Dyscalculia

Action plans for successful learning in mathematics

Glynis Hannell

• Publisher: Routledge
• Year: 2013
• ISBN:
  9781135107536
• Edition: 2
• Topic: Education
• Subtopic: Education General

Based on expert observations of children who experience difficulties with maths this book gives a comprehensive overview of dyscalculia, providing a wealth of information and useful guidance for any practitioner. With a wide range of appropriate and proven intervention strategies it guides readers through the cognitive processes that underpin success in mathematics and gives fascinating insights into why individual students struggle with maths. Readers are taken step-by-step through each aspect of the maths curriculum and each section includes:

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• Examples which illustrate why particular maths difficulties occur

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• Practical 'action plans' which help teachers optimise children's progress in mathematics

This fully revised second edition will bring the new research findings into the practical realm of the classroom. Reflecting current knowledge, Glynis Hannell gives increased emphasis to the importance of training 'number sense' before teaching formalities, the role of concentration difficulties and the importance of teaching children to use strategic thinking. Recognising that mathematical learning has a neurological basis will continue to underpin the text, as this has significant practical implications for the teacher.

Introduction to dyscalculia

Literacy difficulties account for over 90% of the research literature on learning disorders, and yet in every classroom there are an equal number of children struggling with mathematics. This book outlines the essentials of the mathematics learning disorder called dyscalculia and offers numerous practical ways in which these difficulties can be addressed.

Understanding dyscalculia

DOI: 10.4324/9780203074350-1

What is dyscalculia?

The term dyscalculia is used to describe specific difficulties with mathematics. In many ways it is the mathematical equivalent of dyslexia, which is a specific difficulty with literacy.

Pupils with dyscalculia seem to be just as intelligent as their peers. They have been taught in the same way and engaged in the same mathematical activities and yet they encounter distinct difficulties in mastering the basics of mathematical thinking. Appropriate instruction and practice does not produce the expected gains in understanding and competence. As a result, pupils with dyscalculia often fail to acquire the essential concepts that underpin skills in performing mathematical procedures.

The disorder is also sometimes referred to as ‘developmental dyscalculia’, indicating that it is a developmental problem, as distinct from a difficulty that has been acquired through accident, illness, poor teaching or other adverse circumstances.

Although there is general agreement that some individual pupils do, quite clearly, have specific and sometimes severe difficulties with mathematics, there has been considerable professional debate about the precise nature of dyscalculia, its extent and its causes. Over recent years, research has clearly shown that there is a neurological basis for the disorder. Specific areas of the brain are now proven to be of critical importance in the development of mathematical thinking. It has also become increasingly evident that pupils with dyscalculia generally demonstrate a fundamental difficulty in acquiring basic ‘number sense’ (Dehaene, 2011).

These research findings highlight the fact that dyscalculia is a serious learning disorder and not a minor ‘hiccup’ in learning mathematics that can be easily fixed (or glossed over). It is also very evident that difficulties with concentration and strategic thinking also make significant contributions to the impact of the disorder. You will read more about these important aspects of dyscalculia throughout this book.

The word ‘dyscalculia’ means literally a ‘disorder in calculation’. The Department for Education and Skills defines developmental dyscalculia as ‘a condition that affects the ability to acquire arithmetical skills. Dyscalculic learners may have difficulty understanding simple number concepts, lack an intuitive grasp of numbers and have problems learning number facts and procedures.’

In the USA, the National Center for Learning Disabilities defines dyscalculia as ‘a wide range of lifelong learning disabilities involving math. There is no single form of math disability, and difficulties vary from person to person and affect people differently in school and throughout life’.

Mathematics is a complex curriculum area. It requires a wide range of skills across several quite distinct domains, such as number sense, spatial reasoning, verbal reasoning, counting and calculating. Geary (2004) points out that many pupils with dyscalculia can do very well indeed in some domains of the mathematics curriculum and yet have substantial difficulties in others. This reminds us that achievement tests containing a range of mathematical tasks (such as arithmetic, geometry, problem solving and measurement) can be very misleading. Strengths in one area can easily cancel out weaknesses in others. This means, of course, that the overall score may be a very unreliable indicator of the pupil's mathematical ability in specific domains.

Geary also points out that research has concentrated to a very large extent on difficulties with arithmetic and. that other important areas of mathematical ability have been, to a large extent, neglected by the researchers. However, in general it is true to say for the majority of pupils with dyscalculia the primary deficit is in the understanding of basic mathematical concepts, which in turn leads to problems in arithmetic and mathematical problem solving. Of course difficulties in other areas of mathematical thinking, such as spatial reasoning, will also have an impact on the pupil's performance in areas of mathematics which rely on these specific skills.

How common is dyscalculia?

There is general agreement that about 5–7% of pupils have dyscalculia (Shalev, 2007). This means that there will be a very high probability of finding at least one pupil with dyscalculia in every class of 30 children. There may well be two or three pupils with the disorder in the average class.

The consequences of dyscalculia for the individual include longstanding disadvantage in education, employment and life skills. In economic terms it has been calculated that poor numeracy skills in the population costs the UK £2.4 billion a year (Gross, Hudson and Price, 2009)

Geary (2004) comments that some pupils who do poorly in mathematics in one year may perform well in the next, reminding us that the quality of teaching in itself can either create or protect against learning difficulties in mathematics. Many teachers would acknowledge that their own interest, skills and understanding of mathematics are not of the highest order. University staff who provide pre- and post-service teacher education confirm that this is a significant concern and that without appropriate training these teachers will not be well equipped to teach mathematics to the children in their care. Teachers' abilities to analyze their students' mathematical thinking, identify difficulties and offer appropriate instruction will be compromised by their own limitations in this important area of the curriculum (Doerr and English, 2006).

So, in addition to the pupils in your class with a true dyscalculia, you may also be working with other children (with apparently similar difficulties) who have simply had poor learning experiences in earlier years. However, these pupils should improve quickly once they are given appropriate instruction. Pupils with dyscalculia will need more intensive help, and will respond to this much more slowly. Poor response to appropriate instruction is one of the hallmarks of dyscalculia.

Are dyscalculia and dyslexia the same thing?

We know that there is considerable overlap between these two disorders. Butterworth and Yeo (2004) suggest that somewhere between 20% and 60% of pupils have both dyslexia and dyscalculia. Deficits in language and working memory may well create problems in the acquisition of both mathematics and. literacy skills.

Studies such as those by Landerl, et al. (2009) indicate that the primary, underlying difficulty for pupils with dyslexia is a deficit in phonological processing, but that for pupils with dyscalculia there is a an underlying difficulty in processing magnitudes. As with many other studies, it was found that some children had a combination of both disorders.

It is important to remember that reading difficulties may well have a direct and negative impact on a pupil's performance in mathematics. Slow and inaccurate reading will in itself cause errors, reduce practice (because too much time is spent in reading the questions) and lower motivation.

Dyslexia and dyscalculia can exist in isolation from each other. It is fair to say that of the two disorders, dyslexia is usually more readily recognized, and remedied, while mathematical difficulties often seem to go unnoticed. Perhaps this is because mathematics is often seen as an unusually challenging subject, where it is ‘normal’ and therefore acceptable for otherwise capable pupils to have difficulties.

Have you noticed that it is not unusual for adults to say, quite cheerfully, that they were ‘hopeless’ at mathematics, but it is very rare to hear adults admit to being ‘hopeless’ at reading! It does seem as if being ‘hopeless’ at mathematics is accepted as a normal state of affairs. Unfortunately this complacency places pupils with dyscalculia at risk of falling further and further behind in mathematics and facing a range of avoidable disadvantages throughout their lifespan.

What causes dyscalculia?

We do know that there is a strong genetic influence on the development of mathematical skills. Just as we find one family where parents and children are all very capable mathematically, we often identify another family in which difficulties with mathematics are very common.

Obviously, we must remember that environmental factors will play their part in the transmission of a talent for, or a difficulty in, mathematics. A family where parents are mathematically competent may be a very different learning environment to one in which parents are uncertain about basic mathematics themselves.

However, it is clear that biological influences do play a significant role in dyscalculia. For instance, Shalev and Gross-Tur (2001) found that about 50% of the siblings of a pupil with dyscalculia can be expected to have similar difficulties. Parents and siblings of a pupil with dyscalculia are ten times more likely to have dyscalculia than members of the general population.

The brain and mathematics

Some pupils will be blessed with brains that seem purpose-built for mathematics; right from the start it all seems obvious, easy and interesting to them. In contrast, pupils with dyscalculia will find mathematics puzzling, arduous and frustrating, even when they may find other types of learning come very easily to them.

All learning and thinking develops through the evolution of specialized structures within the brain. Some of these structures are equipped to deal with the types of processes involved in mathematics. Between individuals there will naturally be differences in the efficiency with which these structures work. You will find much more information on the role that brain development plays in the acquisition of mathematics (and other learning) in Chapter 2.

It is generally agreed that mathematical competence depends on effective functioning of the pupil's

• number sense,
• visual spatial skills,
• language skills,
• concentration,
• memory.

As you will see as you read this book, successful mathematical thinking often requires the efficient integration of several different types of learning and thinking,

Dyscalculia and number sense

Pupils with dyscalculia frequently lack an intuitive ‘number sense’. They cannot tell at a glance that there are three apples on the plate or guess how many pencils there are in a jar. Instead, they may always need to count each item, one by one, to determine how many item...