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Dr. Yeap Ban Har Marshall Cavendish Institute
Singapore
Slides are available at
www.banhar.blogspot.com
www.facebook.com/MCISingapore
Helping Students
Learn Mathematics What & How of
Singapore Math
Dr. Yeap Ban Har Marshall Cavendish Institute
Singapore
Synopsis
This course focuses on teaching basic skills and concepts including the four basic operations – we will see lessons on addition (grade one) as well as multiplication (grade two) and division (grade three). In addition, we will see a lesson on division involving fraction (grade five). We will one example of practice lesson (refer to the green book). There is a similar course that focuses on problem solving.
area = 225 square miles
population = 5.3 million
durian
“Upon separation from Malaysia in 1965, Singapore
was faced with … high levels of unemployment and
poverty. 70% of Singapore’s households lived in badly
overcrowded conditions, and a third of its people
squatted in slums on the city fringes. Unemployment
averaged 14%, GDP per capita was less than $2,700,
and half of the population was illiterate. “
| Hanusek, Jamison, Jamison & Woessmann 2008
Score 1960-1970s 1980s 1990s 2000s
500’s Japan Hong Kong Japan Korea
Hong Kong Japan Korea
Singapore
Hong Kong Japan Korea
Singapore
400’s Thailand Philippines Singapore Thailand
Malaysia Thailand
Malaysia Thailand
300’s Indonesia Philippines
Indonesia Philippines
Country
GDP per capita in
current USD
2012
Singapore 60,800
Malaysia 16,800
Thailand 9,500
Indonesia 4,900
Philippines 4,400
Source | IMF
| Hanusek, Jamison, Jamison & Woessmann 2008
What is Essential in Mathematics Literacy Let’s look at what international assessment (PISA) for 15-year-olds and Smarter Balanced Assessment for Hawaii State test suggest.
PISA 2012 Assessment
Source | PISA2012
Source | PISA2012
Source | PISA2012
Source | PISA2012
| PISA 2012
Country % of Low Performers
% of High Performers
Mean
Singapore 8.3 40.0 573
Vietnam 14.2 13.3 511
Thailand 49.7 2.6 427
Malaysia 51.8 1.3 421
Indonesia 75.7 0.3 375
OECD 23.1 12.6 494
| PISA 2012
Country % of Low Performers
% of High Performers
Mean
Shanghai 3.8 55.4 613
Singapore 8.3 40.0 573
Hong Kong 8.5 33.7 561
South Korea 9.1 30.9 554
Japan 11.1 23.7 536
Finland 12.3 15.3 519
OECD 23.1 12.6 494
Smarter Balanced Assessment
| Smarter Balanced Assessment
| Smarter Balanced Assessment
| Smarter Balanced Assessment
| Smarter Balanced Assessment
| Smarter Balanced Assessment
| Smarter Balanced Assessment
What is Essential in Mathematics Literacy What should students be learning in mathematics and what are the implications for classroom practices?
What is Essential in Mathematics Literacy What should students be learning in mathematics and what are the implications for classroom practices?
communication
metacognition
number sense
visualization
patterns
The Fundamentals of Singapore Math
Summary of Oahu’s Discussion
Anchor Task
• Problem-solving Approach (Polya)
• Concrete – Pictorial – Abstract Approach (Bruner)
• Work in Groups and Talking (Vygotsky)
• Student-generated Ideas (Piaget)
• Progression from Literal to Abstract Ideas
• Questions for Self-directed Learning
Teacher Board Writing
Mini White Boards
Student Journal
• Promotes communication
• Allows for assessment
Three-Part Lesson Anchor Task Guided Practice Independent Practice
| Common Core State Standards
What Does Teaching for Relational / Conceptual Understand Look Like?
Teaching for Meaning Making
Concrete Materials
Students are given
bags of 6 beans
each
Anchor Task
How many beans in
4 such bags?
Students Talking
Multiple Responses
Count all
Repeated addition
Multiplication
Board Writing
Student Journal
Meaning Making
4 x 6 is the same as 4 bags of
6 beans. Also linking new
materials (multiplication) to old
materials (addition).
Teaching for Meaning Making
How do I know if I
have taught in a
meaningful way?
• Link to previous
knowledge
• Link to a
concrete
scenario
• Students can
extend their
thinking.
Teaching for Meaning Making
Teaching for Meaning Making
Use of Textbooks
Suggest the kind of
anticipated
responses (add
another six, double,
associative
property and
subtraction
strategy)
As a reflection tool
for students at the
end of the
discussion (“Let’s see
how they do it.”)
