Numeracy and mathematics are areas that cause confusion and anxiety for many learners. SENCO Week looks at ways in which teachers can identify and support such pupils in the classroom
Pupils have difficulties with numbers and numerical operations for a variety of reasons, including inadequate or inappropriate first teaching, absence from school resulting in gaps in mathematics learning, and lack of early ‘mathematical’ and language experience in the home. Some experience specific difficulties which may lead to a diagnosis of dyscalculia, or be connected to the learner’s dyslexia (more on this next week). Whatever the causes, the most common areas of concern involve difficulties with:
- the language of mathematics
- learning strategies (including suitable counting strategies) for working out calculations
- choosing appropriate strategies to use in different operations
- understanding place value.
Research has identified three core skills that children need to develop before they can really start to progress with maths: counting; the equality principle; and the language of maths.
Counting
Many children have this skill by the time they start school, but for some, it is a rote exercise that they don’t really understand, often failing to make a one-to-one correspondence between the spoken number ‘name’ and the object. In these cases, the skill must be explicitly taught and practised. Moving beyond the simple level of counting a single group of objects, the child then learns to add together two small groups. This can be done in several ways:
- start with the largest number and ‘count on’ (the ‘min’ strategy)
- retrieve a known number fact from memory (no need to count)
- retrieve a number fact from memory and adjust it to suit (5+6 can be worked out by recalling that 5+5=10, and adding one more to reach 11).
Whereas many children learn quite quickly which method is the fastest/easiest to use, some do not; they can stick at the ‘count all’ stage and need to be shown how to move on to more efficient strategies.
The equality principle
Children may learn how to add together two and three, without really understanding the principle at work. They need to know that 2+3=5 is an equation: it is balanced on both sides. The question, or number story, can be presented in different ways: 2+?=5, ?+3=5 or 2+3=?, but is still the same question. The = sign means ‘the same as’ rather than, as is often thought, meaning ‘makes the answer’. If they understand this, they have a much better chance of moving on successfully to algebra when the time comes.
Mathematical language
Children develop their understanding of mathematical concepts not only through their actions, but also by listening and talking with others. Language is extremely important in this, and learners with general language difficulties will have difficulty in interpreting situations, finding information, conveying meaning and remembering. They will be slow to move from understanding concrete experiences of the ‘real world’ to the more abstract language used to describe and quantify in maths. For these pupils, the introduction of mathematical vocabulary has to be done very carefully, with lots of opportunities for practice and checking. Lack of understanding of terms such as plus, minus, difference, take-away, carry, borrow, exchange etc. can be the cause of early failure with number work. Beginning work on standardised measures and ‘mass’, will not be effective with a child who confuses ‘heavy’ with ‘big’.
As SENCO, you can support colleagues in acknowledging these issues (not only in Foundation Stage and KS1 classes) and finding ways to address them. The list below might provide a useful starting point:
- link mathematics to familiar and relevant contexts
- avoid moving a child onto higher level tasks before easier levels have been fully understood
- give pupils explicit instruction in strategy and then guide/support their practise
- use a variety of objects, images and models
- encourage children to discuss and explain in order to support the development of their mathematical reasoning
- encourage them to make choices about methods used
- use peer tutoring − a child can often explain in terms more readily accessible to a classmate
- support accurate recording by providing squared paper/prepared formats
- establish a routine of ‘estimate − calculate − check’
- display maths terms and symbols on the walls, using particular colours for different operations, eg all blue for subtraction
- take time to explain vocabulary and check understanding
- use number squares with alternate rows shaded for ease of use
- use small numbers to introduce new concepts
- provide time for practice and consolidation at each stage.
This e-bulletin issue was first published in March 2008
About the author: Linda Evans is the author of SENCO Week. She was a teacher/SENCO/adviser/inspector, before joining the publishing world. She now works as a freelance writer, editor and part-time college tutor.