all hawai'i beyond the basics 01
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Dr. Yeap Ban HarMarshall Cavendish Institute
Singaporeyeapbanhar@gmail.com
Slides are available at
www.banhar.blogspot.com
www.facebook.com/MCISingapore
Marshall Cavendish Institute www.mcinstitute.com.sg
SINGAPORE
M AT HBeyond the Basics
St Edward’s School
Florida, USA
Day One
IntroductionWe started the day with an overview of Singapore education
system. We also watched two videos on the Singapore
education system.
See http://www.youtube.com/watch?v=sEn6OKsVoMs and
http://www.youtube.com/watch?v=Km25TAnPbI4
General Overview of Singapore and its Education System
Land 270 sq miles
People 4.7 million
General Overview of Singapore and its Education System
GDP per capita in current U.S. dollars
1965 $510 2010 $43 300
General Overview of Singapore and its Education System
Students 500 000
Teachers 30 000
Principals & Vice-Principals 900
Schools 173 Primary Schools (Primary 1 – 6) 155 Secondary Schools (Secondary 1 – 4) 13 Junior Colleges (JC 1 – 2) 15 Mixed-Level Schools
The data refers to 1-12 school system. Pre-school is not part of the formal educationsystem. The data excludes post-secondary education system which includes institutesof technical education, polytechnics and universities.
Canossa Convent Primary School
Singapore
Universities
Polytechnics
Junior Colleges
Integrated Programmes
National Examination
Secondary Schools
National Examination
Institutes of Technical Education
Primary Schools
National Examination
A detailed schematic diagram of Singapore’s education system is available in Education Statistics Digest
http://www.moe.gov.sg/education/education-statistics-digest/
Singapore Ministry of Education 1997
THINKING SCHOOLS
LEARNING NATION
is singaporewhat
mathematics
Singapore Mathematics: Focus on Thinking
excellentvehicle
an
for the development&improvement ofa person’s intellectual
competenciesMinistry of Education Singapore 2006
Lesson 1We did a lesson on multiplication facts to understand the
emphasis on visualization in learning basic materials. We also
saw the use of an anchor tasks to engage students for an
extended period of time.
Public School in Chile
Lesson 2Can we get the multiplication facts for, say 4, from 2 x 4 and 5 x
4?
Lesson 1 June 18, 2012
2 x 4 = 8
5 x 4 = 20Problem
10 x 4 =
5 x 4 = 20
9 x 4 =
2 x 4 = 8
4 x 4 =
8 x 8 =
7 x 4 =
2 x 4 = 8 6 x 4 =
5 x 4 = 20 3 x 4 =
2 x 4 = 8
This Grade 2 lesson on multiplication facts of 4 centers around using doubling
strategy and adding one row strategy in addition to previewing more advanced
strategies such as using 2 x 4 and 5 x 4 to get 7 x 4 as well as ‘subtraction’ strategy.
The anchor task is to use 2 x 4 and 5 x 4 to obtain all the other facts. The anchor task
allows students to work on one task for an extended period of time.
Da Qiao Primary School
Singapore
Lesson 3Multiplication of multi-digit numbers with emphasis on
visualization.
Lesson 4 June 18, 2012
39 x 6
30 9
6
40 x 6 = 240 39 x 6 =
30 9
Method 1 Method 2
Lesson 4 June 18, 2012
39 x 6
30 9
6
40 x 6 = 240 39 x 6 =
30 9
Method 1 Method 2
Lesson 4Use digits 1 to 9 to make a correct multiplication sentence
=.
Lesson 5We studied a problem that was used with a group with Grade 3
students in hawai’i
Lesson 2 June 18, 2012
Jack
Kyla
had
$2
more
than
Jack
Kyla
gave
$3
Lesson 2 June 18, 2012
Open Lesson at Hawaii, USA
Lesson 5 June 18, 2012
Story 1
Jack had $3.
Jack gave Kyla $2
more.Jack Kyla
Before $3 $1 $5 $19
After $1 $3 $7 ?
What if Kyla
had this
amount
before?
Lesson 5 June 18, 2012
Story 2
Kyla had $3 more than Jack.
Jack
Kyla
Jack gave Kyla $2.
$2
$3
Who had
more money
afterwards?
How much
more?
Kyla had $3 more than Jack.
Jack gave Kyla $2.
How much more did Kyla have than Jack?
Students in Grade 6 may use algebra to deal with Story 2.
Kyla had $(x + 3)
Jack had $x
Then, Jack had $(x – 2)
And Kyla had $(x + 5)
Kyla had $(x + 5) – $(x – 2) or $7 more than Jack.
Lesson 6Question: How do we help students set up the model? Students
are introduced to the idea of using a rectangle to represent
quantities – known and unknown. Paper strips are used. Later,
only diagrams are used. Advanced skills like cutting and
moving are learned in Grades 4, 5 and 6. How is the idea of bar
model introduced in Grades K – 3?
Lesson 3 show a basic bar model solution in Grade 4.
Lesson 6 June 20, 2012
Carl
Ben
$4686
Differentiated instruction
for students who have
difficulty with standard
algorithms. Use number
bonds.
2x + x = 4686
3x = 4686
Students in Grade 7 may use algebra to deal with such situations. Bar
model is actual linear equations in pictorial form.
Lesson 7We studied the strategies to help struggling readers as well as
those weak in representing problem situations.
Lesson 7 June 18, 2012
In the end ... At first …
Alice
Betty
Charmaine
Dolly
20
10
Lesson 7 June 18, 2012
Mahalo
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