MAP101 Hilo, Hawai'i

Dr Yeap Ban [email protected]

Marshall Cavendish Institute Singapore

Presentation slides are available at www.banhar.blogspot.com

Professional DevelopmentSingapore Mathematics

Big Island of Hawai’i 5 – 9 June 2012

www.mcinstitute.com.sgwww.facebook.com/MCISingapore

Day 1

FUNDAMENTALS

of singapore

m a t h

Slides are available at

www.banhar.blogspot.com

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General Overview of Singapore and its Education System

Land 700 sq km

People 4.7 million


GDP per capita in current U.S. dollars

1965 $510 2010 $43 300


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


Institutes of Technical Education

Primary Schools


A detailed schematic diagram of Singapore’s education system is available in Education Statistics Digest

http://www.moe.gov.sg/education/education-statistics-digest/








Curriculum document is available at http://www.moe.gov.sg/

http://www.moe.gov.sg/

Singapore Ministry of Education 1997

THINKING SCHOOLS

LEARNING NATION

Singapore Ministry of Education 2006

“Mathematics is an excellent vehicle for the development

and improvement of a person’s intellectual competencies”

21st Century Competencies FrameworkSingapore Ministry of Education 2011

is singaporewhat

mathematics

Singapore Mathematics: Focus on Thinking

excellentvehicle

an

for the development&improvement ofa person’s intellectual

competenciesMinistry of Education Singapore 2006

FUNDAMENTALS

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110 g

290 g

110 g180 g

Bella puts 180 g brown sugar on the dish.

110 g

290 g

110 g180 g

2 units = 180 g

1 unit = 90 g

3 units = 270 g

Bella puts 270 g brown sugar on the dish.

on an identical dish

Singapore Mathematicsfocuses on the ability tovisualize. For example,bar models are usedextensively.

Bar models were introduced to overcome thepervasive problems students had with word problems– even the basic ones.

Such word problems are used to

help students

Deal with information

Handle and clarify ambiguity –

one dish or two

Develop visualization – bar

models are used extensively

Practice mental strategies –

numbers used are not difficult to

compute

Singapore Math

Visualization

C H E R Y L

C H E R Y L1

C H E R Y L2

C H E R Y L3

C H E R Y L4

C H E R Y L5

C H E R Y L6

C H E R Y L7

C H E R Y L8

C H E R Y L9

C H E R Y L

C H E R Y L

Which letter is 99?

Method 1The positions of 11, 22, 33 are at C, H, E respectively. Positions of multiples of 11 can be located.

Method 2The positions of numbers ending with 1 and 6 can be located ta either ends. Thus 91 or 96 can be located. Subsequently, 99 can be located.

Method 3Numbers ending with 9 are at E. So, 99 is at E too.

Method 4The position for 99 can be found by writing out all the numbers but this is not efficient method.

D A V I D

Method 1The letters under A and I are even. So 99 cannot be there.

Method 2The positions of numbers ending with 9 form a diagonal pattern.

Method 3The numbers under first D increases by 8. Thus 17 + 80 = 97 is under first D. The position for 99 can be worked out.

Method 4The positions of multiples of 8 I is definitely under A. 8 x 12 = 96 is under A. The position of 99 can be worked out.

Method 5Numbers under V is 1 less than multiples of 4. So, 2011 (1 less than 2012) is under V. 99 is less than 100.

Method 2The positions of numbers ending with 9 form a diagonal pattern.

The methods were the ones that participants in Chile came up with.

Another MethodIn a course done in December 2010 with a group of Chilean teachers, there was a method that involves division. For Cheryl, it was 99 : 10.

For David, it was 99 : 8. Are you able to figure out that method?

We did this version in Big Island of Hawai’i.

Kamehameha Schools, Hawaii

Singapore Math at Kamehameha Schools, Hawai’i USA

Singapore Math

Patterns & Generalization

Singapore Mathematics: Focus on Problem Solving

FUNDAMENTALS

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CPA Approach based onJerome Bruner was usedto learn division offractions – using paperfolding and subsequentdrawing.

Singapore Mathematics: Focus on Conceptual Understanding

Singapore Math

Learn New Concept Through

Problem Solving

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Singapore Math

Drill-and-Practice Through

Problem Solving

Singapore Math

Problem Solving Lesson

Anchorvale Primary School,

Singapore

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Further Examples

Singapore Math

Applying Knowledge in

Problem Solving

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Learning Theories

How many 4s are there in 12? 12 ÷ 4 = 3

Marcus gave ¼ of his coin collection to his

sister and ½ of the remainder to his

brother.

As a result, Marcus had 18 coins.

Find the number of coins in his collection

at first.

3 units = 18

8 units = ???

Marcus had 48 coins at first.

MAP101 Hilo, Hawai'i

Education

Transcript of MAP101 Hilo, Hawai'i