Psychology
2012. Vol.3, No.10, 906-911
Published Online October 2012 in SciRes (http://www.SciRP.org/journal/psych) http://dx.doi.org/10.4236/psych.2012.310136
906
Adaptation of Lesson Study and Open Approach for Sustainable
Development of Students’ Mathematical Learning Process
Sampan Thinwiangthong1, Maitree Inprasitha2, Suladda Loipha3
1Faculty of Education, K ho n K a e n U n iv e rsity, Khon Kaen, Thailand
2Center for Research in Mathematics Education, Khon Kaen University, Khon Kaen, Thailand
3Centre of Excellence in Ma t hematics, The Office of Higher Education Commission, Bangkok, Thailand
Received July 7th, 2012; revised August 8th, 2012; accepted September 6th, 2012
This research was aimed to analyze and develop Small-group Mathematical Communication (SMC) as
Mathematical Learning Process (MLP) of the seventh grade students in Ban-beung-neam-beung-krai-
noon school for the school year 2008-2010 by adapting the Lesson Study and Open Approach which were
innovations from Japan in order to be a context as well as guidelines for practice enhancing the students’
MLP. The teaching experiment (Steffe & Thomson, 2000) as a research methodology was used in de-
signing the lesson plan, and studying students’ MLP. The data were collected by using the video-audio
recordings in classroom activities, video-stimulated interviewing the students, and interviewing the
teacher. Data were also analyzed utilizing a video and protocol analysis. The research findings found that
the students had SMC in mathematics classroom adapting Lesson Study and Open Approach. The stu-
dents learned mathematics more meaningfully by themselves based on sharing mathematical ideas in or-
der to create the shared meaning and leading to shared goal. They participated in SMC regularly. As a re-
sult, they developed a “habit of mind” which was led to a sustainable Mathematical Learning Process.
Keywords: Lesson Study; Open Approach; Mathematical Learning Process; Small-Group Mathematical
Communication; Triad Feedback
Introduction
The major point of education is learning reform (Wasee,
2000). After the announcement of National Education Act 1999,
the learning process was focused in Basic Education Curricu-
lum 2001. However, the outcome of education reform from the
first round in a previous decade did not show the emphasis of
the learning in the classroom. Besides, the international study
outcome-TIMSS (1999, 2003) and PISA (2003, 2006), found
that Thai students had lower average score in every mathemat-
ics content than every national students’ total average scores.
Moreover, the findings of evaluation in the National Educa-
tional Quality by the Office of Standard Accreditation and
Educational Quality Assessment (OSE) (second round during
2006-2010), found that most of the students could not reach the
standard level in analytical thinking, synthetic thinking, and
self-studying. Inprasitha (2006) stated that although there was
an attempt of educational reform, most teachers still used the
traditional way of teaching style focusing on the content with-
out emphasizing on the students’ MLP. Fernandez, Cannon, &
Chokshi (2003) suggested that the teachers needed to learn how
to understand their students’ MLP. The teacher, who under-
stands his students’ learning process, would have useful infor-
mation in planning his lesson. Helping mathematics teachers to
understand their students’ MLP was based on an innovation for
changing the traditional classroom into the classroom focusing
on MLP and we need framework for understanding the stu-
dents’ MLP.
The Center for Research in Mathematics Education (CRME)
has adapted both the Lesson Study and Open Approach from
Japan in the mathematics classroom of Thailand since 2002
(Inprasitha, 2007). The Lesson Study (jugyou-kenkyu) came to
be known around the world as a uniquely Japanese method of
lesson improvement which is designed to facilitate the devel-
opment of high quality lessons (Isoda, Stephen, Ohara, & Mi-
yakawa, 2007). The new approach of teaching professional
development for enhancing the MLP was based on Lesson
Study integrating an Open Approach (Loipha & Inprasitha,
2004). In mathematics classroom using the Open Approach, the
students’ various ideas and thoughts would be discussed and
developed mathematically through sophistication by their peer
group and appropriate advice by the teacher. Thus, for the Open
Approach, the class would share their common interest with the
class which emphasizes mathematical discussion and commu-
nication (Nohda, 2000). Mathematical communication was the
students’ important MLP (Emori, 2005), especially, students’
mathematical communication in small group working. However,
most of the Thai mathematics teachers were not able to under-
stand their students’ SMC since the traditional classroom did
not encourage students to express their thinking and feeling.
Moreover, mathematics teachers did not know how to analyze
SMC in classroom. Those problem issues prompted the re-
searchers in determining the following research questions: how
can we develop SMC as the students’ sustainable MLP? And
how can we analyze the students’ SMC?
The Application of Lesson Study and
Open Approach in the Mathematics
Classroom of Thailand
Lesson Study is a cycle in which teachers work together to
consider their long-term goals for students, bring those goals

S. THINWIANGTHONG ET AL.
into life in actual “research lesson,” and collaboratively observe,
discuss, and refine the lessons (Lewis, 2002). Lesson Study was
a teaching professional development which has been improved
and used in Japan for 130 years (Shimizu, 2006). It was devel-
oped and applied in teaching professional development in many
countries around the world, and being recognized as the most
efficient technique to improve and develop the mathematics
teaching. Furthermore, it was also a technique in developing the
sustainable improvement of teaching (Lewis & Perry, 2003).
There were 8 steps of Lesson Study. These include: 1) Problem
identification; 2) Class planning; 3) Class implementation; 4)
Class evaluation and review of results; 5) Reconsideration of
class; 6) Implementation of class based on reconsiderations; 7)
Evaluation and review; and 8) Sharing of results (Stigler &
Hiebert, 1999 cited in Baba, 2007).
Loipha & Inprasitha (2004) proposed that the Lesson Study
was prominent including continuous and regular development
focusing on classroom changes. According to this characteristic,
some kinds of innovations to make changes were needed. These
were carried-out by integrating into the topic to be developed
continuously which was the approach of mathematics teaching
model focusing on Open Approach. Therefore, new method of
teaching professional development for enhancing the mathe-
matics learning, was needed to be based on the approach of
teaching improvement and development according to the steps
of Lesson Study as development of teachers’ collaboration in
working by integrating into mathematics teaching model fo-
cusing on Open Approach which was teaching professional
development in classroom level.
After Assistant Professor Dr. Maitree Inprasitha modified the
Lesson Study in context of Thai class since 2002 until the pre-
sent, there were 3 major phases of the modified Lesson Study.
These in include: 1) Collaboratively Plan; 2) Collaboratively
Do; and 3) Collaboratively See by integrating it with the Open
Approach in order to implement every week in school (Inpra-
sitha, 2008) as shown in Figure 1.
Figure 1 shows the integration of Lesson Study and Open
Approach (Inprasitha, 2008) focus on development of students’
mathematical thinking. The Open Approach included both the
major matter for considering in each phase of Lesson Study,
and teaching approach used by teacher in classroom teaching.
As a teaching approach, it included 4 steps: These were: 1)
Pose the open-ended problem; 2) Students’ learning by them-
Figure 1.
The integration of lesson study and open approach.
selves; 3) Whole class di scussion; and 4 ) Summary through c on-
nection. Nohda (1993 cited in Inprasitha, 2004) stated that in
mathematics classroom using Open Approach, the students’
various ideas and thoughts would be discussed through sophis-
tication by their peer group. Thus, for the mathematics class-
room using Open Approach, it emphasizes mathematical dis-
cussion and communication.
According to the above mentioned, it leads to the first hy-
pothesis that the integration of the Lesson Study and Open Ap-
proach in mathematics classroom could help the students to
perform mathematical communication which is very important
MLP, especially, the SMC. The students would obtain opportu-
nity in creating the mathematical knowledge through SMC.
Small-Group Mathematical Communication as
Mathematical Learning Process
Communication could be classified into educational system
since the education was based on communication (Sierpinska,
1998; Emori, 2005). The students’ mathematics learning based
on mathematical communication included 3 characteristics
which are as follows: Rigorousness, Economy, and Freedom in
communicating the participants’ thinking (Emori, 2005). These
3 characteristics determined “Mathematical”, in “Mathematical
Communication” which included opportunity that will occur
during small group discussion.
Small group discussion is a communication among limited
number of people in a place in order to accomplish Shared Goal
of small group communication, Shared Meaning leading to
Shared Goal as a factor classifying the group from gathering
each person together, and the small group discussion from gen-
eral conversation (Samovar, Henman, & King, 1996). Shared
Goal and Shared Meaning were important aspects of learning
process of small group members.
The good lesson was developed based on students’ natural
thinking and feeling. We needed to know how the students
think and feel in learning mathematics, emotional aspects
should be focused on as well (Emori, 2005). However, the for-
mer studies of Mathematical Communication including Emori’s
(1993, 1997, 2005) findings, only cognitive aspect was studied.
So, this study added the emotional aspect in SMC.
Inprasitha (2001) developed theoretical framework of stu-
dents’ emotional experience in mathematical problem solving,
and explained emotional experience that: when human beings
were facing the interruption, the findings of interruption was to
stimulate physical arousal, and cognitive evaluation. We would
use cognitive evaluation (such as cognitive evaluative schema)
to make sense of interruption. The findings of cognitive evalua-
tion would occur as different kinds of emotion such as surprise,
confusion, enjoyment, or other kinds of emotion.
For this study, the theoretical framework of Emori (2005),
Samovar et al. (1996) and Inprasitha (2001) were used in de-
fining the SMC that: It was the students’ conversation, discus-
sion, argument including rigorousness, economy, and freedom
of thought while they were working in small group in which
they had their shared goal as well as shared meaning during
solving mathematical problems together. Consequently, they
changed their schema, and had emotional experience. The unit
of analysis of SMC developed by the researcher called Triad
Feedback (Thinwiangthong, Loipha, & Pasjuso, 2010; Thin-
wiangthong, 2011) was as follows:
According to Figure 2, whene sender sent message 1 by th

S. THINWIANGTHONG ET AL.
908
Figure 2.
Triad feedback: the unit of analysis of SMC.
conversation or facial expression, it is the evidences that the
sender had Activated Schema 1 (AS1). The receiver received
message 1, and sent message 2 as feedback, and stimulus stimu-
lating the sender’s AS1. So, the sender met the Interruption (I),
and needed Cognitive Evaluative Schema (CES) in order to
make sense for that Interruption. Then, the sender adjusted their
mathematical idea or schema until it became the Activated
Schema 2 (AS2) and expressing the Emotional Experience (EE).
This hypothetical model leads to the second hypothesis that
Triad Feedback can be use to analyze both cognitive and
emotional aspects in SMC.
Research Objectives
1) To develop the Seventh Grade Students’ Small-group
Mathematical Communication as Mathematical Learning Proc-
ess in the Classroom using Lesson Study and Open Approach.
2) To analyze the Small-group Mathematical Communi c ation
of the seventh grade students in classroom using Lesson Study
and Open Approach.
Method
This research study was conducted under the project for pro-
fessional development of mathematics teachers through Lesson
Study and Open Approach which has been implemented by
CRME, Faculty of Education, Khon Kaen University since
2006. This study was conducted during 2009-2011. The teach-
ing experiment based on Steffe & Thomson’ (2000) approach
was used for designing the research method including the fol-
lowing details:
Participants
The participants were 8 seventh-grade students studying in
Ban-beung-neam-beung-krai-noon school. Their age ranged
from 12 - 13 years old. They are familiar with mathematics
classroom adapting Lesson Study and Open Approach. They
voluntarily participated in this study.
Procedure
Document Analysis
The researcher analyzed documents, research studies, and
related theoretical framework of SMC including: Emori’s (1993,
1997, 2005) theoretical framework of Mathematical Commu-
nication, Samovar et al. (1996) theoretical framework of Small
Group Communication, and Inprasitha’s (2001) theoretical
framework of Emotional Experience in order to synthesize
theoretical framework of SMC in classroom using Lesson
Study and Open App r o ach.
Participatory Observation
The researcher participated as a member in Lesson Study
team in conducting collaboratively plan, do, and see: to wit:
1) Collaboratively Plan, implemented every Tuesday Eve-
ning. The member team of Lesson Study including the teacher,
participatory teacher, internship student, researcher, co-re-
searcher, school coordinator, under monitoring and taking care
of the director as well as experts of CRME, collaborated in
developing the open-ended problems, designing the material
and equipment, anticipating the students’ mathematical ideas as
well as response toward the open-ended problem, and under-
standing the students’ SMC. In this step, the members’ conver-
sations were recorded using audio tape recorder.
2) Collaboratively Do, implemented during mathematics
class organized by school in each week. The teacher imple-
mented lesson plan in the classroom. Teaching was observed by
the members of Lesson Study team. The objective of observa-
tion was to know the students’ responses on the open-ended
problem, SMC, the students’ changes in mathematical ideas,
and their emotional expression. In this step, the observer would
take field note to record what were observed in the classroom.
The classroom activities were recorded using a video tape re-
corder.
3) Collaboratively See, implemented in every Thursday
evening. Every group member discussed the outcomes of
teaching observation in different aspects including: the stu-
dents’ responses on open-ended problem, mathematical ideas,
SMC, changes of mathematical ideas, and students’ emotional
expression. The sequence of reflection included: the teacher,
internship students, participatory teacher, co-researcher, re-
searcher, school coordinator, and experts of CRME. The object-
tive of discussion was to improve the lessons. The members’
conversation was recorded using an audio tape recorder.
Video-Stimulated Interview
After class, the researcher concluded the field note into is-
sues regarding to SMC occurring in class, and studied the
classroom video-tape to prepare the students’ interview topics.
For students’ interview, the researcher turned on classroom
video-tape for students to stimulate them to think back while
they were participating in learning activities in class focusing
on interviewing the SMC especially the students’ thought and
feeling occurring while they were performing SMC.

S. THINWIANGTHONG ET AL.
Teacher and Participatory Teacher Interview
After completing the data collection of every lesson, the re-
searcher interviewed teacher and participatory teacher including
interview issues as: What do the classroom adapting Lesson
Study and Open Approach, focus on or give value on? Are the
students learning through classroom adapting Lesson Study and
Open Approach, the same or different from students in tradi-
tional classroom? What does sustainable learning process mean?
Does the classroom adapting Lesson Study and Open Approach
able to develop the students’ sustainable learning process?
How?
Video Analysis
The researcher carefully analyzed video-tape by focusing on
students’ SMC. The students’ thinking and feeling were satis-
factory while they were participating in SMC by considering
the occurrence regularly. Then, the hypothetical model was
constructed to further explain the SMC. The researcher studied
related theories and connected the theories with phenomenon in
practice occurring in the classroom. As a result, the researcher
understood both the components and process of students’ SMC.
Then, the researcher synthesized them as theoretical framework
used to further study the SMC.
Verification of Theoretical Framework
The researcher investigated theoretical framework by col-
lecting supplementary data of SMC, and using the synthetic
theoretical framework in analyzing it to assure that it would be
practical and more reliable.
Instruments
Instruments used to collect data were field note, video- and
audio recorders. They were used for recording the activities in
participatory observation (collaboratively plan, do, see), and
interview sessions. Instrument used to analyze cognitive and
emotional aspects in SMC, was the Triad Feedback-hypothetic-
cal model of SMC.
Data Analysis
For data analysis, video-tape was analyzed and written in
analytic description to reveal details of the SMC. The re-
searcher would like to show the samples of data analysis in
order to reveal the details of SMC. These were as follows:
Topic: Relationship of tw o-dimensiona l geometry, and three-dimensional
one.
Title: Magic Cube
Date and Pl a ce: 5th January 2011, 12:30-13:30 p.m. 7-grade Class.
Problem Situation: Let th e students imagine that if t he cube was cut and
folded it into a flat figure a s only one shee t . How many times do you need
to cut it? And wha t figure it woul d be? Write figure as your imagination as
much as possible.
Item 1St1It’s easy, five cut five times, is that right?
Cut here Message 1
Item 2St2(Show him works heet drawing the f igure
to St1)
Item 3St1
(Look at a figure drawn by St2, consider it,
and count the cut edges)
One, two, thre e. Folded into this figure.
Item 4St2
Is this figure r ight? (Pointing at one’s
own figure. )
Message 2
Item 5St1Wait, wait, wait.
Item 6St3(Looking at figure pointed by St1)
Is it right?
Item 7St2Don’t argue m e.
Item 8St1One, two, three, four, five, six (try to think)
Item 9St3Seven (Looking at St1’s face)
Cognitive
Evaluation of
Interruption
in St1’s
Mental Space
Item 10St1Hey! Seven times. Message 3
St
2
St
1
St
2
St
1
St
2
St
1
Figure 3.
The students’ SMC while solving problem on magic cube.
The analysis of video as the above, was based on framework
of Triad Feedback. St1’ statement in Item 1 that “It’s easy, five
cut five times, is that right? Cut here.” Could help the other
students to understand that St1 cut the cube for five times as
St1’s intention. But, St2 wasn’t certain. So, he handed in his
worksheet written flat figure (see figure in protocol Item 4) for
St1 to look at, and asked St1 in Item 4 that “Is this figure right?”
St2’ actions in handing in the worksheet including flat figure as
well as asking, were messages turning back to St1. Then, St1
found different idea, and reviewed her own idea. St1 tried to
think until she had her new mathematical idea which she never
had this idea before. She spoke Item 10 that “Hey! Seven times”.
According to this communication, St1 and other students of this
group, could be able to communicate as their intention by using
concise message. In addition, it could help St1 to have new
mathematical idea. The communication in this scene consisted
of rigorousness, economy, and freedom in thinking of those
who participated in communication.
Considering the goals of St1 and other students in the group,
found that everyone had one’s goal in finding the number of
times for cutting the cube edges, which was a shared goal of St1
and other students. To accomplish the shared goal, St1 and other
students in group communicated with each other until the
shared meaning regarding to how many times one would cut the
cube edges, was shown. In Item 1-4, other students had shared
meaning with St1 that: one would cut the cube edges for 5 times.
But, after St1 tried to think until she had new idea that: one
needed to cut the cube edges for 7 times. The other students
could understand that: how many times to cut the cube edges,
were 7 times.
After teacher pose open-ended problem on the board, and
distributed single work sheet for students. The student read wo rk-
sheet, and tried to think how many times they had to cut the
edge of a cube. The teacher allows each student think about 5
minutes. Then, the students could speak with their nearby fr iend
as following protocol which according to Figure 3 (St1: the
first Student; St2: the Second Student; St3: the Third Student). St1 presented his idea in Item 1 that: “It’s easy, five cut five times, is that right? Cut here”, could be analyzed that St1 had

S. THINWIANGTHONG ET AL.
910
schema in cutting the cube edges for 5 times, the flat figure
(AS1) as a sheet was occurred. Then, St2 handed in his own
figure of how to cut the cube for St1 to see, and asked in Item 4
that: Is this figure right? St2’ actions in handing in the work-
sheet including figure how to cut the cube as well as asking in
Item 4, were message 2 stimulating AS1. As a result, St1 met
interruption (I) by saying that “Wait, wait, wait.” St1 tried to
think about her own idea which was duration St1 had cognitive
evaluation by using cognitive evaluative schema (CES) to in-
terpret the interruption. St1 considered the correctness as well as
logic of the figure, and the number of cutting. The cognitive
evaluation occurred in St1’s mental space. Then, St1’ schema
was changed. Since St1 spoke with exciting voice in Item 10
that: “Hey! Seven times.” When St1 said in Item 10, it was
message 3 which could be analyzed to show St1’s changed
schema: the schema in cutting the cube for 7 times, the flat one
as only one sheet (AS2). In addition, St1 also expressed his
emotional experience (EE) as the surprise, and excitement.
The Findings from Interviewing the Teacher and
Participat o ry Teacher
The researcher interviewed teacher and participatory teacher
regarding to students’ sustainable learning process. The find-
ings of interview were as follows:
From the Table 1, both the teacher, and participatory teacher
revealed that a class using Lesson Study and Open Approach
focusing on students’ learning process, could help them think
variously, feel more expressively, discuss and shar e their ideas,
and perform SMC regularly. Consequently, this kind of class-
room setting could be able to develop the students’ habit of
mind in solving the problems and sustainable learning process.
Discussions
Mathematics classroom adapting Lesson Study and Open
Approach was the problem solving classroom (Isoda et al.,
2007). This new kind of classroom served to the expectation of
educational reform in Thailand. Moreover, problem solving
classroom was required in many countries around the world.
Because it cultivated the quality citizens in the countries. This
study showed some success in improving the traditional class-
room to be the problem solving classroom.
This study incorporated emotional aspect into mathematical
communication, especially, SMC. According to Hannula et al.
(2004) stated that one important problem in the recent research
on affect is the understanding of the interaction between affect
and cognition. This study provided the teachers and research-
ers’ intensive understanding of affect and cognition in SMC of
students. However, Immordino-Yang (2011) suggested that
cognitive, affective and social neuroscience have the potential
to revolutionize educational theories of learning. This study
does not incorporate neuroscience in the framework of SMC. It
should be more recognized in the SMC future study.
Conclusion
According to the question: How can we develop SMC as the
students’ sustainable MLP? The research findings found that
mathematics classroom adapting the Lesson Study and Open
Approach, could develop the students’ SMC. Since the students
had opportunities to collaborate in solving the open-ended
problem regularly, the students practiced thinking in problem
solving through various solutions. They learned mathematics
meaningfully by themselves based on sharing of mathematical
ideas in order to create the shared meaning leading to the ac-
complishments of shared goals. As they perform SMC, they
develop the “habit of mind” which lead to a sustainable
Mathematical Learning Process.
According to the question that How can we analyze the stu-
dents’ SMC? The research findings found that the theoretical
Table 1.
The fidings from interviewing the teacher and particip ato ry teacher.
Teacher’s answers Participatory teacher’s answers
Questions 1) What does the teacher who used Lesson Study and Open Approach focus on or value?
I focused on students t o h ave first-hand experience, r eal experiment and
practice, self-learning, and present their ideas. Students have different ideas. They are proud they think differently from thei
r
friends. The class provides more freedom to solve problems.
Questions 2) D o the students in classroom who adapt the Lesson Study and Open Approach, the same or different from the other s tudents in traditional
classroom? How?
 The similar issue is: those w ho want to learn and know, c ould be able to
learn similarly both in the c l assroom adapting Lesson S tudy and Open
Approach, and in the traditiona l classroom.
 The different issue is: st udents in the classroom adapting Lesson St udy
and Open Approach, are more expressive, better performance in the
presentation. T hey discuss on solving problem with their friends whil e in
the traditional classroom, the students ask their teacher only.
 Classroom using these innovations, students could sh ow diverge nt
thinking, solve problems by various solutions, and present thei r own
thinking.
 In traditional classroom, students have convergen t thinking or one
solution only .
Questions 3) What does sustaina ble learning process mean?
The students c ould apply knowledge or learned techniques in other situations.
They are able to apply and expand it further. They could learn every place for the rest of their lives. They could solve problems by themselves without place or time limitation. They could apply it.
Questions 4) Could the classroom applying of Lesson Stu dy and Open Approach, develop the students to have sustainable learning process? How?
I think it does . But, it isn’t quick. It depends on how muc h patience the
teacher has. We focus on process rather than product. We provide
instruments f or students so that they would be able to apply those lat er.
I think it does. Since it causes students to think differently and variously until
they could apply to solve problems in different situations. This kind of
classroom could develop sustainable learning process.

S. THINWIANGTHONG ET AL.
framework called Triad Feedback, synthesized by the re-
searcher, could be used to analyze the students’ SMC. It re-
vealed the characteristics of Mathematical Communication,
cognitive aspects as well as emotional aspects of SMC. This
analysis aimed to understand the students’ MLP so that the
teachers or researcher would be able to utilize the students’
thinking and feeling towards the lesson.
Acknowledgements
This research is (partially) supported by the Centre of Excel-
lent in Mathematics, the Commission on Higher Education,
Thailand, and Center for Research in Mathematics Education,
Khon Kaen University, Thailand.
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