Maths at Hardwick

Hardwick Primary School follow the Singapore Maths approach to the teaching of Mathematics. One of the key learning principles behind the approach is the concrete pictorial abstract approach, often referred to as CPA.

The concrete-pictorial-abstract approach, based on research by psychologist Jerome Bruner, suggests that there are three steps (or representations) necessary for pupils to develop understanding of a concept. Reinforcement is achieved by going back and forth between these representations.

Concrete Representation

The enactive stage - a pupil is first introduced to an idea or a skill by acting it out with real objects. In division, for example, this might be done by separating apples into groups of red ones and green ones or by sharing 12 biscuits amongst 6 children. This is a 'hands on' component using real objects and it is the foundation for conceptual understanding.

Pictorial Representation

The iconic stage - a student has 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 symbolic stage - a student is now capable of representing problems by using mathematical notation, for example: 12 ÷ 2 = 6. This is the ultimate mode, for it "is clearly the most mysterious of the three."

Maths – No Problem! textbooks

At Hardwick Primary School we are using ‘Maths - No Problem!’ text books.

Maths - No Problem! is a series of textbooks and workbooks written to meet the requirements of the National Curriculum.

The focus of the series is on teaching to mastery. This research-based approach emphasises problem solving and utilises pupils' core competencies to develop a relational understanding of mathematical concepts.

Consultant and Author: Dr. Yeap Ban Har

UK Consultant: Dr. Anne Hermanson

Authors: Dr. Foong Pui Yee, Lim Li Gek Pearlyn, Wong Oon Hua

The ‘Working - Wall’ 

At Hardwick Primary School we believe the classroom environment is one of the most powerful teaching aids in our class. It should be visually stimulating and lively and should help to develop and engage children's learning. All classroom environments provide the ‘Maths Working-Wall’ at an appropriate level for the age of the children working in that classroom.

The working-wall is a display of the learning process and evolves as each day progresses. It is not static. The purpose of the working wall is to support children’s independence. It evolves as a unit of work unfolds, and is not intended to be a tidy display of finished work.

The working-wall should support independent working and learning: think of the working -wall as an extra adult in the classroom. It can help support children who become stuck and direct children to new tasks when they have self-assessed that they have successfully finished an activity. The working-wall can also support whole class and guided group teaching: models and images, key vocabulary and useful prompts are displayed and referred to by the teacher to support children in their understanding.

Below are examples of Working Walls from Reception to Year 6.

At Hardwick we believe that every child can master an understanding and love of Maths with the right kind of teaching and support.