questions of research, to refine our initial model and its corresponding analytical framework. It opens new perspectives for taking variation into account variation not only for a given task, but also for the enrichment of teachers’ resource systems, and for their professional development.
... On the one hand, Chinese teachers are highly respected and often regarded as knowledge authorities, responsible for teaching through an authoritative teaching style that governs classroom talk (Yu et al., 2019). On the other hand, traditional mathematics teaching emphasizes content knowledge and skills rather than creative thinking and reasoning (Cai et al., 2014;Fan et al., 2004). ...
Although classroom discourse that positions students as active participants benefits both their learning and cognitive development, teachers often find it challenging to implement dialogic instructions in the classroom. This study reports on a video-based teacher professional development (PD) program that leverages visualizations and analytics in supporting teacher change in whole-class dialogue in mathematics classrooms. Both experimental and comparison teachers (n = 24 and 22, respectively) were provided with information on dialogic instructions, and experimental teachers used the Classroom Discourse Analyzer to reflect on videos of their lessons and their peers' lessons in a year-long PD program. The intervention teachers significantly moved toward less dominant classroom talk—they reduced the number of words spoken per lesson, and their students significantly increased the number of words per turn in whole-class discussions, relative to the comparison teachers. Furthermore, analysis of the classroom discourse shows qualitative changes in the intervention teachers' discourse. PD workshop and teacher self-reflection data are analyzed to examine how visualizations and analytics in the PD program may serve as a cross-boundary object to support peer collaboration in reflective practice, and to increase teachers' awareness of their teaching development.
... It is believed that the Confucianism-oriented Chinese culture helps produce diligent pupils and dedicated teachers. China has a single national standards-based curriculum that prescribes uniform textbook contents across the country; even behaviors such as how a teacher opens his/ her lesson is hinted to be attributable to the achievement gap between China and the U.S. (Fan et al., 2004). Such studies are informative, but, their limitation is that they treated mathematics education as compartmentalized activities and failed to see the whole picture of everyday mathematics teaching and learning in the school context. ...
“What is two divided by two thirds?,” the education professor asked. “I know! I know!” Michelle raised her hand, went up to the board, took the chalk, and began her computation. “2 divided by 2/ 3…multiply 3 here and here…cross 3…cross 2…Here you go. It is 3!” Michelle was in her early 30s. She got her Master’s degree from Teachers College before coming to Syracuse for her doctorate. It was a simple problem and a sixth grader in China would most likely give the answer right away. It took her almost 2 minutes. In the United States (U.S.), it has been a popular saying that Chinese students outperform American students in mathematics, and mathematics education in the U.S. is at risk. Indeed, international assessments, such as the Programme for International Student Assessment (P.I.S.A.) of 2015 and 2018, show that students from China are ranked top. A number of factors are claimed to account for Chinese students’ top mathematics performance (Wang & Lin, 2005 ). Stigler and Hiebert ( 1999 ) examined teachers’ classroom instruction. They compared lessons taught by teachers from several countries and found that the American teachers spent a predominant amount of time on procedural matters instead of guiding students to reasoning and problem solving. They concluded that the U.S. teaching culture must be changed so as to improve students’ mathematics achievement. Meanwhile, teachers in the U.S. are identifi ed as particularly weak in mathematics knowledge. Liping Ma ( 1999 ) found that the majority of the Chinese teachers in her study demonstrated more in- depth conceptual understandings of mathematical content and had more knowledge of pedagogical content than the American teachers. It is believed that the Confucianism- oriented Chinese culture helps produce diligent pupils and dedicated teachers. China has a single national standards- based curriculum that prescribes uniform textbook contents across the country; even behaviors such as how a teacher opens his/ her lesson is hinted to be attributable to the achievement gap between China and the U.S. (Fan et al., 2004). Such studies are informative, but, their limitation is that they treated mathematics education as compartmentalized activities and failed to see the whole picture of everyday mathematics teaching and learning in the school context. Bearing this notion in mind, we were engaged in fi eldwork at two elemen�tary schools in a northeastern city in China and started to follow the imple�mentation of the New Mathematics Curriculum Reform (referred to as “the reform” for short). The decade- long investigation revealed that the schools had a data- driven quality control mechanism to monitor, evaluate, and regu�late teachers’ activities throughout the whole teaching process. The data were systematically collected from reviews of lesson plans, observation of teachers’ instruction and professional learning, examples of student work, and results of assessment. Those data provided ample evidence on teachers’ performance and students’ learning. Thus, teachers could receive timely feedback regarding their strengths and shortcomings, and make changes accordingly. This mechanism is to ensure that no student, teacher, or school is left behind. The downside of the quality control mechanism could be that it was rigid, lacked fl exibility, and even restrained individual creativity. Teachers might clone one another. Some teachers might be pressed by tight evaluation and become more concerned with their job security. They would assign an excessive amount of homework to drill students for good test scores at the cost of students’ physical and mental health. P.I.S.A. data show students in China have the highest number of study hours in all participating countries. This might offer a potential explanation for the perplexing phenomenon that Chinese students performed much better than their American peers in solving procedural problems but were not as strong in open- ended problem�solving areas (Cai, 2004 ). The Reform meant to change this, but it has not got there yet. Based on the fieldwork carried out at two elementary schools in northeastern China, the monograph details how local schools enacted the New Mathematics Curriculum Reform that was launched in early 2000. The trajectory of the reform implementation at each school was plotted out. Both schools resorted to a long- standing quality control mechanism and teaching norms to operationalize the reform ideas. The mechanism functioned by placing teachers under measurable supervision and evaluation aligned with the reform. The schools responded to the reform following school people’s raising practical concerns, as well as the established school culture. Merits School arrived at a “two- faced strategy” to cope with the reform. Pioneer School managed to maintain a balance between promoting reform peda�gogy and maintaining good test rankings. Both schools marginally involved parents in the implementation of the reform. This study suggests that to achieve success, reformers need to place equal emphasis on the transform�ation of teachers as well as local policymakers. This book enriches the existing literature on the implementation of math�ematics curriculum reform at the school level and brings insights into the schools’ implementation decisions, which will appeal to policymakers, curric�ulum researchers and administrators.
... Considerable research was conducted to account for Chinese students' achievements in international studies by Chinese scholars and educators. Part of this research was reported through How Chinese learn mathematics (Fan et al., 2004), How Chinese teach mathematics (Fan et al., 2015), and How Chinese teach mathematics and improve teaching (Li & Huang, 2013). The Chinese scholars not only depicted the on-going practice and reform in mathematics education in China from an insider's view, but also examined Chinese mathematics education as a part of international mathematics education. ...
As part of a large reciprocal learning partnership project between Canada and China, this study explored Canadian teachers’ perceptions of mathematics teaching in elementary schools in China. Using reciprocal learning and Activity Theory as the theoretical lens, we collected data, i.e., classroom observations, group discussion, and informal exchanges from teachers in a pair of research sister-schools in Canada and China. Qualitative data analyses revealed four themes in Canadian teachers’ perceptions of the characteristics of Chinese mathematics teaching: an active teacher-student interaction model of questioning-responding, a mathematical knowledge-package summary at the end of each lesson, integration of the history of mathematics into teaching, and the development and implementation of well-structured lessons. Contributions, implications, and limitations of the study in mathematics education and research are discussed.
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The field of mathematics education research has been promoting problem-solving-based mathematics instruction (PS-based MI) to afford opportunities to develop students’ conceptual understanding and problem-solving abilities in mathematics. Given its usefulness, there is still little knowledge in the field about how it can afford such opportunities in real classrooms. In this study, an attempt was made to make in-depth observations of such classrooms from the perspective of variation. We examined the differences in the space of learning provided by two lessons of the same teacher in two Ethiopian primary school classrooms. Based on the literature, we identified three key aspects for analysis: mathematical tasks, lesson structure and classroom interaction patterns. Our analysis showed that, even though both lessons focused on the same topic of solving linear inequalities, they were enacted differently. The lesson that employed a PS-based MI approach constituted a wider space of learning than the lesson employing a conventional approach. This study demonstrates the usefulness of our analytical approach for describing and documenting PS-based MI practice, and for qualitatively interpreting the differences in what is mathematically made available to learn. We suggest that it can provide guidelines for mathematics teachers to reflect upon and to enhance learning spaces in their own classrooms.
Technical Report
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Öğretmenlerden ders kitabının sunduğu pedagojik potansiyeli öğrenme ortamlarında öğrencilerin öğrenmesini destekleyecek biçimde en üst seviyede kullanmaları beklenir. Bu nedenle öğretmenlerin öğrenme ortamlarında ders kitabı kullanımını bütünsel olarak anlamanın onların etkili ders kitabı kullanımını desteklemek için önemli olduğu araştırmacılar tarafından vurgulanmıştır. Rapor edilen bu araştırmanın amacı öğretmenlerin MEB tarafından sağlanan ders kitaplarını öğrenme ortamlarında ne sıklıkla ve hangi amaçla kullandıklarını incelemektir. ................................................................................................................& Teachers are expected to exploit the full pedagogical potential offered by the textbook in a way that promotes students’ learning in learning environments. For this reason, researchers have emphasized that a holistic understanding of teachers’ use of textbooks in learning environments is important in order to support their effective use of textbooks. The aim of the research study reported here is to examine how often and for what purpose(s) teachers use textbooks provided by the Ministry of National Education of Türkiye (MoNE) in learning environments.
In this survey paper we focus on mathematics learning in Chinese contexts, as a way to contribute to broader discussions about mathematical learning. We first review the features of Chinese students’ mathematical learning depicted in the literature, followed by a review of student mathematical learning in recent Chinese research journals. This leads to an introduction of the papers on Chinese students’ learning in this issue. For Chinese students’ learning contexts, we discuss four aspects, namely, classroom instruction, teachers’ professional learning, curriculum materials, and learning outside of school. For each context, we review the literature findings on the identified features, introduce emerged practices and most recent policies under the reformed era, and discuss the relevant papers in this special issue. Whenever possible, we connect findings on Chinese students’ learning with the associated contexts and relate these findings in the Chinese contexts to findings in the broader world context. We conclude this survey paper with possible lessons learned from Chinese students’ learning features and from the varied Chinese contexts. In particular, we discuss these aspects from culturally contextualized and semantically decontextualized dimensions, which is expected to facilitate broad international discourse centering on the three questions proposed at the end of this paper.
This study investigated the characteristics of high-quality mathematics teaching in China following the launch of a new standard curriculum. Data was gathered through video-recorded observations of lessons that won a national teaching contest. We identified and examined the characteristics of the instructional practices through six domains: (1) the mathematics, (2) cognitive demand, (3) classroom management (4) equitable access to mathematical content, (5) agency, authority, and identity, and (6) formative assessment. The results indicated that a well-managed classroom and low level of formative assessment were salient features of the observed lessons. In most cases, though students had a chance to say or explain things, their ideas were not explored or built upon. The majority of the mathematics task designs offered possibilities for “student struggle,” but teaching practices tended to “scaffold away” the challenges, which reduced cognitive demand for students. Good mathematics instructional practices are nested in underlying social and cultural values and norms. Implications for practice and future research are presented.
Concrete materials have a long history in the mathematics classroom, although they have not always been readily accepted or used appropriately. They disappeared when written computational methods arose and little premium was placed on understanding the algorithms being learned. Comenius and Pestalozzi began the process of reintroduction, with Montessori and many others in the present century providing new materials and new rationales for their use, so that today one finds hundreds of ‘manipulatives’ available. Arguments have persisted, however, as to whether common tools from daily life might be better than specially constructed educational materials and whether, in fact, all such materials might do more harm than good. Educational materials are not miracle drugs; their productive use requires planning and foresight.
Contends that individual teachers have ultimate control over what content is taught in their classrooms. Reports a study of the factors which influenced the curriculum decision-making of 18 elementary teachers. (BSR)
This brief report compared the lesson on addition and subtraction of signed whole numbers in three seventh-grade Japanese mathematics textbooks with the corresponding lesson in four U.S. mathematics textbooks. The results indicated that Japanese books contained many more worked-out examples and relevant illustrations than did the U.S. books, whereas the U.S. books contained roughly as many exercises and many more irrelevant illustrations than did the Japanese books. The Japanese books devoted 81% of their space to explaining the solution procedure for worked-out examples compared to 36% in U.S. books; in contrast, the U.S. books devoted more space to unsolved exercises (45%) and interest-grabbing illustrations that are irrelevant to the lesson (19%) than did the Japanese books (19% and 0%, respectively). Finally, one of the four U.S. books and all three Japanese books used meaningful instructional methods emphasizing (a) multiple representations of how to solve worked-out examples using words, symbols, and pictures and (b) inductive organization of material beginning with familiar situations and ending with formal statements of the solution rule. The results are consistent with classroom observations showing that Japanese mathematics instruction tends to emphasize the process of problem solving more effectively than does U.S. mathematics instruction (Stevenson and Stigler, 1992).
The purposes of this investigation were to (a) describe teachers' styles of textbook use and (b) examine the overlap between content taught and textbook content in elementary school mathematics. Using daily teacher logs and a three-dimensional classification system as guides, trained raters generated detailed classifications of all problems presented in books and all content presented to students over the course of an entire school year. The results of analyses of overlap between textbook content and content taught challenge the popular notion that elementary school teachers' content decisions are dictated by the mathematics textbooks they use In each classroom studied, there were important differences between the curriculum of the text and teachers' topic selection, content emphasis, and sequence of instruction.
How educators and researchers define and study school effectiveness continues to be shaped by two divided camps. The policy mechanics attempt to identify particular school inputs, including discrete teaching practices, that raise student achievement. They seek universal remedies that can be manipulated by central agencies and assume that the same instructional materials and pedagogical practices hold constant meaning in the eyes of teachers and children across diverse cultural settings. In contrast, the classroom culturalists focus on the implicitly modeled norms exercised in the classroom and how children are socialized to accept particular rules of participation and authority, linguistic norms, orientations toward achievement, and conceptions of merit and status. It is the culturally constructed meanings attached to instructional tools and pedagogy that sustain this socialization process, not the material character of school inputs per se. This article reviews how these two paths of school-effects research are informed by work conducted within developing countries. First, we discuss the school’s aggregate effect, relative to family background, within impoverished settings. Second, we review recent empirical findings from the Third World on achievement effects from discrete school inputs. An emerging extension of this work also is reviewed: How input effects are conditioned by the social rules of classrooms. Third, we illustrate how future work in the policy-mechanic tradition will be fruitless until cultural conditions are taken into account. And the classroom culturalists may reach a theoretical dead end until they can empirically link classroom processes to alleged effects. We put forward a culturally situated model of school effectiveness—the implications of which are discussed for studying ethnically diverse schools within the West. By bringing together the strengths of these two intellectual camps, researchers can more carefully condition their search for school effects.
Studies of 4 fourth-grade teachers in 2 urban schools in a single school district provide the data for this article. Questions about the roles textbooks play in elementary education and how they come to play those roles were addressed using an ecologically based research approach (interviews and classroom observations)-one that considered teachers' thought and action and the relationships between these, teachers' work within and across subjects, and the fuller context of teachers' conditions of work. Using this approach, we found that the influence of textbooks on classroom instruction and teachers' thinking was somewhat less than the literature would have us expect, that patterns of textbook use and thinking about these materials were not necessarily consistent across subjects even for a single teacher, and that the conditions of elementary teachers' work encouraged selective and variable use of textbook materials.
This article presents a theoretical analysis of how such class conditions as textbook organization and content, compositional characteristics of classes, instructional time, and teachers' beliefs influence the mathematics content that teachers introduce. Propositions concerning the relations among these conditions were examined in light of evidence from detailed case studies undertaken in 9 fourth-grade classes. Although textbook characteristics, class composition, and teacher beliefs were related to the amount and order in which content was presented, instructional time was not. Implications for further study of teacher decision making, textbook content and organization, and the use of instructional time are discussed.
The importance of textbooks to the U.S. mathematics curriculum cannot be overstated. The recent rejection by the California State Board of Education of all fourteen text series submitted for adoption illustrates the public perception of the importance of textbooks. Begle (1973) pointed to data from the National Longitudinal Study of Mathematical Achievement to emphasize the important influence textbooks have on student learning, citing evidence that students learn what is in the text and do not learn topics not covered in the book. The National Advisory Committee on Mathematical Education (1975) acknowledged the importance of textbooks as guides for teachers. Fey (1980) emphasized the important influence of texts and pointed out that text content is usually not ba ed on research. Investigators at the Insti tute for Research on Teaching offer evidence that, at the very least, texts are important exercise sources (see Porter et al. 1986). The overall picture is that to a great extent the textbook defines the content of the mathematics that is taught in U.S. schools.