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Experiencing
                                         Singapore Math
Experiencing Singapore Math
    July 23, 2012 ïź Minneapolis, MN

                Yeap Ban Har
          Marshall Cavendish Institute
                   Singapore

           yeapbanhar@gmail.com

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

                               People
               introduction     ï‚Ą 4.7 million

                               GDP per capita
                                ï‚Ą 1965 USD510

                                ï‚Ą 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
  ï‚Ą 500 000

 Teachers
  ï‚Ą 30 000

 Principals & Vice-Principals
  ï‚Ą 900

 Schools
  ï‚Ą 173 Primary Schools (Primary 1 – 6)
  ï‚Ą 155 Secondary Schools (Secondary 1 – 4)
  ï‚Ą   13 Junior Colleges (JC 1 – 2)                                           Canossa Convent Primary
  ï‚Ą   15 Mixed-Level Schools                                                  School, 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.

                                                        2013
                                        Fourth version of the problem-solving
                                          curriculum will be implemented.
     Page 1
Experiencing
Page 4




         Singapore Math
Experiencing
                                       Singapore Math
 on Visualization
   Fundamentals of Singapore Math

Focus
              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
                              Relational
                              Understanding
                              ï‚Ą   R Skemp

                what & how    Concrete
                              Introduction
                              ï‚Ą   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
              visualization            ï‚Ą   J Bruner
                                       Human
                                       Intelligences
                                       ï‚Ą   H Gardner




             Page 11
King Solomon Academy, London
Experiencing
                               Singapore Math
King Solomon Academy, London
Singapore Math
                      Experiencing
King Solomon Academy, London
Experiencing
                        Singapore Math
Globe Academy, London
Experiencing
                        Singapore Math
Globe Academy, London
Experiencing
                        Singapore Math
Globe Academy, London
Experiencing
                                      Singapore Math
 on Patterns
  Fundamentals of Singapore Math

 Focus
             Yeap Ban Har
       Marshall Cavendish Institute
                Singapore

         yeapbanhar@gmail.com

            Slides are available at
        www.banhar.blogspot.com
Page 3
C H E R Y L
C H E R Y L
1
C H E R Y L
  2
C H E R Y L
    3
C H E R Y L
      4
C H E R Y L
        5
C H E R Y L
          6
C H E R Y L
        7
C H E R Y L
      8
C H E R Y L
    9
C H E R Y L
C H E R Y L
C H E R Y L
C H E R Y L
C H E R Y L
C H E R Y L
      Which letter is 99?
D A V I   D
Experiencing
                                    Singapore Math
Da Qiao Primary School, Singapore
Emphasis on Generalization
                     My Pals Are Here! Mathematics (Second Edition)




                       Explicit instruction to
                     engage in higher-order
                   competencies such as to
                         look for a pattern.
Emphasis on Generalization
                    My Pals Are Here! Mathematics (Second Edition)




                                            There are
                                              sections
                                           devoted to
                                         higher-order
                                       thinking which
                                     includes pattern
                                         observation.
Page 6
Experiencing
                                                          Singapore Math
Junyuan Secondary School, Singapore




                                         Mathematical

               patterns and                  Practices
                                            “Mathematically

              generalization
                                          proficient students
                                       look closely to discern
                                      a pattern or structure.”
Experiencing
                                         Singapore Math
 Fundamentals of Singapore Math

 Challenging Word
Problems using Bar
      Models
            Yeap Ban Har
                                     
      Marshall Cavendish Institute
               Singapore

        yeapbanhar@gmail.com

           Slides are available at
       www.banhar.blogspot.com
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
Page 15




          Singapore Math
Experiencing
Page 15




          Singapore Math
Math in Focus
     Grade 1




                   Experiencing
                Singapore Math
Experiencing
                                          Singapore Math
                              Math in Focus
                                   Grade 2




Escuela de Guetamala, Chile
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 = ïź


           cars             buses

           543               274
Lesson 6             June 20, 2012




      Carl

             $4686
      Ben
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 ïź                         June 18, 2012


      Jack                      $3
                         Jack
           Kyla                 $2

                         Kyla

     gave
                   more

    had
                  than
Lesson ïź             June 18, 2012




           Open Lesson at Hawaii, USA
Lesson ïź                                      June 18, 2012
                                   What if Kyla
Story 1                             had this
Jack had $3.                        amount
                                    before?
Jack gave Kyla $2
more.
                Jack          Kyla
     Before         $3   $1   $5      $19
     After          $1   $3   $7       ?
Lesson ïź                                    June 18, 2012

Story 2
Kyla had $3 more than Jack.    Who had
                              more money
Jack       $2                 afterwards?
                              How much
Kyla            $3               more?


Jack gave Kyla $2.
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 ïź                                    July 23, 2012




         In the end ...   At first 


Alice                                  20



Betty                                       10



Charmaine


 Dolly
Lesson 7   June 18, 2012
Experiencing
                                                       Singapore Math
Junyuan Secondary School, Singapore




                                       Concrete to
          visualization                Visual
         and managing
                                       ï‚Ą   J Bruner
                                       Human
           information                 Intelligences
                                       ï‚Ą   H Gardner
can learn.
                                                        Our students must
                                                                      too.




Google learns from typos and spelling mistakes we all make when searching to help give you
quicker and more accurate search results. So if you type ‘grizzly pears’, we can guess that you
probably meant ‘grizzly bears’.
Goggle does not have a degree in English. We can do this because over the years we’ve
studied how people search and learned what the most common errors are. So it’s good to
know that all those little mistakes aren’t made in vain.
Experiencing
                                        Singapore Math
Experiencing Singapore Math
      July 23, 2012 ïź Minnesota

               Yeap Ban Har
         Marshall Cavendish Institute
                  Singapore

          yeapbanhar@gmail.com

              Slides are available at
         www.banhar.blogspot.com

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Singapore Math Seminar at Minneapolis MN

  • 1. Experiencing Singapore Math Experiencing Singapore Math July 23, 2012 ïź Minneapolis, MN Yeap Ban Har Marshall Cavendish Institute Singapore yeapbanhar@gmail.com Slides are available at www.banhar.blogspot.com
  • 2. Experiencing Singapore Math  Land ï‚Ą 270 sq miles  People introduction ï‚Ą 4.7 million  GDP per capita ï‚Ą 1965 USD510 ï‚Ą 2010 USD43,300 in current USD Junyuan Secondary School, Singapore
  • 3. General Overview of Singapore and its Education System
  • 4. General Overview of Singapore and its Education System  Students ï‚Ą 500 000  Teachers ï‚Ą 30 000  Principals & Vice-Principals ï‚Ą 900  Schools ï‚Ą 173 Primary Schools (Primary 1 – 6) ï‚Ą 155 Secondary Schools (Secondary 1 – 4) ï‚Ą 13 Junior Colleges (JC 1 – 2) Canossa Convent Primary ï‚Ą 15 Mixed-Level Schools School, 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 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
  • 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)
  • 7.
  • 8. "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
  • 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. 2013 Fourth version of the problem-solving curriculum will be implemented. Page 1
  • 10. Experiencing Page 4 Singapore Math
  • 11. Experiencing Singapore Math  on Visualization Fundamentals of Singapore Math Focus Yeap Ban Har Marshall Cavendish Institute Singapore yeapbanhar@gmail.com Slides are available at www.banhar.blogspot.com
  • 12. 110 g 290 g Page 2
  • 13. 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. ? ?
  • 14. Experiencing Singapore Math Escuela de Guetamala, Chile
  • 15. x + 2x = 12 Experiencing Singapore Math
  • 16. Experiencing Singapore Math King Solomon Academy, Londo
  • 18. Globe Academy, London Experiencing Singapore Math
  • 19. Experiencing Singapore Math 3x – 2 = 8 Globe Academy, London
  • 20. Experiencing Singapore Math  Relational Understanding ï‚Ą R Skemp what & how  Concrete Introduction ï‚Ą J Bruner Junyuan Secondary School, Singapore Page 08 Page 13
  • 21. Experiencing Singapore Math Share 3 fourths equally among 3. 3 fourths 3 = 1 fourth Page 5
  • 22. 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
  • 23. 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
  • 29. Experiencing Singapore Math Junyuan Secondary School, Singapore  Concrete to Visual visualization ï‚Ą J Bruner  Human Intelligences ï‚Ą H Gardner Page 11
  • 31. Experiencing Singapore Math King Solomon Academy, London
  • 32. Singapore Math Experiencing King Solomon Academy, London
  • 33. Experiencing Singapore Math Globe Academy, London
  • 34. Experiencing Singapore Math Globe Academy, London
  • 35. Experiencing Singapore Math Globe Academy, London
  • 36.
  • 37. Experiencing Singapore Math  on Patterns Fundamentals of Singapore Math Focus Yeap Ban Har Marshall Cavendish Institute Singapore yeapbanhar@gmail.com Slides are available at www.banhar.blogspot.com
  • 39. C H E R Y L
  • 40. C H E R Y L 1
  • 41. C H E R Y L 2
  • 42. C H E R Y L 3
  • 43. C H E R Y L 4
  • 44. C H E R Y L 5
  • 45. C H E R Y L 6
  • 46. C H E R Y L 7
  • 47. C H E R Y L 8
  • 48. C H E R Y L 9
  • 49. C H E R Y L
  • 50. C H E R Y L
  • 51. C H E R Y L
  • 52. C H E R Y L
  • 53. C H E R Y L
  • 54. C H E R Y L Which letter is 99?
  • 55.
  • 56. D A V I D
  • 57.
  • 58. Experiencing Singapore Math Da Qiao Primary School, Singapore
  • 59. Emphasis on Generalization My Pals Are Here! Mathematics (Second Edition) Explicit instruction to engage in higher-order competencies such as to look for a pattern.
  • 60. Emphasis on Generalization My Pals Are Here! Mathematics (Second Edition) There are sections devoted to higher-order thinking which includes pattern observation.
  • 62.
  • 63.
  • 64. Experiencing Singapore Math Junyuan Secondary School, Singapore Mathematical patterns and Practices “Mathematically generalization proficient students look closely to discern a pattern or structure.”
  • 65. Experiencing Singapore Math Fundamentals of Singapore Math Challenging Word Problems using Bar Models Yeap Ban Har  Marshall Cavendish Institute Singapore yeapbanhar@gmail.com Slides are available at www.banhar.blogspot.com
  • 66. 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. ? ?
  • 67. Experiencing Page 15 Singapore Math
  • 68. Experiencing Page 15 Singapore Math
  • 69. Math in Focus Grade 1 Experiencing Singapore Math
  • 70. Experiencing Singapore Math Math in Focus Grade 2 Escuela de Guetamala, Chile
  • 71.
  • 72. 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 = ïź cars buses 543 274
  • 73. Lesson 6 June 20, 2012 Carl $4686 Ben
  • 74.
  • 75. Differentiated instruction for students who have difficulty with standard algorithms. Use number bonds.
  • 76. 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.
  • 77. Lesson ïź June 18, 2012 Jack $3 Jack Kyla $2 Kyla gave more had than
  • 78. Lesson ïź June 18, 2012 Open Lesson at Hawaii, USA
  • 79.
  • 80.
  • 81.
  • 82. Lesson ïź June 18, 2012 What if Kyla Story 1 had this Jack had $3. amount before? Jack gave Kyla $2 more. Jack Kyla Before $3 $1 $5 $19 After $1 $3 $7 ?
  • 83.
  • 84. Lesson ïź June 18, 2012 Story 2 Kyla had $3 more than Jack. Who had more money Jack $2 afterwards? How much Kyla $3 more? Jack gave Kyla $2.
  • 85. 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.
  • 86. Lesson ïź July 23, 2012 In the end ... At first 
 Alice 20 Betty 10 Charmaine Dolly
  • 87. Lesson 7 June 18, 2012
  • 88. Experiencing Singapore Math Junyuan Secondary School, Singapore  Concrete to visualization Visual and managing ï‚Ą J Bruner  Human information Intelligences ï‚Ą H Gardner
  • 89.
  • 90. can learn. Our students must too. Google learns from typos and spelling mistakes we all make when searching to help give you quicker and more accurate search results. So if you type ‘grizzly pears’, we can guess that you probably meant ‘grizzly bears’. Goggle does not have a degree in English. We can do this because over the years we’ve studied how people search and learned what the most common errors are. So it’s good to know that all those little mistakes aren’t made in vain.
  • 91. Experiencing Singapore Math Experiencing Singapore Math July 23, 2012 ïź Minnesota Yeap Ban Har Marshall Cavendish Institute Singapore yeapbanhar@gmail.com Slides are available at www.banhar.blogspot.com