Michael Farrell considers the mathematics disorder dyscalculia, and looks at ways of supporting students who struggle with its effects
Definition
Mathematics disorder/dyscalculia is defined as, ‘a condition that affects the ability to acquire mathematical skills. Dyscalculic learners may have difficulty understanding simple number concepts, lack an intuitive grasp of numbers, and have problems with learning number facts and procedures. Even if they produce the correct answer or use the correct method, they may do so mechanically and without confidence’ (Department of Education and Skills, 2001).
Curriculum and assessment and organisation
For pupils with mathematics disorder, levels of the curriculum may be lower than age-typical in areas where mathematics is a major component, such as the sciences. The balance of subjects may emphasise mathematics to encourage and support progress. Within subjects, the mathematics elements will be highlighted for support. Small steps of assessment may be used to demonstrate progress in mathematics.
Explicit systematic instruction, with numerous opportunities for students to respond and to talk through their thinking, appears to be helpful to students with mathematics disorder (eg Gersten, Chard, Jayanthi, Baker, Flojo, and Lee, under review). Therefore classroom and group organisation that facilitates this is likely to aid learning.
Pedagogy
Teaching prerequisite skills
The development of skills and understanding necessary in mathematics are hindered if there is not a secure basis of certain prerequisite skills: classification, number, length, area, volume, weight, position and movement. For example, among precursors of understanding weight is that the pupil grasps the conservation of weight, understanding that, if two malleable items weigh the same and one is then made into a different shape, it will still weigh the same as its partner. To teach this, the pupil might begin by reading his weight on scales when standing, then checking the reading when crouching to show that weight is constant. This develops into weighing items and changing their shape and then weighing them again to confirm their weight is the same (Poustie, 2001, pp 22-23).
General approachesSome pupils become anxious when expected to demonstrate competence applying mathematical skills (Battista, 1999). Sometimes difficulties with attention are exacerbated by stress and anxiety about doing mathematics. Reassuring the pupil and trying to make mathematics enjoyable perhaps using games can help reduce anxiety and help the pupil relax and therefore concentrate and attend better. Individual tuition can help ensure early success and reduce the anxiety about possible failure. Using concrete apparatus helps give the pupil experience and understanding of what is being done and a pupil with mathematics disorder may require consolidation using concrete items longer than most pupils. Number lines or a box of physical shapes that are labelled are examples. Concrete material such as Unifix blocks can be useful in developing understanding of computation and other mathematical understanding.
Mathematics and DCD
Bearing in mind the underlying difficulties associated with developmental coordination disorder (DCD) can suggest why certain difficulties arise in mathematics and how they might be tackled. For example because of such difficulties as orientation, the pupil with DCD may have problems understanding and using positional words and phrases such as ‘up’, ‘down’, ‘behind’ and ‘in front’ and linking them to different aspects of spatial relationships. These works need to be explicitly taught and linked with practical experience of the positions they convey. The teacher may begin by applying the words to the position of the pupil’s body, for example teaching the pupil positions such as standing ‘behind’ a tree or ‘in front’ of a tree. Miniature models are then used (a figure representing the pupil and a model of the tree) with the pupil manipulating these to develop and confirm understanding. Next, two-dimensional representations are used such as immediately observed digital photographs (of the pupil standing behind/in front of the tree) and drawings.
Mathematics and reading disorder
Difficulties associated with reading disorder that may relate to mathematics difficulty include: phonological difficulties, auditory perception and auditory processing difficulties; short-term verbal memory difficulties; and sequencing difficulties. For example, it is important that the teacher’s use of language in explaining mathematical relationships corresponds to the student’s comprehension level (Cawley et al, 2001). Difficulties with phonological representations and with auditory processing and auditory perception may make it hard for the pupil with reading disorder to develop a secure understanding of the language of mathematics.
The pupil may have difficulty in acquiring and using mathematical language such as ‘addition’, ‘place value’, ‘decimals’ and ‘fractions’, perhaps having limited experience of mathematical vocabulary receptively and expressively. The teacher can introduce and explain new words and display key words throughout the lesson for example on a board. Wall displays with key words as their focus can be built up as new words are introduced.
References
- Battista, MT (1999) ‘The Mathematical Miseducation of America’s Youth: Ignoring Research and Scientific Study in Education’, Phi Delta Kappan 80, 6, 425-433.
- Cawley, J, Parmar, R, Foley, T, Salmon, S and Roy, S (2001) ‘Arithmetic Performance of Students: Implications for Standards and Programming’, Exceptional Children 67, 3,
- 311 – 328.
- DfES (2001) The National Numeracy Strategy Guidance to Support Pupils with Dyslexia and Dyscalculia, London: DfES.
- Gersten, R, Chard, D, Baker, S Jayanthi, N, Flojo, J and Lee, D (under review) ‘Experimental and Quasi-experimental Research on Instructional Approaches for Teaching Mathematics to Students with Learning Disabilities. A Research Synthesis’, Review of Educational Research.
- Poustie, J (2001) Mathematics Solutions: An Introduction to Dyscalculia Part B – How to Teach Children and Adults who have Specific Learning Difficulties in Mathematics, Taunton: Next Generation.
Dr Michael Farrell is a special education consultant whose recent books include the Effective Teachers’ Guides (Routledge, 2006)
