Keynote Lecture at First International Symposium on Early Mathematics Education

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Keynote Lecture at First International Symposium
on Early Mathematics Education Erikson Institute,
Chicago
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Big Ideas in Early Mathematics
Yeap Ban-Har, Ph.D. National Institute of
Education Nanyang Technological University
Singapore banhar.yeap_at_nie.edu.sg
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Slides are also available on math.nie.edu.sg/T3
Photo PCF Telok Blangah Kindergarten
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overview

• Kindergartens as Part of Informal System
• Early Mathematics in Kindergarten and Grade 1
• Big Ideas in Early Mathematics
• Number Bonds Basic Facts
• Visualization
• Connections
• Communication

Photo PCF Telok Blangah Kindergarten
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kindergarten part of informal schooling
Photo PCF Telok Blangah Kindergarten

• PART 1

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Variation in kindergartens

• Kindergarten is not part of formal schooling.
• Pre-school education varies in types and quality.
• Teachers qualification ranges from O-Levels to
  masters degrees in early childhood. Monthly fees
  range from 65 to more than 1000.

Photo PCF Telok Blangah Kindergarten
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Variation in kindergartens

• Kindergartens that the majority of Singapore
  children attend are run by grass-root
  organizations and they struggle to provide a
  high-quality program due to lack of resources and
  qualified teachers.
• One such provider of kindergarten education is
  the PCF Kindergartens which has 255 kindergartens
  out of 485 kindergartens in Singapore.

Photo PCF Telok Blangah Kindergarten
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Uniformity in primary schools

• The formal education system in Singapore is
  uniform with only public schools, a national
  curriculum, and a single teacher-training
  institute.
• The gaps among children in the first year of
  primary school are large depending on the
  kindergarten education they have received. Some
  children have not attended kindergartens.

Photo St Anthonys Canossian Primary School
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Outcomes
1995
2003
2007
Advanced
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41
38
High
70
74
73
Intermediate
89
92
91
Low
96
98
97
Photo Catholic High School (Primary)
The gaps that were seen in Grade 1 appears to
have been corrected to a large extent by Grade 4.
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How are these gaps corrected?
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Given the present situation, how can teachers be
helped to deliver high-quality programs in
kindergartens?
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corrections in grades one

• Grade 1 and Grade 2 classes have a smaller
  class-size of thirty children per class.
• There is also a learning support program for
  children who are less proficient in mathematics
  and English.

Photo Princess Elizabeth Primary School
How are these gaps corrected?
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corrections in grades one

• Since 2005, Grade 1 and Grade 2 teachers have
  been asked to adopt the SEED Approach. SEED is
  the acronym for Strategies for Effective
  Engagement and Development.
• This effort is to engage the children in the
  learning process. This has brought about a
  greater use of concrete materials in mathematics
  lessons.

Photo Catholic High School (Primary)
How are these gaps corrected?
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corrections in grades one
Conscious effort not to put the disadvantage
children in a position of greater disadvantage.
Textbooks are written for learners of the
language, yet challenging for advanced learners.
Grade 1 Textbook
How are these gaps corrected?
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corrections in grades one
Textbooks are also written simply so that
non-specialist teachers can understand the
mathematics they are teaching. Hopefully, it is
not complicated to put the less educated parents
off helping their kids. Children bring their
books home every day.
Grade 1 Textbook
How are these gaps corrected?
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corrections in grades one

• Further efforts to strengthen primary education
  is evident.
• A high-profile committee reviewed primary
  education in Singapore and made suggestions this
  stage of education can be further improved.

How are these gaps corrected?
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Efforts in pre- school education
While pre-school education sets to remain as part
of informal schooling, the present state of the
situation is deemed far from ideal. Recently, in
an effort to improve pre-school education in
Singapore, the Ministry of Education set up a
pre-school unit. The pedagogy used in developing
mathematics textbooks in primary grades was also
used to produce textbooks for the
kindergartens.
Kindergarten Textbook
What are some efforts to reduce these gaps ?
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Efforts in pre- school education
Five PCF kindergartens have been selected to
engage in lesson study to build teacher
capacity.
Princess Elizabeth Primary School
What are some efforts to reduce these gaps ?
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big ideas in early mathematicsin kindergartens
through grade one

• PART 2

Photo PCF Telok Blangah Kindergarten
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Number Bonds
Number Bonds is emphasized prior to the learning
of addition. Children are given, say, 5 unifix
cubes and guided to see that 1 and 4 make 5, for
example. Others may say that 3 and 2 make 5 or 4
and 1 make 5. Yet others may say that 5 and 0
make 5.
Kindergarten Textbook
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Photo PCF Telok Blangah Kindergarten
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One duck is big. Six ducklings are small.
Photo PCF Telok Blangah Kindergarten
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Photo PCF Telok Blangah Kindergarten
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Photo PCF Telok Blangah Kindergarten
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Photo PCF Telok Blangah Kindergarten
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Photo PCF Telok Blangah Kindergarten
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Grade 1 Textbook
Number Bonds continues to receive attention in
Grade 1.
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Addition Facts
Addition Facts are given emphasis in the first
six months of grade one. The children learn it
in stages as the textbooks distinguished between
Numbers to 10 and Numbers to 20. Count On and
Count All are used in Numbers to 10.
Kindergarten Textbook
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Addition Facts Number Sense
While Count On and Count All are used in Numbers
to 10, Make Ten is given emphasis in Numbers to
20.
Princess Elizabeth Primary School
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Connections
Looking for Patterns is introduced through
exploration with Shapes. Subsequently, this is
done using numbers in a more abstract context.
Princess Elizabeth Primary School
Make Connections to Generalize
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Communication
Articulating ones thoughts orally, at first, and
in written forms using words, pictures, diagrams
and symbols is important.
Maris Stella High (Primary) School
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Connections
Princess Elizabeth Primary School
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Visualization
Visualization is, among other things, the ability
to manipulate visual images without the benefit
of concrete objects. In the Japanese lessons, we
saw children engaged in three-dimensional
visualization (bean-container task) and
two-dimensional visualization (pattern-block
task).
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Visualization
In the learning of Numbers to 10, children use
square tiles to form patterns of 3 and patterns
of 4, for instance. Illustrations in textbooks
were also carefully varied to develop this
competency.
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Are there other big ideas?
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banhar.yeap_at_nie.edu.sg
Children are truly the future of our nation.
Irving Harris
www.banhar.blogspot.com
math.nie.edu.sg/T3
Bina Bangsa School, Indonesia