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Experiencing Singapore Maths
    Merton, London  October 2012

                Yeap Ban Har
          Marshall Cavendish Institute
                   Singapore

           yeapbanhar@gmail.com

               Slides are available at
          www.banhar.blogspot.com
“Singapore” by Yeap Ken Min
Experiencing
                                                                  Singapore Math
                                       Land
                                         270 sq miles

                                         700 sq km


                  introduction         People
                                         5.3 million

                                       GDP per capita
                                         1965 USD500

                                         2011 USD50 000
Junyuan Secondary School, Singapore              in current USD
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, Singapore
     15 Mixed-Level Schools

  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.
                                       Today, about the
                                       same proportion
                                       achieve        the
                                       highest grade in
                                       each of the four
                                       subjects tested.




  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)
Singapore Maths at Merton
Experiencing
                                                                                           Singapore Math
                                             Mathematics is “an excellent
                                         vehicle for the development and
                                               improvement of a person’s
                                                 intellectual competence”.
                  1982                              Ministry of Education Singapore 2006
Introduction of Singapore mathematics
  textbooks as they are known today.                       2001
                                          Introduction of textbooks published by
                        1992                private publishers and approved by
              Introduction of Problem-             Ministry of Education.
                 Solving Curriculum                       2007
                                             New editions of textbooks are
                       1997               published with the introduction of the
                 Thinking Schools                  revised curriculum.
                 Learning Nation
                                                          2013
                                             New editions of textbooks are
                                            published with the revision of the
                                                      curriculum.


     Page 1
Experiencing
Page 4




         Singapore Math
Experiencing
                                                   Singapore Math
                                     Achievement
                          Attitude
           Singapore      71         41

           Hong Kong      67         40

             Taiwan       50         24




Grade 4
             Japan        62         23

          Kazakhstan      89         19

            England       62         16

             Russia       80         16

          International   72         5
Experiencing
                                                   Singapore Math
                                     Achievement
                          Attitude
             Taiwan       37         45

            S Korea       33         40

           Singapore      60         40




Grade 8
           Hong Kong      47         31

             Japan        30         26

            Hungary       30         10

            England       40         8

          International   54         2
Singapore Maths at Merton
Experiencing
                                      Singapore Math
                               Mean
                 Shanghai      600

                Singapore      562

                Hong Kong      555




15 year-olds
                 S Korea       546

                 Taiwan        543

                 Finland       541

               Liechtenstein   536

               International   496
Experiencing
Singapore Math
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
Professional Development at Merton, London
Experiencing
                              Singapore Math
Escuela de Guetamala, Chile
x + 2x = 12




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




                                       Singapore Math
                                       Experiencing
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
Page 5




         Singapore Math
Experiencing
Singapore Math
Experiencing
                                                               Singapore Math
3 fourths  4 = 12 sixteenths  4                     1    3
                                    3 fourths  4 =       ×4
                                                      4
              = 3 sixteenths
Experiencing
Singapore Math




                  Professional Development at Merton, London
Experiencing
                                   Singapore Math
Share 3 fourths equally among 3.




3 fourths  3 = 1 fourth
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
Using bar model to introduce solving
algebraic equations
Solve 7 – 3y = 1 .

             7




     3y             1
Singapore Maths at Merton
Singapore Maths at Merton
Experiencing
                                           Singapore Math
 Experiencing Singapore Math
Emphasis on Number Sense & Visualization
             Yeap Ban Har
      Marshall Cavendish Institute
               Singapore

        yeapbanhar@gmail.com

            Slides are available at
       www.banhar.blogspot.com
Experiencing
Singapore Math
Experiencing
Singapore Math
Experiencing
Singapore Math
Experiencing
Singapore Math
King Solomon Academy, London
Experiencing
                               Singapore Math
King Solomon Academy, London
Singapore Math
                         Experiencing
King Solomon Academy, London
Experiencing
Globe Academy, London




                        Singapore Math
Experiencing
Globe Academy, London




                        Singapore Math
Experiencing
Globe Academy, London




                        Singapore Math
Experiencing
Singapore Math
Experiencing
                                                         Singapore Math
Teaching Multiplication Facts




                                Allfarthing Primary School, London
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)
emphasis
visualization
Experiencing
                                  Singapore Math
3 units = 18
1 units = 18  3 = 6
6 x 8 = 48
There were 48 coins at first.
                                Page 15
Experiencing
Singapore Math

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Singapore Maths at Merton

  • 1. Experiencing Singapore Maths Merton, London  October 2012 Yeap Ban Har Marshall Cavendish Institute Singapore yeapbanhar@gmail.com Slides are available at www.banhar.blogspot.com
  • 3. Experiencing Singapore Math  Land  270 sq miles  700 sq km introduction  People  5.3 million  GDP per capita  1965 USD500  2011 USD50 000 Junyuan Secondary School, Singapore in current USD
  • 4. General Overview of Singapore and its Education System
  • 5. 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, Singapore  15 Mixed-Level Schools 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.
  • 6. 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. Today, about the same proportion achieve the highest grade in each of the four subjects tested. Keon Ming Public School, Singapore
  • 7. 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)
  • 9. Experiencing Singapore Math Mathematics is “an excellent vehicle for the development and improvement of a person’s intellectual competence”. 1982 Ministry of Education Singapore 2006 Introduction of Singapore mathematics textbooks as they are known today. 2001 Introduction of textbooks published by 1992 private publishers and approved by Introduction of Problem- Ministry of Education. Solving Curriculum 2007 New editions of textbooks are 1997 published with the introduction of the Thinking Schools revised curriculum. Learning Nation 2013 New editions of textbooks are published with the revision of the curriculum. Page 1
  • 10. Experiencing Page 4 Singapore Math
  • 11. Experiencing Singapore Math Achievement Attitude Singapore 71 41 Hong Kong 67 40 Taiwan 50 24 Grade 4 Japan 62 23 Kazakhstan 89 19 England 62 16 Russia 80 16 International 72 5
  • 12. Experiencing Singapore Math Achievement Attitude Taiwan 37 45 S Korea 33 40 Singapore 60 40 Grade 8 Hong Kong 47 31 Japan 30 26 Hungary 30 10 England 40 8 International 54 2
  • 14. Experiencing Singapore Math Mean Shanghai 600 Singapore 562 Hong Kong 555 15 year-olds S Korea 546 Taiwan 543 Finland 541 Liechtenstein 536 International 496
  • 16. 110 g 290 g Page 2
  • 17. 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. ? ?
  • 18. Experiencing Singapore Math Professional Development at Merton, London
  • 19. Experiencing Singapore Math Escuela de Guetamala, Chile
  • 20. x + 2x = 12 Experiencing Singapore Math
  • 21. Experiencing Singapore Math Globe Academy, London
  • 22. Edgewood Elementary School, New York Singapore Math Experiencing
  • 23. 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
  • 24. Experiencing Singapore Math  Relational Understanding  R Skemp what & how  Concrete Introduction  J Bruner Junyuan Secondary School, Singapore Page 08 Page 13
  • 25. Experiencing Page 5 Singapore Math
  • 27. Experiencing Singapore Math 3 fourths  4 = 12 sixteenths  4 1 3 3 fourths  4 = ×4 4 = 3 sixteenths
  • 28. Experiencing Singapore Math Professional Development at Merton, London
  • 29. Experiencing Singapore Math Share 3 fourths equally among 3. 3 fourths  3 = 1 fourth
  • 30. 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
  • 31. Experiencing Singapore Math Using bar model to introduce solving algebraic equations Solve 7 – 3y = 1 . 7 3y 1
  • 34. Experiencing Singapore Math Experiencing Singapore Math Emphasis on Number Sense & Visualization Yeap Ban Har Marshall Cavendish Institute Singapore yeapbanhar@gmail.com Slides are available at www.banhar.blogspot.com
  • 40. Experiencing Singapore Math King Solomon Academy, London
  • 41. Singapore Math Experiencing King Solomon Academy, London
  • 46. Experiencing Singapore Math Teaching Multiplication Facts Allfarthing Primary School, London
  • 47. Math in Focus Experiencing Singapore Math
  • 48. Experiencing Math in Focus Singapore Math
  • 49. Math in Focus Experiencing Singapore Math
  • 50. Experiencing Math in Focus Singapore Math
  • 51. Math in Focus Experiencing Singapore Math
  • 52. Experiencing Singapore Math Math in Focus
  • 53. Math in Focus Experiencing Singapore Math
  • 54. Math in Focus Experiencing Singapore Math
  • 55. Math in Focus Experiencing Singapore Math
  • 56. Math in Focus Experiencing Singapore Math
  • 57. Math in Focus Experiencing Singapore Math
  • 58. Experiencing Singapore Math Da Qiao Primary School, Singapore
  • 59. 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.
  • 60. Experiencing Singapore Math Visuals are used to teach concepts – distributive property of multiplication – without using formal terms. Primary Mathematics (Third Edition)
  • 62. Experiencing Singapore Math 3 units = 18 1 units = 18  3 = 6 6 x 8 = 48 There were 48 coins at first. Page 15