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Introduction onto Singapore Maths.

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- 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 - 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. - 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.merriam-webster.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. - 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 self-

government, and increasing emphasis was given to

ensure that Singapore could develop an industrialized

economy. - 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. - Mathematics Curriculum Framework

Beliefs

Interest

Appreciation

M

Monitoring of one’s own

e

Confidence

ta thinking

c

Perseverance

og Self-regulation of learning

At itudes

nition

Numerical calculation

Mathematica

Algebraic manipulation

S

Reasoning,

Spatial visualization

k

l Problem

il

communication &

Data analysis

s

Solving

connections

Measurement

Processes Thinking skills &

Use of mathematical

Concepts

heuristics

tools

Application & modelling

Estimation

Numerical

Algebraic

Geometrical

Statistical

Probabilistic

Analytical - TIMSS 1995 – 2007

Trends in International Mathematics and Science Studies

a

5

3

7

n

9

0

0

tio

Grade 4

9

0

0

a

l

1

2

2

rn

te

In

Advanced

38

38

41

5

High

70

73

74

26

Intermediat

89

91

92

67

e

Low

96

97

98

90 - TIMSS 2007

Trends in International Mathematics and Science Studies

l

a

n

sia

d

re

tio

e

n

o

a

n

ysia

p

rn

o

ila

a

Grade 8

a

la

te

d

g

h

a

In

In

T

M

in

S

Advanced

2

0

3

2

40

High

15

4

12

18

70

Intermediat

46

14

44

50

88

e

Low

75

48

66

82

97

Method Used in Singapore Textbooks - Mathematics is “an excellent vehicle for

the development and improvement of a

person’s intellectual competence”.

Ministry of Education (Singapore) 2006 - 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. - 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. - For example,

3 + 4 = 7

A child who "knows" this number bond should be able to immediately fil

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. - Part & Whole

• Explain to the child that the two smal er

numbers are the ‘parts’ that make the big

number, that is the ‘whole’. - Number

N

Bumb

on er

ds 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 - Number Bonds continues

to receive attention in Grade 1. - Addition

Ad

F d

a ition

cts 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. - 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. - 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. - 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 - Model Drawing

• http://thinkingblocks.com/ - Textbooks
- experien

concre ce

te s - con

fr cr

omete

ptict

o orial - pict

fr orial

om

abtsotract - Variations

Tasks are varied in a systematic way to ensure that

average & struggling learners

can learn well. - Spiral Approach

The spiral approach is where lessons include

mathematical variations within the same grade. - Concrete

To

Pictorial

The concrete

pictorial abstract

approach is used to

help the majority of

learners to develop

strong foundation

in mathematics. - Links between

concrete and

pictorial

representation

must be

carefully

constructed. - conceptual

understanding - Other problem solving strategies

includes:

• Drawing a Picture.

• Looking for a Pattern.

• Guess & Check.

• Making a Systematic List.

• Logical Reasoning.

• Working Backwards. - 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? - 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, al

mathematical y correct solutions are acceptable and there is no

loss of marks if a correct algebraic method is used.