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
use mathematical language to communicate mathematical ideas and arguments
precisely, concisely and logically
develop positive attitudes towards Mathematics including confidence, enjoyment
appreciate the power and structure of Mathematics, including patterns and
relationships, and to enhance their intellectual curiosity
This is a brief overview of Singapore mathematics
curriculum, its framework
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
Reading comprehension is very important for the
students to use the required mathematical
operations to solve the problem.
• Before Singapore self-independence in 1959,
Singapore did not have a unified system of
• Each type of school will teach their own type of
mathematics, using textbooks from different
• A common curriculum was developed only after selfgovernment, and increasing emphasis was given to
ensure that Singapore could develop an
5. Mathematical Framework
• A Mathematical Framework was developed in the
1990s, following a review of mathematics
curriculum, to articulate the principles of
• 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
6. Mathematics Curriculum Framework
Use of mathematical tools
Monitoring of one’s own thinking
Self-regulation of learning
Thinking skills &
Application & modelling
7. TIMSS 1995 – 2007
Trends in International Mathematics and Science Studies
8. TIMSS 2007
Trends in International Mathematics and Science Studies
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
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,
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
emphasized prior to the learning
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
Earlybird Kindergarten Mathematics
15. Number Bonds
continues to receive attention in
emphasis in the first six months
of grade one.
The children learn it in stages as
between Numbers to 10 and
Numbers to 20.
Count On and Count All are used
in Numbers to 10.
17. Focus on Problem Solving
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.
Dylan has 20 toy cars. Mark has 4 less toy cars than Dylan. How
many toy cars does Mark have?
20 – 4 = 16
Answer: Mark has 16 cars all together.
19. 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
20. Basic Steps
on Model Drawing
• Step 1: Read the entire problem
• Step 2: Understand on ‘Who’ is involved in the
• Step 3: Understand on ‘What’ is involved in the
• 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
21. Model Drawing
Tasks are varied in a systematic way to ensure that
average & struggling learners
can learn well.
27. Spiral Approach
The spiral approach is where lessons include
mathematical variations within the same grade.
is used to help the
29. Links between
31. Other problem solving strategies
Drawing a Picture.
Looking for a Pattern.
Guess & Check.
Making a Systematic List.
• 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
• Each bottle holds 100 ml of cough syrup. At most how
many full bottles can you get from 980 ml of cough
• 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?
• 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