Read the extended quote on the following slide from the Cockcroft Report of 1982, written well before the national curriculum came into existence. The quote is discussing maths with mainstream children and is not concerned with those with learning difficulties. Nevertheless, it makes salutary reading.
Mathematics is a difficult subject both to teach and to learn.
One of the reasons why this is so is that mathematics is a hierarchical subject. This
does not mean that there is an absolute order in which it is necessary to study the
subject but that ability to proceed to new work is very often dependent on a sufficient
understanding of one or more pieces of work which have gone before. Whether or not
it is true, as is sometimes suggested, that each person has a 'mathematical ceiling'
(and so far as we are aware no research has been undertaken to establish whether or
not this is the case), it is certainly true that children, and adults, learn mathematics
at greatly differing speeds. A concept which some may comprehend in a single lesson
may require days or even weeks of work by others, and be inaccessible, at least for
the time being, to those who lack understanding of the concepts on which it depends.
This means that there are very great differences in attainment between
children of the same age. A small number reach a standard which enables them to study mathematics at degree level but many others have time to advance only a very short distance along the mathematical road during their years at school. Because of the hierarchical nature of mathematics these pupils do not reach a position from which they are able to tackle the more abstract branches of the subject with understanding or hope of success, though some can and do continue their advance after they have left school.
Department of Education and Science, 1982
What can we take from this quote and how can we apply it to those with SLD?
For pupils with SLD which of the following positions do you hold and why?
- We should teach mathematics through the national curriculum and the national numeracy strategy.
- We should teach mathematics through other subjects.
- We shouldn't teach mathematics at all.
- Another position?
Is mathematical literacy possible for those working consistently on the p-scales (below level 1 of the national curriculum)?
Mathematical literacy has been defined as:
An individual's capacity to identify and understand the role that
mathematics plays in the world, to make well-founded judgments and to use and engage
with mathematics in ways that meet the needs of that individual's life as a constructive,
concerned and reflective citizen.
If the answer to the previous question is no, should we be teaching mathematics as a discrete subject?
Imray (2005) and Lacey (2009) have variously defined the difficulties facing a person with severe learning difficulties as:
- Communication. Numerous writers (for example, Robbins, 1991; Paterson et al, 2006; Porter, 2010) have pointed out that because so much formal maths is related to linguistic ability, those with communication problems are very likely to be at a serious natural disadvantage in learning.
- Difficulties in understanding abstract concepts.
- Difficulties in concentration – especially in holding more than a single piece of information at a time and multi-tasking, so often a requirement of problem solving.
- Information processing difficulties in moving things from short- to long-term memory.
- Inefficient and slow information processing speed.
- Little general knowledge so pupil requires constant contextual referencing for learning to take place.
- Poor strategies for thinking and learning.
- Difficulties with generalisation and problem solving. In the same way that context plays an essential role in aiding the understanding of specific words in particular and language in general (Locke, 1999, Hinchcliffe, 2001), so context is essential for mathematical understanding (Porter, 2010).
Headteachers of SLD schools noted that 'average' ability levels had declined markedly during the 10 years from 1996 to 2006. There was no firm research relating to this, but it was a common enough theme for it to be part of an Ofsted SEND Review (Ofsted, 2006)
A new generation of children with learning difficulties, described by Barry Carpenter as having CLDD (Carpenter, 2010; Carpenter et al, 2010), are presenting with more diverse, fractured and complex difficulties. They are apparent across all sectors, both in mainstream and special schools. Co-morbidity is commonplace, especially in the areas of ASD and ADHD, but also in children who present with extremely spiky profiles, often with particular difficulties in mathematics.
Carpenter, B. (2010) Curriculum Reconciliation and Children with Complex Learning Difficulties and Disabilities. London: Specialist Schools and Academies Trust.
Carpenter, B., Cockbill, B., Egerton, J. and English, J. (2010) Children with complex learning difficulties and disabilities: developing meaningful pathways to personalised learning. The SLD Experience. 58:3-10.
Hinchcliffe V (2001) Tailoring Literacy to Pupils with Special Needs: Bespoke or 'Off the Peg' Strategies? The SLD Experience. 31: 6-9.
Imray, P. (2005) Moving Towards Simple, Understandable and Workable Definitions of SLD and PMLD. The SLD Experience. Issue 42.
Lacey P. (2009) Developing Thinking and Problem Solving Skills. The SLD Experience. Issue 54.
Locke, A. (1999) Why not to teach the literacy hour. The SLD Experience. 24: 2-4.
OECD (2006) PISA 2003 Sample Questions quoted in Clausen-May T (2007) International mathematics tests and pupils with special educational needs. British Journal of Special Education. 34 (3) 154-161.
Ofsted (2006) Inclusion: does it matter where pupils are taught? (HMI 2535) London. Ofsted.
Paterson, S. J., Girelli, L., Butterworth, B. and Karmiloff-Smith, A. (2006) Are numerical impairments syndrome specific? Evidence from Williams syndrome and Down's syndrome. Journal of Child Psychology and Psychiatry. 47 (2) 190-204.
Porter, J. (2010) Developing number awareness and children with severe and profound learning difficulties. The SLD Experience. 57: 3-7.
Robbins, B. (1991) Mathematics for All in Ashdown, R., Carpenter, B., and Bovair, K. (eds) The Curriculum Challenge. London. Falmer Press.
DES (1982) Mathematics Counts (The Cockfroft Report). London. HMSO.