Mathematics lesson teaching methods

55

(http://www.tc.columbia.edu/lessonstudy/timeline.html)

In 2007, the World Association on Lesson Studies was launched in Hong Kong and, since 

then, has been regularly held. In this year, the conference of WALS will be held in Sweden. 

According to Dr. Hiroyuki Kuno, except Japan and Kazakhstan, USA, UK, Singa-

pore, Hong Kong, Thailand, Malaysia, Indonesia, Brunei, Thai, China, Sweden are practic-

ing Lesson Study in their own context. (Kuno 2011 WALS)

The objective of Lesson Study

The objective of Lesson Study is different in each school. There are three types of 

Lesson Study that differ according the objective. The first type focuses on the unified theme 

of Lesson Study, the second type focuses on improving teaching skills and the third type of 

Lesson Study focuses on improving observation skills.

In the first type of Lesson Study, all teachers collaborate with one another, set a unified 

research theme, conduct Lesson Study according to the research theme and collect data or 

information through each Lesson Study. Finally, at the end of the school year, they publish 

a research report. In this type of Lesson Study, each teacher conducts Lesson Study not for 

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themself, but for the unified research theme. Each Lesson Study during the year consists of 

parts of the school-wide Lesson Study process. In this case, discussion of the lesson plan 

becomes more important. Each lesson plan has to relate to the research theme for the school. 

With each Lesson Study cycle, teachers try to attain research outcomes for the unified theme.

The theme of Lesson Study may be:

•  developing  discussion between students

•  developing  critical thinking in students

•  using  group/pair work

•  using ICT tools

•  developing reading skill

•  developing skills of self expression

•  deepening the meaning of number or quantity using concrete objects

In Japan, many schools conduct this type of Lesson Study, and my research paper shows 

the effectiveness of this type of Lesson Study. But this requires a lot of experience in Lesson 

Study and so I do not want to recommend this type of Lesson Study yet for Kazakh teachers

In the second type of Lesson Study, a volunteer teacher conducts Lesson Study inde-

pendently. This teacher sets his/her own research theme, and tries to develop his/her teach-

ing method independently. He/she writes a lesson plan according to the research theme and 

opens the research lesson which is observed by a group of teachers. The lesson is discussed 

with the observers, and then he/she rewrites the lesson plan and opens a second research 

lesson. In this type of Lesson Study, the teacher who opens the research lesson gets feed-

back from the Lesson Study cycle and can improve his/her teaching skills. Lesson Study 

conducted in UK or USA is similar to this type.

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For example, the UK researcher, Dadley(2011) describes the process of Lesson Study 

as an improving process for the teacher. He emphasizes the process of collecting data from 

case pupils who reflect different groups of learner in the class. By observing and interview-

ing case pupils, observers can understand how students learn during the lesson and how 

effective the lesson plan is. 

The USA researcher, Lewis (2002) describes the Lesson Study process as a manage-

ment cycle:

1.  Form a Lesson Study group

2.  Formulate goals for student learning and long term development

3.  Collaboratively plan a research lesson

4.  Conduct the lesson with one team member teaching and others gathering evi-

dence on student learning and development

5.  Discuss the evidence gathered during the lesson, using it to improve the lesson, 

the unit and general instructions.

6.  Teach the revised lesson in another class room

This type of Lesson Study can promote a teacher’s teaching skill. Both researchers 

describe the Lesson Study process with a volunteer group of teachers in the school. There 

is a big difference between Japanese Lesson Study and UK or USA Lesson Study. Lesson 

Study in Japan is conducted by all teachers in the school whereas Lesson Study in UK or 

USA is conducted by a group of volunteer teachers.

In the third type of Lesson Study, all teachers in the faculty open research lessons, at the 

same time observing research lessons of their colleagues. While observing lessons, teachers 

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can share good practice and develop their own teaching skills and observation skills. In this 

type of Lesson Study, teachers can set their own research theme like second type, but it is more 

useful for them to set unified research theme.  In this type of Lesson Study, each teacher will 

open a research lesson once a year, but the focus this time is on the process of observation.

With well developed observation skills, a teacher is able to adequately observe each stu-

dent. Normally when teachers observe lessons, they tend to focus only on the teacher and not on 

the students. Teachers should develop their observation skills in order to focusing on students.

In a classroom there are various kinds of students, talented or gifted students and 

weak students and a teacher should be able to teach all of these students. In order to do this, 

the teacher needs to understand how they are learning, and how they understand the lesson.

Lesson Study encourages teachers to test their assumptions and beliefs, promotes rich 

dialogue amongst teachers, fosters a culture of collegiality and professional development, 

fosters a culture of collegiality and professional development, focuses teachers on students’ 

learning needs and promotes a deeper understanding of the curriculum.

The effectiveness of Lesson Study

Lewis (2002) summarizes the effectiveness of Lesson Study as below:

•  Brings educational goals and standards to life in the classroom

•  Promotes data-based improvement

•  Targets the many student qualities that influence learning

•  Creates a demand for improvement

•  Values teachers

The first point means Lesson Study provides a collaborative process for teachers to 

make sense of educational goals. The second point  means that  teachers can get much data 

by observing the classroom and not only from tests and homework. This data contains the 

following kind of information: 

•  in what ways students’ knowledge and understanding of the topic change over 

the lesson

•  students’ basic personal qualities needed for learning. For example, well-organ-

ized, responsible, and able to listen and respond to one another’s  ideas

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Dudley (2011) summarizes the effectiveness of Lesson Study as below:

•  pupil learning appears in much sharper detail than usual

•  gaps become apparent between what they had assumed was happening when pu-

pils learned and what it actually happening

•  learning is planned that is better matched to the pupil’s needs

•  this is all done in the context of a supportive teaching and learning community

I would summarize the effectiveness of Lesson Study, as getting implicit knowledge 

and developing school culture.

Explicit knowledge and implicit knowledge

If I ask you a question, “How do you develop your teaching skills?” your answer 

may be divided into two, getting knowledge and gaining experience in the classroom. You 

get knowledge from reading books or attending conferences. Explicit knowledge comes 

from reading books or attending conferences. But in many cases, explicit knowledge is not 

enough for practice.

Think about riding bicycle, you can get knowledge from reading book of riding bi-

cycle, it may be useful for you, but it is not enough for you riding bicycle. You have to 

exercise to ride bicycle. Through exercise, you can develop explicit knowledge to implicit 

knowledge.

This also applies to teaching skills. Most part of a teacher’s practice may not be ex-

plained explicitly, teacher’s knowledge of practice is implicit. Explicit knowledge may be 

effective, when developed into implicit knowledge. (Kolb, 1981)

Many teachers gain implicit knowledge through their experience. So, many teachers 

emphasize their own experience. Lesson Study can promote you getting implicit knowledge 

effectively, because Lesson Study promotes your reflection of lesson or observation skill.

Importance of school culture

In addition to having experience of teaching, school culture is important to develop 

teaching skills.

According to a research in Japan, a teacher’s teaching skill is affected not by principal 

leadership, but school culture. Principal leadership affects how to develop school culture.

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My research paper shows the effectiveness of Lesson Study with statistical data. Ac-

cording to my paper, Lesson Study can promote excellent school culture. “Excellent school 

culture”  means  close  communication  between  teachers.  Close  communication  between 

teachers can promote high quality instruction and high test scores of students. USA re-

search papers call excellent school culture “Professional Learning Community”. (Chichibu 

& Kihara, 2013)

Lesson Study can develop school culture

The National Institute for Educational Policy Research of Japan (NIER) surveyed 

2,000 schools (1,000 elementary schools and 1,000 middle schools) in 2010. Toshiya Chi-

chibu played the central role of the survey. The school survey reveals many aspects of Les-

son Study in Japan.

According to the school survey, almost all elementary and middle schools implement 

Lesson Study once or more per year. On average, elementary schools conduct Lesson Study 

10 times per a year, and middle schools implement Lesson Study 5 times per year.

70% of elementary schools and 66% of middle schools have meetings to discuss a 

lesson plan for a research lesson.

The school survey reveals not only actual conditions of Lesson Study, but also of the 

effectiveness of Lesson Study. In order to measure the effects of Lesson Study in schools, 

we developed survey items on “close communication between teachers”, “high quality in-

struction by teachers”, and “test scores of students of the school”. We found that these items 

are significantly associated with one another, and with items on “organizations or sched-

ules” or” methods of Lesson Studies”. 

Furthermore, the school survey reveals the effectiveness of principal and supervi-

sor coaching. Items such as “the principal observes each class daily”, “supervisors of the 

educational office visit the school every year” are associated with items on Lesson Study 

processes.

So, we can see that Lesson Study is effective, and that coaching by principals or su-

pervisors promotes Lesson Study. (Chichibu & Kihara, 2013)

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Differences between the open lesson 

in Kazakhstan and Japanese Lesson Study

In this handbook, I will introduce you how to conduct Lesson Study in your school. 

But you have already conducted similar program; open lesson.

In Kazakhstan, teachers are obliged to open their lessons for observation once or 

twice a year. Teachers in the same school or other schools who don’t have a lesson at the 

time will observe the open lesson. After the lesson the observers give their feedback to the 

teacher who conducted the lesson.

This open lesson is similar to Japanese Lesson Study. In Lesson Study, a volunteer 

teacher will open the lesson and his/her colleague will observe it. This is the research les-

son. There are some differences between the open lesson in Kazakhstan and Japanese Les-

son Study.

One of difference is the forming of a committee and the making of a schedule.

In Lesson Study, not volunteer teacher but all teachers have an obligation to observe 

the research lesson and to join the meeting following the research lesson.

The  committee  of  Lesson  Study  will  decide  the  theme  for  Lesson  Study  and  the 

schedule. 

In the Lesson Study schedule, when they have research lessons, only students of 

the research lesson stay in school and other students will go home early. This means 

that all teachers in the school can join observation of research lesson and post-lesson 

discussion.

During the open lesson in Kazakhstan, observers try to assess the lesson, and give 

feedback to the teacher who opened the lesson. In Japanese Lesson Study, observers can 

give feedback to teachers, but rather use the opportunity to improve their observation skills 

or their teaching skills. In Japanese post-lesson discussion, participant teachers try to un-

derstand the ideas of other teachers. 

62

Kazakhstan

Japan

Open lesson once per year

obligation 

obligation 

Observe the open lesson or 

research lesson

voluntary

obligation

Schedule

For open lesson

For research lesson, meet-

ing for lesson plan, post-

lesson discussion

Committee for Lesson 

Study

none

Decide a schedule or theme 

for Lesson Study

When open lesson or re-

search lesson held

Observed by teachers who 

don’t have a lesson

Other lessons are closed 

and all students except 

those in the research lesson 

go home, so all teachers can 

observe the research lesson

Objective of observation

Give feedback to the teach-

er

Improve observation skill 

of observers

Give feedback to the teacher

Post-lesson discussion

Only discussion with the 

teacher

Discussion within groups 

of 4-6 teachers, sharing the 

outcome of group discus-

sion

Viewpoints of observation 

and discussion

Give feedback or assess the 

teacher

Observe how each student 

learns during the lesson

Consider how to develop 

the lesson

External advisor

none

Sometimes external advi-

sors such as supervisors of 

the administration office or 

university professors are 

asked to join the discussion, 

and asked to give some 

advice to the teachers who 

participated in the meeting

The processes of Lesson Study

Stage1: Preparation by school leadership

You will conduct Lesson Study with all teachers in a faculty or in a school. It is nec-

essary to develop a committee for management and allocating several resources of Lesson 

Study.

At the start of the school year, teachers organize a committee in charge of Lesson 

Study. Members of the committee are delegates of the faculties. In the committee, they will 

discuss and decide the theme and schedule of Lesson Study.

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The theme of Lesson Study shows how teachers try to improve their lesson and chil-

dren. The theme of Lesson Study may be divided into each teacher.

In order to conduct Lesson Study once in a month, timetables should dedicate 

time for whole faculty professional development. Lesson Study can be conducted dur-

ing this time. On the day of the research lesson, only the students in this class stay in 

school and the other students go home, so that all teachers in the school can observe 

the lesson.

Mon

Tue

Wed

Thu

Fri

Sat

1

2

3

4

5

6

 

Lesson Study is held once in a month. The committee for Lesson Study makes a 

schedule for the research lessons and the discussion of the lesson plan. When the research 

lesson is held, the timetable on the day should dedicate time for observers. Meetings for the 

lesson plan can be held two or three weeks before the research lesson.

Month

Teacher who in charge 

of research lesson

Date of research lesson

Date of meeting for 

lesson plan

9

10

11

12

1

2

3

4

5

Stage2: Planning of a research lesson

In Lesson Study, one teacher volunteers to be in charge of research lesson, and to 

write a lesson plan about one month before the research lesson. Then, he/she introduces his/

her lesson plan in a meeting in which the teachers of the same grade or same subject area 

get together. In the meeting, the group of teachers will discuss how to improve the lesson 

plan. When they discuss the lesson plan, they try to improve it according to the theme of 

the Lesson Study set at the beginning of the school year.

64

The teacher then amends the lesson plan based on the discussions with other teachers. 

In some cases, the cycle of meeting and amending is repeated several times. In some other 

cases, the teacher asks for feedback from the principal or a supervisor of the administration 

office. To write and discuss a lesson, it may take one month.

In lesson plans in Kazakhstan, teachers write teacher’s activities in detail, but less ex-

pected students’ reaction. In Japanese lesson plans, it’s more important to note how students 

react to the teacher’s instruction or question.

For example, when students are asked “How to add 37 to 28?”, some will calculate 

30+20=50, 7+8=15, 50+15=65, others will calculate 28=3+25, 37+3=40, 40+25=65, and 

others will calculate 28=13+15, 37+13=50, 50+15=65. In a real lessen, students will show 

unexpected ideas and so the teacher should expect maximum possibility of student’s idea.

In addition to expecting students’ ideas, summarizing process of the lesson is impor-

tant. The objective of this lesson may be “to understand an efficient way of calculation”. 

Students can calculate in various ways, but they should know which is the best way to 

calculate two-digit numbers.

Template of a lesson plan

1 Unit name

2 Date class

3 Objective

4 Criteria

5 Materials

6 Process

  Introduction

        How attract students attention

        Main question:

  Main activity

        Sub question

Estimated students ideas

  Conclusion 

Lesson plan check list

•  details of unit name, date, class, materials

•  learning objectives relates to the school curriculum

•  success criteria relates to the learning objectives

•  relationship between introduction, main activity, conclusion is clear

•  with this lesson plan, whether students will get the objective or not

•  the lesson plan relates to the theme of Lesson Study

•  the lesson plan includes estimated students ideas

Stage3: Observation of the research lesson

The research lesson is conducted by the teacher in his/her class according to the les-

son plan. Teachers in the same faculty observe the research lesson.

Observe the lesson standing up so that student learning can be observed. Avoid talk-

ing to students, when they can’t understand or are not able to concentrate on the lesson as 

this disrupts the lesson. Concentration on observation is necessary.

65

The lesson plan should be given to observers before the lesson. Observers should 

hand the lesson plan, and take notes during the observation. The samples of notes below 

may be useful. 

 (beginning of lesson)

•  Objective of the lesson is clear

•  Students can maintain good posture

•  Students can focus on the lesson

(main activity)

•  Teacher explains clearly

•  Teacher can attract students’ attention

•  Teacher encourages students to express their idea

•  Teacher make students think deeply

•  Teacher writes on blackboard clearly

•  Teacher uses group work appropriately

•  Teacher uses ICT tools appropriately

•  Worksheet or other materials which teacher prepares for the lesson are effective

•  Whether students take notes adequately

•  Whether students understand the lesson

•  Students can express their ideas effectively

•  Students can listen to each other

•  Teacher can respond to students’ expressions, questions, postures, adequately

(conclusion)

•  Conclusion of the lesson relates to the objective

While observing the lesson, don’t focus on the teacher but on the students. If it is dif-

ficult to observe all students, you can focus on some students. When there are not so many 

students, such as less than 10, try to observe all students. 

Share the observations of the case students observed with colleagues. If you share the 

outcome of observation of case students, it will inform you a lot.

Stage4: post-lesson discussion

After the research lesson, observers discuss the research lesson. 

The objective of the post-lesson discussion should not be to evaluate the lesson, but 

to improve the viewpoint of teachers and to deepen reflection by each participant. Some-

times feedback can promote the instructor, but sometimes assessment can discourage the 

instructor.

When Kazakh teachers discuss of open lessons, they try to understand the instruc-

tor’s intention, how students learned during the lesson. Main objective is to develop each 

teacher’s observation skills, but in fact, their teaching methods become similar with obser-

vation each other.

I recommend that the instructor doesn`t join the discussion. The instructor has much 

information of the lesson, so if he/she join the discussion, participants may rely on the 

instructor. The instructor will stay out of the discussion, and will reply to the question of 

observers.

Samples of question to the instructor

•  Why did you use these activities for this lesson?

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