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. In KS1 and KS2 we follow the White Rose 2.0 scheme of learning for maths which includes every objective from the Primary National Curriculum (2014) and breaks each unit down into small steps.
In addition, we supplement using materials from a number of sources, notably:
- 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.
Minute Maths - This step by step programme builds up confidence and speed in rapid recall of addition and subtraction facts in KS1
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 children in KS2 and then KS1 over subsequent years.
Year Group Expectations
By the end of Y1 BRONZE Tables Master Certificate Know 2X,5X,10X tables instantly
By the end of Y2 SILVER Tables Master Certificate Know 3X,4X,8X tables instantly
By the end of Y3 GOLD Tables Master Certificate Know 6X, 7X, 9X tables instantly
By the end of Y4 SUPREME EXPERT Know all tables up to 12X12 instantly
To support and encourage learning these basic facts and other skills, all pupils are individually subscribed to Sumdog - an exciting online learning platform. Children can access Sumdog at home or at school. Teachers can set specific tasks, tailor the questions and monitor how children are progressing. Based around a variety of engaging games, children play against other children in school and around the world.