1. The History of Singapore Maths

2. Programme Based on Established Theories

3. Singapore Maths Teaching Approach

4. Singapore Maths 3-part lessons

5. Questions.

• In 1983 Singapore had poor maths performance in the international league tables and it was ranked 16th out of the 26 countries participating in the SIS study.

• The government realised that this is not good enough for an economy that was entirely depend on its human resources.

• The Singapore Ministry of Education decided to take the best practice research findings from the West and applied them to the classrooms with transformational results.

Programme Based on Established Theories The Based on recommendations from notable experts such as Jerome

Bruner, Richard Skemp and Zoltan Deines.

Bruner: Research on the development of children (1966), Bruner proposed three modes of representation: concrete or action-based (enactive representation), pictorial or image-based (iconic representation) and abstract or language-based (symbolic).

Introduced the term ‘scaffolding’ - to describe how children build on the information they have already mastered.

Bruner proposed the spiral curriculum: a teaching approach in which each subject or skill area is revisited and the material is presented in a logical sequence.

Initially a concept is enacted with “concrete” materials, later it is represented by models (pictures) and then by abstract notation (such a plus or equals sign).

These learning theories are the basis of the Concrete Pictorial Abstract

approach which runs throughout the Singapore Maths Approach.

Richard Skemp - introduced the concept of ‘Relational Understanding

and Instrumental Understanding’.

Skemp distinguishes between the ability to perform a procedure

(instrumental) and the ability to explain the procedure (relational) and

argues that these are two different methods of learning – relational and

instrumental.

Singapore Maths aims for pupils to progress beyond seeing mathematics as

a set of rules or procedures so that they have a relational understanding.

Zoltan Dienes - has introduced the idea of systematic variation. The

idea is that lessons are varied through a series of examples that deal with

the same problem or topic.

Learning of one particular mathematical concept is varied, where the

concept is the same but the pupils are presented with different ways to

perceive a problem and use different ways to to represent the same

concept.

The Singapore Maths approach presents this in a systematic way to ensure

pupils comprehend what they are learning.

Concrete representation The students are first introduced to an idea or a skill by acting it out with real objects. For example in division, sharing 15 sweets amongst 3 children. This is a 'hands on' activity using real objects and it is the foundation for conceptual understanding.

Pictorial representation The students have sufficiently understood the hands-on experiences performed and can now relate them to representations, such as a diagram or picture of the problem. In the case of a division exercise this could be the action of circling objects.

Abstract representation The students are capable of representing problems by using mathematical notation/symbols, for example: addition, subtractions, multiplications or division.

The Same Concept using the CPA Approach

Singapore Textbooks & Workbooks • Textbook 1A and Workbook 1A • Textbook 1B and Workbook 1B

Three-Part Lessons

The Singapore maths textbook is designed based

on 3 parts lesson format.

First Part:

Anchor Task – In the book called is ‘In Focus’. This is were the students work in groups to explore a single problem. It is for the students to show what they know and for the teacher to extend their understanding.

Second Part: Guided Practice – The students practice the work under the guidance of the teacher and it is characterised by talking/discussions and for the teacher to further the student’s understanding OR to support the students if they are struggling. Not much writing at this stage and more focus on practical hands on activities.

Final Part: Independent Practice - At this stage the students move onto independent work to complete the worksheets photocopied from the textbooks. Independent activities can be planned according to the three approaches: Concrete - once the students are confident at this stage they can move onto the Pictorial and only when they have mastered both of these stages, the students can move onto the Abstract work. Students will always end the lesson with independent practice whether it is concrete , pictorial or abstract.

• This approach has changed the children’s attitude towards maths from being less confident and perhaps disliking the subject, to enjoying maths, having fun in problem solving and having high self-esteem!

• The children were able to build their mathematical fluency without the need of rote learning or reciting formulas that they don’t understand.

• It enhanced the children’s learning and understanding of the different topics within the maths curriculum.

How Can I Help My Child with Maths at Home?