Singapore




                                                  Singapore Math in Colorado, USA
    Math
  & Teacher
Preparation
plenary lecture Dr. Yeap Ban Har
MTAP (Tertiary Chapter)
                          Marshall Cavendish Institute
                          Singapore
                          yeapbanhar@gmail.com

www.banhar.blogspot.com
Singapore         This lecture focuses on the
                  whats and hows of Singapore
    Math          Math and the implications on
                  teacher preparation.
  & Teacher
Preparation




                                          Singapore Math in Hawaii, USA
plenary lecture




www.banhar.blogspot.com
Singapore     In particular, the role of
              mathematics in developing
    Math      thinking as well as conceptual
              understanding,      and    the
  & Teacher   central role of problem
Preparation   solving are discussed.




www.banhar.blogspot.com
Kranji Secondary School, Singapore
Singapore
    Math
  & Teacher
Preparation   A framework for teacher
              preparation       to     teach
              mathematics         in      this
              particular way is outlined.
www.banhar.blogspot.com
Singapore Math in The Netherlands
Singapore
    Math
  & Teacher
Preparation
                Singapore Math



www.banhar.blogspot.com
Example 1
How many ½ are there in ¾ ?
Example 1
How many ½ are there in ¾ ?
Example 1
How many ½ are there in ¾ ?
Example 1
How many ½ are there in ¾ ?
Example 1
How many ½ are there in ¾ ?
Prospective   teachers   must
have      a  conceptual
understanding of the
content they teach. They
also          need        the
corresponding
pedagogical knowledge
e.g.     using      concrete
representation and pictorial
representation   to     help
students access abstract
Example 2
Find the value of 51   3.
Example 2
Find the value of 51     3.


Prospective       teachers    must
understand            mathematical
variability      and     perceptual
variability of the mathematics
skill / concept they teach.

What is the emphasis when the
lesson shift from 21 3 to 51 3?
What is the difference between
using base ten block and coins to
Theoretical Underpinnings of Singapore Math
Jerome Bruner
• Spiral Approach
• CPA Approach
Zoltan Dienes
• Variability
Richard Skemp
• Relational Understanding




                   Article on Relational Understanding
Lesson 41   16.08.12
Lesson 41                                  16.08.12

                a
                    b   To prove that angle at
                        centre is equal to 2a + 2b




            a
Northbrooks Secondary
School, Singapore
Lesson 41                                      10.10.11

                  a
                        b   To prove that angle at
                            centre is equal to 2a + 2b



            180o - 2a

                      2a
            a
Lesson 41                                            16.08.12

                a
                    b             To prove that angle at
                                  centre is equal to 2a + 2b




                    2a
                         2b   b
            a
key
   of singapor
mathemati
 focus
cs    e
problem
   solving
thinking
an
excellent
       vehicle
  for the development
   &improvement of
        a person’s intellectual
          competencies
               Ministry of Education Singapore 2006
conceptu
understandi
 al
ng
developin
 visualizatio
g
10

          76
10
x        x   x   10

                      76
x   10
x        x   x   10

                      76 - 20
x   10
Singapore Math in
   London, UK
King Solomon
Academy, London
Singapore Math in The Netherlands
Singapore
    Math
  & Teacher
Preparation
               Professional Learning



www.banhar.blogspot.com
Grade 10



Grades 11 – 12   Polytechnic



         University
Teacher
Preparation
  at NIE

 Professional
 Development
Certificate in Mathematics
                  Teaching (120 h)

                 Course for Math
 Marshall        Specialists (40 h)
Cavendish
 Institute   Course for Math Coaches
                      (40 h)

               Course for Graduate
                Research (40 h)
Pedagogy for Teacher
       Preparation

where mindset is
changed,knowledge is constructe
and the ability to learn, enhanced
Pedagogy for
                 Teacher
              Preparation
Teachers as Learners
Pedagogy for
                 Teacher
              Preparation
Teachers as Observers
Find the distance
between two given
points.
Bina Bangsa School, Jakarta
                      Singapore         Math
                      courses for teachers
                      provides opportunities
                      for teachers to ‘study’
                      lessons.
1st Block     4x2x1
                            2nd Block     4x2x3
                            3rd Block

                Victory Christian International
                School, Manila
Singapore         Math
courses for teachers
provides opportunities
for teachers to ‘study’
lessons.
Pedagogy for
                     Teacher
                  Preparation
Textbooks are written to embody the
learning theories and emphasis of
mathematics learning. Teachers learn
mathematics and how to teach mathematics
from the textbooks.
Thank You

yeapbanhar@gmail.com

www.banhar.blogspot.com
                          Junyuan Secondary
                          School, Singapore

MTAP TL International Convention

  • 1.
    Singapore Singapore Math in Colorado, USA Math & Teacher Preparation plenary lecture Dr. Yeap Ban Har MTAP (Tertiary Chapter) Marshall Cavendish Institute Singapore yeapbanhar@gmail.com www.banhar.blogspot.com
  • 2.
    Singapore This lecture focuses on the whats and hows of Singapore Math Math and the implications on teacher preparation. & Teacher Preparation Singapore Math in Hawaii, USA plenary lecture www.banhar.blogspot.com
  • 3.
    Singapore In particular, the role of mathematics in developing Math thinking as well as conceptual understanding, and the & Teacher central role of problem Preparation solving are discussed. www.banhar.blogspot.com
  • 4.
    Kranji Secondary School,Singapore Singapore Math & Teacher Preparation A framework for teacher preparation to teach mathematics in this particular way is outlined. www.banhar.blogspot.com
  • 5.
    Singapore Math inThe Netherlands Singapore Math & Teacher Preparation Singapore Math www.banhar.blogspot.com
  • 6.
    Example 1 How many½ are there in ¾ ?
  • 7.
    Example 1 How many½ are there in ¾ ?
  • 8.
    Example 1 How many½ are there in ¾ ?
  • 9.
    Example 1 How many½ are there in ¾ ?
  • 10.
    Example 1 How many½ are there in ¾ ? Prospective teachers must have a conceptual understanding of the content they teach. They also need the corresponding pedagogical knowledge e.g. using concrete representation and pictorial representation to help students access abstract
  • 11.
    Example 2 Find thevalue of 51 3.
  • 12.
    Example 2 Find thevalue of 51 3. Prospective teachers must understand mathematical variability and perceptual variability of the mathematics skill / concept they teach. What is the emphasis when the lesson shift from 21 3 to 51 3? What is the difference between using base ten block and coins to
  • 16.
    Theoretical Underpinnings ofSingapore Math Jerome Bruner • Spiral Approach • CPA Approach Zoltan Dienes • Variability Richard Skemp • Relational Understanding Article on Relational Understanding
  • 17.
    Lesson 41 16.08.12
  • 18.
    Lesson 41 16.08.12 a b To prove that angle at centre is equal to 2a + 2b a
  • 19.
  • 20.
    Lesson 41 10.10.11 a b To prove that angle at centre is equal to 2a + 2b 180o - 2a 2a a
  • 21.
    Lesson 41 16.08.12 a b To prove that angle at centre is equal to 2a + 2b 2a 2b b a
  • 25.
    key of singapor mathemati focus cs e
  • 26.
    problem solving
  • 27.
  • 28.
    an excellent vehicle for the development &improvement of a person’s intellectual competencies Ministry of Education Singapore 2006
  • 29.
  • 30.
  • 32.
    10 76 10
  • 33.
    x x x 10 76 x 10
  • 34.
    x x x 10 76 - 20 x 10
  • 36.
  • 37.
  • 38.
    Singapore Math inThe Netherlands Singapore Math & Teacher Preparation Professional Learning www.banhar.blogspot.com
  • 39.
    Grade 10 Grades 11– 12 Polytechnic University
  • 40.
    Teacher Preparation atNIE Professional Development
  • 41.
    Certificate in Mathematics Teaching (120 h) Course for Math Marshall Specialists (40 h) Cavendish Institute Course for Math Coaches (40 h) Course for Graduate Research (40 h)
  • 42.
    Pedagogy for Teacher Preparation where mindset is changed,knowledge is constructe and the ability to learn, enhanced
  • 43.
    Pedagogy for Teacher Preparation Teachers as Learners
  • 44.
    Pedagogy for Teacher Preparation Teachers as Observers
  • 45.
    Find the distance betweentwo given points. Bina Bangsa School, Jakarta Singapore Math courses for teachers provides opportunities for teachers to ‘study’ lessons.
  • 46.
    1st Block 4x2x1 2nd Block 4x2x3 3rd Block Victory Christian International School, Manila Singapore Math courses for teachers provides opportunities for teachers to ‘study’ lessons.
  • 47.
    Pedagogy for Teacher Preparation Textbooks are written to embody the learning theories and emphasis of mathematics learning. Teachers learn mathematics and how to teach mathematics from the textbooks.
  • 48.