Singapore Math Strategies for U.S. Schools White Plains NY March 2012 yeap ban har marshall cavendish institute Primary 3 Mathematics Lesson Study on Mass CHIJ Our Lady of Good Counsel, Singapore SESSION ONE Overview & Fundamentals of Singapore Mathematics
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Singapore MathStrategies for U.S. SchoolsW h i t e P l a i n s N Y M a rc h
2 0 1 2
yeap ban har marshall cavendish institute
Primary 3 Mathematics Lesson Study on MassCHIJ Our Lady of Good Counsel, Singapore
SESSION ONEOverview &
Fundamentals of Singapore Mathematics
Introduction
Anchor Green Primary School, Singapore
General Overview of Singapore and its Education System
Land 700 sq km
People 4.7 million
General Overview of Singapore and its Education System
GDP per capita in current U.S. dollars1965 $510 2010 $43 300
General Overview of Singapore and its Education System
The data refers to 1-12 school system. Pre-school is not part of the formal education system. The data excludes post-secondary education system which includes institutes of technical education, polytechnics and universities.
Canossa Convent Primary School, Singapore
Singapore Mathematics: Background
1992 Problem-Solving Curriculum
1997 Thinking Schools, Learning Nation
2004 Teach Less, Learn More2010 Professional Learning Communities2011 21st Century Competencies
Singapore Ministry of Education 1992, 2001, 2007, 2013
Singapore Ministry of Education 2006
“Mathematics is an excellent vehicle for the development
and improvement of a person’s intellectual competencies”
Singapore Mathematics: What & How
What to Teach?
How to Teach?
Case Study 1
As the instructor demonstrates the lesson, study what is it that the teacher wants students to
learn. This is a Grade 6 problem involving fraction and ratio.
Singapore Examination & Assessment Board 2012
Case Study 1 16 units = $120
20 units =
04 units = $120 4 04 units = $30
20 units = $30 x 5 20 units = $150
John had $150 at first.
Case Study 1
what is it that the teacher wants
students to learn
Singapore MathStrategies for U.S. SchoolsW h i t e P l a i n s N Y M a rc h
2 0 1 2
Fundamentals of Singapore Mathematics
SESSION ONEOverview &
Fundamentals of Singapore Mathematics
Focus on Problem Solving Focus on Thinking
Focus on Managing Information Focus on Visualization
Focus on Generalization
Focus on Number Sense
Focus on Communication
Singapore MathStrategies for U.S. SchoolsW h i t e P l a i n s N Y M a rc h
2 0 1 2
yeap ban har marshall cavendish institute
Pathlight School, Singapore
SESSION TWOMathematical Problem Solving including Bar
Models
Case Study 3
Tom has some sweets.Jerry has 5 sweets more than Tom.Later, Tom gives Jerry 2 sweets.Who has more sweets now?
Primary 3 Lesson Study Kong Hwa School
5
2
22
Who has more sweets now?How many more?
Tom Jerry
Before x x + 5
After x – 2 x + 7
Case Study 3
Tom has 9 sweets.Jerry has 5 sweets more than Tom.How many sweets does Jerry have?
9
5
Tom
Jerry
9 + 5 = 14
Jerry has 14 sweets.
Case Study 3
Tom has 9 sweets.Jerry has 5 sweets more than Tom.Later, Tom gives Jerry 2 sweets.Who has more sweets now? How many more?
9
5
Tom
Jerry
2
2
9 – 2 = 7
9 + 5 + 2 =16
16 – 7 = 9
Jerry has 9 more sweets than Tom.
Case Study 3
One day, 543 cars and 274 buses pass through a toll booth. How many cars and buses pass through the toll booth?
Math in Focus Grade 2
543
274
cars
buses
543 + 274 =
543 274
cars buses
543 + 274 =
543 + 274 =
543 + 274 =
543 + 274 =
543 + 274 =
543 + 274 =
Multiplication is taught with a focus on meaning, visualization, and making connections.
Case Study 6
Sam is twice as old as Terry. Vanessa is three times as old as Terry.Their total ages is 72 years. Find their ages.
Sam
Terry
72 6 =
Terry is 12 years old. Sam is 24 years old.
Vanessa
72
60
12 1
2
Vanessa is 36 years old.
Case Study 6
Sam is twice as old as Terry. Vanessa is three times as old as Terry.Their total ages is 72 years. Find their ages.
Sam is twice as old as Terry. Vanessa is 36 years old.Their total ages is 72 years. Find their ages.
Differentiation for Struggling Learners
Case Study 6
Sam is twice as old as Terry. Vanessa is three times as old as Terry Sam.Their total ages is 72 years. Find their ages.
Terry Sam Sam is twice as old as Terry. Vanessa is three times as old as Terry.Their total ages is 72 years. Find their ages.
Differentiation for Advanced Learners
Case Study 2
As the instructor demonstrates the lesson, study what is it that the teacher wants students to
learn. This is a task from a Grade 6 textbook to motivate
the learning of algebra.
Primary Mathematics (Standards Edition) Grade 6
Singapore MathStrategies for U.S. SchoolsW h i t e P l a i n s N Y M a rc h
2 0 1 2
yeap ban har marshall cavendish institute
Primary 3 Mathematics Lesson Study on MassCHIJ Our Lady of Good Counsel, Singapore
REVIEW & CONSOLIDATEOpening Lecture
Average Learners High
Achievement
International Studies
Students in Singapore have demonstrated high achievement and positive attitude towards mathematics.
In Trends in Mathematics and Science Study, about 40% of Singapore’s 4th and 8th graders are in the Advanced International Benchmark (the international average is 5% and 2% respectively).
Advanced
Intermediate
Low
High
199
5
200
3
200
7
38 4138
70 7473
89 9291
96 9897
Gra
de 4
Inte
rnati
on
al
5
26
67
90
Advanced
Intermediate
Low
High
Aver
age
Hon
g Ko
ng
Sing
apor
e
2 4031
15 7064
46 8885
75 9794
S. K
orea
Taiw
an
4540
7171
8690
9598
Gra
de 8
Junyuan Secondary School, Singapore
TIMSSTrends in International Mathematics and Science Studies
Advanced
Intermediate
Low
High
Gra
de 4
19
95
38
70
89
96
TIMSSTrends in International Mathematics and Science Studies
Gra
de 8
19
9942
77
94
99
Fuchun Primary School, Singapore
Advanced
Intermediate
Low
High
Gra
de 4
19
95
38
70
89
96
TIMSSTrends in International Mathematics and Science Studies
Gra
de 8
19
9942
77
94
99
Gra
de 4
20
03
Gra
de 8
20
07
38
73
91
97
40
70
88
97
Fuchun Primary School, Singapore
The attitude index for Singapore students in TIMSS is also relatively high compared to other high-performing countries.
Also, the majority of students in Singapore opt to study mathematics in Grades 11 and 12 when they are no longer required to.
Marsiling Secondary School, Singapore
Singapore
Taiwan
Japan
Hong Kong
Att
itude
Ach
ievem
en
t
71 41
67 40
50 24
62 23
Gra
de 4
Kazakhstan
Russia
International
England
89 19
62 16
80 16
72 5
Taiwan
Singapore
Hong Kong
S Korea
Att
itude
Ach
ievem
en
t
37 45
33 40
60 40
47 31
Gra
de 8
Japan
England
International
Hungary
30 26
30 10
40 8
54 2
High achievement was not a given. In 1960, among 30 615 candidates who sat for the first Primary School Leaving Examination, 45% of the candidates passed.
Keon Ming Public School, Singapore
Score 1960-1970s 1980s 1990s 2000s
500 Japan JapanKorea
Hong Kong
JapanKorea
SingaporeHong Kong
JapanKorea
Hong KongSingapore
400 Thailand SingaporeThailand
The Philippines
MalaysiaThailand
MalaysiaThailand
300 IndonesiaThe Philippines
IndonesiaThe Philippines
Reference: E. Hanusek, D. Jamison, E. Jamison & L. Woessmann (2008)
All major international tests (literacy, science and mathematics) between 1964 and 2003 were placed on a common scale. Selected countries shown in the table.
Average Learners High
Achievement
Pedagogy
Math in Focus
Pensar sin Limites (Spanish Edition)
Pensar sin Limites (Spanish Edition)
Maths Champion (Indonesian Edition)
Primary Mathematics (Standards Edition)
Primary Mathematics (Standards Edition)
Singapore MathStrategies for U.S. SchoolsW h i t e P l a i n s N Y M a rc h
2 0 1 2
yeap ban har marshall cavendish institute
Primary 3 Mathematics Lesson Study on MassCHIJ Our Lady of Good Counsel, Singapore
SESSION THREEDifferentiated
Instruction
“… over-emphasising procedural skills without understanding the underlying
mathematical principles should be avoided.”
Ministry of Education 2006
My Pals Are Here! Mathematics (Second Edition)
Singapore MathStrategies for U.S. SchoolsW h i t e P l a i n s N Y M a rc h
2 0 1 2
yeap ban har marshall cavendish institute
Primary 3 Mathematics Lesson Study on MassCHIJ Our Lady of Good Counsel, Singapore
Jack and Kyla share $300.Jack gets twice as much as Kyla.How much does Kyla get?
Jack
Kyla
$300 3 = $100
Kyla gets $100.
Case Study 5
Natalia’s bag is 12 kg heavier than Peter’s. The total mass of the two bags is 58 kg. How heavy is Natalia’s bag? How heavy is Peter’s bag?
Natalia
Peter
12
58 – 12 = 46
46 2 = 23
23 + 12 = 35
Natalia’s bag is 35 kg. Peter’s bag is 23 kg.
Case Study 7
Mrs. Lee used ¼ of the flour she bought to make cookies and a third of the remainder to bake a cake. She then has 3.6 kg of flour left. How much flour did she buy?
Case Study 7
Mrs. Lee used ¼ of the flour she bought to make cookies and ½ of the remainder to bake a cake. She then has 3.6 kg of flour left. How much flour did she buy?
Case Study 7
Mrs. Lee used ¼ of the flour she bought to make cookies and ¼ of the remainder to bake a cake. She then has 3.6 kg of flour left. How much flour did she buy?
Case Study 7
Mrs Lee used ¼ of the flour she bought to make cookies and ½ of the remainder to bake a cake. She then has 3.6 kg of flour left. How much flour did she buy?
Jason, Edward and Sam had a total of $837. Jason had the least amount of money. The ratio of Edward’s money to Sam’s money was 4 : 3 at first. Jason and Edward each spent a third of their money. Given that the three boys had $648 left, how much did Jason have at first? An example of novel assessment task from a Singapore school. This is for Grade 6.$837 - $648 = $189$189 x 3 = $567This is Jason and Edward’s money at first.
$837 - $567 = $270This is Sam’s money at first.
With this it is possible to find Edward’s hence Jason’s amount easily. Did you get $360 for Edward and $207 for Jason?
Homework for Bar Model
Case Study 8
Pablo is twice as tall as Wynn. Wynn is 20 cm taller than Zena.Pablo is 100 cm taller than Zena.Find their heights in meters.
Pablo
Wynn
Zena
Case Study 9
Rosa made paper cranes to fill a glass jar. She made 4 more cranes each day than the day before. After 10 days, she has made 250 cranes. How many paper cranes did she make on the last day?
Day 1
Day 2
Day 3
4
4 4
Day 4 4 4 4
Case Study 9
Rosa made paper cranes to fill a glass jar. She made 4 more cranes each day than the day before. After 4 days, she has made 52 cranes. How many paper cranes did she make on the last day?