Developing Critical Thinking Through Singapore Math
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Transcript of Developing Critical Thinking Through Singapore Math
raisingcritical thinkersthrough
singapore mathDr Yeap Ban Har
National Institute of EducationNanyang Technological University
Singapore
Slides are available for download.
May 2010
Keys Grade School, Manila, The Philippines
internationalperspectives onmathematics
teaching
Tanjong Pagar PCF Kindergarten Singapore
What counts as mathematical proficiency?
procedural fluency
conceptual reasoning
Keys Grade School, Manila, The Philippines
strategic competence
K E Y S1 2 3 45 6 7 89 10 11 12
3948 ?Keys Grade School, Manila, The Philippines
adaptive reasoning
17
710
17 – 3
Keys Grade School, Manila, The Philippines
productive disposition
Keys Grade School, Manila, The Philippines
What counts as mathematical proficiency?
their understandingin a variety of
complex situations
mathz4kidz Learning Centre, Penang, Malaysia
This whole shape
stands for 1.
Trends inMathematics& Science Studies
applyand knowledge
What does this stand
for?
Trends inMathematics& Science Study
explaintheir reasoningmathz4kidz Learning Centre, Penang, Malaysia
Math for Developing Intellectual Competence
Mathematics as a vehicle to develop and improve a person’s intellectual competence.
Princess Elizabeth Primary School, Singapore
education
Bina Bangsa School, Bandung, Indonesia
mathematics
Ministry of Education Singapore 2006
an excellent vehicle for the development and improvement of
a person’s intellectual competence
“
”
using to develop
mathematicschildren’s
intelligence
Keys Grade School, Manila, The Philippines
4 7
47
11
47 – 11 Edgewood Elementary School, New York, USA
Edge
woo
d El
emen
tary
Sch
ool,
New
Yor
k
Edgewood Elementary School, New York, USA
What is Singapore Math?Challenging Materials
Meiling and Raja started on a 36-km cycling trip at the same time. They cycled at the same speed for the first 12 km. For the remaining 24 km, Meiling cycled at a faster speed. She arrived at the finishing point 10 minutes before Raja who was 4 km behind her. Raja did not change his speed throughout the trip and he completed the trip at 11 10.
(a) At what time did the trip start?(b) What was Meiling’s average speed for the remaining 24 km of the trip in m/min?
(PSLE Grade 6)MeilingRaja
Raja: 10 min 4 km
Raja: 10 min 4 km
??? min 36 km
Raja: 90 min 36 km
11 10 hrs 10 10 hrs 09 40 hrsRaja, and hence Meiling, started the trip at 09 40.
Raja: First 12 km 30 min Raja: Last 24 km 60 min
Meiling: Last 24 km 50 min
Meiling: 24000 m 50 min
Meiling: 2400 m 5 minMeiling: 480 m 1 min
Meiling’s average speed was 480 m/min for the last part of the trip.
The total number of stamps in Album A, Album B and Album C was 444 at first. Dennis gave away 3/5 of the stamps from Album A, put 24 more new stamps into Album B and added some stamps into Album C until the number of stamps in Album C became three times its original number. The ratio of the number of stamps in Album A to that in Album B to that in Album C became 2 : 5 : 9. How many more stamps were there in Album C than Album A in the end?
(Teck Whye Primary School, Grade 6)
Album A
Album B
Album C
The total number of stamps in Album A, Album B and Album C was 444 at first. Dennis gave away 3/5 of the stamps from Album A, put 24 more new stamps into Album B and added some stamps into Album C until the number of stamps in Album C became three times its original number. The ratio of the number of stamps in Album A to that in Album B to that in Album C became 2 : 5 : 9. How many more stamps were there in Album C than Album A in the end?
(Teck Whye Primary School, Grade 6)
Album A
Album B
Album C
13 units 444 + 24 = 4681 unit 468 ÷ 13 = 36
468
390 78
7 units ?7 units 36 x 7 = 210 + 42 = 252There were 252 more stamps in Album C than Album A in the end.
210
5
1
8
3
High Student Achievement
Advanced
Intermediate
Low
High
1995
2003
2007
38 4138
70 7473
89 9291
96 9897
Grade 4
Catholic High School (Primary), Singapore
TIMSSTrends in International Maths and Science Studies
Advanced
Intermediate
Low
High
Swed
en
Med
ian
U S
A
3 105
24 4026
69 7767
93 9590
Grade 4
Elementary School in Japan
TIMSSTrends in International Maths and Science Studies
Japa
n
Sing
apor
e
4123
7461
9289
9898
Advanced
Intermediate
Low
High
Aver
age
Hon
g Ko
ng
Sing
apor
e
2 4031
15 7064
46 8885
75 9794
Grade 8
Telok Kurau Primary School
TIMSSTrends in International Maths and Science Studies
Kore
a
Taiw
an
4540
7171
8690
9598
Northlight School, Singapore
Advanced
Intermediate
Low
High
AVER
AGE
MAL
AYSI
A
SIN
GAP
ORE
TIMSS 2007
2 402
15 7018
46 8850
75 9782
Grade 8
Advanced
Intermediate
Low
High
Gra
de 4
41
74
92
98
Singapore
Catholic High School (Primary)
TIMSSTrends in International Maths and Science Studies
Gra
de 8
40
70
88
97
Advanced
Intermediate
Low
High
Gra
de 4
10
40
77
95
U S A
Catholic High School (Primary)
TIMSSTrends in International Maths and Science Studies
Gra
de 8
6
31
67
92
Advanced
Intermediate
Low
High
Gra
de 4
16
48
79
94
England
Catholic High School (Primary)
TIMSSTrends in International Maths and Science Studies
Gra
de 8
8
35
69
90
Advanced
Intermediate
Low
High
Gra
de 4
5
26
67
90
International
Catholic High School (Primary)
TIMSSTrends in International Maths and Science Studies
Gra
de 8
2
15
46
75
Using Mathematics to Develop Intelligent Behaviors
intelligent
what arebehaviors?
1000- 124
mathematics& intelligent
behaviors
1000- 124
199
1000- 124
999- 124 875
876
forlooking
connections
Bina Bangsa School, Bandung, Indonesia
ability
explainto
A Grade 6 US textbook written using the Singapore Pedagogy
mathematics& intelligent
behaviours
34
÷3 = 3 x 43
= 4
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
5 cm
5 cm5 cm
11 cm
4 cm
Area = (11 + 5) ÷ 2 x 4
ability knowledge
to use
Key Success Factors
Princess Elizabeth Primary School, Singapore
Some of us come from
English-speaking
homes. Some of us don’t. I
speak Malay at home.
This is what help me learn mathematics well.…
Factors That Contribute to High Achievement Level in Mathematics
We like our teacher.Once, she was absent for two days. We missed her. She told
she had to learn new things to teach us better.
North Vista Primary School, Singapore
teacherquality
National Institute of Education, Singapore
Keys Grade School, Manila, The Philippines
Keys Grade School, Manila, The Philippines
x
professional developmentin-service
Keys Grade School. Manila, The Philippines
Hougang Primary School, Singapore
parentalexpectations
Seminar for Parents on Problem Solving
Last Saturday, Mum and Dad went to school – to learn the
model method so they can help me with schoolwork. But Mum
said she did not get it. In the end I had to teach her.
Teaching Every Child
singaporemath
Bruner’stheory
Photos: Princess Elizabeth Primary School, Singapore
We use concrete materials to learn mathematics.
Keys Grade School, Manila, The Philippines
singaporemath
emphasis onconcrete topictorial to abstract
representations
Catholic High School (Primary) Singapore
singaporemath
especially onthe model method
mathz4kidz Learning Center, Malaysia
Telok Kurau Primary School, Singapore
A lion weighs 135 kg. A cow weigh 87 kg more than the lion. An elephant weighs 139 more than the cow. How heavy is the elephant? (Primary 2)
bruner’s theoryconcrete
mathz4kidz Learning Centre, Penang, Malaysia
concreteexperiences
mathz4kidz Learning Centre, Penang, Malaysia
pictorialconcreteto
from
mathz4kidz Learning Centre, Penang, Malaysia
abstractpictorialto
from
All Kids Are Intelligent Series
symbols
mathz4kidz Learning Centre, Penang, Malaysia
concrete
A Public School in Chile
usingmaterials
Ateneo Grade School, Manila, The Philippines
Vygotsky’s Theory
Children Learn in Social
Situations
Fuch
un P
rimar
y Sc
hool
, Sin
gapo
re
interaction
conceptual
Bina Bangsa School, Semarang, Indonesia
skemp’s
understandingtheory
Keys Grade School, Manila, The Philippines
Keys Grade School, Manila, The Philippines
singaporemath
thank you
www.askyeapbanhar.blogspot.com
www.math.nie.edu.sg/T3
www.mathz4kidz.com