Transcript 日本の数学教育に関する教師教育 - The Math Forum

Teacher Training in Japanese
Mathematics Education
Toshikazu Ikeda
Yokohama National University
Yoshiaki Kuwahara
Shinmei Junior High School
Outline
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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)
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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)
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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)
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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
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In 2001
Ministry of Education, Culture, Sports,
Science and Technology is planning to
integrate teacher training university,
keeping the quota of 10,000 students.
Pre-Service Education
All
PCMI 2002: Toshikazu Ikeda, Yoshiaki Kuwahara
Nothing
Example in Yokohama National
University
In 1997: Faculty of Education
Quota of students
15000 → 10000
→ Faculty of Education and Human Sciences
◇Pre-service education: 230 students
Focus on Elementary School Education
◇Establishment of New Courses: 230 students
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 education
in 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
Curriculum of mathematics education in YNU
1
2
Calculus
Ⅰ-Ⅳ
Algebra
Ⅰ-Ⅳ
3
4
Observation of
Classroom
teaching
Introduction to
Math.
Geometry
Ⅰ-Ⅳ
Probability &
StatisticⅠ-Ⅳ
Teaching methods
of elementary math.
Lesson plan
& observation
Problem solving and
mathematical thinking
Analysis of
Classroom teaching
Contents taught in
Secondary math.
Teaching Practice
[elementary level]
(4 weeks)
Development of
Teaching material
Assessment
Report to graduate
Teaching Practice
[secondary level]
(2 weeks)
PCMI 2002: Toshikazu Ikeda, Yoshiaki Kuwahara
In Case of Yokohama National University
(For Elementary School Teacher)
Introduction to Mathematics for elementary school teachers
Core
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
technology
Option
Presentation
１．Mathematics for teachers
２．Mathematics for a real world
３．Mathematics for a joy
PCMI 2002: Toshikazu Ikeda, Yoshiaki Kuwahara
Option:
Mathematics for a real world
Selection of problem in each group
12 groups composed of 5 members
Problem Solving
Preparation of Presentation
Presentation, Assessing each other
Mathematical points of view: 5points
Presentation: 5points
PCMI 2002: Toshikazu Ikeda, Yoshiaki Kuwahara
ＴＲＹ
Goal Post
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
It is possible for player
probability when attempting to make a goal kick.
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?”
Law of 72
５％ → ７２÷５＝１４．４
３％ → ７２÷３＝２４
１％ → ７２÷１＝７２
１５ years
２４ years
７２ years
PCMI 2002: Toshikazu Ikeda, Yoshiaki Kuwahara
Eyesight
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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
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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 on
the ship
Training in ministry of education
Guidance of students' course to take after guraduation, Training for new industrial technology teachers
Dispatched to the Abroad ,Japanese school
New teacher
Prefecture training
After
5 years
Training
Experienced Teacher Training
After
15 years
Training
Dispatched to the Master Course in teacher training university
Training for the Curriculum coordinator
Training for the Administrator
Principal,Vice-Principal
City
Town
Ward
School
Individual
(private)
Annnual Training Program for All teachers
Study in a school
Group Resarch & training
Individual Resarch & trariing
PCMI 2002: Toshikazu Ikeda, Yoshiaki Kuwahara
Classification of Teacher Training
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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
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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 9０ 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
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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)
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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
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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
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To a Company
To Abroad
Language Training
Japanese School
Inspection of various countries
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To a Master Course in teacher training
university (Study & Research)
PCMI 2002: Toshikazu Ikeda, Yoshiaki Kuwahara
Collaboration
on the Daily work
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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
② Observation of
an actual classroom
teaching
③ Analytical
discussion about the
classroom teaching
① Discussion
about a lesson plan
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Pre-service education:
One of the tools to assess a classroom teaching
Examinations to become a teacher:
Demonstration of classroom teaching
PCMI 2002: Toshikazu Ikeda, Yoshiaki Kuwahara
Lesson plan – it’s history
Before world war Ⅱ
Teacher’s Students’
activity
activity
After world war Ⅱ
Students’ Remark on
activity
teaching
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
School attached to
prefectures
University
Style 5
In a Prefecture,
Academic
From all of the Company
prefectures
PCMI 2002: Toshikazu Ikeda, Yoshiaki Kuwahara
Society
&
Five styles of a Lesson Study
in Japan (in-service education)
Main Aim of L.S.
Methods to disseminate
Style1
to attain
objectives
the
Style2
to promote
development
professional
Style3
to develop and spread new Call for attendance at the
contents and approaches
beginning of semester
Style4
to develop and spread new
Announcement
contents and approaches
Homepage
Style5
to cultivate activity of lesson Announcement, Journal,
study
Homepage
school
Announcement
Convey from older
teachers
to
younger
teachers
PCMI 2002: Toshikazu Ikeda, Yoshiaki Kuwahara
，
Lesson Study Triangle
Relation between
children and teacher
children
teacher
Relation
between
children
and
material
material
Relation
between teacher
and material
Strong Relation
Between two
components
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?
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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.
Check 3 in the following figure !
Answers of students
Students’ own problem
Why did we
derive a variety
of ideas ?
PCMI 2002: Toshikazu Ikeda, Yoshiaki Kuwahara
Learn to see material
Identifying mathematical essential points
To identify essential and a wide range of
mathematical ideas
Ex: Division with a remainder “13÷5 = “
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.
[ Aim of teacher ]
The quotient is 2
and the remainder is 3
PCMI 2002: Toshikazu Ikeda, Yoshiaki Kuwahara
Learn to see material
Identifying 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
Is there any students’ ideas ignored by
teacher’s selfish judgment?
Which animal do you think is the biggest among a lion,
a frog and a turtle made by the clay ?
Focus of teacher: Measuring Volume
Let’s measure the weight
of three animals to
compare the volume
Um… Are there
other ideas ?
It is not appropriate for teacher to
ignore student’s idea in this situation.
PCMI 2002: Toshikazu Ikeda, Yoshiaki Kuwahara
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.
15, July
Summary
If you have the panel,
please show us at the
beginning.
S = (a+b)×ｈ÷２
PCMI 2002: Toshikazu Ikeda, Yoshiaki Kuwahara
a
h
b
Future Issues to be discussed in Japan
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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．
If you have a chance to teach the same topic next
time, how do you want to treat them?
Is there any alternative
teaching methods?
What is the points that is
useful in a future teaching?
PCMI 2002: Toshikazu Ikeda, Yoshiaki Kuwahara
Future Issues to be discussed in Japan
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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
Total
31,000
Total
12,000
14
12
10
Ppulation
(1000
students)
8
小学校
中学校
高校
6
4
Number of
Teachers in 2002
2
0
1990
1992 1994
1996
1998
Elementary:407,000 Junior High: 255,000 Senior High: 266,000
(Male):(Female)
(Male):(Female)
(Male):(Female)
=2:3
=3:2
=5:2
PCMI 2002: Toshikazu Ikeda, Yoshiaki Kuwahara