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
Presentation Math Workshop#May 25th New Help our teachers understa...guest80c0981
This is presented by a Math teacher,in Army Burn Hall College For Girls ,Abbottabad.
The target group was the teachers of school section. There were certain activities also performed an demonstrated in order to introduce new teaching methodologies and to prepare our teachers to meet the need of the day.
Umber
Presentation Math Workshop#May 25th New Help our teachers understa...guest80c0981
This is presented by a Math teacher,in Army Burn Hall College For Girls ,Abbottabad.
The target group was the teachers of school section. There were certain activities also performed an demonstrated in order to introduce new teaching methodologies and to prepare our teachers to meet the need of the day.
Umber
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This session will focus on teacher actions, which promote problem solving and reasoning in early years classrooms. We will workshop some tasks and have opportunities for discussion.
Connect with Maths ~ supporting the teaching of maths ONLINE
Join a Connect with Maths community today http://www.aamt.edu.au/Communities
AAMT website: http://www.aamt.edu.au
This Connect with Maths Early Years Learning in Mathematics community webinar discusses the importance of talk as part of a quality mathematical learning environment for young children. Denise makes links to the Early Years Learning Framework and the Australian Curriculum and share some ideas for facilitating mathematical talk with young children.
Connect with Maths ~Maths leadership series- Session 3- the right knowledgeRenee Hoareau
Connect with Maths ~Maths leadership series- Session 3- the right knowledge presented by Rob Proffitt-White
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This workshop targets teachers and school leaders and aims to upskill their assessment literacy by:
• Creating cognitive activation tasks that promote critical thinking in all students
• Ensuring a consistent and shared responsibility for numeracy transfer
• Differentiating tasks through a focus on the proficiency strands
• Classifying the different problem solving types.
Connect with Maths ~ supporting the teaching of mathematics ONLINE
Engaging All Students community ~ http://connectwith.engaging.aamt.edu.au
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Connect with Maths~ Teaching maths through problem solvingRenee Hoareau
Connect with Maths Early Years Learning in Mathematics community
Teaching Maths Through Problem Solving: Facilitating Student Reasoning
Presenter: Louise Hodgson
This session will focus on teacher actions, which promote problem solving and reasoning in early years classrooms. We will workshop some tasks and have opportunities for discussion.
Connect with Maths ~ supporting the teaching of maths ONLINE
Join a Connect with Maths community today http://www.aamt.edu.au/Communities
AAMT website: http://www.aamt.edu.au
This Connect with Maths Early Years Learning in Mathematics community webinar discusses the importance of talk as part of a quality mathematical learning environment for young children. Denise makes links to the Early Years Learning Framework and the Australian Curriculum and share some ideas for facilitating mathematical talk with young children.
Connect with Maths ~Maths leadership series- Session 3- the right knowledgeRenee Hoareau
Connect with Maths ~Maths leadership series- Session 3- the right knowledge presented by Rob Proffitt-White
The right knowledge – A clear valuing and understanding of mathematical content, the connections and a working knowledge of the proficiency strands underpins successful teaching
This workshop targets teachers and school leaders and aims to upskill their assessment literacy by:
• Creating cognitive activation tasks that promote critical thinking in all students
• Ensuring a consistent and shared responsibility for numeracy transfer
• Differentiating tasks through a focus on the proficiency strands
• Classifying the different problem solving types.
Connect with Maths ~ supporting the teaching of mathematics ONLINE
Engaging All Students community ~ http://connectwith.engaging.aamt.edu.au
Teacher Effectiveness Impacts Student Success in PreK and Kindergarten MathETA hand2mind
Core PD 'Where's the Math?' course on early childhood math professional development, by Juanita V. Copley, Ph.D., focuses on equipping teachers with the content knowledge and instructional strategies to ensure that young children encounter good mathematics instruction in their early years of schooling.
PSLE Mathematics Seminar
Association of Mathematics Educators
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Nanyang Technological University
This seminar was conducted at Singapore Polytechnic.
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3 april '13 (everyone) on Singapore Maths for ICBB / PSLE Math
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
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
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.
17.
18.
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.
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
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.