Progression in Learning Maths
Generally speaking, learning, and especially learning in maths, moves through three phases:
- Concrete - this means that you actually do something, or move something or play with something, usually with your hands. In maths this could mean using counters, blocks or a number line.
- Pictorial - this means that you can show what you have done with your hands using pictures or diagrams.
- Abstract - this means that you can use symbols to show what you have done with your hands or pictures. You can also 'see' it in your head.
We use these developmental stages to support learning. So you would tend to see the youngest children (but not exclusively) doing maths with objects, talking about what they are doing, showing and sharing maths. As children get older, they will begin to write maths down, possibly as diagrams or pictures. Finally, when they are ready, maths will take on more numbers, 'sums', symbols and signs.
Our calculation policy shows in great detail how we use this sequence to develop the four operations of addition, subtraction, multiplication and division.
Maths Documents - Calculation Policy
Our planning and provision is very carefully thought through to ensure that each stage of learning builds on the firm foundations of what has gone before. Our planning structure has been derived and adapted from materials put together by the White Rose Maths Hub - a group of schools and maths professionals who focus on developing excellence in maths. We build on this structure using materials from a number of sources, notably:
- The White Rose Hub produce some of their own resources
- www.nrich.org - This resource was originally set up and run by Cambridge University.
- www.ncetm.org.uk - National College for Excellence in the Teaching of Mathematics
- www.atm.org.uk - The Association of Teachers of Maths
- www.mathletics.co.uk - This a comprehensive online learning platform for pupils but also contains a wealth of resources for teachers.
As mentioned above, practical handling of materials is a vital step in learning mathematic concepts. We use a number of learning aids - 'manipulatives' - to support children as they get to grips with number and calculation.
With the youngest children, we use Numicon materials. Each tile represents a different number and they can be combined and arranged to give a clear visual image for a number of maths concepts.
As children get older, we begin to use Dienes' Blocks which are particularly useful for understanding how our 10 based number system works, and for demonstrating how calculations work.
Once children have firmly grasped the 10's concepts with blocks, this enables them to work with Place Value Counters to represent numbers and calculations.
Basic Skills for Number
In our maths teaching, we aim to develop three main types of mathematical thinking and skill : -
- The ability to manipulate, recall and apply maths - FLUENCY
- The ability to solve maths-based tasks - PROBLEM SOLVING
- The ability to explain, justify, probe, apply logic - REASONING
We believe that, without a solid foundation in knowledge, recall and application of basic number facts, pupils will be held back in developing these forms of thinking. We put a lot of emphasis, therefore, on ensuring children know the addition and subtraction facts to 20 and the multiplication and division facts to 12X12.
Number Whizz - This step by step programme was devised by us and introduced as a pilot to our Year 2 in Sept 2016. Based on Numicon, this ensures children can accurately and rapidly recall number facts up to 20. Each step covers 5 number fact families.
Tables Master - Devised and introduced as a pilot in 2015/16 with the then Year 6 children, this similar step by step programme requires children to know their multiplication facts for each table instantly. To become a Tables Master, children have to complete all 144 tables facts, jumbled, up in a timed test. Presentation of the Tables Master certificate takes place in assembly - where children are expected to answer random questions instantly! This approach proved very successful and was rolled out to Year 5 and Year 4 children over the last academic year.
To support and encourage learning these basic facts and other skills, all pupils are individually subscribed to two online learning platforms. Children are able to access these platforms in lessons, at home or in clubs run by the school. Teachers can set specific tasks, tailor the question asked and monitor how children are progessing. Based around a variety of engaging games, children play against other children in school and around the world.
Assessment and Learning
We make sure that pupils know what we are trying to help them achieve. By sharing details of their learning with them, children can see how their learning is developing, what they have achieved and what their next steps need to be. This helps them to see the ‘bigger picture’ and to get interested in how they are learning, as well as what they are learning (metacognition).
For this reason, we use ‘ I Can’ sheets – which set out clearly for pupils, staff, parents/carers how children are doing and where they are going next.