Use assessment to build on pupils' existing knowledge and understanding

1

Assessment should be used not only to track pupils' learning but also to provide teachers with information about what pupils do and do not know
This should inform the planning of future lessons and the focus of targeted support
Effective feedback will be an important element of teachers' response to assessment
Feedback should be specific and clear, encourage and support further effort, and be given sparingly
Teachers not only have to address misconceptions but also understand why pupils may persist with errors
Knowledge of common misconceptions can be invaluable in planning lessons to address errors before the arise

Use manipulatives and representations

2

Manipulatives (physical opbjects used to teach maths) and representations (such as number lines or graphs) can help pupils engage with mathematical ideas
However, manipulatives and representations are just tools: how they are used is essential
They need to be used purposefully and appropriately to have an impact
There must be a clear rationale for using a particular manipulative or representation to teach a specific mathematical concept
Manipulatives should be temporary; they should act as a 'scaffold' that can be removed once independence is achieved

Teach pupils strategies for solving problems

3

If pupils lack a well-rehearsed and readily available method to solve a problem they need to draw on problem-solving strategies to make sense of the unfamiliar situation
Select problem-solving tasks for which pupils do not have ready-made solutions
Teach them to use and compare different approaches
Show them how to interrogate and use their existing knowledge to solve problems
Use worked examples to enable them to analyse the use of different strategies
Require pupils to monitor, reflect on, and communicate their problem solving

Enable pupils to develop a rich network of mathematical knowledge

4

Emphasise the many connections between mathematical facts, procedures and concepts
Ensure that pupils develop fluent recall of facts
Teach pupils to understand procedures
Teach pupils to consciously choose between mathematical strategies
Build on pupils' informal understanding of sharing and proportionality to introduce procedures
Teach pupils that fractions and decimals extend the number system beyond whole numbers
Teach pupils to recognise and use mathematical structure

Develop pupils' independence and motivation

5

Encourage pupils to take responsibility for, and play and active role in, their own learning
This requires pupils to develop metacognition - the ability to independently plan, monitor and evaluation their thinking and learning
Initially, teachers may have to model metacognition by describing their own thinking
Provide regular opportunities for pupils to develop metacognition by encouraging them to explain their thinking to themselves and others
Avoid doing too much too early
Positive attitudes are important, but there is scant evidence on the most effective ways to foster them
School leaders should ensure that all staff, including non-teaching staff, encourage enjoyment in maths for all children

Use tasks and resources to challenge and support pupils' mathematics

6

Tasks and resources are just tools - they will not be effective if they are used inappropriately by the teacher
Use assessment of pupils' strengths and weaknesses to inform your choice of task
Use tasks to address pupil misconceptions
Provide examples and non-examples of concepts
Use stories and problems to help pupils understand mathematics
Use tasks to build conceptual knowledge in tandem with procedural knowledge
Technology is not a silver bullet - it has to be used judiciously and less costly resources may be more effective

Use structured interventions to provide additional support

7

Selection should be guided by pupil assessment
Interventions should start early, be evidence-based and be carefully planned
Interventions should include explicit and systematic instruction
Even the best-designed implementation will not work if implementation is poor
Support pupils to understand how interventions are connected to whole-class instruction
Interventions should motivate pupils - not bore them or cause them to be anxious
If interventions cause pupils to miss activities they enjoy, or content they need to learn, teachers should ask if the interventions are really necessary
Avoid 'intervention fatigue'. Interventions do not always need to be time-consuming or intensive to be effective

Support pupils to make a successful transition between primary and secondary school

8

There is a large dip in mathematical attainment and attitudes towards maths as children move from primary to secondary school
Primary and secondary schools should develop shared understandings of curriculum, teaching and learning
When pupils arrive in Year 7, quickly attain a good understanding of their strengths and weaknesses
Structured intervention support may be required for Year 7 pupils who are struggling to make progress
Carefully consider how pupils are allocated to maths classes
Setting is likely to lead to a widening of the attainment gap between disadvantaged pupils and their peers, because the former are more likely to be assigned to lower groups

Maths (MA)

Use assessment to build on pupils' existing knowledge and understanding

Use assessment to build on pupils' existing knowledge and understanding

1

Use manipulatives and representations

Use manipulatives and representations

2

Teach pupils strategies for solving problems

Teach pupils strategies for solving problems

3

Enable pupils to develop a rich network of mathematical knowledge

Enable pupils to develop a rich network of mathematical knowledge

4

Develop pupils' independence and motivation

Develop pupils' independence and motivation

5

Use tasks and resources to challenge and support pupils' mathematics

Use tasks and resources to challenge and support pupils' mathematics

6

Use structured interventions to provide additional support

Use structured interventions to provide additional support

7

Support pupils to make a successful transition between primary and secondary school

Support pupils to make a successful transition between primary and secondary school

8

General

General Maths Information