Experiencing
                                       Singapore Math
Experiencing Singapore Math
      Newark  East Brunswick

              Yeap Ban Har
        Marshall Cavendish Institute
                 Singapore

          yeapbanhar@gmail.com

             Slides are available at
         www.banhar.blogspot.com
Experiencing
                                                           Singapore Math
                                Land
                                  270 sq miles

                                People
                introduction      4.7 million

                                GDP per capita
                                  1965 USD510

                                  2010 USD43,300
                                          in current USD
Junyuan Secondary School,
Singapore
General Overview of Singapore and
      its Education System
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)                                           Canossa Convent Primary School,
     15 Mixed-Level Schools                                                  Singapore

  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.
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
Experiencing
                                                                                                Singapore Math
 All major international tests (literacy, science and mathematics) between 1964
 and 2003 were placed on a common scale. Selected countries shown in the table.

      Score             1960-1970s                1980s                 1990s          2000s
       500                  Japan                Japan                  Japan         Japan
                                                 Korea                  Korea         Korea
                                               Hong Kong              Singapore     Hong Kong
                                                                      Hong Kong     Singapore
       400                Thailand            Singapore               Malaysia       Malaysia
                                               Thailand               Thailand       Thailand
                                            The Philippines
       300                                                          Indonesia       Indonesia
                                                                  The Philippines The Philippines
Reference: E. Hanusek, D. Jamison, E. Jamison & L. Woessmann (2008)
"Solving problems is central to mathematical proficiency
and is articulated to a varying degree across the
international curricula. Singapore applies the highest
degree of specificity to it, placing it at the centre of all
mathematical learning.“

            Review of the National Curriculum in England Research Report
                                             UK Department for Education
Experiencing
                                                                                      Singapore Math
                  1982
Introduction of Singapore mathematics
  textbooks as they are known today.
                                         Mathematics is “an excellent
                                          vehicle for the development
                        1992           and improvement of a person’s
              Introduction of Problem-       intellectual competence”.
                Solving Curriculum             Ministry of Education Singapore 2006

                       1997                              2001
                 Thinking Schools       Introduction of textbooks published by
                 Learning Nation          private publishers and approved by
                                                 Ministry of Education.
                                                        2007
                                           New editions of textbooks are
                                        published with the introduction of the
                                                 revised curriculum.
     Page 1
Experiencing
Page 4




         Singapore Math
Experiencing
                                  Singapore Math
Experiencing Singapore Math
         Spiral Approach

         Yeap Ban Har
   Marshall Cavendish Institute
            Singapore

     yeapbanhar@gmail.com

        Slides are available at
    www.banhar.blogspot.com
543 + 274 = 
543 + 274 = 
543 + 274 = 
543 + 274 = 
543 + 274 = 
543 + 274 = 
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




 cars            543


 buses     274
                                         543 + 274 = 


          cars            buses

          543              274
emphasis
  spiral
Experiencing
Singapore Math
Experiencing
                                  Singapore Math
Experiencing Singapore Math
         Visual Approach

         Yeap Ban Har
   Marshall Cavendish Institute
            Singapore

     yeapbanhar@gmail.com

        Slides are available at
    www.banhar.blogspot.com
110 g




        290 g   Page 2
2 units = 290 g – 110 g = 180 g
            1 units = 180 g   2 = 90 g
110 g

            3 x 90 g = 270 g
            Bella puts 270 g sugar on the dish.

   ?    ?
Experiencing
                              Singapore Math
Escuela de Guetamala, Chile
x + 2x = 12




                 Experiencing
              Singapore Math
Experiencing
                  Singapore Math
King Solomon Academy, Londo
Edgewood Elementary School, New York
Globe Academy, London




                           Experiencing
                        Singapore Math
Experiencing
                                     Singapore Math
3x – 2 = 8




             Globe Academy, London
Experiencing
                                                                   Singapore Math
            Experiencing Singapore Math
Initial Concrete Experiences & Building Conceptual Understanding

                        Yeap Ban Har
                  Marshall Cavendish Institute
                           Singapore

                    yeapbanhar@gmail.com

                       Slides are available at
                  www.banhar.blogspot.com
Experiencing
                                               Singapore Math
                              Relational
                              Understanding
                                 R Skemp

                what & how    Concrete
                              Introduction
                                 J Bruner


Junyuan Secondary School,
Singapore



                                             Page 08
                                             Page 13
Experiencing
                                    Singapore Math
Share 3 fourths equally among 3.




3 fourths 3 = 1 fourth




                                   Page 5
Experiencing
                                                               Singapore Math
Share 3 fourths equally between 2.




 3 fourths 2
= 6 eighths 2               Share 3 fourths equally among 4.
= 3 eighths



                             3 fourths 4
                            = 12 sixteenths 4
                            = 3 sixteenths
Experiencing
                                                 Singapore Math
12 cookies   4

12 pieces    4

12 sixteenths    4

12 tenths    4       12 cookies    4 cookies

12 x   4             12 pieces    4 pieces

                     12 x   4x




                                               Page 13
Experiencing
Singapore Math
Experiencing
Singapore Math
Experiencing
Singapore Math
Experiencing
Singapore Math
Experiencing
Singapore Math
Experiencing
                                                       Singapore Math
Junyuan Secondary School, Singapore

                                       Concrete to
                                       Visual
                                          J Bruner

              visualization            Variation
                                          Z Dienes
                                       Human
                                       Intelligences
                                          H Gardner



             Page 11
Math in Focus




                   Experiencing
                Singapore Math
Experiencing
Math in Focus




                Singapore Math
Math in Focus




                   Experiencing
                Singapore Math
Experiencing
Math in Focus




                Singapore Math
Math in Focus




              Experiencing
           Singapore Math
Experiencing
                Singapore Math
Math in Focus
Math in Focus




                   Experiencing
                Singapore Math
Math in Focus




                   Experiencing
                Singapore Math
Math in Focus




                   Experiencing
                Singapore Math
Math in Focus




                   Experiencing
                Singapore Math
Math in Focus




                   Experiencing
                Singapore Math
Experiencing
                                    Singapore Math
Da Qiao Primary School, Singapore
Experiencing
                                                                              Singapore Math
                                Primary Mathematics (Third Edition)




See Ho, S. Y. & Yeap, B. H. (2011). Development of Visualization Skills in
Singapore Primary School Mathematics Textbooks. Paper presented at PME-35
Angkara, Turkey.
See also Yeap, B. H. (2011). The Emphasis of Primary-Level Textbooks in
Singapore on Higher-Order Thinking Skills. Paper presented at International
Conference on School Mathematics Textbooks Shanghai, China.
Experiencing
                                Singapore Math
Visuals are used to
teach concepts –
distributive property of
multiplication – without
using formal terms.




     Primary Mathematics (Third Edition)

Administrators Symposium at East Brunswick

  • 1.
    Experiencing Singapore Math Experiencing Singapore Math Newark  East Brunswick Yeap Ban Har Marshall Cavendish Institute Singapore yeapbanhar@gmail.com Slides are available at www.banhar.blogspot.com
  • 2.
    Experiencing Singapore Math  Land  270 sq miles  People introduction  4.7 million  GDP per capita  1965 USD510  2010 USD43,300 in current USD Junyuan Secondary School, Singapore
  • 3.
    General Overview ofSingapore and its Education System
  • 4.
    General Overview ofSingapore 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) Canossa Convent Primary School,  15 Mixed-Level Schools Singapore 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.
  • 5.
    High achievement wasnot 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
  • 6.
    Experiencing Singapore Math All major international tests (literacy, science and mathematics) between 1964 and 2003 were placed on a common scale. Selected countries shown in the table. Score 1960-1970s 1980s 1990s 2000s 500 Japan Japan Japan Japan Korea Korea Korea Hong Kong Singapore Hong Kong Hong Kong Singapore 400 Thailand Singapore Malaysia Malaysia Thailand Thailand Thailand The Philippines 300 Indonesia Indonesia The Philippines The Philippines Reference: E. Hanusek, D. Jamison, E. Jamison & L. Woessmann (2008)
  • 8.
    "Solving problems iscentral to mathematical proficiency and is articulated to a varying degree across the international curricula. Singapore applies the highest degree of specificity to it, placing it at the centre of all mathematical learning.“ Review of the National Curriculum in England Research Report UK Department for Education
  • 9.
    Experiencing Singapore Math 1982 Introduction of Singapore mathematics textbooks as they are known today. Mathematics is “an excellent vehicle for the development 1992 and improvement of a person’s Introduction of Problem- intellectual competence”. Solving Curriculum Ministry of Education Singapore 2006 1997 2001 Thinking Schools Introduction of textbooks published by Learning Nation private publishers and approved by Ministry of Education. 2007 New editions of textbooks are published with the introduction of the revised curriculum. Page 1
  • 10.
    Experiencing Page 4 Singapore Math
  • 11.
    Experiencing Singapore Math Experiencing Singapore Math Spiral Approach Yeap Ban Har Marshall Cavendish Institute Singapore yeapbanhar@gmail.com Slides are available at www.banhar.blogspot.com
  • 12.
    543 + 274= 
  • 13.
    543 + 274= 
  • 14.
    543 + 274= 
  • 15.
    543 + 274= 
  • 16.
    543 + 274= 
  • 17.
    543 + 274= 
  • 18.
    One day, 543cars and 274 buses pass through a toll booth. How many cars and buses pass through the toll booth? Math in Focus Grade 2 cars 543 buses 274 543 + 274 =  cars buses 543 274
  • 19.
  • 20.
  • 21.
    Experiencing Singapore Math Experiencing Singapore Math Visual Approach Yeap Ban Har Marshall Cavendish Institute Singapore yeapbanhar@gmail.com Slides are available at www.banhar.blogspot.com
  • 22.
    110 g 290 g Page 2
  • 23.
    2 units =290 g – 110 g = 180 g 1 units = 180 g 2 = 90 g 110 g 3 x 90 g = 270 g Bella puts 270 g sugar on the dish. ? ?
  • 24.
    Experiencing Singapore Math Escuela de Guetamala, Chile
  • 25.
    x + 2x= 12 Experiencing Singapore Math
  • 26.
    Experiencing Singapore Math King Solomon Academy, Londo
  • 27.
  • 28.
    Globe Academy, London Experiencing Singapore Math
  • 29.
    Experiencing Singapore Math 3x – 2 = 8 Globe Academy, London
  • 30.
    Experiencing Singapore Math Experiencing Singapore Math Initial Concrete Experiences & Building Conceptual Understanding Yeap Ban Har Marshall Cavendish Institute Singapore yeapbanhar@gmail.com Slides are available at www.banhar.blogspot.com
  • 31.
    Experiencing Singapore Math  Relational Understanding  R Skemp what & how  Concrete Introduction  J Bruner Junyuan Secondary School, Singapore Page 08 Page 13
  • 32.
    Experiencing Singapore Math Share 3 fourths equally among 3. 3 fourths 3 = 1 fourth Page 5
  • 33.
    Experiencing Singapore Math Share 3 fourths equally between 2. 3 fourths 2 = 6 eighths 2 Share 3 fourths equally among 4. = 3 eighths 3 fourths 4 = 12 sixteenths 4 = 3 sixteenths
  • 34.
    Experiencing Singapore Math 12 cookies 4 12 pieces 4 12 sixteenths 4 12 tenths 4 12 cookies 4 cookies 12 x 4 12 pieces 4 pieces 12 x 4x Page 13
  • 35.
  • 36.
  • 37.
  • 38.
  • 39.
  • 40.
    Experiencing Singapore Math Junyuan Secondary School, Singapore  Concrete to Visual  J Bruner visualization  Variation  Z Dienes  Human Intelligences  H Gardner Page 11
  • 41.
    Math in Focus Experiencing Singapore Math
  • 42.
  • 43.
    Math in Focus Experiencing Singapore Math
  • 44.
  • 45.
    Math in Focus Experiencing Singapore Math
  • 46.
    Experiencing Singapore Math Math in Focus
  • 47.
    Math in Focus Experiencing Singapore Math
  • 48.
    Math in Focus Experiencing Singapore Math
  • 49.
    Math in Focus Experiencing Singapore Math
  • 50.
    Math in Focus Experiencing Singapore Math
  • 51.
    Math in Focus Experiencing Singapore Math
  • 52.
    Experiencing Singapore Math Da Qiao Primary School, Singapore
  • 53.
    Experiencing Singapore Math Primary Mathematics (Third Edition) See Ho, S. Y. & Yeap, B. H. (2011). Development of Visualization Skills in Singapore Primary School Mathematics Textbooks. Paper presented at PME-35 Angkara, Turkey. See also Yeap, B. H. (2011). The Emphasis of Primary-Level Textbooks in Singapore on Higher-Order Thinking Skills. Paper presented at International Conference on School Mathematics Textbooks Shanghai, China.
  • 54.
    Experiencing Singapore Math Visuals are used to teach concepts – distributive property of multiplication – without using formal terms. Primary Mathematics (Third Edition)