Teacher Training in Japanese Mathematics Education Toshikazu Ikeda Yokohama National University...

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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

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

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

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

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

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

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

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

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

4Report to graduate

Curriculum of mathematics education in YNU

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

１． Mathematics for teachers 　２． Mathematics for a real world

３． Mathematics for a joy

OptionPresentationtechnology

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

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.

“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

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. 　　　　　　　　　　　　　　　　　　　　

Mirror Problem

Problem What size of mirror do we need at least in order to see the whole body?

Reflector of bicycle

Reflector of bicycle is shining even though light flood into it from any angles. What is the structure of reflector?

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

Classification of Teacher Training

Public Training (National,Prefecture,City/Town/Ward, School)

Private training (Individual research,society,Other Training & research circle)

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 ）

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

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 ）

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

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)

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

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

Lesson plan – it’s history

　Teacher’s 　activity

Students’ activity

　Students’ 　activity

Remark on 　teaching

Before world war Ⅱ After world war Ⅱ

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

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

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

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?

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?

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?

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 !

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.

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.

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

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

h If you have the panel,please show us at the

beginning.

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

What is the points that is useful in a future

teaching?

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.

The number of new teachers & the number of teachers

Ppulation(1000

students)

19901992199419961998

?¬Sw?Z’†Sw?Z?,?Z

Total12,00

Total31,00

Elementary:407,000(Male):(Female)

Junior High: 255,000(Male):(Female)

Senior High: 266,000 (Male):(Female)

Number of Teachers in

Teacher Training in Japanese Mathematics Education Toshikazu Ikeda Yokohama National University...

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