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Teacher Training in Japanese Mathematics Education
Toshikazu IkedaYokohama National University
Yoshiaki KuwaharaShinmei Junior High School
PCMI 2002: Toshikazu Ikeda, Yoshiaki Kuwahara
Outline
States and issues in Japanese teacher training
Pre-service education : Example in Yokohama National University
In-service education Lesson Study
PCMI 2002: Toshikazu Ikeda, Yoshiaki Kuwahara
First Report by the Education Personnel Training Council (1997)
Improvement of the teacher training curriculum ① Wide understanding of liberal arts ② Problem Solving Ability, Humanity ③ Knowledge and skills of subject matters
The number of credits for subjects concerning teaching methods of mathematics
→ From about 2 credits to 8 credits
PCMI 2002: Toshikazu Ikeda, Yoshiaki Kuwahara
Second Report by the Education Personnel Training Council (1998)
Promotion of reeducation of currently employed teachers through master course
System of night master course for teachers is gradually introduced in teacher training university
PCMI 2002: Toshikazu Ikeda, Yoshiaki Kuwahara
Third Report by the Education Personnel Training Council (1999)
Facilitation of cooperation in the cultivation, appointment and training of teachers
Deeper cooperation is expected
University
Board of education School
PCMI 2002: Toshikazu Ikeda, Yoshiaki Kuwahara
Issue in teacher training university
In 2001 Ministry of Education, Culture, Sports, Science and Te
chnology is planning to integrate teacher training university, keeping the quota of 10,000 students.
Pre-Service Education
All Nothing
PCMI 2002: Toshikazu Ikeda, Yoshiaki Kuwahara
Example in Yokohama National University
In 1997: Faculty of Education
→ Faculty of Education and Human Sciences ◇
Pre-service education: 230 students
Focus on Elementary School Education ◇ Establi
shment of New Courses: 230 students
Quota of students15000 → 10000
In 2000: Introduction of a New Curriculum based on first report by the Education
Personnel Training Council
PCMI 2002: Toshikazu Ikeda, Yoshiaki Kuwahara
Aims in mathematics education
in Yokohama National University [Mathematical points of view] ① To foster students’ ability to think
mathematically ② To enable students to understand
mathematical concepts and ideas existing behind elementary and secondary mathematics.
③ To foster students’ ability to represent mathematically
④ To foster students’ ability to utilize technology
PCMI 2002: Toshikazu Ikeda, Yoshiaki Kuwahara
Aims in mathematics educationin Yokohama National University
[Educational points of view] ⑤ To enable students to understand the objectives and contents of mathematics
⑥ To enable students to understand Teaching methods including assessment of mathematics
⑦ To foster students’ ability to construct and analyze a classroom teaching
⑧ To foster students’ ability to utilize the textbook of mathematics
PCMI 2002: Toshikazu Ikeda, Yoshiaki Kuwahara
Introduction toMath.
Observation ofClassroom teaching
CalculusⅠ-Ⅳ
AlgebraⅠ-Ⅳ
Geometry
Ⅰ-Ⅳ
Probability & StatisticⅠ-Ⅳ
Teaching Practice[elementary level]
(4 weeks)
Teaching Practice[secondary level]
(2 weeks)
Teaching methods of elementary math.
Problem solving and mathematical thinking
Analysis of Classroom teaching
Contents taught in Secondary math.
Development of Teaching material
Assessment
Lesson plan& observation
1
2
3
4Report to graduate
Curriculum of mathematics education in YNU
PCMI 2002: Toshikazu Ikeda, Yoshiaki Kuwahara
In Case of Yokohama National University (For Elementary School Teacher)
Introduction to Mathematics for elementary school teachers
Mathematical concepts and ideas existing behind elementary mathematics
1. Number and operation 2. Quantity and measurement 3. Figures 4. Relation between number and quantity 5. Way of mathematical thinking
Core
1. Mathematics for teachers 2. Mathematics for a real world
3. Mathematics for a joy
OptionPresentationtechnology
PCMI 2002: Toshikazu Ikeda, Yoshiaki Kuwahara
Option:Mathematics for a real world
Presentation, Assessing each other Mathematical points of view: 5points Presentation: 5points
Selection of problem in each group
12 groups composed of 5 members
Problem SolvingPreparation of Presentation
PCMI 2002: Toshikazu Ikeda, Yoshiaki Kuwahara
GOAL KICKS IN RUGBY
In rugby, a chance to score a goal is given after a try. The probability of a successful goal is influenced by the position where the goal kick is made. How should you decide the position with the largest probability when attempting to make a goal kick.
TRY
Goal Post
It is possible for player to kick in any place
on the blue line.
PCMI 2002: Toshikazu Ikeda, Yoshiaki Kuwahara
“How many years does it take to make money double?”
5% → 72 ÷5=14.4 15 years3% → 72 ÷3=24 24 years1% → 72 ÷1=72 72 years
Law of 72
PCMI 2002: Toshikazu Ikeda, Yoshiaki Kuwahara
Eyesight
I heard that Eyesight of Inuit is more than 5.0. If it is true, how can Inuit see far away compared with us.
PCMI 2002: Toshikazu Ikeda, Yoshiaki Kuwahara
Mirror Problem
Problem What size of mirror do we need at least in order to see the whole body?
PCMI 2002: Toshikazu Ikeda, Yoshiaki Kuwahara
Reflector of bicycle
Reflector of bicycle is shining even though light flood into it from any angles. What is the structure of reflector?
PCMI 2002: Toshikazu Ikeda, Yoshiaki Kuwahara
In-service teacher training in Japan
National New teacher Training in ministry of educationtraining onthe ship
Guidance of students' course to take after guraduation, Training for new industrial technology teachers
Dispatched to the Abroad ,Japanese school
New teacher Experienced Teacher TrainingPrefecturetraining After After
5 years 15 yearsTraining Training
Dispatched to the Master Course in teacher training university
Training for the Curriculum coordinator
Training for the AdministratorPrincipal,Vice-Principal
CityTown Annnual Training Program for All teachersWard
School Study in a school
Individual(private) Group Resarch & training
Individual Resarch & trariing
PCMI 2002: Toshikazu Ikeda, Yoshiaki Kuwahara
Classification of Teacher Training
Public Training (National,Prefecture,City/Town/Ward, School)
Private training (Individual research,society,Other Training & research circle)
PCMI 2002: Toshikazu Ikeda, Yoshiaki Kuwahara
Public Training for in-service Teachers
New teachers Training Experienced Teachers Training
(After 5 years & After 10 years )
Dispatched Training (Master course in teacher training university, Company, Abroad )
PCMI 2002: Toshikazu Ikeda, Yoshiaki Kuwahara
New teachers Training
・ About 9 0 times training during first year
60 times in School , 30 times out of School
・ Leading Teacher in charge guide New Teacher one by one.
・ Extensive training Lecture,Lesson study,Management
PCMI 2002: Toshikazu Ikeda, Yoshiaki Kuwahara
Experienced Teacher Training After 5 years 5 ~ 6 times training in 6th years Group Training in each theme (Class Management , Students Guidance, Problems to be solved (Bullying etc) After 15 years 3~5 times training in 15th years Optional Course Training each interest (Subject ,Class Management , Students Guidance, Problem to be solved )
PCMI 2002: Toshikazu Ikeda, Yoshiaki Kuwahara
An example in mathematics education
In case of Junior High School Teachers
Contents: ・ Explanation of the National Curriculum
・ Developing New teaching materials for Team Teaching or Optional Course
・ Collaboration by Experienced Teachers
PCMI 2002: Toshikazu Ikeda, Yoshiaki Kuwahara
Dispatched Training To a Company To Abroad
Language Training Japanese School Inspection of various countries
To a Master Course in teacher training university (Study & Research)
PCMI 2002: Toshikazu Ikeda, Yoshiaki Kuwahara
Collaboration on the Daily work
Daily discussion in the Teachers’ Room Regarding to mathematics teaching Progress of classroom teaching The way of Assessment Teaching Materials Exchange views
PCMI 2002: Toshikazu Ikeda, Yoshiaki Kuwahara
Lesson Study as teacher training
Pre-service education: One of the tools to assess a classroom teaching Examinations to become a teacher:
Demonstration of classroom teaching
① Discussion about a lesson plan
② Observation of an actual classroom
teaching
③ Analytical discussion about the classroom teaching
PCMI 2002: Toshikazu Ikeda, Yoshiaki Kuwahara
Lesson plan – it’s history
Teacher’s activity
Students’ activity
Students’ activity
Remark on teaching
Before world war Ⅱ After world war Ⅱ
PCMI 2002: Toshikazu Ikeda, Yoshiaki Kuwahara
Five styles of a Lesson Study
in Japan (in-service education)
Scale of L.S. By Whom
Style 1 In a school Principal & Teachers
Style 2 In a City/Prefecture
Teachers themselves
Style 3 In a City/Prefecture Board of Education
Style 4 From all of the prefectures
School attached to University
Style 5 In a Prefecture, From all of the prefectures
Academic Society & Company
PCMI 2002: Toshikazu Ikeda, Yoshiaki Kuwahara
Five styles of a Lesson Study
in Japan (in-service education)
Main Aim of L.S. Methods to disseminate
Style1 to attain the school objectives
Announcement
Style2 to promote professional development
Convey from older teachers to younger teachers
Style3 to develop and spread new contents and approaches
Call for attendance at the beginning of semester
Style4 to develop and spread new contents and approaches
Announcement , Homepage
Style5 to cultivate activity of lesson study
Announcement, Journal,Homepage
PCMI 2002: Toshikazu Ikeda, Yoshiaki Kuwahara
Relation between children and
teacher
Relation between
teacher and material
Relation between children
and material
Strong Relation Between two components
Lesson Study Triangle
children
materialteacher
PCMI 2002: Toshikazu Ikeda, Yoshiaki Kuwahara
Effectiveness of Lesson Study
Lesson study might be effective for teacher in the following points in particular.
① learn to see material ・ Can teacher identify mathematical
essential points of materials? ・ Does teacher deprive of students’
opportunity to think mathematically?
PCMI 2002: Toshikazu Ikeda, Yoshiaki Kuwahara
Effectiveness of Lesson Study
② learn to see students ・ Can teacher understand what students
understand? ・ Can students understand teacher’s asking
questions? ・ Does teacher ignore of students’ ideas by
his/her selfish reason? ・ Can teacher accept and evaluate students’
ideas appropriately? ・ Can students discuss cooperatively?
PCMI 2002: Toshikazu Ikeda, Yoshiaki Kuwahara
Effectiveness of Lesson Study
① learn to see material + ② learn to see students ・ Can teacher develop the material by considering
both mathematical essential points and students’ interest?
・ Can students find out their own problems from the original problem that teacher presents at first?
・ Can teacher assist students’ cooperative discussion and summarize the mathematical essential ideas derived from their discussion?
PCMI 2002: Toshikazu Ikeda, Yoshiaki Kuwahara
What do you consider important when introducing a mathematics lesson?
(3) To make students clarify an ambiguous situation.
Answers of students
Why did we derive a
variety of ideas ?
Students’ own problem
Check 3 in the following figure !
PCMI 2002: Toshikazu Ikeda, Yoshiaki Kuwahara
Learn to see materialIdentifying mathematical essential points
To identify essential and a wide range of mathematical ideas
Ex: Division with a remainder “13÷5 = “
[ Aim of teacher ] The quotient is 2
and the remainder is 3
If I had two more, the quotient would
become 3
The quotient is 3 with a lack of 2
No, your idea is not good.
PCMI 2002: Toshikazu Ikeda, Yoshiaki Kuwahara
Learn to see materialIdentifying mathematical essential points
Wide and deep mathematical insights are required for a teacher.
Ex: Division with a remainder “13÷5 = “
Mathematical essential points
[ Aim of teacher ]The quotient varies
based on the situation
Teacher can pick up students’ mutter as well as focus on mathematically essential points.
PCMI 2002: Toshikazu Ikeda, Yoshiaki Kuwahara
Let’s measure the weight of three
animals to compare the volume
Which animal do you think is the biggest among a lion, a frog and a turtle made by the clay ?
Um… Are there other ideas ?
It is not appropriate for teacher to ignore student’s idea in this situation.
Is there any students’ ideas ignored by teacher’s selfish judgment?
Focus of teacher: Measuring Volume
PCMI 2002: Toshikazu Ikeda, Yoshiaki Kuwahara
15, July
Are mathematical essential ideas elicited from students’ collaborative discussion summarized at the end of lesson?
Students developed the formula to calculate the area of trapezoid.
At the end of lesson, teacher put the panel on the blackboard.
Summary
S = (a+b)× h ÷ 2
a
b
h If you have the panel,please show us at the
beginning.
PCMI 2002: Toshikazu Ikeda, Yoshiaki Kuwahara
Future Issues to be discussed in Japan
It is necessary for teachers to discuss the issues that are useful in a future teaching. Namely, it is expected for teachers to discuss the following questions for instance .
Is there any alternative teaching methods?
If you have a chance to teach the same topic next time, how do you want to treat
them?
What is the points that is useful in a future
teaching?
PCMI 2002: Toshikazu Ikeda, Yoshiaki Kuwahara
Future Issues to be discussed in Japan
We often observed the stereotyped classroom teaching. (ex. Understand a problem - solving individually -Presentation by students - Negotiation)
The most important thing for teacher is to accept students’ ideas and evaluate them flexibility. If a teacher couldn’t do so, students might not come to life.
PCMI 2002: Toshikazu Ikeda, Yoshiaki Kuwahara
PCMI 2002: Toshikazu Ikeda, Yoshiaki Kuwahara
The number of new teachers & the number of teachers
0
2
4
6
8
10
12
14
Ppulation(1000
students)
19901992199419961998
?¬Sw?Z’†Sw?Z?,?Z
Total12,00
0
Total31,00
0
Elementary:407,000(Male):(Female)
=2:3
Junior High: 255,000(Male):(Female)
=3:2
Senior High: 266,000 (Male):(Female)
=5:2
Number of Teachers in
2002