Practical support for identifying and meeting need

Cognition and learning

Here are some key principles to bear in mind when supporting mathematical learning:
(Taken from Big ideas in mastery ©NCETM)

Coherence

Small steps are easier to take.
Focus on one key point each lesson allows for deep and sustainable learning.
Certain images, techniques and concepts are important pre-cursors to later ideas. Getting the sequencing of these right is an important skill in planning and teaching for mastery.
When something has been deeply understood and mastered, it can and should be used in the next steps of learning.

Representation and structure

The representation needs to pull out the concept being taught, and in particular the key difficulty point. It exposes the structure.
In the end, they need to be able to do the maths without the representation.
A stem sentence describes the representation and helps them move to working in the abstract (“ten tenths is equivalent to one whole”) and could be seen as a representation in itself.
There will be some key representations which they will meet time and again.
Pattern and structure are related but different: They may have seen a pattern without understanding the structure which causes that pattern.

Variation

The central idea of teaching with variation is to highlight the essential features of a concept or idea through varying the non-essential features.
When giving examples of a mathematical concept, it is useful to add variation to emphasise: What it is (as varied as possible) and what it is not.
When constructing a set of activities/questions it is important to consider what connects the examples; what mathematical structures are being highlighted?
Variation is not the same as variety – careful attention needs to be paid to what aspects are being varied (and what is not being varied) and for what purpose.

Fluency

Fluency demands more of learners than memorisation of a single procedure or collection of facts. It encompasses a mixture of efficiency, accuracy and flexibility.
Quick and efficient recall of facts and procedures is important for learners’ to keep track of sub problems, think strategically and solve problems.
Fluency demands the flexibility to move between different contexts and representations of mathematics, to recognise relationships and make connections and to make appropriate choices from a whole toolkit of methods, strategies and approaches.

Mathematical thinking

Mathematical thinking is central to deep and sustainable learning of mathematics.
Taught ideas that are understood deeply are not just ‘received’ passively but worked on by the learner. They need to be thought about, reasoned with and discussed.
Mathematical thinking involves: Looking for pattern in order to discern structure, looking for relationships and connecting ideas as well as reasoning logically, explaining, conjecturing and proving.

Learning environment

Concrete resources are provided, e.g. number lines, objects, counters, Numicon, Cuisenaire rods and Dienes. Click here for KS3>.
Explicit teaching of strategies to minimise the impact of limited working memory> when completing calculations, e.g. use of a whiteboard for jotting down key information.
Opportunities to teach a concept back to an adult/peer to check understanding.
Time to jot down key points/calculations.
Opportunities to apply their skills and to build their mathematical language in practical situations (Primary> and KS3> examples).
Discussion of mathematical investigations> to inform the development of mathematical language and to enable them to analyse and understand what they have seen.
A differentiated maths help resource pack, including vocabulary mats>, is provided.

Access to the curriculum

Quality First multisensory teaching is in place that focuses on intent, implementation and impact.
Structured programmes are in place, e.g. First Class @ Number.
Repetition and reinforcement to embed the meaning of new concepts before moving on.
An understanding of maths facts is reinforced using diagrams and models.
Songs, games, stories>, rhymes and mnemonics are used to highlight procedures.
Exploit the many forms of mathematical representation, (e.g. pie charts, number lines, abacus and bar charts) and the connections between them. (Primary> and KS3> examples).
Multiple examples of new concepts provided with examples taken from real life rather than talking in the abstract.
New learning is linked with what they already know at the start of the lesson.

Learning environment

A profile of maths skills, including strengths and areas for development, is created.
A chart/resource to show the focus of each lesson and how successive lessons or topics link together to develop an area of mathematics work. This could include symbols, images or objects to make it more accessible.
Time to discuss mathematical errors/misconceptions> to prevent them becoming inhibited by fear of making mistakes. Emphasise the importance of processes and problem solving to avoid the culture of getting the ‘right answer’.
Resources, such as times tables and number squares, to allow access to higher levels of math.
Mnemonics and visual prompt cards to assist in the memorising of rules, formulae and tables.
Graphic organisers> are provided to break down activities into smaller steps.

Access to the curriculum

Reinforcement and constant rehearsal of specific skills through appropriate game and problem solving> activities.
The same concept or process is presented with a variety of words, symbols, models and images.
Mathematical symbols are presented in different colours to prevent confusion between symbols where a difference in orientation is all that distinguishes one from another, e.g. + and x.
ICT> is available to enable them to switch quickly between different representations.
Targets set by a specialist teacher.

Learning environment

Attention is given to celebrate strengths in other areas.
There is direct intervention to target identified needs.
Opportunities to make choices are woven into the activities, e.g. selecting numbers and devising calculations.
Regular checks to ensure understanding.
Kinaesthetic and visual supports in place, e.g. bead strings to teach place value and calculations.
Pre-prepared formats provided for calculations, graphs and tables.
Recording using numeral cards or circling numerals on number lines rather than writing them.

Access to the curriculum

Evidenced based 1:1 structured intervention in place to target gaps and reinforce concepts (e.g. Every Child Counts) with frequent opportunities for overlearning.
Timetabled sessions to revise and consolidate what has been learned that includes game based activities with concrete apparatus.
Precision Teaching> is used.
Mathematics Plan set by a specialist teacher.
Highly skilled/trained staff that are familiar with the needs of pupils with mathematical needs.

University of Cambridge