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Teaching Mathematics Effectively for the 21st Century

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Title: Slide 1 Author: Yeap Banhar Last modified by: Yeap Banhar Created Date: 2/9/2009 9:39:49 AM Document presentation format: On-screen Show (4:3) – PowerPoint PPT presentation

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Title: Teaching Mathematics Effectively for the 21st Century

1
Teaching Mathematics Effectively for the 21st
Century
Yeap Ban-Har, Ph.D. National Institute of
Education Nanyang Technological University
Singapore banhar.yeap_at_nie.edu.sg
2
Catholic High School (Primary)
The MPK Lecture Teaching Mathematics Effectively
to Engage Students for the 21st Century
3
introduction
Wellington Primary School
4
• Move 3 sticks to make 2 squares.

5
• Move 3 sticks to make 2 squares.

6
• Move 3 sticks to make 2 squares.

7
• Move 3 sticks to make 3 squares.

8
• Move 3 sticks to make 3 squares.

9
• Move 3 sticks to make 3 squares.

10
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?
11
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

Fairfield Methodist Primary School
12
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?

13
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?

14
34 20 14
54 34 20
34
54
15
3 x 7 21
21 girls wear goggles.
Kurikulum yang membantu murid-murid dengan
kemampuan biasa / rata-rata mencapai prestasi
yang tinggi.
21 anak perempuan memakai kacamata renang
A Curriculum That Helps Average Students Reach
High Achievement
16
(No Transcript)
17
Mathematics Curriculum Framework
18
TIMSS Trends in International Maths and Science
Studies
1995
2003
2007
38
41
38
High
70
74
73
Intermediate
89
92
91
Low
96
98
97
Catholic High School (Primary)
19
TIMSS Trends in International Maths and Science
Studies
Sweden
Median
U S A
Japan
Singapore
3
10
5
41
23
High
24
40
26
74
61
Intermediate
69
77
67
92
89
Low
93
95
90
98
98
Elementary School in Japan
20
TIMSS Trends in International Maths and Science
Studies
Average
Hong Kong
Singapore
Korea
Taiwan
2
40
31
45
40
High
15
70
64
71
71
Intermediate
46
88
85
86
90
Low
75
97
94
95
98
Telok Kurau Primary School
21
TIMSS Trends in International Maths and Science
Studies
Average
Indonesia
Thailand
Malaysia
Singapore
2
3
0
40
2
High
15
12
4
70
18
Intermediate
46
44
14
88
50
Low
75
66
48
97
82
Effective Methods in Teaching Mathematics
22
effective
mathematics
teaching
Bina Bangsa School, Indonesia
23
Primary Mathematics 1A
Pedagogical Principle Bruner Prinsip Pedagogi
Bruner
24
Number Bonds
PCF Kindergarten Telok Blangah
25
Number Bonds
PCF Kindergarten Telok Blangah
26
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.
27
Division Pembagian
My Pals Are Here! Mathematics 1B
28
Division Pembagian
Photo Princess Elizabeth Primary School
29
Division Pembagian
My Pals Are Here! Mathematics 1B
30
summary
Elementary School in Chile
31
Skemp
• Understanding in mathematics
• relational
• (conceptual)
• instrumental
• (procedural)
• conventional
• Teaching for conceptual understanding is given
emphasis in Singapore Math.

Pedagogical Principle Skemp Prinsip Pedagogi
Skemp
Primary Mathematics Standards Edition Grade 6
32
Skemp
Pedagogical Principle Skemp Prinsip Pedagogi
Skemp
• Matematika Singapura menitik-beratkan pengajaran

Primary Mathematics Standards Edition Grade 6
33
Fraction Division Pembagian Pecahan
Primary Mathematics Standards Edition Grade 6
34
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
1 1/3 atau 3 x 4/3.
Primary Mathematics Standards Edition Grade 6
35
summary
Scarsdale Middle School New York
36
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
37
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
38
Pedagogical Principle Dienes Prinsip Pedagogi
Dienes
39
Pedagogical Principle Dienes Prinsip Pedagogi
Dienes
40
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
41
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
42
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 Variasi dari segi
Matematika
30
43
effective
teaching
44
Pictorial Before Abstract
Gambar sebelum abstrak
45
Perceptual Variation
Variasi dari segi persepsi
Primary Mathematics Standards Edition
46
Mathematical Variation
Variasi dari segi matematika
47
Penekanan pada pemaparan visual dan variasi
sistematis memperkuat pemahaman konsep
Emphasis on pictorial representation and
systematic variation to enhance conceptual
understanding
48
TIMSS Trends in International Maths and Science
Studies
Singapore
41
40
High
74
70
Intermediate
92
88
Low
98
97
Catholic High School (Primary)
49
TIMSS Trends in International Maths and Science
Studies
U S A
10
6
High
40
31
Intermediate
77
67
Low
95
92
Catholic High School (Primary)
50
TIMSS Trends in International Maths and Science
Studies
England
16
8
High
48
35
Intermediate
79
69
Low
94
90
Catholic High School (Primary)
51
TIMSS Trends in International Maths and Science
Studies
International
5
2
High
26
15
Intermediate
67
46
Low
90
75
Catholic High School (Primary)
52
conclusion
PCF Kindergarten Pasir Ris
53
Fuchun Primary School
Mathematics is an excellent vehicle for the
development and improvement of a persons
intellectual competence .. Ministry of Education
2006
Matematika adalah kendaraan / alat yang
hebat untuk membangun dan memperbaiki kompetensi
dan intelektual seseorang
54
Patterns
Bina Bangsa School Bandung
55
Patterns
Bina Bangsa School Bandung
56
Visualization
SD Negeri in Palembang
57
Visualization
Teacher Training for LEAP Programme for Public
School Teachers in Manila
58
Communication
mathz4kidz Learning Centre in Malaysia
59
Communication
Pathlight School
60
Primary Mathematics Syllabus 2007
Primary 2 Wellington Primary School
61
Balestier Hill Primary School
Fuchun Primary School
Primary Mathematics Syllabus 2007
62
Princess Elizabeth Primary School
63
Children are truly the future of our nation.
Irving Harris