Transcript Slide 1

Teaching
Mathematics
Effectively
for the 21st
Century
Yeap Ban-Har, Ph.D.
National Institute of Education
Nanyang Technological University
Singapore
[email protected]
Catholic High School (Primary)
The MPK Lecture
Teaching
Mathematics
Effectively to
Engage Students
for the 21st
Century
introduction
Wellington Primary School
Task
• Move 3 sticks to make 2 squares.
Task
• Move 3 sticks to make 2 squares.
Task
• Move 3 sticks to make 2 squares.
Task
• Move 3 sticks to make 3 squares.
Task
• Move 3 sticks to make 3 squares.
Task
• Move 3 sticks to make 3 squares.
A Problem
from Singapore Classroom
• 88 children took part in a swimming
competition. 1/3 of the boys and 3/7 of the
girls wore swimming goggles. Altogether 34
children wore swimming goggles.
How many girls wore swimming goggles on
that day?
Fairfield Methodist Primary School
88 anak mengikuti perlombaan berenang. 1/3 anak laki-laki dan 3/7 anak perempuan
memakai kacamata renang. Total ada 34 anak yang memakai kacamata renang.
Berapa jumlah anak perempuan yang memakai kacamata renang pada hari itu?
A Problem
from Singapore Classroom
• 88 anak mengikuti perlombaan berenang. 1/3
anak laki-laki dan 3/7 anak perempuan
memakai kacamata renang.
Total ada 34 anak yang memakai kacamata
renang.
Berapa jumlah anak perempuan yang
memakai kacamata renang pada hari itu?
Fairfield Methodist Primary School
88 anak mengikuti perlombaan berenang. 1/3 anak laki-laki dan 3/7 anak perempuan
memakai kacamata renang. Total ada 34 anak yang memakai kacamata renang.
Berapa jumlah anak perempuan yang memakai kacamata renang pada hari itu?
• 88 children took part in a swimming competition. 1/3 of the boys and 3/7
of the girls wore swimming goggles. Altogether 34 children wore
swimming goggles.
How many girls wore swimming goggles on that day?
88 anak mengikuti perlombaan berenang. 1/3 anak laki-laki dan 3/7 anak perempuan
memakai kacamata renang. Total ada 34 anak yang memakai kacamata renang.
Berapa jumlah anak perempuan yang memakai kacamata renang pada hari itu?
88
34
54
• 88 children took part in a swimming competition. 1/3 of the boys and 3/7
of the girls wore swimming goggles. Altogether 34 children wore
swimming goggles.
How many girls wore swimming goggles on that day?
34 – 20 = 14
34
54 – 34 = 20
54
3 x 7 = 21
21 girls wear goggles.
21 anak perempuan memakai kacamata renang
A Curriculum
That Helps
Average
Students
Reach High
Achievement
Kurikulum yang
membantu
murid-murid
dengan
kemampuan
biasa / rata-rata
mencapai prestasi
yang tinggi.
Mathematics Curriculum Framework
Beliefs
Interest
Appreciation
Confidence
Perseverance
Numerical calculation
Algebraic manipulation
Spatial visualization
Data analysis
Measurement
Use of mathematical tools
Estimation
Monitoring of one’s own thinking
Self-regulation of learning
Mathematical
Problem
Solving
Concepts
Numerical
Algebraic
Geometrical
Statistical
Probabilistic
Analytical
Reasoning,
communication &
connections
Thinking skills &
heuristics
Application & modelling
TIMSS
Grade 4
1995
2003
2007
Trends in International Maths and Science Studies
Advanced
38
38
41
High
70
73
74
Intermediate
89
91
92
Low
96
97
98
Catholic High School (Primary)
TIMSS
Grade 4
Sweden
Median
USA
Japan
Singapore
Trends in International Maths and Science Studies
Advanced
3
5
10
23
41
High
24
26
40
61
74
Intermediate
69
67
77
89
92
Low
93
90
95
98
98
Elementary School in Japan
TIMSS
Average
Hong Kong
Singapore
Korea
Taiwan
Trends in International Maths and Science Studies
Advanced
2
31
40
40
45
High
15
64
70
71
71
Intermediate
46
85
88
90
86
Low
75
94
97
98
95
Grade 8
Telok Kurau Primary School
TIMSS
Average
Indonesia
Thailand
Malaysia
Singapore
Trends in International Maths and Science Studies
Advanced
2
0
3
2
40
High
15
4
12
18
70
Intermediate
46
14
44
50
88
Low
75
48
66
82
97
Grade 8
Effective Methods in Teaching Mathematics
effective
mathematics
teaching
Bina Bangsa School, Indonesia
Primary Mathematics 1A
Pedagogical
Principle:
Bruner
Prinsip Pedagogi:
Bruner
Number
Bonds
PCF Kindergarten Telok Blangah
Number
Bonds
PCF Kindergarten Telok Blangah
Bruner
Division
Pembagian
The concrete 
pictorial  abstract
approach is used to
help the majority of
learners to develop
strong foundation in
mathematics.
National Institute of Education
Pendekatan kongkret  gambar  abstrak, dipergunakan untuk
menolong sebagian besar pelajar untuk membangun dasar matematika yang kuat.
Division
Pembagian
My Pals Are Here! Mathematics 1B
Division
Pembagian
Photo: Princess Elizabeth Primary School
Division
Pembagian
My Pals Are Here! Mathematics 1B
summary
Elementary School in Chile
Skemp
Understanding in mathematics
• relational
(conceptual)
• instrumental
(procedural)
• conventional
Teaching for conceptual
understanding is given
emphasis in Singapore Math.
Primary Mathematics Standards Edition Grade 6
Pedagogical
Principle:
Skemp
Prinsip
Pedagogi:
Skemp
Skemp
Matematika Singapura menitik-beratkan
pengajaran pada pemahaman konsep.
Primary Mathematics Standards Edition Grade 6
Pedagogical
Principle:
Skemp
Prinsip
Pedagogi:
Skemp
Fraction
Division
Pembagian
Pecahan
Primary Mathematics Standards Edition Grade 6
3 kue dibagi secara rata kepada beberapa anak. Setiap anak mendapatkan ¾
bagian kue. Berapa anak yang mendapatkan ¾ bagian kue?
Jika Anda memotong 1 bagian penuh menjadi
¾ bagian, Anda mendapatkan 1 dan 1/3
tiga seperempat. Jadi, di dalam 3 bagian
penuh ada 3 x 1 1/3 atau 3 x 4/3.
Primary Mathematics Standards Edition Grade 6
summary
Scarsdale Middle School New York
How to make sure the butterfly cannot fly
How do you get a butterfly?
First there is the egg which hatches into a caterpillar. The caterpillar eats and grows. At the right time, it
makes a cocoon out of its own body. While in the cocoon, the caterpillar changes into a butterfly.
When the butterfly is ready, it starts to break through the cocoon. First a hole appears. Then the
butterfly struggles to come out through the hole. This can take a few hours.
If you try to "help" the butterfly by cutting the cocoon, the butterfly will come out easily but it will never
fly. Your "help" has destroyed the butterfly.
The butterfly can fly because it has to struggle to come out. The pushing forces lots of enzymes from the
body to the wing tips. This strengthens the muscles, and reduces the body weight. In this way, the
butterfly will be able to fly the moment it comes out of the cocoon. Otherwise it will simply fall to the
ground, crawl around with a swollen body and shrunken wings, and soon die.
If the butterfly is not left to struggle to come out of the cocoon, it will never fly.
We can learn an important lesson from the butterfly.
If we do not have struggles and challenges in our work, we will never grow strong and capable. If life
has no difficulties, we will become weak and helpless.
Lim Siong Guan Head, Civil Service
Dienes
Dienes encouraged the use of
variation in mathematics education –
perceptual
variation
and
mathematical variation.
Dienes menganjurkan penggunaan
variasi
dalam
pengajaran
matematika - variasi persepsi dan
variasi matematika.
Pedagogical
Principle:
Dienes
Prinsip Pedagogi:
Dienes
Primary Mathematics Standards Edition
Pedagogical
Principle:
Dienes
Prinsip Pedagogi:
Dienes
Pedagogical
Principle:
Dienes
Prinsip Pedagogi:
Dienes
Jane berlatih piano selama ¾ jam per hari.
Berapa menit dia berlatih setiap harinya?
1 jam = 60 menit
60 ÷ 4 = 15
15 x 3 = 45
¾ x 60 = 45
Mathematical
Variation
Variasi dari segi
Matematika
Di sebuah kelas, 2/5 muridnya memakai kacamata.
a) Berapa bagiankah murid yang tidak memakai kacamata?
b) Jika 16 murid memakai kacamata, berapa jumlah murid seluruhnya?
16
Di sebuah kelas, 2/5 muridnya memakai kacamata.
a) Berapa bagiankah murid yang tidak memakai kacamata?
b) Jika 16 murid memakai kacamata, berapa jumlah murid seluruhnya?
16
Nicole membeli 30 butir telur. Dia memakai 2/3 telur yang dibeli untuk memanggang kue.
Berapa telur yang tersisa?
Mathematical
Variation
30
Variasi dari segi
Matematika
effective
teaching
Keys Grade School , Manila
Pictorial Before
Abstract
Gambar sebelum abstrak
Perceptual
Variation
Variasi dari segi persepsi
Primary Mathematics Standards Edition
Mathematical
Variation
Variasi dari segi matematika
Penekanan pada pemaparan visual
dan variasi sistematis
memperkuat pemahaman konsep
Emphasis on
pictorial
representation
and systematic
variation to
enhance
conceptual
understanding
TIMSS
Singapore
Grade 4
Grade 8
Trends in International Maths and Science Studies
Advanced
41
40
High
74
70
Intermediate
92
88
Low
98
97
Catholic High School (Primary)
TIMSS
USA
Grade 4
Grade 8
Trends in International Maths and Science Studies
Advanced
10
6
High
40
31
Intermediate
77
67
Low
95
92
Catholic High School (Primary)
TIMSS
England
Grade 4
Grade 8
Trends in International Maths and Science Studies
Advanced
16
8
High
48
35
Intermediate
79
69
Low
94
90
Catholic High School (Primary)
TIMSS
International
Grade 4
Grade 8
Trends in International Maths and Science Studies
Advanced
5
2
High
26
15
Intermediate
67
46
Low
90
75
Catholic High School (Primary)
conclusion
PCF Kindergarten Pasir Ris
Fuchun Primary School
Mathematics is an
excellent vehicle for
the development and
improvement of a
person’s intellectual
competence ..
Ministry of Education 2006
Matematika adalah kendaraan / alat yang hebat
untuk membangun dan memperbaiki kompetensi
dan intelektual seseorang …
Bina Bangsa School Bandung
Patterns
Bina Bangsa School Bandung
Patterns
Visualization
SD Negeri in Palembang
Visualization
Teacher Training for LEAP Programme
for Public School Teachers in Manila
Communication
mathz4kidz Learning Centre in Malaysia
Pathlight School
Communication
Primary Mathematics Syllabus 2007
Primary 2
Wellington Primary School
Balestier Hill
Primary School
Fuchun Primary School
Primary Mathematics Syllabus 2007
Princess Elizabeth Primary School
“Children are truly the
future of our nation. “
Irving Harris