This document provides an overview of the aims and framework of Singapore's mathematics education system. The key points are: - The aims of Singapore math education are to develop skills in number, measurement, problem solving, logical reasoning, and positive attitudes towards math. - The mathematical framework emphasizes mathematical problem solving and its five interrelated components: concepts, skills, processes, attitudes and metacognition. - Singapore's approach emphasizes number bonds and word problems from an early age using concrete, pictorial, and abstract representations to build a strong conceptual foundation. Model drawing is a key problem solving strategy taught. - Textbooks and instruction use varied tasks, a spiral approach, and focus on developing understanding rather than ro

1. Singapore Maths
Aim of Mathematics Education:
• The aim of mathematics education, as stated by Singapore's Ministry
of Education (MOE), are to enable pupils to:
•
acquire and apply skills and knowledge relating to number, measure and space in
mathematical situations that they will meet in life
•
acquire mathematical concepts and skills necessary for a further study in
Mathematics and other disciplines
•
develop the ability to make logical deduction and induction as well as to explicate
their mathematical thinking and reasoning skills through solving of mathematical
problems
•
use mathematical language to communicate mathematical ideas and arguments
precisely, concisely and logically
•
develop positive attitudes towards Mathematics including confidence, enjoyment
and perseverance
•
appreciate the power and structure of Mathematics, including patterns and
relationships, and to enhance their intellectual curiosity

2. Introduction
This is a brief overview of Singapore mathematics
curriculum, its framework
and
its rationale and underlying goals
through the usage of
Number Bonds & Word Problems.

3. Mathematics as a Whole
•
•
•
Mathematics is the science of numbers and their
operations, interrelations, combinations,
generalizations, and abstractions and of space
configurations and their structure, measurement,
transformations, and generalizations (Merriam
Webster Dictionary http://www.merriamwebster.com/dictionary/mathematics).
The mathematics of a problem is the calculations
that are involved in it. In Singapore the solving of
mathematical word problems is a major
component both within the instructional program
as well as during formal assessments. Research
has indicated that both language and semantic
structures play a part in determining pupils’
performance in the solving of mathematical word
problems.
Reading comprehension is very important for the
students to use the required mathematical
operations to solve the problem.

4. Prior
• Before Singapore self-independence in 1959,
Singapore did not have a unified system of
education.
• Each type of school will teach their own type of
mathematics, using textbooks from different
countries.
• A common curriculum was developed only after selfgovernment, and increasing emphasis was given to
ensure that Singapore could develop an
industrialized economy.

5. Mathematical Framework
• A Mathematical Framework was developed in the
1990s, following a review of mathematics
curriculum, to articulate the principles of
mathematical teaching.
• It has remained largely the same over the years,
retaining mathematical problem solving as its core,
and the five inter-related components of concepts,
skills, processes, attitudes and metacognition.
• Minor revisions were made to stress new initiatives
such as thinking skills, information technology and
National Education.

6. Mathematics Curriculum Framework
Beliefs
Interest
Appreciation
Confidence
Perseverance
Numerical calculation
Algebraic manipulation
Spatial visualization
Data analysis
Measurement
Use of mathematical tools
Estimation
Monitoring of one’s own thinking
Self-regulation of learning
Mathematical
Problem
Solving
Concepts
Numerical
Algebraic
Geometrical
Statistical
Probabilistic
Analytical
Reasoning,
communication &
connections
Thinking skills &
heuristics
Application & modelling

7. TIMSS 1995 – 2007
Grade 4
1995
2003
2007
International
Trends in International Mathematics and Science Studies
Advanced
38
38
41
5
High
70
73
74
26
Intermediate
89
91
92
67
Low
96
97
98
90

8. TIMSS 2007
International
Indonesia
Thailand
Malaysia
Singapore
Trends in International Mathematics and Science Studies
Advanced
2
0
3
2
40
High
15
4
12
18
70
Intermediate
46
14
44
50
88
Low
75
48
66
82
97
Grade 8
Method Used in Singapore Textbooks

9. Mathematics is “an excellent vehicle for
the development and improvement of a
person’s intellectual competence”.
Ministry of Education (Singapore) 2006

10. Uniqueness of Singapore Maths
•
•
•
•
•
That is, the Concrete-Pictorial-Abstract
approach.
The students are provided with the necessary
learning experiences beginning with the
concrete and pictorial stages.
Followed by the abstract stage to enable them
to learn mathematics meaningfully.
This approach encourages active thinking
process, communication of mathematical
ideas and problem solving.
This helps develop the foundation students
will need for more advance mathematics.

11. Number Bonds
The focus on number sense right from the start.
Number bonds is taught before addition.
From Wikipedia, the free encyclopedia:
In mathematics education at primary school level, a number
bond (sometimes alternatively called an addition fact) is a
simple addition sum which has become so familiar that a child
can recognise it and complete it almost instantly, with recall as
automatic as that of an entry from a multiplication
table in multiplication.

12. For example,
3+4=7
A child who "knows" this number bond should be able to immediately fill
in any one of these three numbers if it was missing, given the other two,
without having to "work it out".
Having acquired some familiar number bonds, children should also soon
learn how to use them to develop strategies to complete more
complicated sums, for example by navigating from a new sum to an
adjacent number bond they know, i.e. 5 + 2 and 4 + 3 are both number
bonds that make 7; or by strategies like "making ten", for example
recognising that 7 + 6 = 7 + (3 + 3) = (7 + 3) + 3 = 13.

13. Part & Whole
• Explain to the child that the two smaller
numbers are the ‘parts’ that make the big
number, that is the ‘whole’.

14. 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.
Earlybird Kindergarten Mathematics

15. Number Bonds
continues to receive attention in
Grade 1.

16. Addition
Facts Facts
Addition
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.

19. Focus on Problem Solving
(Model Drawing)
The Singapore curriculum focuses on problem solving.
So does the national test.
It is no wonder that’s schools place a lot of emphasis
on problem solving.

20. ☻☻☻☻☻
☻☻☻☻☻
18
–
5
☻☻☻☻☻
☻☻☻
=
–
10
5
+
=
Dylan has 20 toy cars. Mark has 4 less toy cars than Dylan. How
many toy cars does Mark have?
20
DYLAN
MARK
20 – 4 = 16
?
Answer: Mark has 16 cars all together.
=
4

21. Model Drawing?
• Bar modeling is used as a tool to help students
solve arithmetic and algebraic word problems.
• The model method requires students to draw
diagrams in the form of rectangular bars to
represent known and unknown quantities, as
well as the relationships between the
quantities.

22. Basic Steps
on Model Drawing
• Step 1: Read the entire problem
• Step 2: Understand on ‘Who’ is involved in the
problem
• Step 3: Understand on ‘What’ is involved in the
problem
• Step 4: Draw a universe of ‘Equal length’
• Step 5: Read each sentence one at a time
• Step 6: Put the question mark in place
» (what you are looking for)
• Step 7: Work the computations
» to the side or underneath
• Step 8: Answer the question in complete sentence

23. Model Drawing
• http://thinkingblocks.com/

24. Textbooks

25. concrete
experiences

26. from
concrete
to
pictorial

27. from
pictorial
to
abstract

28. Variations
Tasks are varied in a systematic way to ensure that
average & struggling learners
can learn well.

29. Spiral Approach
The spiral approach is where lessons include
mathematical variations within the same grade.

30. Concrete
To
Pictorial
The concrete 
pictorial 
abstract approach
is used to help the
majority of
learners to
develop strong
foundation in
mathematics.

31. Links between
concrete and
pictorial
representation
must be
carefully
constructed.

32. conceptual
understanding

34. Other problem solving strategies
includes:
•
•
•
•
•
•
Drawing a Picture.
Looking for a Pattern.
Guess & Check.
Making a Systematic List.
Logical Reasoning.
Working Backwards.

35. Examples
• Each box contains 4 pieces of cookies. How many
boxes are needed to contain 36 cookies?
• Each bottle holds 100 ml of cough syrup. At least how
many bottles are needed to hold 980 ml of cough
syrup?
• Each bottle holds 100 ml of cough syrup. At most how
many full bottles can you get from 980 ml of cough
syrup?
• Alvin has 2 brothers. Brian has 2 brothers. Chris has 2
brothers. Alvin, Brian, Chris and their brothers went
into a van. How many boys are there in the van?

36. Conclusion
• Other than the model drawing approach, pupils are also
taught different problem solving methods. They are
encouraged to try different approaches and have the
flexibility to choose the method that works best for them in
solving the problems. They are also encouraged to present
their solutions clearly so that these can be understood.
• While pupils are not required to use algebra to solve word
problems in the Primary Six Leaving Examination for
Mathematics, they are also not restricted to the use of any
one particular method. In the marking of examination itself,
all mathematically correct solutions are acceptable and
there is no loss of marks if a correct algebraic method is
used.

37. Websites
• http://www.thesingaporemaths.com/
• http://www.singaporemath.com/Default
.asp
• http://www.edcrisch.com/edcrisch/web
/Index.asp
• http://www.moe.edu.sg/
• http://www.testpapers.com.sg/index.ht
ml
• http://www.sgbox.com/
• http://www.topschoolexampapers.com/
• http://thinkingblocks.com/