SlideShare a Scribd company logo
Full Terms & Conditions of access and use can be found at
http://www.tandfonline.com/action/journalInformation?journalCode=ujrc20
Download by: [University of Newcastle, Australia] Date: 21 February 2017, At: 22:04
Journal of Research in Childhood Education
ISSN: 0256-8543 (Print) 2150-2641 (Online) Journal homepage: http://www.tandfonline.com/loi/ujrc20
An Examination of the Implementation of
Mathematics Lessons in a Chinese Kindergarten
Classroom in the Setting of Standards Reform
Bi Ying Hu, Sarah Quebec Fuentes, Jingjing Ma, Feiwei Ye & Sherron
Killingsworth Roberts
To cite this article: Bi Ying Hu, Sarah Quebec Fuentes, Jingjing Ma, Feiwei Ye & Sherron
Killingsworth Roberts (2017) An Examination of the Implementation of Mathematics Lessons in
a Chinese Kindergarten Classroom in the Setting of Standards Reform, Journal of Research in
Childhood Education, 31:1, 53-70, DOI: 10.1080/02568543.2016.1244581
To link to this article: http://dx.doi.org/10.1080/02568543.2016.1244581
Published online: 04 Jan 2017.
Submit your article to this journal
Article views: 7
View related articles
View Crossmark data
An Examination of the Implementation of Mathematics Lessons in
a Chinese Kindergarten Classroom in the Setting of Standards
Reform
Bi Ying Hua
, Sarah Quebec Fuentesb
, Jingjing Mab
, Feiwei Yec
,
and Sherron Killingsworth Robertsd
a
University of Macau, Taipa, Macao; b
Texas Christian University, Fort Worth, Texas; c
Zhejiang Normal University,
Zhejiang, China; d
University of Central Florida, Orlando, Florida
ABSTRACT
In China, the 2001 Kindergarten Education Guidelines (Trial), or New Outline,
delineates what constitutes high-quality, developmentally appropriate practices
in all early childhood education curriculum domains, including mathematics.
The New Outline is known for advocating a child-centered, play-based approach
to teaching and learning, a significant change from teacher-directed instruction.
Research highlights a gap between the intended practices set forth in the New
Outline and the enacted practices in Chinese kindergarten classrooms. This
descriptive study examines the implementation of 10 mathematics lessons,
delivered over a 6-month period, from one Chinese kindergarten classroom in
light of the New Outline. The analysis revealed that the lessons reflected aspects
of the New Outline. However, overall, the lessons lacked critical components to
provide students with opportunities to construct an understanding of the
mathematics and become independent learners in five areas: (1) opportunities
to inspire autonomous and life-long learning, (2) strategies for differentiated
instruction, (3) use of resources to represent mathematics concepts, (4) student-
centered instructional approaches, and (5) ways to foster communication.
ARTICLE HISTORY
Received 9 December 2014
Accepted 27 August 2015
KEYWORDS
China; kindergarten;
mathematics curriculum
reform
Children’s early success with mathematics sets a solid foundation for their later academic achievements
(Duncan et al., 2007). During the kindergarten year, children are formally being introduced to basic
mathematics concepts critical for later mastery of complex concepts and skills (Van Luit & Schopman,
2000). The quality of kindergarten mathematics teaching, including instructional and motivational
support, directly affects children’s learning experiences and success with mathematics (Sarama &
Clements, 2004).
In China, the Kindergarten Education Guidelines (Trial) (Ministry of Education, 2001), also called
the New Outline, delineates what constitutes high-quality, developmentally appropriate practices in
all early childhood education1
(ECE) curriculum domains, including mathematics (Hu, 2011; Wang,
2008). The New Outline is known for advocating a child-centered, play-based approach to teaching
and learning, a sharp contrast to teacher-directed instruction. Although the current Chinese kin-
dergarten mathematics standards from the New Outline promote the teaching of mathematics for the
long-term goal of better understanding the world, grounding teaching in children’s daily lives and
activities and using problem solving as a driving motivator, the New Outline lacks guidance on how
teachers might achieve these reform-oriented ideas (Ministry of Education, 2001).
Through a descriptive study of the implementation of 10 mathematics lessons, delivered over a
6-month period, from one Chinese kindergarten classroom, the purpose of the present research is
CONTACT Sarah Quebec Fuentes s.quebec.fuentes@tcu.edu College of Education, Texas Christian University, TCU Box
297920, Fort Worth, TX 76129.
Color versions of one or more of the figures in the article can be found online at www.tandfonline.com/ujrc.
© 2017 Association for Childhood Education International
JOURNAL OF RESEARCH IN CHILDHOOD EDUCATION
2017, VOL. 31, NO. 1, 53–70
http://dx.doi.org/10.1080/02568543.2016.1244581
to evaluate the lessons in light of the New Outline. This article provides a historical overview on
the development of curriculum standards for Chinese kindergarten mathematics since 1904 and
Chinese scholars’ views toward the newer child-centered curriculum movement. The methods
for conducting the descriptive study, including an analysis of the New Outline, are described.
Aspects of the 10 lessons, which align and do not align with the practices endorsed by the New
Outline, are identified, and, based on these findings, implications and directions for future research
are discussed.
Curriculum standards development in Chinese early childhood education
The history of kindergarten curriculum standards in China can be traced back to 1904, when the Qing
government promulgated regulations for early education. However, the government of the Republic
Ministry of Education did not announce China’s first kindergarten curriculum standards until 1932
(Tang, 2005). The standards were divided into three parts, namely, objectives, scope and sequences, and
key teaching methods. A group of ECE scholars, who understood not only Western theories, but also
China’s realities, drafted China’s first national curriculum standards (Tang, 2005). This first set of standards
attended to physical exercise, emphasized developing children’s creativity and imagination, and embedded
ways to honor children’s learning interests. The standards also expected ECE programs to nurture
children’s aesthetic and emotional development as well as qualities such as self-confidence and persever-
ance through flexible and active teaching methodologies (Wang, 2004). Moreover, in addition to general
requirements, the standards also addressed minimum requirements to be adaptable to the different regions
of China, which had varying educational opportunities. At that time, the ECE curriculum standards
seemed to embrace the idea of child-centered teaching.
This trend of embracing child-centered teaching ceased upon the founding of the People’s Republic of
China (PRC) in 1949. Since then, the government has issued three kindergarten curriculum standards, in
1952, 1981, and 2001 (Wang, 2004). Due to political influences, the 1952 Provisional Kindergarten Teaching
Outline (Ministry of Education in People’s Republic of China, 1952) adopted the educational concepts
embraced by the Soviet Union at that time. The provisional outline of 1952 advised practitioners to focus
on age and individual differences of children, and it organized guidelines for teaching around six subjects:
physical education, language, environmental awareness, art, music, and arithmetic. For each subject, the
outline included objectives, curriculum frameworks, teaching foci, and teaching equipment. Influenced by
Piaget’s cognitive development theory (Piaget, 1926), the 1952 provisional outline emphasized the sys-
tematic and logical coherence of mathematics. Instead of showing connections among the six subjects, each
subject was taught separately.
In 1981, the Ministry of Education of the PRC issued the 1981 Kindergarten Education Outline,
which clearly stated that the goal for kindergarten education was for students to develop fully in all
domains (i.e., physical education, language, environmental awareness, art, music, and arithmetic)
and to build a solid foundation for primary education. Notably, the 1981 Outline changed its title
from Teaching Outline (Ministry of Education of People’s Republic of China, 1952) to Education
Outline (Ministry of Education in People’s Republic of China, 1981) to reflect the consensus among
ECE scholars that the main responsibilities of a kindergarten are teaching and caring for young
children. The 1981 Outline stressed the importance of play in teaching and learning, emphasizing
that preschoolers should not be given tests and homework. In fact, the 1981 Kindergarten Education
Outline emphasized the importance of meeting teaching and content requirements through activ-
ities, observation, and connections with everyday life. However, due to inadequate ECE teacher
training, teachers used lecture as the main instructional method, and so kindergartens resembled
elementary schools (Wang, 2004). Similar to the 1952 Provisional Kindergarten Teaching Outline, the
1981 Kindergarten Education Outline kept distinctive boundaries across the six subjects. The 1981
Kindergarten Education Outline referred to mathematics as arithmetic and placed great emphasis on
mastering basic mathematical skills within specified content areas. Standards were written in
succinct language to allow for teachers to understand and transfer them into teaching objectives
54 B. Y. HU ET AL.
(e.g., “Students can identify even and odd numbers within 10”). According to Chen (2005), the 1981
Outline did not take children’s learning interests into account; instead, it catered to teachers’
preferred teaching style: lecture-based, whole-class instruction. Chen (2005) explained that the
more the guidelines focus on content, the more likely teachers will deliver the mathematics content
via whole-class instruction, instead of integrating the content into play and/or using a thematic unit
approach.
In 1997, the National Association for the Education of Young Children (NAEYC) published
Developmentally Appropriate Practice in Early Childhood Programs (Bredekamp & Copple,
1997), which advocated for a reform-oriented approach to teaching and learning; that is,
children should learn science and mathematics concepts through hands-on discovery and self-
construction of meaning. Meanwhile, an increased concern about the lack of focus on children’s
interests and teachers’ dominant use of whole-group teaching methods led Chinese ECE
scholars to call for curriculum reform. This curriculum reform, which was influenced by the
NAEYC publication, sought to minimize the distinct subject approach to the ECE curriculum
and advocated for the use of an integrated thematic unit approach. As a result, the Chinese
Ministry of Education (2001) produced the Kindergarten Education Guidelines (Trial) (also
called the New Outline), which endorsed the use of an integrated curricular approach to
kindergarten education. The New Outline divided the kindergarten curriculum into five
domains: health, language, social studies, science, and art. As a consequence, mathematics was
incorporated into the science domain in the New Outline. Compared to the 1981 Outline, the
New Outline made significant adjustments concerning kindergarten mathematics, including
changes in objectives, content, and instructional methodology. The mathematics objectives,
according to the New Outline, are to “experience quantitative relationships through daily life
and play, and gain a sense of the importance as well as fun of learning mathematics” (Ministry
of Education, 2001, p. 34).
Chinese ECE scholars favored the new standards’ move toward a child-centered curriculum and
instructional approach (Chen, 2005; Pan, 2005; Wu, 2003). Chen (2005) believed that the succinctly
expressed mathematics standards reduce the emphasis on solely teaching mathematics content; the
standards reflect the fun in teaching and learning and stress the importance of learning mathematics
through daily life experiences. Pan (2005) also expressed that the New Outline minimizes the goal of
mastering instructional content and stresses building connections with other disciplines, thereby
enriching instruction. Another feature of the New Outline, according to Pan (2005), is the emphasis
on children’s self-construction of knowledge and the cultivation of children’s positive attitudes
toward and competencies in mathematics, all of which, in turn, positively lessen the teachers’ roles
as knowledge disseminators and their heavy reliance on the use of direct, whole-group instruction.
ECE scholars also acknowledge challenges in implementing the practices promoted by the New
Outline (Hu, 2011; Lin, 2004; Su & Cai, 2006; Wang, 2004; Zhu & Zhang, 2008). As the kindergarten
mathematics standards reform continues, scholars (e.g., Lin, 2004; Su & Cai, 2006) have suggested
accentuating the process and outcomes of mathematics standards in regard to teaching and learning,
instead of being limited to mathematics content objectives. However, Wang (2004) has pointed out
an existing gap between instruction envisioned in the New Outline and mathematics teaching in
Chinese kindergartens. Therefore, this shift introduces challenges for teachers whose professional
knowledge and skills, previous experiences as learners, and cultural beliefs do not align with the
current reform (Dunphy, 2009; Huo, 2004; Pan, 2005). Scholars have gradually recognized that the
goal for such mathematics reform should be focused on effective teaching, and providing instruc-
tional support to teachers.
Teacher development, in fact, has been identified as an important aspect of successful school
reform (Dossey, 2007; Remillard & Bryans, 2004; Sun, 2008) and is addressed in the New Outline.
There is a section for teacher professionalization and training that states:
JOURNAL OF RESEARCH IN CHILDHOOD EDUCATION 55
Local educational administrative departments should develop effective, ongoing teacher training programs.
Teacher professional-development training institutions shall view conducting necessary training for new
curriculum implementation as the main task and ensure the synchronization of the training with curriculum
reform. (Ministry of Education, 2001, Teacher Professionalization and Training section, para. 2)
However, according to Wang (2004), Chinese teachers need additional development in the areas
of building upon children’s ideas and cultivating children’s critical thinking as the New Outline
suggests. Further, preschool teachers have noted a lack of instructional support in implementing the
new integrated curriculum outlined in the reform (Hu, 2011). Therefore, the purpose of the present
study is to examine the implementation of 10 mathematics lessons from a curriculum that was
created to meet the standards of the New Outline, in one Chinese kindergarten classroom in light of
the recommendations in New Outline.
Method
A descriptive study was conducted due to the dynamic relationship between education reform at the
macro- and microlevels. First, successful education reform at the national level requires effective
implementation of reform in local schools (Borko, Wolf, Simone, & Uchiyama, 2003). Second,
detailed analysis of the implementation of reform within classrooms can provide rich and concrete
evidence for the improvement of education reform (Ross, McDougall, Hogaboam-Gray, & LeSage,
2003).
Setting and participants
The researchers purposively selected one kindergarten to participate in the study because the school
used a mathematics curriculum, which was designed to align with the New Outline. Founded in 1954
and located in Hangzhou, Zhejiang, Kindergarten A is considered a high-quality public kindergarten
and currently serves 230 children, ages 2 to 6, on two campuses with a total of 42 staff members.
Kindergarten A has two kindergarten classes, each with 35 students (ages 5 and 6); both classes use
an integrated provincial curriculum called Life, Practice/Fulfill, and Wisdom. Developed by ECE
faculty and experienced teachers to celebrate the spirit of the New Outline, the provincial curriculum
embraces a child-centered approach to classroom teaching and learning. As an integrated curricu-
lum, it uses thematic units to organize grade-level content and learning activities, guided by the New
Outline. The complete curriculum, which covers all five previously named subject area domains, also
includes (1) children’s books, (2) a teachers’ guide, (3) art materials, (4) mathematics manipulatives,
(5) pictures to hang in the classroom, (5) audiocassettes, and (7) a teacher’s resource booklet.
The teacher of one of the kindergarten classes agreed to participate in the study and has a
bachelor’s degree in ECE from a local normal university. This teacher has 5 years of teaching
experience, 3 ½ of which have been at Kindergarten A. Life, Practice/Fulfill, and Wisdom is the
third curriculum that the teacher has used.
Instrument
The Classroom Observation of Early Mathematics Environment and Teaching (COEMET) (Sarama &
Clements, 2007) was used by the researchers to analyze the 10 mathematics lessons. The COEMET is
an observational tool specifically designed to evaluate mathematics instruction in early childhood
settings. The instrument has three sections: Classroom Culture (nine items under two subscales);
Specific Math Activity (SMA), for any activity directly involving the teacher (19 items under seven
subscales); and Mini SMA, a brief description of any activity, such as centers, that does not directly
involve the teacher. Refer to the appendix for a list of the nine subscales and 28 items. Twenty-four of
the items are scored on a 5-point Likert-type scale (strongly disagree = 1, disagree = 2, neutral = 3,
agree = 4, and strongly agree = 5). For each item, the rater indicates his or her level of agreement with
56 B. Y. HU ET AL.
each statement with respect to the observed instruction. For the remaining four items (1, 2, 4, and 15),
the approximate percentage of occurrence is documented (i.e., 0% = 1, 1%–25% = 2, 26%–50% = 3,
51%–75% = 4, and 76%–100% = 5). Not Applicable (NA) may be used for any of the items. Sarama
and Clements (2007) reported strong interrater reliability (r = .88) and internal consistency (>.94) for
the instrument in their study.
Although the COEMET is an instrument from the United States, which is one of the countries
that influenced the development of the New Outline (Li, 2007; Wu, 2001), an analysis of the New
Outline was conducted to ensure that the COEMET was appropriate to use in a Chinese context. The
New Outline consists of a brief introduction providing the reason for its creation and nine sections,
which are further divided into 20 subsections, describing the reform details. These nine sections
include the goal of curriculum reform, the structure of curricula, curriculum standards, teaching
process, development and management of curricular programs, curriculum evaluation, curriculum
management, teacher professionalization and training, and organization and implementation of
curriculum reform. Even though there is one section that specifically addresses instruction (i.e.,
teaching process), references to instruction are found throughout the various sections of the New
Outline. Therefore, two researchers coded all references to instruction in the nine sections of the New
Outline. This process resulted in 36 codes, such as real-world connections, individual needs,
enthusiasm for learning, discussion, and problem solving. Through the sorting of the 36 codes,
five overarching categories emerged. The first two columns in Table 1 present the five overarching
categories and their descriptions.
To determine if the COEMET was suitable for analyzing instruction in a Chinese classroom in the
era of the New Outline, the researchers determined whether each COEMET item aligned with one of
the aforementioned overarching categories. The results of the item alignment are in the third column
of Table 1. With the exception of three items (2, 7, and 10), all remaining items were aligned with
one of the overarching categories. Item 2 references the actions of any support staff. Although the
described actions align with the New Outline, there was not any support staff in the kindergarten
Table 1. Overarching categories from analysis of the new outline and corresponding Classroom Observation of Early Mathematics
Environment and Teaching (COEMET) items.
Overarching Category Description COEMET Items
Category
Mean
Expectations and outcomes Foster students’ lifelong learning skills by helping
them develop the ability to learn and apply
knowledge independently and stimulating their
curiosity and interest in learning.
8, 9, 18 2.07
Developmental dimensions Meet the mental and physical needs of students
based on their developmental characteristics
(e.g., age group and individual) through
appropriate teaching and learning strategies.
11, 13, 16, 17, 24, 25, 27, 28 3.10
Resources and connections Utilize various educational resources and learning
tools, including technology, from both inside and
outside of the classroom to help students develop
connections between learning and real life, their
family, community, and society.
4, 5 2.50
Active learning Encourage active learning and engagement
through exploration, experimentation,
investigation, collecting and analyzing
information, observation, questioning, problem
solving, hands-on activities, and playing games.
12, 14, 26 3.17
Interaction and
communication
Promote students’ abilities to communicate and
cooperate with each other and the teacher by
actively interacting with students.
1, 3, 6, 15, 19, 20, 21, 22, 23 3.09
Note. For items 1, 2, 4, and 15, 1 = 0%, 2 = 1%–25%, 3 = 26%–50%, 4 = 51%–75%, and 5 = 76%–100%. For the remaining items,
1 = strongly disagree, 2 = disagree, 3 = neutral, 4 = agree, and 5 = strongly agree.
JOURNAL OF RESEARCH IN CHILDHOOD EDUCATION 57
classroom examined in this study. In contrast, Items 7 and 10 relate to the content knowledge of the
teacher, which is not addressed in the New Outline. Therefore, these three items were eliminated
from the analysis. Overall, the alignment process shows that the COEMET is relevant to Chinese
lesson implementation under the New Outline.
Procedure
The researchers collected three forms of data: videotaped lessons, observation field notes, and
teacher interviews. Upon receiving consent, a research assistant visited the kindergarten class
regularly to observe and videotape mathematics lessons. From January 2011 to June 2011, a total
of 10 lessons (each approximately 30–45 minutes in length) were observed and videotaped once
every other week to ensure that data included representative lessons across the semester. Table 2
shows the theme, title, and content areas for each observed lesson. The videotape captured the
teacher’s whole-class instruction and accompanying student-teacher interactions. The research
assistant took field notes during center activities and individual work time to document teacher-
student and student-student interactions as well as the overall action within the classroom. The
research assistant also interviewed the teacher two times. The interviews were semistructured and
ranged in length from 40 to 80 minutes. The focus of the first interview, which occurred at the
beginning of the research period, was on the teacher’s views about and implementation of the
Provincial Curriculum. The second interview was conducted toward the end of the research period
and addressed the support the teacher received via the curriculum materials.
Data analysis
Two research assistants, graduate students majoring in ECE, analyzed the 10 videotaped mathe-
matics lessons using the COEMET. In line with Sarama and Clements’ (2007) suggestion, the
research assistants studied a self-training packet with detailed instructions for assessment procedures
and examples of classroom episodes for ease and accuracy of coding. Individually, the research
assistants watched, rewatched, and scored each videotaped lesson. For the first two lessons, the
research assistants discussed discrepancies in scores to reach consensus. The research assistants
individually scored the third lesson with an interrater reliability of 0.80. After the discussion of
scores in the first two phases, the research assistants individually scored the remaining seven lessons,
reaching an overall interrater reliability of 0.85. In addition, the researchers identified classroom
episodes aligning with each item and its corresponding rating for every lesson. To summarize the
ratings, a numerical score was assigned to each rating (or approximate percentage for items 1, 2, 4,
and 15); that is, 1 = strongly disagree (or 0%), 2 = disagree (or 1%–25%), 3 = neutral (or 26%–50%), 4
= agree (or 51%–75%), and 5 = strongly agree (or 76–100%). Using these values, the mean score for
each item over the 10 lessons was calculated (the appendix). To examine the lesson implementation
with respect to the New Outline, the mean score for each of the overarching categories (fourth
Table 2. Theme, title, and content area for lessons observed during the research period.
Theme Lesson Title (Content Area)
New year 1. Dumpling party (Number and Operations)
2. Addition when the sum is 7 (Number and Operations)
I am going to elementary school 3. Telling left from right (Measurement)
4. My new seat (Number and Operations)
5. Subtraction when the minuend is 7 (Number and Operations)
6. 10-yuan market (Number and Operations)
Animal kingdom 7. Fun categorizing (Data Analysis)
8. Creating story problems I (Number and Operations)
9. Creating story problems II (Number and Operations)
Good-bye kindergarten 10. Phone number of friends (Number and Operations)
58 B. Y. HU ET AL.
column in Table 1) for the 10 lessons was also determined. The transcripts of the two interviews
served as a supporting data source to corroborate or not corroborate the findings from the analysis
of the lessons and were coded according to the five overarching categories described in Table 1.
Findings
The appendix shows mean scores over the 10 lessons for each COEMET item. The lowest mean
score was 1, and the highest was 5. (Item 2 was rated as NA, because the teacher did not have any
support staff.) The fourth column in Table 1 gives the mean scores for each of the overarching
categories, which stemmed from the analysis of the New Outline. The category means ranged from a
minimum mean score of 2.07 to a maximum of 3.17. The following sections, organized according to
the five overarching categories, elaborate on the findings from the COEMET. One of the 10 observed
lessons, Addition When the Sum is 7 (Table 2), is used as a representative lesson to exemplify the
implementation of the lessons as indicated by the category means.
This lesson, Addition When the Sum is 7, addresses the content area of number and operations,
specifically the part-part-whole number relationship and its connection to the operation of addition and
the commutative property. As indicated by its title, the lesson focused on different ways to make seven.
Figure 1 shows the section of the Provincial Curriculum Teacher’s Guide (The Committee on Provincial
Kindergarten Curriculum Guide, 2009) for this lesson, including the objectives, materials, and lesson
procedure. The teacher loosely followed the recommendations made in the Teacher’s Guide. The enacted
lesson consisted of three parts: whole-class instruction (13.5 minutes), individual student practice (24 min-
utes), and a return to whole-class instruction (4 minutes). During the initial period of whole-class
instruction, the teacher reviewed addition when the sum is 6 using flashcards and introduced different
ways of making seven (5 + 2 = 7, 1 + 6 = 7, 2 + 5 = 7, 3 + 4 = 7, 5 + 2 = 7, and 6 + 1 = 7) by telling stories. (For
Figure 1. The section, and the English translation, of the provincial curriculum teacher’s guide for the lesson Addition When the
Sum is 7.
JOURNAL OF RESEARCH IN CHILDHOOD EDUCATION 59
an example, refer to the Resources and Connections section.) During this time, the students modeled the
stories using manipulatives. For the second part of the lesson, students worked individually on practice
problems (Figures 2 and 3) while the teacher walked around the classroom helping struggling students and
answering students’ questions. The teacher closed the lesson with a short period of whole-class instruction
during which she addressed students’ problems and misconceptions.
Expectations and outcomes
The expectations and outcomes category refers to the teacher’s role in developing independent and
inquisitive learners. The category mean for expectations and outcomes (M = 2.07) reflects the means
for the three items aligned with the category: Item 8 (M = 1.7), Item 9 (M = 1.8), and Item 18
(M = 2.7). Items 8 and 9 reference a teacher’s enthusiasm for learning mathematics, and Item 18
references a teacher’s acknowledgment and support of students’ efforts. As demonstrated in the
Addition When the Sum is 7 lesson, the teacher engaged the students with stories at the opening of
the lesson. (Refer to the Resources and Connections for examples of the opening stories.) Her actions
Figure 2. One of the student independent practice pages for Addition When the Sum is 7 lesson.
Figure 3. A second student independent practice page for Addition When the Sum is 7 lesson.
60 B. Y. HU ET AL.
and responses to students, in the various segments of the lesson, often minimized student autonomy
in developing an understanding of the content. For example, after letting students use bottle caps to
show the number of monkeys in a tree for a story that represented the equation, 1 + 6 = 7, she said,
“I like Lily’s (pseudonym) way of arranging. She put one monkey on one side, and put the other six
on the other side.” The teacher then proceeded to ask students for the equation that represented the
situation; instead, she could have followed up by asking if the other students demonstrated the story
in a different manner. For a story about crocodiles, she wanted students to use bottle caps to
represent two crocodiles and five crocodiles. One of the students tried to take more bottle caps from
the basket even though he already had an adequate amount. In response, the teacher stopped the
student, arranged the bottle caps for him, and said, “Don’t pick. Put them separately and then you
can differentiate them.” The teacher could have used this opportunity to have the student explain his
reasoning for wanting more bottle caps and to represent the story on his own.
Developmental dimensions
The developmental dimensions category reflects the modification of instructional strategies to meet
the various needs of students. The category mean for developmental dimensions was M = 3.10. The
item means ranged from M = 1 for Item 28, reflecting the teacher’s ability to adapt tasks and
discussions to a variety of student developmental levels, to M = 4.2 for Item 17, reflecting the
teacher’s mathematical expectations of students. The teacher was familiar with the various develop-
mental levels of the students and attempted to provide differentiated instruction to meet their
individual needs. For example, during the second interview, she stated:
Most students are able to understand; four to five students with weaker learning abilities may not get it immediately;
there are also one to two students who are able to do it only under supervision. . . . During the activities, for students
who can learn by themselves, I only need to check their work; for students with weaker learning abilities, I have to
give one-on-one instruction, but there certainly is not enough time to do it for every student.
As previously described, in the middle of the Addition When the Sum is 7 lesson, the teacher
worked one-on-one with struggling students and responded to student questions while they worked
independently on the practice problems. Based on working with the students, she determined the
common student difficulties and addressed them in the closing whole-class instruction (Item 27),
opening with: “Many of you didn’t get today’s problems. First of all. . . .” She proceeded to review
three of the problems from the independent practice.
Even though the teacher realized the range of developmental levels among the students, she
acknowledged challenges to meet their various needs.
For those who haven’t gotten enlightened, no matter how I teach them, they still don’t get it. I have no idea
what to do if they still don’t get it. I don’t know how to teach them since I’ve already tried everything. Maybe
it’s because his developmental level is not there yet.
For instance, she worked one-on-one with a student, who was not able to figure out how to solve
one of the independent practice problems (first question on left-hand side of Figure 3).
Teacher: There are seven circles in this box in total. How many circles are here now? [Pointing at
the visible circles.]
Student: Two circles.
Teacher: Ah? How many circles can you see?
Student: [Slid a pencil along the visible circles.]
Teacher: How many?
Student: Seven.
Teacher: You can already see seven? How many circles?
Student: [Pointed and counted two out of four visible circles.]
Teacher: Ah?
JOURNAL OF RESEARCH IN CHILDHOOD EDUCATION 61
Student: Two circles.
Teacher: [Pointed at the visible circles.] One, two, three, four. How many circles?
Student: [Hesitated.] Four circles.
Teacher: You can see four circles, but there is supposed to be seven circles. A piece of paper covered
the other ones. How many are covered?
Student: One?
Teacher: Seven in total. [Pointed and counted the visible circles again.] One, two, three, four.
[Pointed at the blank area of the box.] Draw them. [The student did not know what to do.]
Teacher: Seven in total. You draw as many of the circles that have been covered.
[The student still did not know what to do.]
Teacher: You look at this. [Pointed and counted the visible circles.] One, two, three, four. . . . Count
and draw at the same time. [Drew in the blank area of the box.] Five, six, seven. Can you
do this? How many were covered?
Student: Seven?
Teacher: How many were covered!
Student: Three?
Teacher: Three, yes. Now here [pointed at the next problem], you count and draw.
Throughout the dialogue, the student remained confused. The teacher completed the problem for
the student, rather than helping him develop an understanding of the underlying concept (e.g., Items
26 and 28). As the interaction progressed, the teacher became increasingly impatient. In response to
a question about how the provision of a rationale for the lesson objectives would support her
instruction, the teacher acknowledged her lack of patience: “It would make teachers’ theoretical
knowledge richer. Also, I would understand the reasons why a certain objective was included when I
teach children. Then probably I would have more patience.” The teacher contributes her frustration,
in part, to not understanding the concepts underlying lesson objectives.
Resources and connections
The resources and connections category describes the use of resources and tools to guide students in
making connections between classroom learning and the real world. The category mean for resources and
connections was M = 2.50, which reflects a low item mean of M = 1 for Item 4 pertaining to student use of
mathematics software on computers and a fairly high item mean of M = 4 for Item 5 pertaining to the use of
materials for mathematics such as manipulatives. Even though there was technology available in the
classroom, the students did not use technology in any of the lessons. Although recommended in the
curriculum materials, the teacher did not use any form of technology such as computers during the whole-
class instruction segment of the lesson.
Because there are so many things for teachers to do, usually we [only have time to] plan the lessons based on
our prior experience. For example, the curriculum mentions the PowerPoint activities. I cannot provide these.
What should I do? I don’t have the ability [to make them] anyway. So, I can only use the pictures and draw
them by myself. Eventually, all the lesson plans look the same no matter what curriculum you are using.
As the teacher mentioned, she used concrete materials during whole-class instruction. To engage
students with the content of the lesson, she told stories to introduce the various ways to make seven.
Teacher: In the forest, there is a herd of elephants. At the moment, one elephant feels hungry. So,
he searched and searched and found a lot of banana trees. He ran to a banana tree and
started to eat bananas. Then, his older brother came and ate the bananas with him. . . .
Later, they asked the younger brother to join them. The parents of the elephants
discovered that all of their children were gone and came to find them. They started to
eat bananas altogether. How many elephants are under the banana tree now?
62 B. Y. HU ET AL.
Students: Five!
Teacher: Let’s count them.
Teacher and Students: One, two, three, four, five.
Teacher: From a distance, two chubby elephants approached them. What do they want?
Students: Eat the bananas!
Teacher: Yes, they want to taste them too.
Throughout the telling of the story, the teacher used cutouts of elephants to mirror the action and
ultimately represent the equation 5 + 2 = 7. Similarly, for other ways of making seven, the teacher
shared five additional stories about monkeys (1 + 6 = 7), crocodiles (2 + 5 = 7), lollipops (3 + 4 = 7), red
packets filled with money, a gift children often receive from elders on the New Year (5 + 2 = 7), and
dumplings (6 + 1 = 7). The teacher provided students the opportunity to work with manipulatives
during this portion of the lesson; that is, the students modeled each of the stories with bottle caps.
Active learning
The active learning category refers to instructional strategies that promote student engagement. The
mean for this category was M = 3.17. The item means were M = 3, M = 2.7, and M = 3.8 for Items 12
(lesson engagement), 14 (management strategies), and 26 (opportunities for mathematical reflection),
respectively. The teacher acknowledged the value of exploration and hands-on activities: “No matter
whether it’s mathematics or science, the outcome would be better if you let students engage and explore.”
However, the teacher believed that the larger class size prohibited her from utilizing investigative
activities. “The situation is often that there are too many children and too few teachers. . . . This is not
a problem that I can solve.” In the whole-class portion of the Addition When the Sum is 7 lesson, the
students were actively involved in representing the various stories using bottle caps, following the
teacher’s model. For an example, refer to the Resources and Connections section.
Similar situations occurred when the teacher was helping students during the independent practice
portion of the lesson. For instance, a student was having difficulty with the problem on the left-hand side
of Figure 3. The handout provided three ways of making 7: 6 and 1, 2 and 5, and 4 and 3 (every other row
starting with the first row). The students were supposed to generate the other three ways to make 7: 1 and
6, 5 and 2, and 3 and 4. The teacher worked with a student, who was struggling with the problem.
Teacher: You need to divide seven game sticks into two groups, which number hasn’t been used yet?
Student: [No response.]
Teacher: Six has been used, two has been used, and four has been used. Which number hasn’t been
used yet? . . . Two sticks have been put here, four sticks have been put here, and six have
been put here. There are seven in total. Which number has not been used? . . . Which
number has not been used? . . . Which number has not been used?
Student: Five.
Teacher: After you used the five sticks, how many sticks are left? . . . 1, 2, 3, 4, 5. Five have been put
here. How many are left?
Student: Two.
Teacher: Where are you going to put them?
[The student pointed at the cell on the left in which she just drew five tally marks.]
Teacher: Five sticks have been already put here. The lines go like this [pointing at the two lines that
connect the seven game sticks and the two columns, respectively]. Five sticks are here
[pointing at the left column]. Where will you put the other two sticks?
[The student hesitantly pointed at the correct cell.]
Teacher: Draw them.
The teacher continued to help the student in a similar manner for the remaining two rows. Unlike
the opening activity, for this problem, the students needed to generate the different ways to make
JOURNAL OF RESEARCH IN CHILDHOOD EDUCATION 63
seven. When the teacher helped the struggling student, the task was reduced to a procedure in which
the student was told where to write her answer. The student did not understand the purpose of the
problem and continued to need help to complete the entire task.
Interaction and communication
The interaction and communication category emphasizes the teacher’s role in fostering classroom
discourse. The category mean for interaction and communication was M = 3.09. The item means
ranged from M = 2 for Item 23 (the teacher supported the listener’s understanding) to M = 5 for
Items 1 and 15 reflecting a teacher’s level of interaction. The teacher in this study regularly engaged
with the students during the whole-class instruction and individual student practice segments of the
lessons. While the students were working individually, she was interacting with the students 100% of
the time. In these interactions, the teacher tended to tell the students how to complete the problem
from a procedural perspective rather than help the students build an understanding of the content.
(Refer to the Developmental Dimensions and Active Learning sections for examples.)
Similarly, during whole-class instruction, the teacher regularly asked the students questions. For
instance, at the end of the elephant story (resources and connections), the teacher prompted the
students:
Teacher: Now, how many elephants are there under the tree?
Students: Seven!
Teacher: How did you calculate it?
Students: 5 + 2 = 7.
Teacher: How many elephants are here [points to left side]?
Students: Five.
Teacher: What about here [points to right side]?
Students: Two.
Teacher: In the middle, add them up. There are seven in total.
Teacher with Students: Five plus two is seven.
Teacher: Then if the plus sign stays the same and I switch the positions of two and five, what is the
result?
Students: It is still seven!
Teacher: [Writes 2 + 5 on the board.] Two plus five, I switched them. What is the result?
Students: Seven.
Teacher: How many?
Students: Seven.
Teacher: I heard somebody said six. The result stays the same.
With the exception of one time, the teacher asked a question every time she spoke. She asked
closed questions looking for a single answer. As an alternative, she could have asked students to
clarify or justify their thinking or to evaluate the thinking of others, means of assessing student
understanding or lack thereof (e.g., Items 21, 22, and 23).
Discussion
The present descriptive study offers an evaluation over 10 mathematics lessons from one Chinese
kindergarten classroom teacher’s practice with respect to the mathematics curriculum standards in
the New Outline and provides excerpts from one of the 10 lessons to illustrate the COEMET ratings.
Specifically, the teacher’s instruction was examined according to the five overarching categories,
which stemmed from an analysis of the New Outline: expectations and outcomes, developmental
dimensions, resources and connections, active learning, and interaction and communication. On the
surface, the implementation of the lessons reflected the expectations put forth in the New Outline.
64 B. Y. HU ET AL.
However, upon closer examination, the students did not have opportunities to construct an under-
standing of the mathematics and become independent learners. In what follows, the evaluation of the
implemented lessons is discussed in more detail for each of the five categories.
Expectations and outcomes, one of the overarching categories of the New Outline, focuses on students
developing life-long learning capabilities. More specifically, kindergarten science teaching should “sti-
mulate children’s curiosity and desire to explore things as well as develop cognitive ability” (Ministry of
Education, 2001, Science section, para. 1). To meet these expectations, teachers need to provide
opportunities for students to become autonomous learners. In the present study, during whole-class
instruction, the students were highly engaged. However, the instruction was teacher directed. The
students followed the teacher’s approach to representing a problem minimizing any alternative
approaches suggested by students and focusing only on correct student responses. These findings parallel
Tang’s (2006) description of Chinese kindergarten teachers’ practice and views of students. Tang argues
that, in the majority of Chinese kindergartens, students are perceived as reliant on teachers. Students “are
virtually under the control of teachers in that the whole learning process is designed and implemented
according to the teacher’s prescription without taking children’s own initiatives into account” (Tang,
2006, p. 345). If teachers believe that students are not capable of learning autonomously, then their
instruction will reflect a great deal of teacher control (Chen, as cited in Tang, 2006).
Teacher control, as represented by a focus on specific procedures and responses, can lead to a
failure to address the various developmental dimensions of students. However, meeting the diverse
needs of students is an integral part of the New Outline. All overarching principles for kindergarten
education address respect for students’ developmental dimensions. For instance, the sixth over-
arching principle states: “Kindergarten should emphasize children’s individual differences, and
provide children with opportunities and conditions to achieve their potential and develop further
from their existing levels” (Ministry of Education, 2001, Part 1 section, para. 6). This principle aligns
with the tenets of differentiated instruction, which integrates a collection of pedagogical strategies to
address the distinctive needs of individual students (Watts-Taffe et al., 2012). Like the philosophical
stance of the New Outline, Gregory and Chapman (2002) contend, “Differentiation is not a set of
tools, but a belief system educators embrace to meet the unique needs of every learner” (p. 2). The
teacher in the current study acknowledged the range of developmental levels among her students.
She provided support for the students who struggled with one-on-one instruction. However, with a
large class size, she was not able to help all struggling students individually. Howard and Aleman
(2008) consider content and pedagogical content knowledge as a contributing factor to a teacher’s
ability to address diverse learners. The teacher experienced challenges helping students. Unable to
modify how she provided support, the teacher often resorted to giving the answer to the students.
She contributed her frustration to a lack of subject matter knowledge and effective strategies.
Differentiating instruction is difficult, and teachers are often not prepared to provide instruction
responsive to students’ needs (Bofferding, Kemmerle, & Murata, 2012; Neville, 2010). However,
developmentally appropriate instructional support is critical as it contributes to children’s increased
task engagement (Pakarinen et al., 2010; Turner et al., 2002).
One means of engaging students is using resources and connections, including manipulatives and
technology. Technology is a major component of the teaching process section in the New Outline.
Teachers need to “fully take advantage of informational technology to provide a variety of educa-
tional environments and powerful learning tools for students’ learning and development” (Ministry
of Education, 2001, Teaching Process section, para. 2). The teacher and her students did not use any
form of technology in the lessons observed. She explained that the curriculum recommends the use
of technology, such as PowerPoint activities, but did not provide the resources nor did she have the
time to generate them. However, the teacher did use manipulatives in combination with contexts
that connect to students’ interests. According to the New Outline, “Teachers should let children use
senses, be hands-on and minds-on, discover and solve problems, encourage children’s cooperation,
and actively involve children in exploration activities” (Ministry of Education, 2001, Guidance
section, para. 2). For the Addition When the Sum is 7 lesson, she presented multiple stories to
JOURNAL OF RESEARCH IN CHILDHOOD EDUCATION 65
represent the various ways to make 7. For each story, she used cutouts to model the story, and the
students followed along using bottle caps. The students’ involvement included actively manipulating
the objects; that is, they were hands-on. Because the students were expected to follow the teacher’s
actions, their involvement was not necessarily minds-on.
Being hands-on and minds-on are integral parts of active learning (Andrews & Trafton, 2002);
that is, instructional approaches that involve “students in doing things and thinking about the things
they are doing” (Bonwell & Eison, 1991, p. 2). To be considered active learning, student engagement
in activities must include sense-making opportunities, including hypothesizing, observing, analyzing,
evaluating, and synthesizing the objects of focus (Bonwell & Eison, 1991; Katz, 2002). Similarly, the
New Outline states: “[Education] should . . . help children learn to use the methods of observation,
comparison, analysis, reasoning, etcetera to conduct exploration activities” (Ministry of Education,
2001, Guidance section, para. 1). As previously discussed, the teacher’s instruction (whole class and
one-on-one) was engaging but did not meet the requisites of active learning by being hands-on and
minds-on. She attributed some of her challenges to a large class size and a lack of materials, two
barriers documented in the literature (Bonwell & Eison, 1991).
Interaction and communication also promotes sense making (Andrews & Trafton, 2002).
Students should “explore ideas with their peers and be able to use adaptive ways to express their
findings and communicate” (Ministry of Education, 2001, Objective section, para. 4). By sharing
their ideas and listening to the ideas of others, students have opportunities to articulate, refine, and
revise their understanding. Scott, Mortimer, and Aguiar (2006) delineate a framework for classifying
classroom interactions by integrating two dimensions: interactive or noninteractive and dialogic or
authoritative. According to this framework, the teacher’s mode of communication is interactive/
authoritative. She interacts with her students regularly. However, she questions students, leading
them toward a specific approach and/or answer (Scott et al., 2006). The teacher follows an initiation-
response-evaluation interaction pattern (Mehan, 1979). She asks closed-ended questions, the student(s)
respond, and she evaluates the response. Further, when working one-on-one with students, who do not
follow her line of questioning, she struggled with altering her approach to a task. Wang (2004) also
found that Chinese teachers need additional development in the areas of building upon students’ ideas
and cultivating students’ critical thinking.
The implemented lessons reflected aspects of the New Outline; however, overall, the lessons
lacked critical components that foster student sense making. For instance, the teacher recognized
and attempted to support the range of leaners in her classroom but did not have the repertoire of
instructional strategies to do so. Her instruction was hands-on, by making connections to students’
interests and utilizing manipulatives, but it was not necessarily minds-on, the combination of which
is necessary to engage students in active learning. The teacher interacted with the students regularly,
but the interaction did not provide the students with opportunities to develop their own ideas about
the mathematics. These findings provide insights into areas in which Chinese kindergarten teachers
potentially need support to meet the expectations set forth in the New Outline.
Conclusion
Although conducted in a Chinese context, the present study has implications for the potential, or
lack thereof, for education reform as implemented through standards documents. Effective imple-
mentation of reform at the local level strongly influences the success of reform at the national level
(Borko et al., 2003). Therefore, examining instructional practices at the local level can provide insight
about how to support teachers in understanding and enacting the reform and corresponding
standards, authentically rather than superficially. This is of particular importance when the reform
reflects a significant shift in classroom practices.
The release of the New Outline marks a transition of the role of the teacher from knowledge
disseminator to facilitator of learning through play, self-discovery, and problem solving. Meeting the
expectations set forth in the New Outline requires a change in perception about the role of the
66 B. Y. HU ET AL.
teacher and the student. Chinese teachers have been traditionally taught through direct, didactic
instruction and most have never observed anyone, nor have the skills to deliver inquiry-based
kindergarten teaching. Further, the Chinese collectivist culture teaches respect for authority figures;
teachers feel obligated to gain a sense of control of the class, which translates into teacher-directed
lessons. Chinese teachers also need to believe that students are able to be active participants in
their learning.
The evaluation of the 10 implemented lessons from one Chinese kindergarten classroom in the
present study confirms previous findings about a disconnect between the type of instruction
supported through the New Outline and its implementation in Chinese kindergarten classrooms
(Tang, 2006; Wang, 2004). Further, the analysis of the New Outline provides a framework for future
studies and the design of professional development opportunities. Specifically, all of the references to
instruction in the New Outline were coded and organized into five overarching categories:
● Expectations and outcomes: Learning opportunities, which inspire autonomous and lifelong
learners.
● Developmental dimensions: Differentiated instructional approaches, including multiple ways to
continuously assess students’ prior knowledge and skills, identify individual student’s needs,
and accommodate those needs.
● Resources and connections: Provision of various resources, including manipulatives and tech-
nology, as well as effective means of utilizing the resources to represent mathematical concepts
and make connections to the more abstract representations.
● Active learning: Instructional approaches, which facilitate sustained interactions with key
mathematics ideas to refine views, promote conceptual understanding, and enhance problem-
solving and reasoning processes (i.e., hands-on and minds-on).
● Interaction and communication: Strategies to foster interactive/dialogic communication (Scott
et al., 2006) in which teachers build upon students’ ideas by providing opportunities for
students to share their thinking and listen and respond to the thinking of others.
The present study only examined 10 lessons from one Chinese kindergarten classroom. A larger
scale evaluation of the implementation of the Chinese curricular reform needs to be conducted, and
the framework presented herein can guide the analysis.
Ma and Yuan (2007) have suggested that high-quality kindergarten mathematics teaching lies in
providing support and evaluative systems for teachers. The framework can also be used to evaluate
individual teacher’s practice and design professional development centered on areas of needed
improvement. The professional development should center on teachers’ daily practice, be long
term, and cultivate teachers’ perspectives about teaching and learning mathematics (Collopy,
2003). Educative curriculum materials, designed for student and teacher learning, can also be a
means of supporting teacher development in the recommended areas (Hu, Fuentes, Wang, & Yie,
2013; Collopy, 2003; Davis & Krajcik, 2005).
By providing a descriptive analysis of 10 lessons from one Chinese kindergarten classroom in the
era of the New Outline, the present study informs teacher educators, future researchers, and policy-
makers of areas of evaluation and potential improvement in the implementation of education reform
in Chinese kindergartens. Future research can focus on effective ways to implement professional
development for teachers to facilitate student-centered learning. In parallel, research can examine
teachers’ beliefs and practices regarding developmentally appropriate mathematics curricula and
instruction as well as the effects of professional development on teachers’ practice. These efforts will
contribute to closing the gap between the intended and implemented curriculum, enhance teacher
quality, improve student learning, and bring to life the spirit of the New Outline.
JOURNAL OF RESEARCH IN CHILDHOOD EDUCATION 67
Note
1. In China, early childhood education programs (or preschools) serve children ages 3–6 and include the
kindergarten year.
References
Andrews, A. G., & Trafton, P. R. (2002). Little kids-Powerful problem solvers: Math stories from a kindergarten
classroom. Portsmouth, NH: Heinemann.
Bofferding, L., Kemmerle, M., & Murata, A. (2012). Making 10 my way. Teaching Children Mathematics, 19(3), 164–173.
doi:10.5951/teacchilmath.19.3.0164
Bonwell, C. C., & Eison, J. A. (1991). Active learning: Creating excitement in the classroom. Washington, DC: The
George Washington University.
Borko, H., Wolf, S. A., Simone, G., & Uchiyama, P. (2003). Schools in transition: Reform efforts and school capacity in
Washington state. Educational Evaluation and Policy Analysis, 25(2), 171–201. doi:10.3102/01623737025002171
Bredekamp, S., & Copple, C. (1997). Developmentally appropriate practice in early childhood programs. Washington,
DC: National Association for the Education of Young Children.
Chen, X. J. (2005). 关于幼儿园数学教育变革的思考 [On kindergarten math education reform]. Theoretical
Construction, 7–8, 20–22.
Collopy, R. (2003). Curriculum materials as a professional development tool: How a mathematics textbook affected
two teachers’ learning. Elementary School Journal, 103(3), 287–311. doi:10.1086/499727
The Committee on Provincial Kindergarten Curriculum Guide. (2009). Teachers’ guide for instructional activities
design. Zhejiang, China: New Times Press.
Davis, E. A., & Krajcik, J. S. (2005). Designing educative curriculum materials to promote teacher learning.
Educational Researcher, 34(3), 3–14. doi:10.3102/0013189X034003003
Dossey, J. (2007). Looking back, looking ahead. In C. R. Hirsch (Ed.), Perspectives on the design and development of
school mathematics curricula (pp. 185–199). Reston, VA: National Council of Teachers of Mathematics.
Duncan, G., Dowsett, C. A., Magnuson, K., Huston, A., Klebanov, P., & Japel, C. (2007). School readiness and later
achievement. Developmental Psychology, 43, 1428–1446. doi:10.1037/0012-1649.43.6.1428
Dunphy, E. (2009). Early childhood mathematics teaching: Challenges, difficulties and priorities of teachers of young
children in primary schools in Ireland. International Journal of Early Years Education, 17(1), 3–16. doi:10.1080/
09669760802699829
Gregory, G. H., & Chapman, C. (2002). Differentiated instruction in inclusive classrooms. Boston, MA: Pearson.
Howard, T. C., & Aleman, G. R. (2008). Teacher capacity for diverse learners: What do teachers need to know? In M.
Cochran-Smith, S. Feiman-Nemser, & D. J. McIntyre (Eds.), Handbook of research on teacher education: Enduring
questions in changing contexts (pp. 156–174). New York, NY: Routledge Taylor & Francis Group.
Hu, B. (2011). Exploring the cultural relevance of developmentally appropriate practices from the point view of
preschool teachers in Beijing. The 2011 Yearbook of the Texas A&M University-Corpus Christi’s Center for
Educational Development, Evaluation, and Research, 1–23.
Hu, B., Fuentes, S., Wang, C., & Yie, F. (2013). A case study of the implementation of Chinese kindergarten
mathematics curriculum. International Journal of Mathematics and Science, 12(1), 193–217.
Huo, J. (2004).《幼儿园教育指导纲要》实施过程中教师适应行为的调查研究 [Investigations on the teachers’
adaptive actions during the implementation process of GPE] (master’s thesis). Liao Ning Normal University,
Dalian, China.
Katz, L. G. (2002). Foreword. In A. G. Andrews & P. R. Trafton (Eds.), Little kids-Powerful problem solvers: Math
stories from a kindergarten classroom (pp. xi–xiii). Portsmouth, NH: Heinemann.
Li, M. (2007). 试析美国幼儿教育课程模式的理论流派及其启示 [An exploratory analysis of the theory genre and
insights from U.S. preschool curriculum models]. Comparative Education Studies, 11, 69–74.
Lin, Y. (2004). 中国幼儿数学教育课程的反思和构建 [Reconsideration and construction of Chinese early childhood
mathematics education]. Journal of Shanxi Normal University (Philosophy and Social Science Edition), 33(1), 117–121.
Ma, J., & Yuan, D. (2007). 《从学前班到8年级的课程焦点:追求连贯性》报告评述[A commentary on curricu-
lum focal points for prekindergarten through Grade 8 mathematics: A quest for coherence report]. Comparative
Education Review, 204(5), 48–52.
Mehan, H. (1979). Learning lessons: Social organization in the classroom. Cambridge, MA: Harvard University Press.
Ministry of Education in People’s Republic of China. (1952). Temporary regulations for kindergarten education (draft).
Ministry of Education in People’s Republic of China. (1981). The guideline for kindergarten Education (trial version).
Shangdong Education, 10, 4–8.
Ministry of Education in People’s Republic of China. (2001). The guideline for kindergarten education (trial version).
Retrieved from http://www.moe.gov.cn/publicfiles/business/htmlfiles/moe/s7054/201403/xxgk_166067.html
68 B. Y. HU ET AL.
Neville, E. (2010). Utilizing a school-university collaborative partnership to design, present, and support pre-K-12
coursework on differentiated instruction. School-University Partnerships, 4(2), 92–95.
Pakarinen, E., Kiuru, N., Lerkkanen, M., Poikkeus, A., Siekkinen, M., & Nurmi, J. (2010). Classroom organization and
teacher stress predict learning motivation in kindergarten children. European Journal of Psychology of Education, 25,
281–300. doi:10.1007/s10212-010-0025-6
Pan, Y. (2005). 对我国当前幼儿园数学教育政策的反思[Reflection on the current policy for kindergarten mathe-
matics education]. Theoretical Construction, 3, 9–11.
Piaget, J. (1926). The language and thought of the child. London, England: Routledge & Kegan Paul.
Remillard, J. T., & Bryans, M. B. (2004). Teachers’ orientations toward mathematics curriculum materials: Implications
for teacher learning. Journal for Research in Mathematics Education, 35(5), 352–388. doi:10.2307/30034820
Ross, J. A., McDougall, D., Hogaboam-Gray, A., & LeSage, A. (2003). A survey measuring elementary teachers’
implementation of standards-based mathematics teaching. Journal for Research in Mathematics Education, 34(4),
344–363. doi:10.2307/30034787
Sarama, J., & Clements, D. (2004). Building blocks for early childhood mathematics. Early Childhood Research
Quarterly, 19, 181–189. doi:10.1016/j.ecresq.2004.01.014
Sarama, L., & Clements, D. H. (2007). Manual for Classroom Observation (COEMET)-Version 3 (Unpublished
version).
Scott, P. H., Mortimer, E. F., & Aguiar, O. G. (2006). The tension between authoritative and dialogic discourse: A
fundamental characteristic of meaning making interactions in high school lessons. Science Education, 90, 605–631.
doi:10.1002/sce.20131
Su, G., & Cai, Q. (2006). 幼教课程改革研究[Research on early childhood curriculum reform]. Curriculum and
Instruction, 12, 14–15.
Sun, X. (2008). Mathematics curriculum standards of China: Its process, strategies, outcomes and difficulties. In Z.
Usiskin & E. Willmore (Eds.), Mathematics curriculum in pacific rim countries – China, Japan, Korea, and Singapore
(pp. 73–82). Charlotte, NC: Information Age Publishing.
Tang, F. (2006). The child as active learner: Views, practices, and barriers in Chinese early childhood education.
Childhood Education, 82(6), 342–346. doi:10.1080/00094056.2006.10522859
Tang, S. (2005). 中国农村幼儿教育的发展与变革[On the development and reform of Chinese country preschool
education]. Career Development and Management, 38(6), 38–40.
Turner, J. C., Midgley, C., Meyer, D. K., Gheen, M., Anderman, E., Kang, Y., & Patrick, H. (2002). The classroom
environment and students’ reports of avoidance behaviors in mathematics: A multi-method study. Journal of
Educational Psychology, 94, 88–106. doi:10.1037/0022-0663.94.1.88
Van Luit, J. E. H., & Schopman, E. A. M. (2000). Improving early numeracy of young children with special needs.
Remedial and Special Education, 21(1), 27–40. doi:10.1177/074193250002100105
Wang, C. (2004). 中国学前课程百年发展与变革的历史研究 [A history study of the development and changes of
preschool curriculum and its enlightenments in the past century in China]. Beijing, China: Educational Science
Press.
Wang, C. (2008). 中国学前课程百年发展变革的特点和启示 [Characteristics of development and changes of pre-
school curriculum and its enlightenments in the past century in China]. Educational Research, 9, 93–97.
Watts-Taffe, S., Laster, B. P., Broach, L., Marinak, B., Connor, C. M., & Walker-Dalhouse, D. (2012). Differentiated
instruction: Making informed teacher decisions. Reading Teacher, 66(4), 303–314. doi:10.1002/trtr.2012.66.issue-4
Wu, C. (2003). 我国数学教育的改革探索 [Exploring mathematics education reform in China]. Studies in Preschool
Education, 10, 48–49.
Wu, D. (2001). 美国数学课程标准的思想和启示[U.S. mathematics curriculum standards: Ideas and enlighten-
ments]. Journal of Shenzhen Institute of Education, 2, 82–85.
Zhu, J., & Zhang, J.. (2008). Contemporary trends and developments in early childhood education in China.
International Journal of Early Years Education, 28(20), 173–182.
JOURNAL OF RESEARCH IN CHILDHOOD EDUCATION 69
Appendix: Classroom Observation of Early Mathematics Environment and Teaching
(COEMET) items and teacher mean scores for each item over 10 observed lessons
COEMET Sections, Subscales, and Items Item Mean
Classroom Culture
Environment and Interaction
1. Teacher actively interacted with and was responsive to children. 5
2. Other staff (e.g., aide) actively interacted with and was responsive to children. NA
3. The teacher used teachable moments as they occurred to develop math ideas. 3.1
4. Children took turns using computers with math software. 1
5. The environment showed signs of mathematics: materials for mathematics, including specific math
manipulatives, were available and mathematics was enacted and/or discussed around them.
4
6. Children’s math work and/or other signs of mathematical thinking were on display. 3.1
Personal Attributes of the Teacher
7. The teacher appeared to be knowledgeable and confident about mathematics. 3.5
8. The teacher showed she believed that math learning can and should be enjoyable. 1.7
9. The teacher showed curiosity about and/or enthusiasm for math ideas and/or connections to other
ideas or real-world situations.
1.8
Specific Math Activity
Mathematical Focus
10. The teacher displayed an understanding of mathematics concepts. 2.7
11. The mathematical content was appropriate for the developmental levels of the children in his class. 4
Organization, Teaching Approaches, Interactions
12. The teacher began by engaging and focusing children’s mathematical thinking. 3
13. The pace of the activity was appropriate for the developmental levels/needs of the children and
the purpose of the activity.
3
14. The teacher’s management strategies enhanced the quality of the activity. 2.7
15. The teacher was actively involved in the activity for what percentage of time (beyond setup or
introduction).
5
16. The teaching strategies used were appropriate for the development levels/needs of the children
and purposes of the activity.
3.2
Expectations
17. The teacher had high but realistic mathematical expectations of children. 4.2
18. The teacher acknowledged and/or reinforced children’s effort, persistence, and/or concentration. 2.7
Eliciting children’s solution methods
19. The teacher asked children to share, clarify, and/or justify their ideas. 2.7
20. The teacher facilitated children’s responding. 2.4
21. The teacher encouraged children to listen to and evaluate others’ thinking/ideas. 2.2
Supporting children’s conceptual understanding
22. The teacher supported the describer’s thinking. 2.3
23. The teacher supported the listener’s understanding. 2
24. The teacher provided “just enough” support. 2.6
Extending children’s mathematical thinking
25. The teacher built on and/or elaborated children’s mathematical ideas and strategies. 2.8
26. The teacher encouraged mathematical reflection. 3.8
Assessment and Instructional Adjustment
27. The teacher observed and listened to children, taking notes as appropriate (only need notes in
small groups).
4
28. The teacher adapted tasks and discussions to accommodate the range of children’s abilities and
development.
1
Note. For items 1, 2, 4, and 15, 1 = 0%, 2 = 1–25%, 3 = 26–50%, 4 = 51–75%, and 5 = 76–100%. For the remaining items,
1 = strongly disagree, 2 = disagree, 3 = neutral, 4 = agree, and 5 = strongly agree.
70 B. Y. HU ET AL.

More Related Content

Similar to An Examination of the Implementation of Mathematics Lessons in a Chinese Kindergarten Classroom in the Setting of Standards Reform.pdf

Appraisal of colleges of education social studies curriculum vis à-vis the j...
 Appraisal of colleges of education social studies curriculum vis à-vis the j... Appraisal of colleges of education social studies curriculum vis à-vis the j...
Appraisal of colleges of education social studies curriculum vis à-vis the j...
Alexander Decker
 
Algebra Problem-Solving Equity Challenges
Algebra Problem-Solving Equity ChallengesAlgebra Problem-Solving Equity Challenges
Algebra Problem-Solving Equity Challenges
Martha Brown
 
The Hidden Curriculum In Education
The Hidden Curriculum In EducationThe Hidden Curriculum In Education
The Hidden Curriculum In Education
Beth Salazar
 
Curriculum integration in social studies as predictor of academic performance...
Curriculum integration in social studies as predictor of academic performance...Curriculum integration in social studies as predictor of academic performance...
Curriculum integration in social studies as predictor of academic performance...
Alexander Decker
 
Secondary level-mathematics-curriculum-of-kerala
Secondary level-mathematics-curriculum-of-keralaSecondary level-mathematics-curriculum-of-kerala
Secondary level-mathematics-curriculum-of-kerala
kgbiju
 
2Modern Childhood ClassroomThe Curricu.docx
2Modern Childhood ClassroomThe Curricu.docx2Modern Childhood ClassroomThe Curricu.docx
2Modern Childhood ClassroomThe Curricu.docx
tamicawaysmith
 
Dr. William Allan Kritsonis & Steven Norfleet
Dr. William Allan Kritsonis & Steven NorfleetDr. William Allan Kritsonis & Steven Norfleet
Dr. William Allan Kritsonis & Steven Norfleet
guestfa49ec
 
Dr. William Kritsonis, Dissertation Chair
Dr. William Kritsonis, Dissertation ChairDr. William Kritsonis, Dissertation Chair
Dr. William Kritsonis, Dissertation Chair
guestfa49ec
 
An Analysis of Teachers’ Pedagogical Content Knowledge on Number Sense Learni...
An Analysis of Teachers’ Pedagogical Content Knowledge on Number Sense Learni...An Analysis of Teachers’ Pedagogical Content Knowledge on Number Sense Learni...
An Analysis of Teachers’ Pedagogical Content Knowledge on Number Sense Learni...
AJHSSR Journal
 
Ex Ed English- research paper
Ex Ed English- research paperEx Ed English- research paper
Ex Ed English- research paper
Pendarvis Ben
 
Modular and Recorded Video Lessons in Teaching Music, Arts, Physical Educati...
Modular and Recorded Video Lessons in  Teaching Music, Arts, Physical Educati...Modular and Recorded Video Lessons in  Teaching Music, Arts, Physical Educati...
Modular and Recorded Video Lessons in Teaching Music, Arts, Physical Educati...
Research Publish Journals (Publisher)
 
Action research for Strategic Intervention Materials
Action research for Strategic Intervention MaterialsAction research for Strategic Intervention Materials
Action research for Strategic Intervention Materials
Kristine Barredo
 
Influence of the differences in social studies teachers’ curriculum conceptio...
Influence of the differences in social studies teachers’ curriculum conceptio...Influence of the differences in social studies teachers’ curriculum conceptio...
Influence of the differences in social studies teachers’ curriculum conceptio...
Alexander Decker
 
EwingMonsenKielblock2017online-Teachersattitudestowardsinclusiveeducation-Acr...
EwingMonsenKielblock2017online-Teachersattitudestowardsinclusiveeducation-Acr...EwingMonsenKielblock2017online-Teachersattitudestowardsinclusiveeducation-Acr...
EwingMonsenKielblock2017online-Teachersattitudestowardsinclusiveeducation-Acr...
ximenaoyarzo2
 
Barry Carpenter- Decoding complexity lecture script
Barry Carpenter- Decoding complexity lecture script Barry Carpenter- Decoding complexity lecture script
Barry Carpenter- Decoding complexity lecture script
Swiss Cottage Development and Research Centre
 
FORMATIVE ASSESSMENT PRACTICES IN THE MALAYSIAN ENGLISH LANGUAGE PRIMARY CLAS...
FORMATIVE ASSESSMENT PRACTICES IN THE MALAYSIAN ENGLISH LANGUAGE PRIMARY CLAS...FORMATIVE ASSESSMENT PRACTICES IN THE MALAYSIAN ENGLISH LANGUAGE PRIMARY CLAS...
FORMATIVE ASSESSMENT PRACTICES IN THE MALAYSIAN ENGLISH LANGUAGE PRIMARY CLAS...
indexPub
 
Curriculum innovation in the Philippines (BASIC.pptx
Curriculum innovation in the Philippines (BASIC.pptxCurriculum innovation in the Philippines (BASIC.pptx
Curriculum innovation in the Philippines (BASIC.pptx
Alleli Faith Leyritana
 
The influence of the asei pdsi approach on students' views and
The influence of the asei pdsi approach on students' views andThe influence of the asei pdsi approach on students' views and
The influence of the asei pdsi approach on students' views and
Alexander Decker
 
Ie usahk qualitative journal of education second revision
Ie usahk qualitative journal of education second revisionIe usahk qualitative journal of education second revision
Ie usahk qualitative journal of education second revision
steyngm1
 
Impact of audiovisual aids in teaching home economics in secondary schools
Impact of audiovisual aids in teaching home economics in secondary schoolsImpact of audiovisual aids in teaching home economics in secondary schools
Impact of audiovisual aids in teaching home economics in secondary schools
ResearchWap
 

Similar to An Examination of the Implementation of Mathematics Lessons in a Chinese Kindergarten Classroom in the Setting of Standards Reform.pdf (20)

Appraisal of colleges of education social studies curriculum vis à-vis the j...
 Appraisal of colleges of education social studies curriculum vis à-vis the j... Appraisal of colleges of education social studies curriculum vis à-vis the j...
Appraisal of colleges of education social studies curriculum vis à-vis the j...
 
Algebra Problem-Solving Equity Challenges
Algebra Problem-Solving Equity ChallengesAlgebra Problem-Solving Equity Challenges
Algebra Problem-Solving Equity Challenges
 
The Hidden Curriculum In Education
The Hidden Curriculum In EducationThe Hidden Curriculum In Education
The Hidden Curriculum In Education
 
Curriculum integration in social studies as predictor of academic performance...
Curriculum integration in social studies as predictor of academic performance...Curriculum integration in social studies as predictor of academic performance...
Curriculum integration in social studies as predictor of academic performance...
 
Secondary level-mathematics-curriculum-of-kerala
Secondary level-mathematics-curriculum-of-keralaSecondary level-mathematics-curriculum-of-kerala
Secondary level-mathematics-curriculum-of-kerala
 
2Modern Childhood ClassroomThe Curricu.docx
2Modern Childhood ClassroomThe Curricu.docx2Modern Childhood ClassroomThe Curricu.docx
2Modern Childhood ClassroomThe Curricu.docx
 
Dr. William Allan Kritsonis & Steven Norfleet
Dr. William Allan Kritsonis & Steven NorfleetDr. William Allan Kritsonis & Steven Norfleet
Dr. William Allan Kritsonis & Steven Norfleet
 
Dr. William Kritsonis, Dissertation Chair
Dr. William Kritsonis, Dissertation ChairDr. William Kritsonis, Dissertation Chair
Dr. William Kritsonis, Dissertation Chair
 
An Analysis of Teachers’ Pedagogical Content Knowledge on Number Sense Learni...
An Analysis of Teachers’ Pedagogical Content Knowledge on Number Sense Learni...An Analysis of Teachers’ Pedagogical Content Knowledge on Number Sense Learni...
An Analysis of Teachers’ Pedagogical Content Knowledge on Number Sense Learni...
 
Ex Ed English- research paper
Ex Ed English- research paperEx Ed English- research paper
Ex Ed English- research paper
 
Modular and Recorded Video Lessons in Teaching Music, Arts, Physical Educati...
Modular and Recorded Video Lessons in  Teaching Music, Arts, Physical Educati...Modular and Recorded Video Lessons in  Teaching Music, Arts, Physical Educati...
Modular and Recorded Video Lessons in Teaching Music, Arts, Physical Educati...
 
Action research for Strategic Intervention Materials
Action research for Strategic Intervention MaterialsAction research for Strategic Intervention Materials
Action research for Strategic Intervention Materials
 
Influence of the differences in social studies teachers’ curriculum conceptio...
Influence of the differences in social studies teachers’ curriculum conceptio...Influence of the differences in social studies teachers’ curriculum conceptio...
Influence of the differences in social studies teachers’ curriculum conceptio...
 
EwingMonsenKielblock2017online-Teachersattitudestowardsinclusiveeducation-Acr...
EwingMonsenKielblock2017online-Teachersattitudestowardsinclusiveeducation-Acr...EwingMonsenKielblock2017online-Teachersattitudestowardsinclusiveeducation-Acr...
EwingMonsenKielblock2017online-Teachersattitudestowardsinclusiveeducation-Acr...
 
Barry Carpenter- Decoding complexity lecture script
Barry Carpenter- Decoding complexity lecture script Barry Carpenter- Decoding complexity lecture script
Barry Carpenter- Decoding complexity lecture script
 
FORMATIVE ASSESSMENT PRACTICES IN THE MALAYSIAN ENGLISH LANGUAGE PRIMARY CLAS...
FORMATIVE ASSESSMENT PRACTICES IN THE MALAYSIAN ENGLISH LANGUAGE PRIMARY CLAS...FORMATIVE ASSESSMENT PRACTICES IN THE MALAYSIAN ENGLISH LANGUAGE PRIMARY CLAS...
FORMATIVE ASSESSMENT PRACTICES IN THE MALAYSIAN ENGLISH LANGUAGE PRIMARY CLAS...
 
Curriculum innovation in the Philippines (BASIC.pptx
Curriculum innovation in the Philippines (BASIC.pptxCurriculum innovation in the Philippines (BASIC.pptx
Curriculum innovation in the Philippines (BASIC.pptx
 
The influence of the asei pdsi approach on students' views and
The influence of the asei pdsi approach on students' views andThe influence of the asei pdsi approach on students' views and
The influence of the asei pdsi approach on students' views and
 
Ie usahk qualitative journal of education second revision
Ie usahk qualitative journal of education second revisionIe usahk qualitative journal of education second revision
Ie usahk qualitative journal of education second revision
 
Impact of audiovisual aids in teaching home economics in secondary schools
Impact of audiovisual aids in teaching home economics in secondary schoolsImpact of audiovisual aids in teaching home economics in secondary schools
Impact of audiovisual aids in teaching home economics in secondary schools
 

More from Nancy Ideker

Sell Essays Online
Sell Essays OnlineSell Essays Online
Sell Essays Online
Nancy Ideker
 
Beliefs Essay
Beliefs EssayBeliefs Essay
Beliefs Essay
Nancy Ideker
 
Van Gogh Essay
Van Gogh EssayVan Gogh Essay
Van Gogh Essay
Nancy Ideker
 
Welfare Essays
Welfare EssaysWelfare Essays
Welfare Essays
Nancy Ideker
 
Printable Paper, Graph Paper With One Line Per Inch And
Printable Paper, Graph Paper With One Line Per Inch AndPrintable Paper, Graph Paper With One Line Per Inch And
Printable Paper, Graph Paper With One Line Per Inch And
Nancy Ideker
 
Essay Money Cannot Buy H
Essay Money Cannot Buy HEssay Money Cannot Buy H
Essay Money Cannot Buy H
Nancy Ideker
 
100 Self-Introduction
100 Self-Introduction100 Self-Introduction
100 Self-Introduction
Nancy Ideker
 
Who Can I Pay To Write A Paper For Me - Write My Custom Paper.
Who Can I Pay To Write A Paper For Me - Write My Custom Paper.Who Can I Pay To Write A Paper For Me - Write My Custom Paper.
Who Can I Pay To Write A Paper For Me - Write My Custom Paper.
Nancy Ideker
 
Mrs. BoydS Site Research Paper
Mrs. BoydS Site Research PaperMrs. BoydS Site Research Paper
Mrs. BoydS Site Research Paper
Nancy Ideker
 
How To Write Impressive College Entrance Essays
How To Write Impressive College Entrance EssaysHow To Write Impressive College Entrance Essays
How To Write Impressive College Entrance Essays
Nancy Ideker
 
16 Best Images Of Persuasive Writing Worksh
16 Best Images Of Persuasive Writing Worksh16 Best Images Of Persuasive Writing Worksh
16 Best Images Of Persuasive Writing Worksh
Nancy Ideker
 
Essay Writing Service In Australia - Essay Writing Service By Top
Essay Writing Service In Australia - Essay Writing Service By TopEssay Writing Service In Australia - Essay Writing Service By Top
Essay Writing Service In Australia - Essay Writing Service By Top
Nancy Ideker
 
How To Write A Law Essay Like A Pro CustomEssay
How To Write A Law Essay Like A Pro CustomEssayHow To Write A Law Essay Like A Pro CustomEssay
How To Write A Law Essay Like A Pro CustomEssay
Nancy Ideker
 
How To Write An Explanatory Essay Topics, Outline, Ex
How To Write An Explanatory Essay Topics, Outline, ExHow To Write An Explanatory Essay Topics, Outline, Ex
How To Write An Explanatory Essay Topics, Outline, Ex
Nancy Ideker
 
How To Write An Introduction Paragraph Of A Research
How To Write An Introduction Paragraph Of A ResearchHow To Write An Introduction Paragraph Of A Research
How To Write An Introduction Paragraph Of A Research
Nancy Ideker
 
013 Essay Example What Is Diversity Essays On In Coll
013 Essay Example What Is Diversity Essays On In Coll013 Essay Example What Is Diversity Essays On In Coll
013 Essay Example What Is Diversity Essays On In Coll
Nancy Ideker
 
Paragraph Writing (Simple, Five Sentence F
Paragraph Writing (Simple, Five Sentence FParagraph Writing (Simple, Five Sentence F
Paragraph Writing (Simple, Five Sentence F
Nancy Ideker
 
Printable Kindergarten Writing Paper Template
Printable Kindergarten Writing Paper TemplatePrintable Kindergarten Writing Paper Template
Printable Kindergarten Writing Paper Template
Nancy Ideker
 
Reddit.Com Us Papers Writing Service - Malta Blu
Reddit.Com Us Papers Writing Service - Malta BluReddit.Com Us Papers Writing Service - Malta Blu
Reddit.Com Us Papers Writing Service - Malta Blu
Nancy Ideker
 
How To Write An Expository Thesis. Expository Essay
How To Write An Expository Thesis. Expository EssayHow To Write An Expository Thesis. Expository Essay
How To Write An Expository Thesis. Expository Essay
Nancy Ideker
 

More from Nancy Ideker (20)

Sell Essays Online
Sell Essays OnlineSell Essays Online
Sell Essays Online
 
Beliefs Essay
Beliefs EssayBeliefs Essay
Beliefs Essay
 
Van Gogh Essay
Van Gogh EssayVan Gogh Essay
Van Gogh Essay
 
Welfare Essays
Welfare EssaysWelfare Essays
Welfare Essays
 
Printable Paper, Graph Paper With One Line Per Inch And
Printable Paper, Graph Paper With One Line Per Inch AndPrintable Paper, Graph Paper With One Line Per Inch And
Printable Paper, Graph Paper With One Line Per Inch And
 
Essay Money Cannot Buy H
Essay Money Cannot Buy HEssay Money Cannot Buy H
Essay Money Cannot Buy H
 
100 Self-Introduction
100 Self-Introduction100 Self-Introduction
100 Self-Introduction
 
Who Can I Pay To Write A Paper For Me - Write My Custom Paper.
Who Can I Pay To Write A Paper For Me - Write My Custom Paper.Who Can I Pay To Write A Paper For Me - Write My Custom Paper.
Who Can I Pay To Write A Paper For Me - Write My Custom Paper.
 
Mrs. BoydS Site Research Paper
Mrs. BoydS Site Research PaperMrs. BoydS Site Research Paper
Mrs. BoydS Site Research Paper
 
How To Write Impressive College Entrance Essays
How To Write Impressive College Entrance EssaysHow To Write Impressive College Entrance Essays
How To Write Impressive College Entrance Essays
 
16 Best Images Of Persuasive Writing Worksh
16 Best Images Of Persuasive Writing Worksh16 Best Images Of Persuasive Writing Worksh
16 Best Images Of Persuasive Writing Worksh
 
Essay Writing Service In Australia - Essay Writing Service By Top
Essay Writing Service In Australia - Essay Writing Service By TopEssay Writing Service In Australia - Essay Writing Service By Top
Essay Writing Service In Australia - Essay Writing Service By Top
 
How To Write A Law Essay Like A Pro CustomEssay
How To Write A Law Essay Like A Pro CustomEssayHow To Write A Law Essay Like A Pro CustomEssay
How To Write A Law Essay Like A Pro CustomEssay
 
How To Write An Explanatory Essay Topics, Outline, Ex
How To Write An Explanatory Essay Topics, Outline, ExHow To Write An Explanatory Essay Topics, Outline, Ex
How To Write An Explanatory Essay Topics, Outline, Ex
 
How To Write An Introduction Paragraph Of A Research
How To Write An Introduction Paragraph Of A ResearchHow To Write An Introduction Paragraph Of A Research
How To Write An Introduction Paragraph Of A Research
 
013 Essay Example What Is Diversity Essays On In Coll
013 Essay Example What Is Diversity Essays On In Coll013 Essay Example What Is Diversity Essays On In Coll
013 Essay Example What Is Diversity Essays On In Coll
 
Paragraph Writing (Simple, Five Sentence F
Paragraph Writing (Simple, Five Sentence FParagraph Writing (Simple, Five Sentence F
Paragraph Writing (Simple, Five Sentence F
 
Printable Kindergarten Writing Paper Template
Printable Kindergarten Writing Paper TemplatePrintable Kindergarten Writing Paper Template
Printable Kindergarten Writing Paper Template
 
Reddit.Com Us Papers Writing Service - Malta Blu
Reddit.Com Us Papers Writing Service - Malta BluReddit.Com Us Papers Writing Service - Malta Blu
Reddit.Com Us Papers Writing Service - Malta Blu
 
How To Write An Expository Thesis. Expository Essay
How To Write An Expository Thesis. Expository EssayHow To Write An Expository Thesis. Expository Essay
How To Write An Expository Thesis. Expository Essay
 

Recently uploaded

MATATAG CURRICULUM sample lesson exemplar.docx
MATATAG CURRICULUM sample lesson exemplar.docxMATATAG CURRICULUM sample lesson exemplar.docx
MATATAG CURRICULUM sample lesson exemplar.docx
yardenmendoza
 
3. Maturity_indices_of_fruits_and_vegetable.pptx
3. Maturity_indices_of_fruits_and_vegetable.pptx3. Maturity_indices_of_fruits_and_vegetable.pptx
3. Maturity_indices_of_fruits_and_vegetable.pptx
UmeshTimilsina1
 
DepEd School Calendar 2024-2025 DO_s2024_008
DepEd School Calendar 2024-2025 DO_s2024_008DepEd School Calendar 2024-2025 DO_s2024_008
DepEd School Calendar 2024-2025 DO_s2024_008
Glenn Rivera
 
C# Interview Questions PDF By ScholarHat.pdf
C# Interview Questions PDF By ScholarHat.pdfC# Interview Questions PDF By ScholarHat.pdf
C# Interview Questions PDF By ScholarHat.pdf
Scholarhat
 
Java MCQ Questions and Answers PDF By ScholarHat
Java MCQ Questions and Answers PDF By ScholarHatJava MCQ Questions and Answers PDF By ScholarHat
Java MCQ Questions and Answers PDF By ScholarHat
Scholarhat
 
Benchmarking Sustainability: Neurosciences and AI Tech Research in Macau - Ke...
Benchmarking Sustainability: Neurosciences and AI Tech Research in Macau - Ke...Benchmarking Sustainability: Neurosciences and AI Tech Research in Macau - Ke...
Benchmarking Sustainability: Neurosciences and AI Tech Research in Macau - Ke...
Alvaro Barbosa
 
INSIDE OUT - PowerPoint Presentation.pptx
INSIDE OUT - PowerPoint Presentation.pptxINSIDE OUT - PowerPoint Presentation.pptx
INSIDE OUT - PowerPoint Presentation.pptx
RODELAZARES3
 
Introduction to Google Productivity Tools for Office and Personal Use
Introduction to Google Productivity Tools for Office and Personal UseIntroduction to Google Productivity Tools for Office and Personal Use
Introduction to Google Productivity Tools for Office and Personal Use
Excellence Foundation for South Sudan
 
Codeavour 5.0 International Impact Report - The Biggest International AI, Cod...
Codeavour 5.0 International Impact Report - The Biggest International AI, Cod...Codeavour 5.0 International Impact Report - The Biggest International AI, Cod...
Codeavour 5.0 International Impact Report - The Biggest International AI, Cod...
Codeavour International
 
Lecture Notes Unit4 Chapter13 users , roles and privileges
Lecture Notes Unit4 Chapter13 users , roles and privilegesLecture Notes Unit4 Chapter13 users , roles and privileges
Lecture Notes Unit4 Chapter13 users , roles and privileges
Murugan146644
 
ASP.NET Core Interview Questions PDF By ScholarHat.pdf
ASP.NET Core Interview Questions PDF By ScholarHat.pdfASP.NET Core Interview Questions PDF By ScholarHat.pdf
ASP.NET Core Interview Questions PDF By ScholarHat.pdf
Scholarhat
 
C Interview Questions PDF By Scholarhat.pdf
C Interview Questions PDF By Scholarhat.pdfC Interview Questions PDF By Scholarhat.pdf
C Interview Questions PDF By Scholarhat.pdf
Scholarhat
 
Dr. Nasir Mustafa CERTIFICATE OF APPRECIATION "NEUROANATOMY"
Dr. Nasir Mustafa CERTIFICATE OF APPRECIATION "NEUROANATOMY"Dr. Nasir Mustafa CERTIFICATE OF APPRECIATION "NEUROANATOMY"
Dr. Nasir Mustafa CERTIFICATE OF APPRECIATION "NEUROANATOMY"
Dr. Nasir Mustafa
 
React Interview Question PDF By ScholarHat
React Interview Question PDF By ScholarHatReact Interview Question PDF By ScholarHat
React Interview Question PDF By ScholarHat
Scholarhat
 
slidesgo-mastering-the-art-of-listening-insights-from-robin-sharma-2024070718...
slidesgo-mastering-the-art-of-listening-insights-from-robin-sharma-2024070718...slidesgo-mastering-the-art-of-listening-insights-from-robin-sharma-2024070718...
slidesgo-mastering-the-art-of-listening-insights-from-robin-sharma-2024070718...
MANIVALANSR
 
SD_Integrating 21st Century Skills in Classroom-based Assessment.pptx
SD_Integrating 21st Century Skills in Classroom-based Assessment.pptxSD_Integrating 21st Century Skills in Classroom-based Assessment.pptx
SD_Integrating 21st Century Skills in Classroom-based Assessment.pptx
elwoodprias1
 
Brigada Eskwela 2024 PowerPoint Update for SY 2024-2025
Brigada Eskwela 2024 PowerPoint Update for SY 2024-2025Brigada Eskwela 2024 PowerPoint Update for SY 2024-2025
Brigada Eskwela 2024 PowerPoint Update for SY 2024-2025
ALBERTHISOLER1
 
PRESS RELEASE - UNIVERSITY OF GHANA, JULY 16, 2024.pdf
PRESS RELEASE - UNIVERSITY OF GHANA, JULY 16, 2024.pdfPRESS RELEASE - UNIVERSITY OF GHANA, JULY 16, 2024.pdf
PRESS RELEASE - UNIVERSITY OF GHANA, JULY 16, 2024.pdf
nservice241
 
11. Post harvest quality, Quality criteria and Judgement.pptx
11. Post harvest quality, Quality criteria and Judgement.pptx11. Post harvest quality, Quality criteria and Judgement.pptx
11. Post harvest quality, Quality criteria and Judgement.pptx
UmeshTimilsina1
 
JavaScript Interview Questions PDF By ScholarHat
JavaScript Interview  Questions PDF By ScholarHatJavaScript Interview  Questions PDF By ScholarHat
JavaScript Interview Questions PDF By ScholarHat
Scholarhat
 

Recently uploaded (20)

MATATAG CURRICULUM sample lesson exemplar.docx
MATATAG CURRICULUM sample lesson exemplar.docxMATATAG CURRICULUM sample lesson exemplar.docx
MATATAG CURRICULUM sample lesson exemplar.docx
 
3. Maturity_indices_of_fruits_and_vegetable.pptx
3. Maturity_indices_of_fruits_and_vegetable.pptx3. Maturity_indices_of_fruits_and_vegetable.pptx
3. Maturity_indices_of_fruits_and_vegetable.pptx
 
DepEd School Calendar 2024-2025 DO_s2024_008
DepEd School Calendar 2024-2025 DO_s2024_008DepEd School Calendar 2024-2025 DO_s2024_008
DepEd School Calendar 2024-2025 DO_s2024_008
 
C# Interview Questions PDF By ScholarHat.pdf
C# Interview Questions PDF By ScholarHat.pdfC# Interview Questions PDF By ScholarHat.pdf
C# Interview Questions PDF By ScholarHat.pdf
 
Java MCQ Questions and Answers PDF By ScholarHat
Java MCQ Questions and Answers PDF By ScholarHatJava MCQ Questions and Answers PDF By ScholarHat
Java MCQ Questions and Answers PDF By ScholarHat
 
Benchmarking Sustainability: Neurosciences and AI Tech Research in Macau - Ke...
Benchmarking Sustainability: Neurosciences and AI Tech Research in Macau - Ke...Benchmarking Sustainability: Neurosciences and AI Tech Research in Macau - Ke...
Benchmarking Sustainability: Neurosciences and AI Tech Research in Macau - Ke...
 
INSIDE OUT - PowerPoint Presentation.pptx
INSIDE OUT - PowerPoint Presentation.pptxINSIDE OUT - PowerPoint Presentation.pptx
INSIDE OUT - PowerPoint Presentation.pptx
 
Introduction to Google Productivity Tools for Office and Personal Use
Introduction to Google Productivity Tools for Office and Personal UseIntroduction to Google Productivity Tools for Office and Personal Use
Introduction to Google Productivity Tools for Office and Personal Use
 
Codeavour 5.0 International Impact Report - The Biggest International AI, Cod...
Codeavour 5.0 International Impact Report - The Biggest International AI, Cod...Codeavour 5.0 International Impact Report - The Biggest International AI, Cod...
Codeavour 5.0 International Impact Report - The Biggest International AI, Cod...
 
Lecture Notes Unit4 Chapter13 users , roles and privileges
Lecture Notes Unit4 Chapter13 users , roles and privilegesLecture Notes Unit4 Chapter13 users , roles and privileges
Lecture Notes Unit4 Chapter13 users , roles and privileges
 
ASP.NET Core Interview Questions PDF By ScholarHat.pdf
ASP.NET Core Interview Questions PDF By ScholarHat.pdfASP.NET Core Interview Questions PDF By ScholarHat.pdf
ASP.NET Core Interview Questions PDF By ScholarHat.pdf
 
C Interview Questions PDF By Scholarhat.pdf
C Interview Questions PDF By Scholarhat.pdfC Interview Questions PDF By Scholarhat.pdf
C Interview Questions PDF By Scholarhat.pdf
 
Dr. Nasir Mustafa CERTIFICATE OF APPRECIATION "NEUROANATOMY"
Dr. Nasir Mustafa CERTIFICATE OF APPRECIATION "NEUROANATOMY"Dr. Nasir Mustafa CERTIFICATE OF APPRECIATION "NEUROANATOMY"
Dr. Nasir Mustafa CERTIFICATE OF APPRECIATION "NEUROANATOMY"
 
React Interview Question PDF By ScholarHat
React Interview Question PDF By ScholarHatReact Interview Question PDF By ScholarHat
React Interview Question PDF By ScholarHat
 
slidesgo-mastering-the-art-of-listening-insights-from-robin-sharma-2024070718...
slidesgo-mastering-the-art-of-listening-insights-from-robin-sharma-2024070718...slidesgo-mastering-the-art-of-listening-insights-from-robin-sharma-2024070718...
slidesgo-mastering-the-art-of-listening-insights-from-robin-sharma-2024070718...
 
SD_Integrating 21st Century Skills in Classroom-based Assessment.pptx
SD_Integrating 21st Century Skills in Classroom-based Assessment.pptxSD_Integrating 21st Century Skills in Classroom-based Assessment.pptx
SD_Integrating 21st Century Skills in Classroom-based Assessment.pptx
 
Brigada Eskwela 2024 PowerPoint Update for SY 2024-2025
Brigada Eskwela 2024 PowerPoint Update for SY 2024-2025Brigada Eskwela 2024 PowerPoint Update for SY 2024-2025
Brigada Eskwela 2024 PowerPoint Update for SY 2024-2025
 
PRESS RELEASE - UNIVERSITY OF GHANA, JULY 16, 2024.pdf
PRESS RELEASE - UNIVERSITY OF GHANA, JULY 16, 2024.pdfPRESS RELEASE - UNIVERSITY OF GHANA, JULY 16, 2024.pdf
PRESS RELEASE - UNIVERSITY OF GHANA, JULY 16, 2024.pdf
 
11. Post harvest quality, Quality criteria and Judgement.pptx
11. Post harvest quality, Quality criteria and Judgement.pptx11. Post harvest quality, Quality criteria and Judgement.pptx
11. Post harvest quality, Quality criteria and Judgement.pptx
 
JavaScript Interview Questions PDF By ScholarHat
JavaScript Interview  Questions PDF By ScholarHatJavaScript Interview  Questions PDF By ScholarHat
JavaScript Interview Questions PDF By ScholarHat
 

An Examination of the Implementation of Mathematics Lessons in a Chinese Kindergarten Classroom in the Setting of Standards Reform.pdf

  • 1. Full Terms & Conditions of access and use can be found at http://www.tandfonline.com/action/journalInformation?journalCode=ujrc20 Download by: [University of Newcastle, Australia] Date: 21 February 2017, At: 22:04 Journal of Research in Childhood Education ISSN: 0256-8543 (Print) 2150-2641 (Online) Journal homepage: http://www.tandfonline.com/loi/ujrc20 An Examination of the Implementation of Mathematics Lessons in a Chinese Kindergarten Classroom in the Setting of Standards Reform Bi Ying Hu, Sarah Quebec Fuentes, Jingjing Ma, Feiwei Ye & Sherron Killingsworth Roberts To cite this article: Bi Ying Hu, Sarah Quebec Fuentes, Jingjing Ma, Feiwei Ye & Sherron Killingsworth Roberts (2017) An Examination of the Implementation of Mathematics Lessons in a Chinese Kindergarten Classroom in the Setting of Standards Reform, Journal of Research in Childhood Education, 31:1, 53-70, DOI: 10.1080/02568543.2016.1244581 To link to this article: http://dx.doi.org/10.1080/02568543.2016.1244581 Published online: 04 Jan 2017. Submit your article to this journal Article views: 7 View related articles View Crossmark data
  • 2. An Examination of the Implementation of Mathematics Lessons in a Chinese Kindergarten Classroom in the Setting of Standards Reform Bi Ying Hua , Sarah Quebec Fuentesb , Jingjing Mab , Feiwei Yec , and Sherron Killingsworth Robertsd a University of Macau, Taipa, Macao; b Texas Christian University, Fort Worth, Texas; c Zhejiang Normal University, Zhejiang, China; d University of Central Florida, Orlando, Florida ABSTRACT In China, the 2001 Kindergarten Education Guidelines (Trial), or New Outline, delineates what constitutes high-quality, developmentally appropriate practices in all early childhood education curriculum domains, including mathematics. The New Outline is known for advocating a child-centered, play-based approach to teaching and learning, a significant change from teacher-directed instruction. Research highlights a gap between the intended practices set forth in the New Outline and the enacted practices in Chinese kindergarten classrooms. This descriptive study examines the implementation of 10 mathematics lessons, delivered over a 6-month period, from one Chinese kindergarten classroom in light of the New Outline. The analysis revealed that the lessons reflected aspects of the New Outline. However, overall, the lessons lacked critical components to provide students with opportunities to construct an understanding of the mathematics and become independent learners in five areas: (1) opportunities to inspire autonomous and life-long learning, (2) strategies for differentiated instruction, (3) use of resources to represent mathematics concepts, (4) student- centered instructional approaches, and (5) ways to foster communication. ARTICLE HISTORY Received 9 December 2014 Accepted 27 August 2015 KEYWORDS China; kindergarten; mathematics curriculum reform Children’s early success with mathematics sets a solid foundation for their later academic achievements (Duncan et al., 2007). During the kindergarten year, children are formally being introduced to basic mathematics concepts critical for later mastery of complex concepts and skills (Van Luit & Schopman, 2000). The quality of kindergarten mathematics teaching, including instructional and motivational support, directly affects children’s learning experiences and success with mathematics (Sarama & Clements, 2004). In China, the Kindergarten Education Guidelines (Trial) (Ministry of Education, 2001), also called the New Outline, delineates what constitutes high-quality, developmentally appropriate practices in all early childhood education1 (ECE) curriculum domains, including mathematics (Hu, 2011; Wang, 2008). The New Outline is known for advocating a child-centered, play-based approach to teaching and learning, a sharp contrast to teacher-directed instruction. Although the current Chinese kin- dergarten mathematics standards from the New Outline promote the teaching of mathematics for the long-term goal of better understanding the world, grounding teaching in children’s daily lives and activities and using problem solving as a driving motivator, the New Outline lacks guidance on how teachers might achieve these reform-oriented ideas (Ministry of Education, 2001). Through a descriptive study of the implementation of 10 mathematics lessons, delivered over a 6-month period, from one Chinese kindergarten classroom, the purpose of the present research is CONTACT Sarah Quebec Fuentes s.quebec.fuentes@tcu.edu College of Education, Texas Christian University, TCU Box 297920, Fort Worth, TX 76129. Color versions of one or more of the figures in the article can be found online at www.tandfonline.com/ujrc. © 2017 Association for Childhood Education International JOURNAL OF RESEARCH IN CHILDHOOD EDUCATION 2017, VOL. 31, NO. 1, 53–70 http://dx.doi.org/10.1080/02568543.2016.1244581
  • 3. to evaluate the lessons in light of the New Outline. This article provides a historical overview on the development of curriculum standards for Chinese kindergarten mathematics since 1904 and Chinese scholars’ views toward the newer child-centered curriculum movement. The methods for conducting the descriptive study, including an analysis of the New Outline, are described. Aspects of the 10 lessons, which align and do not align with the practices endorsed by the New Outline, are identified, and, based on these findings, implications and directions for future research are discussed. Curriculum standards development in Chinese early childhood education The history of kindergarten curriculum standards in China can be traced back to 1904, when the Qing government promulgated regulations for early education. However, the government of the Republic Ministry of Education did not announce China’s first kindergarten curriculum standards until 1932 (Tang, 2005). The standards were divided into three parts, namely, objectives, scope and sequences, and key teaching methods. A group of ECE scholars, who understood not only Western theories, but also China’s realities, drafted China’s first national curriculum standards (Tang, 2005). This first set of standards attended to physical exercise, emphasized developing children’s creativity and imagination, and embedded ways to honor children’s learning interests. The standards also expected ECE programs to nurture children’s aesthetic and emotional development as well as qualities such as self-confidence and persever- ance through flexible and active teaching methodologies (Wang, 2004). Moreover, in addition to general requirements, the standards also addressed minimum requirements to be adaptable to the different regions of China, which had varying educational opportunities. At that time, the ECE curriculum standards seemed to embrace the idea of child-centered teaching. This trend of embracing child-centered teaching ceased upon the founding of the People’s Republic of China (PRC) in 1949. Since then, the government has issued three kindergarten curriculum standards, in 1952, 1981, and 2001 (Wang, 2004). Due to political influences, the 1952 Provisional Kindergarten Teaching Outline (Ministry of Education in People’s Republic of China, 1952) adopted the educational concepts embraced by the Soviet Union at that time. The provisional outline of 1952 advised practitioners to focus on age and individual differences of children, and it organized guidelines for teaching around six subjects: physical education, language, environmental awareness, art, music, and arithmetic. For each subject, the outline included objectives, curriculum frameworks, teaching foci, and teaching equipment. Influenced by Piaget’s cognitive development theory (Piaget, 1926), the 1952 provisional outline emphasized the sys- tematic and logical coherence of mathematics. Instead of showing connections among the six subjects, each subject was taught separately. In 1981, the Ministry of Education of the PRC issued the 1981 Kindergarten Education Outline, which clearly stated that the goal for kindergarten education was for students to develop fully in all domains (i.e., physical education, language, environmental awareness, art, music, and arithmetic) and to build a solid foundation for primary education. Notably, the 1981 Outline changed its title from Teaching Outline (Ministry of Education of People’s Republic of China, 1952) to Education Outline (Ministry of Education in People’s Republic of China, 1981) to reflect the consensus among ECE scholars that the main responsibilities of a kindergarten are teaching and caring for young children. The 1981 Outline stressed the importance of play in teaching and learning, emphasizing that preschoolers should not be given tests and homework. In fact, the 1981 Kindergarten Education Outline emphasized the importance of meeting teaching and content requirements through activ- ities, observation, and connections with everyday life. However, due to inadequate ECE teacher training, teachers used lecture as the main instructional method, and so kindergartens resembled elementary schools (Wang, 2004). Similar to the 1952 Provisional Kindergarten Teaching Outline, the 1981 Kindergarten Education Outline kept distinctive boundaries across the six subjects. The 1981 Kindergarten Education Outline referred to mathematics as arithmetic and placed great emphasis on mastering basic mathematical skills within specified content areas. Standards were written in succinct language to allow for teachers to understand and transfer them into teaching objectives 54 B. Y. HU ET AL.
  • 4. (e.g., “Students can identify even and odd numbers within 10”). According to Chen (2005), the 1981 Outline did not take children’s learning interests into account; instead, it catered to teachers’ preferred teaching style: lecture-based, whole-class instruction. Chen (2005) explained that the more the guidelines focus on content, the more likely teachers will deliver the mathematics content via whole-class instruction, instead of integrating the content into play and/or using a thematic unit approach. In 1997, the National Association for the Education of Young Children (NAEYC) published Developmentally Appropriate Practice in Early Childhood Programs (Bredekamp & Copple, 1997), which advocated for a reform-oriented approach to teaching and learning; that is, children should learn science and mathematics concepts through hands-on discovery and self- construction of meaning. Meanwhile, an increased concern about the lack of focus on children’s interests and teachers’ dominant use of whole-group teaching methods led Chinese ECE scholars to call for curriculum reform. This curriculum reform, which was influenced by the NAEYC publication, sought to minimize the distinct subject approach to the ECE curriculum and advocated for the use of an integrated thematic unit approach. As a result, the Chinese Ministry of Education (2001) produced the Kindergarten Education Guidelines (Trial) (also called the New Outline), which endorsed the use of an integrated curricular approach to kindergarten education. The New Outline divided the kindergarten curriculum into five domains: health, language, social studies, science, and art. As a consequence, mathematics was incorporated into the science domain in the New Outline. Compared to the 1981 Outline, the New Outline made significant adjustments concerning kindergarten mathematics, including changes in objectives, content, and instructional methodology. The mathematics objectives, according to the New Outline, are to “experience quantitative relationships through daily life and play, and gain a sense of the importance as well as fun of learning mathematics” (Ministry of Education, 2001, p. 34). Chinese ECE scholars favored the new standards’ move toward a child-centered curriculum and instructional approach (Chen, 2005; Pan, 2005; Wu, 2003). Chen (2005) believed that the succinctly expressed mathematics standards reduce the emphasis on solely teaching mathematics content; the standards reflect the fun in teaching and learning and stress the importance of learning mathematics through daily life experiences. Pan (2005) also expressed that the New Outline minimizes the goal of mastering instructional content and stresses building connections with other disciplines, thereby enriching instruction. Another feature of the New Outline, according to Pan (2005), is the emphasis on children’s self-construction of knowledge and the cultivation of children’s positive attitudes toward and competencies in mathematics, all of which, in turn, positively lessen the teachers’ roles as knowledge disseminators and their heavy reliance on the use of direct, whole-group instruction. ECE scholars also acknowledge challenges in implementing the practices promoted by the New Outline (Hu, 2011; Lin, 2004; Su & Cai, 2006; Wang, 2004; Zhu & Zhang, 2008). As the kindergarten mathematics standards reform continues, scholars (e.g., Lin, 2004; Su & Cai, 2006) have suggested accentuating the process and outcomes of mathematics standards in regard to teaching and learning, instead of being limited to mathematics content objectives. However, Wang (2004) has pointed out an existing gap between instruction envisioned in the New Outline and mathematics teaching in Chinese kindergartens. Therefore, this shift introduces challenges for teachers whose professional knowledge and skills, previous experiences as learners, and cultural beliefs do not align with the current reform (Dunphy, 2009; Huo, 2004; Pan, 2005). Scholars have gradually recognized that the goal for such mathematics reform should be focused on effective teaching, and providing instruc- tional support to teachers. Teacher development, in fact, has been identified as an important aspect of successful school reform (Dossey, 2007; Remillard & Bryans, 2004; Sun, 2008) and is addressed in the New Outline. There is a section for teacher professionalization and training that states: JOURNAL OF RESEARCH IN CHILDHOOD EDUCATION 55
  • 5. Local educational administrative departments should develop effective, ongoing teacher training programs. Teacher professional-development training institutions shall view conducting necessary training for new curriculum implementation as the main task and ensure the synchronization of the training with curriculum reform. (Ministry of Education, 2001, Teacher Professionalization and Training section, para. 2) However, according to Wang (2004), Chinese teachers need additional development in the areas of building upon children’s ideas and cultivating children’s critical thinking as the New Outline suggests. Further, preschool teachers have noted a lack of instructional support in implementing the new integrated curriculum outlined in the reform (Hu, 2011). Therefore, the purpose of the present study is to examine the implementation of 10 mathematics lessons from a curriculum that was created to meet the standards of the New Outline, in one Chinese kindergarten classroom in light of the recommendations in New Outline. Method A descriptive study was conducted due to the dynamic relationship between education reform at the macro- and microlevels. First, successful education reform at the national level requires effective implementation of reform in local schools (Borko, Wolf, Simone, & Uchiyama, 2003). Second, detailed analysis of the implementation of reform within classrooms can provide rich and concrete evidence for the improvement of education reform (Ross, McDougall, Hogaboam-Gray, & LeSage, 2003). Setting and participants The researchers purposively selected one kindergarten to participate in the study because the school used a mathematics curriculum, which was designed to align with the New Outline. Founded in 1954 and located in Hangzhou, Zhejiang, Kindergarten A is considered a high-quality public kindergarten and currently serves 230 children, ages 2 to 6, on two campuses with a total of 42 staff members. Kindergarten A has two kindergarten classes, each with 35 students (ages 5 and 6); both classes use an integrated provincial curriculum called Life, Practice/Fulfill, and Wisdom. Developed by ECE faculty and experienced teachers to celebrate the spirit of the New Outline, the provincial curriculum embraces a child-centered approach to classroom teaching and learning. As an integrated curricu- lum, it uses thematic units to organize grade-level content and learning activities, guided by the New Outline. The complete curriculum, which covers all five previously named subject area domains, also includes (1) children’s books, (2) a teachers’ guide, (3) art materials, (4) mathematics manipulatives, (5) pictures to hang in the classroom, (5) audiocassettes, and (7) a teacher’s resource booklet. The teacher of one of the kindergarten classes agreed to participate in the study and has a bachelor’s degree in ECE from a local normal university. This teacher has 5 years of teaching experience, 3 ½ of which have been at Kindergarten A. Life, Practice/Fulfill, and Wisdom is the third curriculum that the teacher has used. Instrument The Classroom Observation of Early Mathematics Environment and Teaching (COEMET) (Sarama & Clements, 2007) was used by the researchers to analyze the 10 mathematics lessons. The COEMET is an observational tool specifically designed to evaluate mathematics instruction in early childhood settings. The instrument has three sections: Classroom Culture (nine items under two subscales); Specific Math Activity (SMA), for any activity directly involving the teacher (19 items under seven subscales); and Mini SMA, a brief description of any activity, such as centers, that does not directly involve the teacher. Refer to the appendix for a list of the nine subscales and 28 items. Twenty-four of the items are scored on a 5-point Likert-type scale (strongly disagree = 1, disagree = 2, neutral = 3, agree = 4, and strongly agree = 5). For each item, the rater indicates his or her level of agreement with 56 B. Y. HU ET AL.
  • 6. each statement with respect to the observed instruction. For the remaining four items (1, 2, 4, and 15), the approximate percentage of occurrence is documented (i.e., 0% = 1, 1%–25% = 2, 26%–50% = 3, 51%–75% = 4, and 76%–100% = 5). Not Applicable (NA) may be used for any of the items. Sarama and Clements (2007) reported strong interrater reliability (r = .88) and internal consistency (>.94) for the instrument in their study. Although the COEMET is an instrument from the United States, which is one of the countries that influenced the development of the New Outline (Li, 2007; Wu, 2001), an analysis of the New Outline was conducted to ensure that the COEMET was appropriate to use in a Chinese context. The New Outline consists of a brief introduction providing the reason for its creation and nine sections, which are further divided into 20 subsections, describing the reform details. These nine sections include the goal of curriculum reform, the structure of curricula, curriculum standards, teaching process, development and management of curricular programs, curriculum evaluation, curriculum management, teacher professionalization and training, and organization and implementation of curriculum reform. Even though there is one section that specifically addresses instruction (i.e., teaching process), references to instruction are found throughout the various sections of the New Outline. Therefore, two researchers coded all references to instruction in the nine sections of the New Outline. This process resulted in 36 codes, such as real-world connections, individual needs, enthusiasm for learning, discussion, and problem solving. Through the sorting of the 36 codes, five overarching categories emerged. The first two columns in Table 1 present the five overarching categories and their descriptions. To determine if the COEMET was suitable for analyzing instruction in a Chinese classroom in the era of the New Outline, the researchers determined whether each COEMET item aligned with one of the aforementioned overarching categories. The results of the item alignment are in the third column of Table 1. With the exception of three items (2, 7, and 10), all remaining items were aligned with one of the overarching categories. Item 2 references the actions of any support staff. Although the described actions align with the New Outline, there was not any support staff in the kindergarten Table 1. Overarching categories from analysis of the new outline and corresponding Classroom Observation of Early Mathematics Environment and Teaching (COEMET) items. Overarching Category Description COEMET Items Category Mean Expectations and outcomes Foster students’ lifelong learning skills by helping them develop the ability to learn and apply knowledge independently and stimulating their curiosity and interest in learning. 8, 9, 18 2.07 Developmental dimensions Meet the mental and physical needs of students based on their developmental characteristics (e.g., age group and individual) through appropriate teaching and learning strategies. 11, 13, 16, 17, 24, 25, 27, 28 3.10 Resources and connections Utilize various educational resources and learning tools, including technology, from both inside and outside of the classroom to help students develop connections between learning and real life, their family, community, and society. 4, 5 2.50 Active learning Encourage active learning and engagement through exploration, experimentation, investigation, collecting and analyzing information, observation, questioning, problem solving, hands-on activities, and playing games. 12, 14, 26 3.17 Interaction and communication Promote students’ abilities to communicate and cooperate with each other and the teacher by actively interacting with students. 1, 3, 6, 15, 19, 20, 21, 22, 23 3.09 Note. For items 1, 2, 4, and 15, 1 = 0%, 2 = 1%–25%, 3 = 26%–50%, 4 = 51%–75%, and 5 = 76%–100%. For the remaining items, 1 = strongly disagree, 2 = disagree, 3 = neutral, 4 = agree, and 5 = strongly agree. JOURNAL OF RESEARCH IN CHILDHOOD EDUCATION 57
  • 7. classroom examined in this study. In contrast, Items 7 and 10 relate to the content knowledge of the teacher, which is not addressed in the New Outline. Therefore, these three items were eliminated from the analysis. Overall, the alignment process shows that the COEMET is relevant to Chinese lesson implementation under the New Outline. Procedure The researchers collected three forms of data: videotaped lessons, observation field notes, and teacher interviews. Upon receiving consent, a research assistant visited the kindergarten class regularly to observe and videotape mathematics lessons. From January 2011 to June 2011, a total of 10 lessons (each approximately 30–45 minutes in length) were observed and videotaped once every other week to ensure that data included representative lessons across the semester. Table 2 shows the theme, title, and content areas for each observed lesson. The videotape captured the teacher’s whole-class instruction and accompanying student-teacher interactions. The research assistant took field notes during center activities and individual work time to document teacher- student and student-student interactions as well as the overall action within the classroom. The research assistant also interviewed the teacher two times. The interviews were semistructured and ranged in length from 40 to 80 minutes. The focus of the first interview, which occurred at the beginning of the research period, was on the teacher’s views about and implementation of the Provincial Curriculum. The second interview was conducted toward the end of the research period and addressed the support the teacher received via the curriculum materials. Data analysis Two research assistants, graduate students majoring in ECE, analyzed the 10 videotaped mathe- matics lessons using the COEMET. In line with Sarama and Clements’ (2007) suggestion, the research assistants studied a self-training packet with detailed instructions for assessment procedures and examples of classroom episodes for ease and accuracy of coding. Individually, the research assistants watched, rewatched, and scored each videotaped lesson. For the first two lessons, the research assistants discussed discrepancies in scores to reach consensus. The research assistants individually scored the third lesson with an interrater reliability of 0.80. After the discussion of scores in the first two phases, the research assistants individually scored the remaining seven lessons, reaching an overall interrater reliability of 0.85. In addition, the researchers identified classroom episodes aligning with each item and its corresponding rating for every lesson. To summarize the ratings, a numerical score was assigned to each rating (or approximate percentage for items 1, 2, 4, and 15); that is, 1 = strongly disagree (or 0%), 2 = disagree (or 1%–25%), 3 = neutral (or 26%–50%), 4 = agree (or 51%–75%), and 5 = strongly agree (or 76–100%). Using these values, the mean score for each item over the 10 lessons was calculated (the appendix). To examine the lesson implementation with respect to the New Outline, the mean score for each of the overarching categories (fourth Table 2. Theme, title, and content area for lessons observed during the research period. Theme Lesson Title (Content Area) New year 1. Dumpling party (Number and Operations) 2. Addition when the sum is 7 (Number and Operations) I am going to elementary school 3. Telling left from right (Measurement) 4. My new seat (Number and Operations) 5. Subtraction when the minuend is 7 (Number and Operations) 6. 10-yuan market (Number and Operations) Animal kingdom 7. Fun categorizing (Data Analysis) 8. Creating story problems I (Number and Operations) 9. Creating story problems II (Number and Operations) Good-bye kindergarten 10. Phone number of friends (Number and Operations) 58 B. Y. HU ET AL.
  • 8. column in Table 1) for the 10 lessons was also determined. The transcripts of the two interviews served as a supporting data source to corroborate or not corroborate the findings from the analysis of the lessons and were coded according to the five overarching categories described in Table 1. Findings The appendix shows mean scores over the 10 lessons for each COEMET item. The lowest mean score was 1, and the highest was 5. (Item 2 was rated as NA, because the teacher did not have any support staff.) The fourth column in Table 1 gives the mean scores for each of the overarching categories, which stemmed from the analysis of the New Outline. The category means ranged from a minimum mean score of 2.07 to a maximum of 3.17. The following sections, organized according to the five overarching categories, elaborate on the findings from the COEMET. One of the 10 observed lessons, Addition When the Sum is 7 (Table 2), is used as a representative lesson to exemplify the implementation of the lessons as indicated by the category means. This lesson, Addition When the Sum is 7, addresses the content area of number and operations, specifically the part-part-whole number relationship and its connection to the operation of addition and the commutative property. As indicated by its title, the lesson focused on different ways to make seven. Figure 1 shows the section of the Provincial Curriculum Teacher’s Guide (The Committee on Provincial Kindergarten Curriculum Guide, 2009) for this lesson, including the objectives, materials, and lesson procedure. The teacher loosely followed the recommendations made in the Teacher’s Guide. The enacted lesson consisted of three parts: whole-class instruction (13.5 minutes), individual student practice (24 min- utes), and a return to whole-class instruction (4 minutes). During the initial period of whole-class instruction, the teacher reviewed addition when the sum is 6 using flashcards and introduced different ways of making seven (5 + 2 = 7, 1 + 6 = 7, 2 + 5 = 7, 3 + 4 = 7, 5 + 2 = 7, and 6 + 1 = 7) by telling stories. (For Figure 1. The section, and the English translation, of the provincial curriculum teacher’s guide for the lesson Addition When the Sum is 7. JOURNAL OF RESEARCH IN CHILDHOOD EDUCATION 59
  • 9. an example, refer to the Resources and Connections section.) During this time, the students modeled the stories using manipulatives. For the second part of the lesson, students worked individually on practice problems (Figures 2 and 3) while the teacher walked around the classroom helping struggling students and answering students’ questions. The teacher closed the lesson with a short period of whole-class instruction during which she addressed students’ problems and misconceptions. Expectations and outcomes The expectations and outcomes category refers to the teacher’s role in developing independent and inquisitive learners. The category mean for expectations and outcomes (M = 2.07) reflects the means for the three items aligned with the category: Item 8 (M = 1.7), Item 9 (M = 1.8), and Item 18 (M = 2.7). Items 8 and 9 reference a teacher’s enthusiasm for learning mathematics, and Item 18 references a teacher’s acknowledgment and support of students’ efforts. As demonstrated in the Addition When the Sum is 7 lesson, the teacher engaged the students with stories at the opening of the lesson. (Refer to the Resources and Connections for examples of the opening stories.) Her actions Figure 2. One of the student independent practice pages for Addition When the Sum is 7 lesson. Figure 3. A second student independent practice page for Addition When the Sum is 7 lesson. 60 B. Y. HU ET AL.
  • 10. and responses to students, in the various segments of the lesson, often minimized student autonomy in developing an understanding of the content. For example, after letting students use bottle caps to show the number of monkeys in a tree for a story that represented the equation, 1 + 6 = 7, she said, “I like Lily’s (pseudonym) way of arranging. She put one monkey on one side, and put the other six on the other side.” The teacher then proceeded to ask students for the equation that represented the situation; instead, she could have followed up by asking if the other students demonstrated the story in a different manner. For a story about crocodiles, she wanted students to use bottle caps to represent two crocodiles and five crocodiles. One of the students tried to take more bottle caps from the basket even though he already had an adequate amount. In response, the teacher stopped the student, arranged the bottle caps for him, and said, “Don’t pick. Put them separately and then you can differentiate them.” The teacher could have used this opportunity to have the student explain his reasoning for wanting more bottle caps and to represent the story on his own. Developmental dimensions The developmental dimensions category reflects the modification of instructional strategies to meet the various needs of students. The category mean for developmental dimensions was M = 3.10. The item means ranged from M = 1 for Item 28, reflecting the teacher’s ability to adapt tasks and discussions to a variety of student developmental levels, to M = 4.2 for Item 17, reflecting the teacher’s mathematical expectations of students. The teacher was familiar with the various develop- mental levels of the students and attempted to provide differentiated instruction to meet their individual needs. For example, during the second interview, she stated: Most students are able to understand; four to five students with weaker learning abilities may not get it immediately; there are also one to two students who are able to do it only under supervision. . . . During the activities, for students who can learn by themselves, I only need to check their work; for students with weaker learning abilities, I have to give one-on-one instruction, but there certainly is not enough time to do it for every student. As previously described, in the middle of the Addition When the Sum is 7 lesson, the teacher worked one-on-one with struggling students and responded to student questions while they worked independently on the practice problems. Based on working with the students, she determined the common student difficulties and addressed them in the closing whole-class instruction (Item 27), opening with: “Many of you didn’t get today’s problems. First of all. . . .” She proceeded to review three of the problems from the independent practice. Even though the teacher realized the range of developmental levels among the students, she acknowledged challenges to meet their various needs. For those who haven’t gotten enlightened, no matter how I teach them, they still don’t get it. I have no idea what to do if they still don’t get it. I don’t know how to teach them since I’ve already tried everything. Maybe it’s because his developmental level is not there yet. For instance, she worked one-on-one with a student, who was not able to figure out how to solve one of the independent practice problems (first question on left-hand side of Figure 3). Teacher: There are seven circles in this box in total. How many circles are here now? [Pointing at the visible circles.] Student: Two circles. Teacher: Ah? How many circles can you see? Student: [Slid a pencil along the visible circles.] Teacher: How many? Student: Seven. Teacher: You can already see seven? How many circles? Student: [Pointed and counted two out of four visible circles.] Teacher: Ah? JOURNAL OF RESEARCH IN CHILDHOOD EDUCATION 61
  • 11. Student: Two circles. Teacher: [Pointed at the visible circles.] One, two, three, four. How many circles? Student: [Hesitated.] Four circles. Teacher: You can see four circles, but there is supposed to be seven circles. A piece of paper covered the other ones. How many are covered? Student: One? Teacher: Seven in total. [Pointed and counted the visible circles again.] One, two, three, four. [Pointed at the blank area of the box.] Draw them. [The student did not know what to do.] Teacher: Seven in total. You draw as many of the circles that have been covered. [The student still did not know what to do.] Teacher: You look at this. [Pointed and counted the visible circles.] One, two, three, four. . . . Count and draw at the same time. [Drew in the blank area of the box.] Five, six, seven. Can you do this? How many were covered? Student: Seven? Teacher: How many were covered! Student: Three? Teacher: Three, yes. Now here [pointed at the next problem], you count and draw. Throughout the dialogue, the student remained confused. The teacher completed the problem for the student, rather than helping him develop an understanding of the underlying concept (e.g., Items 26 and 28). As the interaction progressed, the teacher became increasingly impatient. In response to a question about how the provision of a rationale for the lesson objectives would support her instruction, the teacher acknowledged her lack of patience: “It would make teachers’ theoretical knowledge richer. Also, I would understand the reasons why a certain objective was included when I teach children. Then probably I would have more patience.” The teacher contributes her frustration, in part, to not understanding the concepts underlying lesson objectives. Resources and connections The resources and connections category describes the use of resources and tools to guide students in making connections between classroom learning and the real world. The category mean for resources and connections was M = 2.50, which reflects a low item mean of M = 1 for Item 4 pertaining to student use of mathematics software on computers and a fairly high item mean of M = 4 for Item 5 pertaining to the use of materials for mathematics such as manipulatives. Even though there was technology available in the classroom, the students did not use technology in any of the lessons. Although recommended in the curriculum materials, the teacher did not use any form of technology such as computers during the whole- class instruction segment of the lesson. Because there are so many things for teachers to do, usually we [only have time to] plan the lessons based on our prior experience. For example, the curriculum mentions the PowerPoint activities. I cannot provide these. What should I do? I don’t have the ability [to make them] anyway. So, I can only use the pictures and draw them by myself. Eventually, all the lesson plans look the same no matter what curriculum you are using. As the teacher mentioned, she used concrete materials during whole-class instruction. To engage students with the content of the lesson, she told stories to introduce the various ways to make seven. Teacher: In the forest, there is a herd of elephants. At the moment, one elephant feels hungry. So, he searched and searched and found a lot of banana trees. He ran to a banana tree and started to eat bananas. Then, his older brother came and ate the bananas with him. . . . Later, they asked the younger brother to join them. The parents of the elephants discovered that all of their children were gone and came to find them. They started to eat bananas altogether. How many elephants are under the banana tree now? 62 B. Y. HU ET AL.
  • 12. Students: Five! Teacher: Let’s count them. Teacher and Students: One, two, three, four, five. Teacher: From a distance, two chubby elephants approached them. What do they want? Students: Eat the bananas! Teacher: Yes, they want to taste them too. Throughout the telling of the story, the teacher used cutouts of elephants to mirror the action and ultimately represent the equation 5 + 2 = 7. Similarly, for other ways of making seven, the teacher shared five additional stories about monkeys (1 + 6 = 7), crocodiles (2 + 5 = 7), lollipops (3 + 4 = 7), red packets filled with money, a gift children often receive from elders on the New Year (5 + 2 = 7), and dumplings (6 + 1 = 7). The teacher provided students the opportunity to work with manipulatives during this portion of the lesson; that is, the students modeled each of the stories with bottle caps. Active learning The active learning category refers to instructional strategies that promote student engagement. The mean for this category was M = 3.17. The item means were M = 3, M = 2.7, and M = 3.8 for Items 12 (lesson engagement), 14 (management strategies), and 26 (opportunities for mathematical reflection), respectively. The teacher acknowledged the value of exploration and hands-on activities: “No matter whether it’s mathematics or science, the outcome would be better if you let students engage and explore.” However, the teacher believed that the larger class size prohibited her from utilizing investigative activities. “The situation is often that there are too many children and too few teachers. . . . This is not a problem that I can solve.” In the whole-class portion of the Addition When the Sum is 7 lesson, the students were actively involved in representing the various stories using bottle caps, following the teacher’s model. For an example, refer to the Resources and Connections section. Similar situations occurred when the teacher was helping students during the independent practice portion of the lesson. For instance, a student was having difficulty with the problem on the left-hand side of Figure 3. The handout provided three ways of making 7: 6 and 1, 2 and 5, and 4 and 3 (every other row starting with the first row). The students were supposed to generate the other three ways to make 7: 1 and 6, 5 and 2, and 3 and 4. The teacher worked with a student, who was struggling with the problem. Teacher: You need to divide seven game sticks into two groups, which number hasn’t been used yet? Student: [No response.] Teacher: Six has been used, two has been used, and four has been used. Which number hasn’t been used yet? . . . Two sticks have been put here, four sticks have been put here, and six have been put here. There are seven in total. Which number has not been used? . . . Which number has not been used? . . . Which number has not been used? Student: Five. Teacher: After you used the five sticks, how many sticks are left? . . . 1, 2, 3, 4, 5. Five have been put here. How many are left? Student: Two. Teacher: Where are you going to put them? [The student pointed at the cell on the left in which she just drew five tally marks.] Teacher: Five sticks have been already put here. The lines go like this [pointing at the two lines that connect the seven game sticks and the two columns, respectively]. Five sticks are here [pointing at the left column]. Where will you put the other two sticks? [The student hesitantly pointed at the correct cell.] Teacher: Draw them. The teacher continued to help the student in a similar manner for the remaining two rows. Unlike the opening activity, for this problem, the students needed to generate the different ways to make JOURNAL OF RESEARCH IN CHILDHOOD EDUCATION 63
  • 13. seven. When the teacher helped the struggling student, the task was reduced to a procedure in which the student was told where to write her answer. The student did not understand the purpose of the problem and continued to need help to complete the entire task. Interaction and communication The interaction and communication category emphasizes the teacher’s role in fostering classroom discourse. The category mean for interaction and communication was M = 3.09. The item means ranged from M = 2 for Item 23 (the teacher supported the listener’s understanding) to M = 5 for Items 1 and 15 reflecting a teacher’s level of interaction. The teacher in this study regularly engaged with the students during the whole-class instruction and individual student practice segments of the lessons. While the students were working individually, she was interacting with the students 100% of the time. In these interactions, the teacher tended to tell the students how to complete the problem from a procedural perspective rather than help the students build an understanding of the content. (Refer to the Developmental Dimensions and Active Learning sections for examples.) Similarly, during whole-class instruction, the teacher regularly asked the students questions. For instance, at the end of the elephant story (resources and connections), the teacher prompted the students: Teacher: Now, how many elephants are there under the tree? Students: Seven! Teacher: How did you calculate it? Students: 5 + 2 = 7. Teacher: How many elephants are here [points to left side]? Students: Five. Teacher: What about here [points to right side]? Students: Two. Teacher: In the middle, add them up. There are seven in total. Teacher with Students: Five plus two is seven. Teacher: Then if the plus sign stays the same and I switch the positions of two and five, what is the result? Students: It is still seven! Teacher: [Writes 2 + 5 on the board.] Two plus five, I switched them. What is the result? Students: Seven. Teacher: How many? Students: Seven. Teacher: I heard somebody said six. The result stays the same. With the exception of one time, the teacher asked a question every time she spoke. She asked closed questions looking for a single answer. As an alternative, she could have asked students to clarify or justify their thinking or to evaluate the thinking of others, means of assessing student understanding or lack thereof (e.g., Items 21, 22, and 23). Discussion The present descriptive study offers an evaluation over 10 mathematics lessons from one Chinese kindergarten classroom teacher’s practice with respect to the mathematics curriculum standards in the New Outline and provides excerpts from one of the 10 lessons to illustrate the COEMET ratings. Specifically, the teacher’s instruction was examined according to the five overarching categories, which stemmed from an analysis of the New Outline: expectations and outcomes, developmental dimensions, resources and connections, active learning, and interaction and communication. On the surface, the implementation of the lessons reflected the expectations put forth in the New Outline. 64 B. Y. HU ET AL.
  • 14. However, upon closer examination, the students did not have opportunities to construct an under- standing of the mathematics and become independent learners. In what follows, the evaluation of the implemented lessons is discussed in more detail for each of the five categories. Expectations and outcomes, one of the overarching categories of the New Outline, focuses on students developing life-long learning capabilities. More specifically, kindergarten science teaching should “sti- mulate children’s curiosity and desire to explore things as well as develop cognitive ability” (Ministry of Education, 2001, Science section, para. 1). To meet these expectations, teachers need to provide opportunities for students to become autonomous learners. In the present study, during whole-class instruction, the students were highly engaged. However, the instruction was teacher directed. The students followed the teacher’s approach to representing a problem minimizing any alternative approaches suggested by students and focusing only on correct student responses. These findings parallel Tang’s (2006) description of Chinese kindergarten teachers’ practice and views of students. Tang argues that, in the majority of Chinese kindergartens, students are perceived as reliant on teachers. Students “are virtually under the control of teachers in that the whole learning process is designed and implemented according to the teacher’s prescription without taking children’s own initiatives into account” (Tang, 2006, p. 345). If teachers believe that students are not capable of learning autonomously, then their instruction will reflect a great deal of teacher control (Chen, as cited in Tang, 2006). Teacher control, as represented by a focus on specific procedures and responses, can lead to a failure to address the various developmental dimensions of students. However, meeting the diverse needs of students is an integral part of the New Outline. All overarching principles for kindergarten education address respect for students’ developmental dimensions. For instance, the sixth over- arching principle states: “Kindergarten should emphasize children’s individual differences, and provide children with opportunities and conditions to achieve their potential and develop further from their existing levels” (Ministry of Education, 2001, Part 1 section, para. 6). This principle aligns with the tenets of differentiated instruction, which integrates a collection of pedagogical strategies to address the distinctive needs of individual students (Watts-Taffe et al., 2012). Like the philosophical stance of the New Outline, Gregory and Chapman (2002) contend, “Differentiation is not a set of tools, but a belief system educators embrace to meet the unique needs of every learner” (p. 2). The teacher in the current study acknowledged the range of developmental levels among her students. She provided support for the students who struggled with one-on-one instruction. However, with a large class size, she was not able to help all struggling students individually. Howard and Aleman (2008) consider content and pedagogical content knowledge as a contributing factor to a teacher’s ability to address diverse learners. The teacher experienced challenges helping students. Unable to modify how she provided support, the teacher often resorted to giving the answer to the students. She contributed her frustration to a lack of subject matter knowledge and effective strategies. Differentiating instruction is difficult, and teachers are often not prepared to provide instruction responsive to students’ needs (Bofferding, Kemmerle, & Murata, 2012; Neville, 2010). However, developmentally appropriate instructional support is critical as it contributes to children’s increased task engagement (Pakarinen et al., 2010; Turner et al., 2002). One means of engaging students is using resources and connections, including manipulatives and technology. Technology is a major component of the teaching process section in the New Outline. Teachers need to “fully take advantage of informational technology to provide a variety of educa- tional environments and powerful learning tools for students’ learning and development” (Ministry of Education, 2001, Teaching Process section, para. 2). The teacher and her students did not use any form of technology in the lessons observed. She explained that the curriculum recommends the use of technology, such as PowerPoint activities, but did not provide the resources nor did she have the time to generate them. However, the teacher did use manipulatives in combination with contexts that connect to students’ interests. According to the New Outline, “Teachers should let children use senses, be hands-on and minds-on, discover and solve problems, encourage children’s cooperation, and actively involve children in exploration activities” (Ministry of Education, 2001, Guidance section, para. 2). For the Addition When the Sum is 7 lesson, she presented multiple stories to JOURNAL OF RESEARCH IN CHILDHOOD EDUCATION 65
  • 15. represent the various ways to make 7. For each story, she used cutouts to model the story, and the students followed along using bottle caps. The students’ involvement included actively manipulating the objects; that is, they were hands-on. Because the students were expected to follow the teacher’s actions, their involvement was not necessarily minds-on. Being hands-on and minds-on are integral parts of active learning (Andrews & Trafton, 2002); that is, instructional approaches that involve “students in doing things and thinking about the things they are doing” (Bonwell & Eison, 1991, p. 2). To be considered active learning, student engagement in activities must include sense-making opportunities, including hypothesizing, observing, analyzing, evaluating, and synthesizing the objects of focus (Bonwell & Eison, 1991; Katz, 2002). Similarly, the New Outline states: “[Education] should . . . help children learn to use the methods of observation, comparison, analysis, reasoning, etcetera to conduct exploration activities” (Ministry of Education, 2001, Guidance section, para. 1). As previously discussed, the teacher’s instruction (whole class and one-on-one) was engaging but did not meet the requisites of active learning by being hands-on and minds-on. She attributed some of her challenges to a large class size and a lack of materials, two barriers documented in the literature (Bonwell & Eison, 1991). Interaction and communication also promotes sense making (Andrews & Trafton, 2002). Students should “explore ideas with their peers and be able to use adaptive ways to express their findings and communicate” (Ministry of Education, 2001, Objective section, para. 4). By sharing their ideas and listening to the ideas of others, students have opportunities to articulate, refine, and revise their understanding. Scott, Mortimer, and Aguiar (2006) delineate a framework for classifying classroom interactions by integrating two dimensions: interactive or noninteractive and dialogic or authoritative. According to this framework, the teacher’s mode of communication is interactive/ authoritative. She interacts with her students regularly. However, she questions students, leading them toward a specific approach and/or answer (Scott et al., 2006). The teacher follows an initiation- response-evaluation interaction pattern (Mehan, 1979). She asks closed-ended questions, the student(s) respond, and she evaluates the response. Further, when working one-on-one with students, who do not follow her line of questioning, she struggled with altering her approach to a task. Wang (2004) also found that Chinese teachers need additional development in the areas of building upon students’ ideas and cultivating students’ critical thinking. The implemented lessons reflected aspects of the New Outline; however, overall, the lessons lacked critical components that foster student sense making. For instance, the teacher recognized and attempted to support the range of leaners in her classroom but did not have the repertoire of instructional strategies to do so. Her instruction was hands-on, by making connections to students’ interests and utilizing manipulatives, but it was not necessarily minds-on, the combination of which is necessary to engage students in active learning. The teacher interacted with the students regularly, but the interaction did not provide the students with opportunities to develop their own ideas about the mathematics. These findings provide insights into areas in which Chinese kindergarten teachers potentially need support to meet the expectations set forth in the New Outline. Conclusion Although conducted in a Chinese context, the present study has implications for the potential, or lack thereof, for education reform as implemented through standards documents. Effective imple- mentation of reform at the local level strongly influences the success of reform at the national level (Borko et al., 2003). Therefore, examining instructional practices at the local level can provide insight about how to support teachers in understanding and enacting the reform and corresponding standards, authentically rather than superficially. This is of particular importance when the reform reflects a significant shift in classroom practices. The release of the New Outline marks a transition of the role of the teacher from knowledge disseminator to facilitator of learning through play, self-discovery, and problem solving. Meeting the expectations set forth in the New Outline requires a change in perception about the role of the 66 B. Y. HU ET AL.
  • 16. teacher and the student. Chinese teachers have been traditionally taught through direct, didactic instruction and most have never observed anyone, nor have the skills to deliver inquiry-based kindergarten teaching. Further, the Chinese collectivist culture teaches respect for authority figures; teachers feel obligated to gain a sense of control of the class, which translates into teacher-directed lessons. Chinese teachers also need to believe that students are able to be active participants in their learning. The evaluation of the 10 implemented lessons from one Chinese kindergarten classroom in the present study confirms previous findings about a disconnect between the type of instruction supported through the New Outline and its implementation in Chinese kindergarten classrooms (Tang, 2006; Wang, 2004). Further, the analysis of the New Outline provides a framework for future studies and the design of professional development opportunities. Specifically, all of the references to instruction in the New Outline were coded and organized into five overarching categories: ● Expectations and outcomes: Learning opportunities, which inspire autonomous and lifelong learners. ● Developmental dimensions: Differentiated instructional approaches, including multiple ways to continuously assess students’ prior knowledge and skills, identify individual student’s needs, and accommodate those needs. ● Resources and connections: Provision of various resources, including manipulatives and tech- nology, as well as effective means of utilizing the resources to represent mathematical concepts and make connections to the more abstract representations. ● Active learning: Instructional approaches, which facilitate sustained interactions with key mathematics ideas to refine views, promote conceptual understanding, and enhance problem- solving and reasoning processes (i.e., hands-on and minds-on). ● Interaction and communication: Strategies to foster interactive/dialogic communication (Scott et al., 2006) in which teachers build upon students’ ideas by providing opportunities for students to share their thinking and listen and respond to the thinking of others. The present study only examined 10 lessons from one Chinese kindergarten classroom. A larger scale evaluation of the implementation of the Chinese curricular reform needs to be conducted, and the framework presented herein can guide the analysis. Ma and Yuan (2007) have suggested that high-quality kindergarten mathematics teaching lies in providing support and evaluative systems for teachers. The framework can also be used to evaluate individual teacher’s practice and design professional development centered on areas of needed improvement. The professional development should center on teachers’ daily practice, be long term, and cultivate teachers’ perspectives about teaching and learning mathematics (Collopy, 2003). Educative curriculum materials, designed for student and teacher learning, can also be a means of supporting teacher development in the recommended areas (Hu, Fuentes, Wang, & Yie, 2013; Collopy, 2003; Davis & Krajcik, 2005). By providing a descriptive analysis of 10 lessons from one Chinese kindergarten classroom in the era of the New Outline, the present study informs teacher educators, future researchers, and policy- makers of areas of evaluation and potential improvement in the implementation of education reform in Chinese kindergartens. Future research can focus on effective ways to implement professional development for teachers to facilitate student-centered learning. In parallel, research can examine teachers’ beliefs and practices regarding developmentally appropriate mathematics curricula and instruction as well as the effects of professional development on teachers’ practice. These efforts will contribute to closing the gap between the intended and implemented curriculum, enhance teacher quality, improve student learning, and bring to life the spirit of the New Outline. JOURNAL OF RESEARCH IN CHILDHOOD EDUCATION 67
  • 17. Note 1. In China, early childhood education programs (or preschools) serve children ages 3–6 and include the kindergarten year. References Andrews, A. G., & Trafton, P. R. (2002). Little kids-Powerful problem solvers: Math stories from a kindergarten classroom. Portsmouth, NH: Heinemann. Bofferding, L., Kemmerle, M., & Murata, A. (2012). Making 10 my way. Teaching Children Mathematics, 19(3), 164–173. doi:10.5951/teacchilmath.19.3.0164 Bonwell, C. C., & Eison, J. A. (1991). Active learning: Creating excitement in the classroom. Washington, DC: The George Washington University. Borko, H., Wolf, S. A., Simone, G., & Uchiyama, P. (2003). Schools in transition: Reform efforts and school capacity in Washington state. Educational Evaluation and Policy Analysis, 25(2), 171–201. doi:10.3102/01623737025002171 Bredekamp, S., & Copple, C. (1997). Developmentally appropriate practice in early childhood programs. Washington, DC: National Association for the Education of Young Children. Chen, X. J. (2005). 关于幼儿园数学教育变革的思考 [On kindergarten math education reform]. Theoretical Construction, 7–8, 20–22. Collopy, R. (2003). Curriculum materials as a professional development tool: How a mathematics textbook affected two teachers’ learning. Elementary School Journal, 103(3), 287–311. doi:10.1086/499727 The Committee on Provincial Kindergarten Curriculum Guide. (2009). Teachers’ guide for instructional activities design. Zhejiang, China: New Times Press. Davis, E. A., & Krajcik, J. S. (2005). Designing educative curriculum materials to promote teacher learning. Educational Researcher, 34(3), 3–14. doi:10.3102/0013189X034003003 Dossey, J. (2007). Looking back, looking ahead. In C. R. Hirsch (Ed.), Perspectives on the design and development of school mathematics curricula (pp. 185–199). Reston, VA: National Council of Teachers of Mathematics. Duncan, G., Dowsett, C. A., Magnuson, K., Huston, A., Klebanov, P., & Japel, C. (2007). School readiness and later achievement. Developmental Psychology, 43, 1428–1446. doi:10.1037/0012-1649.43.6.1428 Dunphy, E. (2009). Early childhood mathematics teaching: Challenges, difficulties and priorities of teachers of young children in primary schools in Ireland. International Journal of Early Years Education, 17(1), 3–16. doi:10.1080/ 09669760802699829 Gregory, G. H., & Chapman, C. (2002). Differentiated instruction in inclusive classrooms. Boston, MA: Pearson. Howard, T. C., & Aleman, G. R. (2008). Teacher capacity for diverse learners: What do teachers need to know? In M. Cochran-Smith, S. Feiman-Nemser, & D. J. McIntyre (Eds.), Handbook of research on teacher education: Enduring questions in changing contexts (pp. 156–174). New York, NY: Routledge Taylor & Francis Group. Hu, B. (2011). Exploring the cultural relevance of developmentally appropriate practices from the point view of preschool teachers in Beijing. The 2011 Yearbook of the Texas A&M University-Corpus Christi’s Center for Educational Development, Evaluation, and Research, 1–23. Hu, B., Fuentes, S., Wang, C., & Yie, F. (2013). A case study of the implementation of Chinese kindergarten mathematics curriculum. International Journal of Mathematics and Science, 12(1), 193–217. Huo, J. (2004).《幼儿园教育指导纲要》实施过程中教师适应行为的调查研究 [Investigations on the teachers’ adaptive actions during the implementation process of GPE] (master’s thesis). Liao Ning Normal University, Dalian, China. Katz, L. G. (2002). Foreword. In A. G. Andrews & P. R. Trafton (Eds.), Little kids-Powerful problem solvers: Math stories from a kindergarten classroom (pp. xi–xiii). Portsmouth, NH: Heinemann. Li, M. (2007). 试析美国幼儿教育课程模式的理论流派及其启示 [An exploratory analysis of the theory genre and insights from U.S. preschool curriculum models]. Comparative Education Studies, 11, 69–74. Lin, Y. (2004). 中国幼儿数学教育课程的反思和构建 [Reconsideration and construction of Chinese early childhood mathematics education]. Journal of Shanxi Normal University (Philosophy and Social Science Edition), 33(1), 117–121. Ma, J., & Yuan, D. (2007). 《从学前班到8年级的课程焦点:追求连贯性》报告评述[A commentary on curricu- lum focal points for prekindergarten through Grade 8 mathematics: A quest for coherence report]. Comparative Education Review, 204(5), 48–52. Mehan, H. (1979). Learning lessons: Social organization in the classroom. Cambridge, MA: Harvard University Press. Ministry of Education in People’s Republic of China. (1952). Temporary regulations for kindergarten education (draft). Ministry of Education in People’s Republic of China. (1981). The guideline for kindergarten Education (trial version). Shangdong Education, 10, 4–8. Ministry of Education in People’s Republic of China. (2001). The guideline for kindergarten education (trial version). Retrieved from http://www.moe.gov.cn/publicfiles/business/htmlfiles/moe/s7054/201403/xxgk_166067.html 68 B. Y. HU ET AL.
  • 18. Neville, E. (2010). Utilizing a school-university collaborative partnership to design, present, and support pre-K-12 coursework on differentiated instruction. School-University Partnerships, 4(2), 92–95. Pakarinen, E., Kiuru, N., Lerkkanen, M., Poikkeus, A., Siekkinen, M., & Nurmi, J. (2010). Classroom organization and teacher stress predict learning motivation in kindergarten children. European Journal of Psychology of Education, 25, 281–300. doi:10.1007/s10212-010-0025-6 Pan, Y. (2005). 对我国当前幼儿园数学教育政策的反思[Reflection on the current policy for kindergarten mathe- matics education]. Theoretical Construction, 3, 9–11. Piaget, J. (1926). The language and thought of the child. London, England: Routledge & Kegan Paul. Remillard, J. T., & Bryans, M. B. (2004). Teachers’ orientations toward mathematics curriculum materials: Implications for teacher learning. Journal for Research in Mathematics Education, 35(5), 352–388. doi:10.2307/30034820 Ross, J. A., McDougall, D., Hogaboam-Gray, A., & LeSage, A. (2003). A survey measuring elementary teachers’ implementation of standards-based mathematics teaching. Journal for Research in Mathematics Education, 34(4), 344–363. doi:10.2307/30034787 Sarama, J., & Clements, D. (2004). Building blocks for early childhood mathematics. Early Childhood Research Quarterly, 19, 181–189. doi:10.1016/j.ecresq.2004.01.014 Sarama, L., & Clements, D. H. (2007). Manual for Classroom Observation (COEMET)-Version 3 (Unpublished version). Scott, P. H., Mortimer, E. F., & Aguiar, O. G. (2006). The tension between authoritative and dialogic discourse: A fundamental characteristic of meaning making interactions in high school lessons. Science Education, 90, 605–631. doi:10.1002/sce.20131 Su, G., & Cai, Q. (2006). 幼教课程改革研究[Research on early childhood curriculum reform]. Curriculum and Instruction, 12, 14–15. Sun, X. (2008). Mathematics curriculum standards of China: Its process, strategies, outcomes and difficulties. In Z. Usiskin & E. Willmore (Eds.), Mathematics curriculum in pacific rim countries – China, Japan, Korea, and Singapore (pp. 73–82). Charlotte, NC: Information Age Publishing. Tang, F. (2006). The child as active learner: Views, practices, and barriers in Chinese early childhood education. Childhood Education, 82(6), 342–346. doi:10.1080/00094056.2006.10522859 Tang, S. (2005). 中国农村幼儿教育的发展与变革[On the development and reform of Chinese country preschool education]. Career Development and Management, 38(6), 38–40. Turner, J. C., Midgley, C., Meyer, D. K., Gheen, M., Anderman, E., Kang, Y., & Patrick, H. (2002). The classroom environment and students’ reports of avoidance behaviors in mathematics: A multi-method study. Journal of Educational Psychology, 94, 88–106. doi:10.1037/0022-0663.94.1.88 Van Luit, J. E. H., & Schopman, E. A. M. (2000). Improving early numeracy of young children with special needs. Remedial and Special Education, 21(1), 27–40. doi:10.1177/074193250002100105 Wang, C. (2004). 中国学前课程百年发展与变革的历史研究 [A history study of the development and changes of preschool curriculum and its enlightenments in the past century in China]. Beijing, China: Educational Science Press. Wang, C. (2008). 中国学前课程百年发展变革的特点和启示 [Characteristics of development and changes of pre- school curriculum and its enlightenments in the past century in China]. Educational Research, 9, 93–97. Watts-Taffe, S., Laster, B. P., Broach, L., Marinak, B., Connor, C. M., & Walker-Dalhouse, D. (2012). Differentiated instruction: Making informed teacher decisions. Reading Teacher, 66(4), 303–314. doi:10.1002/trtr.2012.66.issue-4 Wu, C. (2003). 我国数学教育的改革探索 [Exploring mathematics education reform in China]. Studies in Preschool Education, 10, 48–49. Wu, D. (2001). 美国数学课程标准的思想和启示[U.S. mathematics curriculum standards: Ideas and enlighten- ments]. Journal of Shenzhen Institute of Education, 2, 82–85. Zhu, J., & Zhang, J.. (2008). Contemporary trends and developments in early childhood education in China. International Journal of Early Years Education, 28(20), 173–182. JOURNAL OF RESEARCH IN CHILDHOOD EDUCATION 69
  • 19. Appendix: Classroom Observation of Early Mathematics Environment and Teaching (COEMET) items and teacher mean scores for each item over 10 observed lessons COEMET Sections, Subscales, and Items Item Mean Classroom Culture Environment and Interaction 1. Teacher actively interacted with and was responsive to children. 5 2. Other staff (e.g., aide) actively interacted with and was responsive to children. NA 3. The teacher used teachable moments as they occurred to develop math ideas. 3.1 4. Children took turns using computers with math software. 1 5. The environment showed signs of mathematics: materials for mathematics, including specific math manipulatives, were available and mathematics was enacted and/or discussed around them. 4 6. Children’s math work and/or other signs of mathematical thinking were on display. 3.1 Personal Attributes of the Teacher 7. The teacher appeared to be knowledgeable and confident about mathematics. 3.5 8. The teacher showed she believed that math learning can and should be enjoyable. 1.7 9. The teacher showed curiosity about and/or enthusiasm for math ideas and/or connections to other ideas or real-world situations. 1.8 Specific Math Activity Mathematical Focus 10. The teacher displayed an understanding of mathematics concepts. 2.7 11. The mathematical content was appropriate for the developmental levels of the children in his class. 4 Organization, Teaching Approaches, Interactions 12. The teacher began by engaging and focusing children’s mathematical thinking. 3 13. The pace of the activity was appropriate for the developmental levels/needs of the children and the purpose of the activity. 3 14. The teacher’s management strategies enhanced the quality of the activity. 2.7 15. The teacher was actively involved in the activity for what percentage of time (beyond setup or introduction). 5 16. The teaching strategies used were appropriate for the development levels/needs of the children and purposes of the activity. 3.2 Expectations 17. The teacher had high but realistic mathematical expectations of children. 4.2 18. The teacher acknowledged and/or reinforced children’s effort, persistence, and/or concentration. 2.7 Eliciting children’s solution methods 19. The teacher asked children to share, clarify, and/or justify their ideas. 2.7 20. The teacher facilitated children’s responding. 2.4 21. The teacher encouraged children to listen to and evaluate others’ thinking/ideas. 2.2 Supporting children’s conceptual understanding 22. The teacher supported the describer’s thinking. 2.3 23. The teacher supported the listener’s understanding. 2 24. The teacher provided “just enough” support. 2.6 Extending children’s mathematical thinking 25. The teacher built on and/or elaborated children’s mathematical ideas and strategies. 2.8 26. The teacher encouraged mathematical reflection. 3.8 Assessment and Instructional Adjustment 27. The teacher observed and listened to children, taking notes as appropriate (only need notes in small groups). 4 28. The teacher adapted tasks and discussions to accommodate the range of children’s abilities and development. 1 Note. For items 1, 2, 4, and 15, 1 = 0%, 2 = 1–25%, 3 = 26–50%, 4 = 51–75%, and 5 = 76–100%. For the remaining items, 1 = strongly disagree, 2 = disagree, 3 = neutral, 4 = agree, and 5 = strongly agree. 70 B. Y. HU ET AL.