Pedagogical Approaches in Singapore Mathematics

3rd December 2013

Programme09:30 – 10:15

1 An Introduction To The Math Curriculum In Singapore.

2 Singapore Math

3 Learning Styles

4 CPA Approach

10:15 – 10:30

5 Refreshments

10:30 – 11:30

6 VisualisationBar Model DrawingPatterns

An Introduction To The Math Curriculum In Singapore.

Let’s start with a story….

How is this related to Math?

The Mathematical Problem Solving Framework

Ministry of Education, (2013), Primary Mathematics Teaching and Learning Syllabus, Retrieved from http://www.moe.gov.sg/education/syllabuses/sciences/files/maths-primary-2013.pdf

Emphasis on Problem Solving

Problem solving must ‘be the focus of school mathematics’.

An Agenda for Action, USA, (1980)

Problem solving is ‘at the heart of mathematics.’

Cockcroft Report, UK, (1982)

‘The learning of mathematics also provides an excellent vehicle to train the mind, and to develop the capacity to think logically, abstractly, critically and creatively.’

Ministry of Education, (2013), Primary Mathematics Teaching and Learning Syllabus, Retrieved from http://www.moe.gov.sg/education/syllabuses/sciences/files/maths-primary-2013.pdf

• In 1960, the general passing rate for the national examinations was 45%.

• In 2013, the general passing rate for the national examinations was 97.5%.

How did we fare?

TIMSS 2011

‘In TIMSS 2011 students from Singapore were ranked in the first two positions for both the subjects and grades.’

National Institute of Education, Singapore, An Overview of TIMSS 2011, Retrieved from http://www.nie.edu.sg/files/cics/An%20overview%20of%20TIMSS%202011.pdf

Singapore Math

What is Singapore Maths?

It is the way we teach math to give every child the opportunity to succeed.•Learners who are struggling will learn enough to move on to the next level.•Learners who are average will be able to move on to a higher level.•Learners who are advanced will be challenged.

How Did We Do It?• Professional development of teachers.• Consistent pedagogies that facilitate

learning.• Emphasis on problem solving• High stakes national examinations that

include problem solving.

The Goal of the Singapore Math Curriculum

‘The overarching goal of the mathematics curriculum is to ensure that all students will achieve a level of mastery of mathematics that will serve them well in life, and for those who have the interest and ability, to pursue mathematics at the highest possible level.’Ministry of Education, (2013), Primary Mathematics Teaching and Learning Syllabus, Retrieved from http://www.moe.gov.sg/education/syllabuses/sciences/files/maths-primary-2013.pdf

Syllabus Design

• The Spiral Curriculum.• Modelled after Jerome Brunner’s Constructivist Theory.• Learners construct new ideas or concepts based on

their current or past knowledge.• Curriculum organized in a spiral manner so that

students continually build upon what they have already learned.

Learning Styles.

Learning Styles

• Tactile Learners

• Visual Learners

• Verbal/ Auditory Learners

Tactile Learners

• Also referred to as the Bodily-Kinesthetic learning style.

• Students in this category tend to• Be the ones who cannot sit still in class.• Be physically active and very involved in sports.• Be the ones who get bored in a lecture.• Would rather take an engine apart then try to put it back

together without reading the manual.

Visual Learners

• Also referred to as the Spatial learning style.• Students in this category tend to

• Doodle away in class on their notepad while the teacher is talking. Occasionally, they will be ‘dreaming’.

• Have very good spatial sense which in turn gives them a very good sense of direction.

• Be very good with their art work.• Be very attracted to colors, images and pictures.

Auditory Learners

• Also known as the Aural learning style or referred to as the Verbal Learner.

• Students in this category tend to• Be the teacher’s pet because he is always attentive in class,

reads all the notes and does all the homework.• Be very good with music and anything rhythmic.• Like reading and writing.

How are we going to be able to engage students with different learning styles in a math lesson, in the same classroom?

How are we going to do ALL that moving, drawing and talking in a math lesson?

The answer lies in the pedagogy.

CPA Approach

Common Pedagogical Approach

• CPA approach• Built upon Jerome Brunner’s Theory of Representation.

• In order for children to learn anything abstract, they will need to be moved from the concrete representation then to the pictorial representation then the abstract representation.

• Not confined to the learning of mathematics.

Enactive Representation

Iconic Representation

Symbolic Representation

The CPA Approach

• A tool for understanding of concepts before procedural fluency.

• A tool to lead up to visualisation.• A tool to lead to the identification of

patterns.• Eventually, leads to the solving of complex

word problems.

CPA Approach

How are you going to teach ? 21

21

CPA Approach

• Concrete materials to allow for tactile

learners to get a feel of what is .

• Pictorial and Abstract representations are

used concurrently for learners to progress

to abstract understanding.

21

21