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Mentari - Catholic Education Council (MPK) SeminarJanuary 2010Teaching Mathematics in Effectively for the 21st Century
Citation preview
Teaching Mathematics Effectively for the 21st Century
Yeap Ban-Har, Ph.D.National Institute of Education
Nanyang Technological University Singapore
The MPK Lecture
Teaching Mathematics Effectively to
Engage Students for the 21st
Century
Catholic High School (Primary)
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.
• 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?
A Problem from Singapore Classroom
Fairfield Methodist Primary School
88 anak mengikuti perlombaan berenang. 1/3 anak laki-laki dan 3/7 anak perempuanmemakai kacamata renang. Total ada 34 anak yang memakai kacamata renang. Berapa jumlah anak perempuan yang memakai kacamata renang pada hari itu?
• 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
Fairfield Methodist Primary School
• 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?
34
88
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?
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?
34
54 – 34 = 2034 – 20 = 14
54
3 x 7 = 21
21 girls wear goggles.
A Curriculum That Helps
Average Students
Reach High Achievement
21 anak perempuan memakai kacamata renangKurikulum yang
membantu murid-murid
dengan kemampuan
biasa / rata-ratamencapai prestasi
yang tinggi.
Mathematics Curriculum Framework
Mathematical Problem
Solving
Attitudes
Metacognition
Proc
esse
s
Concepts
SkillsNumericalAlgebraic
GeometricalStatistical
ProbabilisticAnalytical
Reasoning, communication & connectionsThinking skills & heuristicsApplication & modelling
Numerical calculationAlgebraic
manipulationSpatial visualization
Data analysisMeasurement
Use of mathematical tools
Estimation
Monitoring of one’s own thinkingSelf-regulation of learning
BeliefsInterest
AppreciationConfidence
Perseverance
Advanced
Intermediate
Low
High
38 4138
70 7473
89 9291
96 9897
Grade 4
Catholic High School (Primary)
TIMSSTrends in International Maths and Science Studies
Advanced
Intermediate
Low
High
3 105
24 4026
69 7767
93 9590
Grade 4
Elementary School in Japan
TIMSSTrends in International Maths and Science Studies
4123
7461
9289
9898
Advanced
Intermediate
Low
High
2 4031
15 7064
46 8885
75 9794
Grade 8
Telok Kurau Primary School
TIMSSTrends in International Maths and Science Studies
4540
7171
8690
9598
Advanced
Intermediate
Low
High
2 30
15 124
46 4414
75 6648
Grade 8
Effective Methods in Teaching Mathematics
TIMSSTrends in International Maths and Science Studies
402
7018
8850
9782
mathematicsteaching
effective
Bina Bangsa School, Indonesia
Pedagogical Principle:
BrunerPrinsip Pedagogi:
Bruner
Primary Mathematics 1A
Number Bonds
PCF Kindergarten Telok Blangah
Number Bonds
PCF Kindergarten Telok Blangah
Bruner
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.
DivisionPembagian
My Pals Are Here! Mathematics 1B
DivisionPembagian
Photo: Princess Elizabeth Primary School
DivisionPembagian
My Pals Are Here! Mathematics 1B
DivisionPembagian
summary
Elementary School in Chile
Skemp
Understanding in mathematics • relational (conceptual) • instrumental (procedural)• conventional
Teaching for conceptual understanding is given emphasis in Singapore Math.
Pedagogical Principle:
SkempPrinsip
Pedagogi: Skemp
Primary Mathematics Standards Edition Grade 6
Skemp
Matematika Singapura menitik-beratkan pengajaran pada pemahaman konsep.
Pedagogical Principle:
SkempPrinsip
Pedagogi: Skemp
Primary Mathematics Standards Edition Grade 6
Fraction Division
Pembagian Pecahan
Primary Mathematics Standards Edition Grade 6
Primary Mathematics Standards Edition Grade 6
3 kue dibagi secara rata kepada beberapa anak. Setiap anak mendapatkan ¾bagian 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.
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
Primary Mathematics Standards Edition
Pedagogical Principle:
DienesPrinsip Pedagogi:
Dienes
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:
DienesPrinsip Pedagogi:
Dienes
Pedagogical Principle:
DienesPrinsip 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
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
Mathematical Variation
Variasi dari segi Matematika
Nicole membeli 30 butir telur. Dia memakai 2/3 telur yang dibeli untuk memanggang kue.Berapa telur yang tersisa?
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
30
Mathematical Variation
Variasi dari segi Matematika
effective
Keys Grade School , Manila
teaching
Pictorial Before Abstract
Gambar sebelum abstrak
Primary Mathematics Standards Edition
Perceptual Variation
Variasi dari segi persepsi
Mathematical Variation
Variasi dari segi matematika
Emphasis on pictorial
representation and systematic
variation to enhance
conceptual understanding
Penekanan pada pemaparan visualdan variasi sistematis
memperkuat pemahaman konsep
Advanced
Intermediate
Low
High
41
74
92
98
Singapore
Catholic High School (Primary)
TIMSSTrends in International Maths and Science Studies
40
70
88
97
Advanced
Intermediate
Low
High
10
40
77
95
U S A
Catholic High School (Primary)
TIMSSTrends in International Maths and Science Studies
6
31
67
92
Advanced
Intermediate
Low
High
16
48
79
94
England
Catholic High School (Primary)
TIMSSTrends in International Maths and Science Studies
8
35
69
90
Advanced
Intermediate
Low
High
5
26
67
90
International
Catholic High School (Primary)
TIMSSTrends in International Maths and Science Studies
2
15
46
75
conclusion
PCF Kindergarten Pasir Ris
Mathematics is an excellent vehicle for
the development and improvement of a
person’s intellectual competence ..
Ministry of Education 2006
Fuchun Primary School
Matematika adalah kendaraan / alat yang hebatuntuk membangun dan memperbaiki kompetensi
dan intelektual seseorang …
Bina Bangsa School Bandung
Patterns
Patterns
Bina Bangsa School Bandung
SD Negeri in PalembangVisualization
Teacher Training for LEAP Programme for Public School Teachers in Manila
Visualization
mathz4kidz Learning Centre in MalaysiaCommunication
Pathlight School
Communication
Primary 2 Wellington Primary School
Primary Mathematics Syllabus 2007
Balestier HillPrimary School
Fuchun Primary School
Primary Mathematics Syllabus 2007
Princess Elizabeth Primary School
“Children are truly the future of our
nation. “Irving Harris