1. Parents’ Information Evening Real Life Learning Academy Trust
Singapore Maths
Parents’ Information Evening
Real Life Learning Academy Trust

2. What is Singapore maths?
Process of teaching and learning that is based on decades of educational theory and research.
Singapore is consistently one of the top performing countries in the World for maths.
99% of pupils in Singapore opt to take A’Level maths because “it is easy.”
The system is referred to as the ‘Singapore method’ as it is an approach that we take to teaching maths.

3. Historic picture Singapore was:
Lagging behind in the PISA tables (Programme for International Student Assessment) early 1980s
Qualifications and employment was necessary in this country to avoid the recession compared to other Asian countries.
Maths was taught through the ‘English’ method:
Procedure, memorisation, computation

4. Action Undertook wide ranging study of educational theory
Development of a system that:
Challenges top third
Enables middle third to perform highly
Allows lower third to obtain competency and does not
disadvantage them in any way

5. Singapore method
The key principles of the Singapore Maths method are based on the works of several educational researchers from Vygotsky, Skemp, Piaget, Bruner to name a few. ‘Learning is not because my teacher told me so. Learning is because I figured it out.’ (Piaget)

6. Concrete, Pictorial and Abstract
In his research on the development of children (1966), Jerome Bruner (child psychologist) proposed three modes of representation: concrete or action-based, pictorial or image-based and abstract or language-based CPA
CONCRETE
Concrete is the “doing” stage, using concrete objects to model problems, this brings concepts to life by allowing children to experience and handle physical objects themselves. Every new abstract concept is learned first with a “concrete” or physical experience.
For example, if a problem is about adding up two baskets of fruit , the children might first handle actual fruit before progressing to handling counters or cubes which are used to represent the fruit.

7. Concrete, Pictorial and Abstract
Pictorial is the “seeing” stage, using representations of the objects to model problems. This stage encourages children to make a mental connection between the physical object and abstract levels of understanding by drawing.
Building or drawing a model makes it easier for children to grasp concepts they may find more difficult, such as fractions, as it helps them visualise the problem and make it more accessible.

9. Concrete, Pictorial, Abstract
Only once a child has demonstrated that they have a solid understanding of the “concrete” and “pictorial” representations of the problem, can the teacher introduce the more “abstract” concept.
Children are introduced to the concept at a symbolic level, using only numbers, notation, and mathematical symbols.
3 + 2 = 5

10. The lesson
methods/concrete-pictorial-abstract/
This video shows how CPA is implemented into a Singapore maths lesson.
Pictorial

11. An example lesson....
Each lesson begins with an anchor task (real life story or problem)
Exploration: Children would spend around 10 minutes exploring this problem, often working collaboratively with a partner, discussing and drawing out ideas.
Practical, concrete investigation draws the maths out (apparatus)
Communication and peer support are a key factor
Visualisation is central (imagine) and pictorial representation (show me)
Structure: After observing the children and their ideas, the teacher will then ask them to share their thoughts as a class and bring methods and explanations together. It is also a time to steer the children in the right direction if they need more guidance. .
Challenged to communicate methods in as many different ways as possible
Explanations and reasoning are crucial parts to the lessons with good mathematical vocabulary. (differentiation)

12. Start of a KS2 lesson –Anchor task.

13. Share methods/ideas.
Challenge: What if there were between 40 and 100 pebbles?
What pattern do we notice?
Would 144 be a common multiple, why?

14. Journaling
Children now record their understanding of the problem and how they solved it inside their own Maths Journal.
Children are encouraged to find more than one way to solve the problem, often driven by the ideas discussed in the lesson
Consistency across the school helps children develop a structured recording method.

15. KS1
An example of pupil’s work for this lesson.

16. There are other examples of journaling on your tables for KS1 and KS2 along with some example textbooks and workbooks.

17. How the lesson will then develop
Guided practise and individual work then follow for the remainder of the lesson.

18. Where are we at in RLLAT?
Initial research began over a year ago when the National Curriculum emphasis became more focused on problem solving and reasoning.
We want our children to understand the relevance of maths in the lives they lead.
Training for staff began in September ready for launch this academic year.
All year groups from 1 – 6 are implementing this method
Currently working alongside Foundation Stage staff to develop the Early Years Curriculum in-line with the approach
Qualified specialists are support us throughout the year.

19. What impact has it had so far?
Initial feedback from our pupil voice has been very positive with comments such as:
Staff thoroughly enjoyed the training and saw maths in a different light. The new approach enables pupils of all abilities to make progress, giving them independence in their own learning and allowing them to explore maths in a purposeful, problem solving context.

20. HOW does this prepare our children for the national tests?
KS1 – Arithmetic paper and Reasoning Paper
KS2 – Arithmetic paper and 2 Problem Solving and Reasoning Papers
National Curriculum Purpose of Study states:
‘A high quality mathematical education therefore provides a foundation for understanding the world, the ability to reason mathematically, an appreciation of the beauty and power of mathematics, and a sense of enjoyment and curiosity about the subject.’

21. HOW does this prepare our children for the national tests?
National Curriculum Aims:
become fluent in the fundamentals of mathematics, including through varied and frequent practice with increasingly complex problems over time, so that pupils develop conceptual understanding and the ability to recall and apply knowledge rapidly and accurately.

22. reason mathematically by following a line of enquiry, conjecturing relationships and generalisations, and developing an argument, justification or proof using mathematical language
can solve problems by applying their mathematics to a variety of routine and non-routine problems with increasing sophistication, including breaking down problems into a series of simpler steps and persevering in seeking solutions.

23. Thank you Many thanks for your attendance this evening.
We hope we have adequately introduced the Singapore Maths approach and underlined why it suits our school.