Dyscalculia: from Science to Education

Brian Butterworth

• Publisher: Routledge
• Year: 2018
• Print ISBN: 9781138688605
• eBook ISBN: 9781134969456
• Edition: 1
• Topic: Education
• Subtopic: Education General

Dyscalulia is caused by developmental differences in the structures and patterns of activation in the brain. Affected learners require timely and tailored interventions, informed and shaped by neurological findings.

In this ground-breaking text, Professor Butterworth explains the latest research in the science of dyscalculia in a clear non-technical way. Crucially, he shows that dyscalculia is caused by a core deficit in the ability to accurately and swiflty represent the number of objects in a set, an ability that underpins learning arithmetic, and clearly differentiates dyscalculia from other forms of early maths learning difficulties. Butterworth uniquely links research to pedagogical practice, to explain how science can be used for the identification of dyscalculia, and for the development of strategies to best help affected learners acquire arithmetical competence. The text provides robust interventions that focus on helping pupils to strengthen their ability to process numerosities and link them to the familiar number symbols, counting words and digits. It shows that science has clear and specific implications both for assessment and intervention.

A landmark publication for the dyscalculia community, Dyscalculia: From Science to Education will become an essential resource for teachers, professionals, parents and sufferers, as well as for university courses that include specific learning disabilities.

CHAPTER

1

What is dyscalculia? It’s not just being bad at maths

We all know that maths is an important life skill, even though many people are happy to admit that they are “crap at maths”. By contrast, most people are not be prepared to say that they are bad at grammar, speaking or reading. In fact, poor maths is a more of a handicap in the workplace than poor literacy (Bynner & Parsons, 1997). Men and women with poor numeracy, have poorer educational prospects, earn less, and are more likely to be unemployed, in trouble with the law, and be sick (Parsons & Bynner, 2005).

The importance of mathematics instruction has been stressed, quite rightly, in many official reports in the UK, the US and other nations. Napoleon famously said that mathematics is “intimately connected with the prosperity of the state”. In his foreword to the Cockcroft report on maths teaching in 1982, Sir Keith Joseph, Secretary of State for Education and Science, wrote, “Few subjects are as important to the future of the nation as mathematics” (Cockcroft, 1982). Since Cockcroft, in the UK alone there has been Professor Adrian Smith’s report on post-14 maths (Smith, 2004), and Sir Peter Williams’s report on primary maths (Williams, 2008). Similarly, the US National Research Council (National Research Council. Committee on Early Childhood Mathematics, 2009) noted that: “The new demands of international competition in the 21st century require a workforce that is competent in and comfortable with mathematics;” and to that end: “The committee [of experts] was charged with examining existing research in order to develop appropriate mathematics learning objectives for preschool children; providing evidence-based insights related to curriculum, instruction, and teacher education for achieving these learning objectives” (p. 1). In 2011, the OECD’s report, The High Cost of Low Educational Performance, demonstrated that the standard of maths drives GDP growth: the standard in 1960 was a good predictor of economic growth up to 2000; and the improvement in educational standards from 1975 to 2000 was highly correlated with improvement in economic growth. In particular, the report looked at the potential effects of improving standards in maths. So, for example, they found that if the UK improved the standard of the 11% of children who failed to reach the PISA minimum level (which is not very high), to the minimum level, then the effect on GDP (Gross domestic product) growth would be about 0.44%. Not much you might think, but with an average rate of GDP growth of 1.5%, this would be a massive and cumulative increase of nearly one-third. The accountancy firm, KPMG, estimated the cost to the UK of poor maths in terms of lost direct and indirect taxes, unemployment benefits, justice costs, and additional educational costs, was £2.4 billion per year (Gross et al., 2009).

One cause of poor mathematical ability is developmental dyscalculia,¹ which is a handicap people are born with and which can persist into adulthood. In this way, it is comparable with dyslexia, which is also a condition someone is born with and persists into adulthood. I will deal with characteristics and causes of dyscalculia, as well as how to help in the following chapters. Unfortunately for dyscalculics, their teachers and their parents, dyscalculia does not have a high public profile. As the UK government’s chief scientific adviser wrote: “Developmental dyscalculia is currently the poor relation of dyslexia, with a much lower public profile. But the consequences of dyscalculia are at least as severe as those for dyslexia” (Beddington et al., Nature, 2008, summarizing Government Office of Science report: Mental Capital and Wellbeing).

Terminology

It is not surprising that many people have become confused about dyscalculia. Here are some terms that are widely used. I list their principal official users, and also some of the scientists associated with each term. The pioneer Ladislav Kosc was the first to use the term dyscalculia to refer to a specific developmental condition. He defined it as follows:

Developmental dyscalculia is a structural disorder of mathematical abilities which has its origin in a genetic or congenital disorder of those parts of the brain that are the direct anatomico-physiological substrate of the maturation of the mathematical abilities adequate to age, without a simultaneous disorder of general mental functions.

(1970a, cited in 1974, p 47)

This is essentially the definition that I will use, modified in the light of subsequent research. It stresses its congenital and neurological basis, which many studies have neglected.

Kosc was careful to distinguish dyscalculia from just being bad at maths. He wrote:

If a person has had inadequate instruction, or if a child because of neurosis, objective illness, or fatigue is not able to demonstrate his potential abilities or directly acquired knowledge or skills adequately, this is not a disorder of these abilities as such but merely a deficit which is called … pseudo-dyscalculia.

(Kosc, 1974, p. 49)

• Dyscalculia or developmental dyscalculia (Kosc, US Department of Education, and many scientific papers, this book)
• Specific disorder of arithmetical skills (ICD 10, see below)
• Mathematics disorder (DSM IV, see below)
• Specific learning disorder with impairment in mathematics (DSM 5, see below)
• Mathematics/mathematical learning difficulty, MLD (Mazzocco, Geary, and many scientific papers).

So what is dyscalculia? Different authorities use different terminologies, and different criteria, and these official definitions, however vague, incoherent and unfounded, are nevertheless important from a practical point of view.

Dyscalculia is whatever your authorities think it is

Dyscalculia, or the local term for it, is whatever your authorities think it is. This may enable the parent, teacher, and sufferer, to request special help. This can be special help with exams, along the lines that dyslexics get help with exams in terms of extra time and the opportunity to use computers if handwriting is difficult. It can also mean help with learning. Again, dyslexics can get specialized teaching. There are places in the world where this approach can be useful, for example, Italy’s Law 170 (see Box 1.1). This law provides for both recognition of the condition and help for overcoming its consequences.

Box 1.1 Italy’s Law 170

Nuove norme in materia di disturbi specifici di apprendimento in ambito scolastico (New regulations concerning specific disorders of learning).

• Article 1.1. The present law recognizes dyslexia, dysgraphia, dysorthographia and dyscalculia as Specific Learning Disabilities.… They manifest themselves in cases of adequate cognitive capacities, and in absence of neurological or sensory deficits. Yet, they constitute an important limitation for daily activities.
• Article 1.5. The present law refers to dyscalculia as a specific deficit which manifests itself as a difficulty in grasping the automatisms of calculation and number processing.
• Article 2 states among other things, that there will be appropriate teaching to realize potential, a reduction in social and emotional consequence, train teachers appropriately, make people aware of the problem, promote early diagnosis and rehabilitation, and ensure equal opportunities to develop social and professional capacities.

The Individuals with Disabilities Education Act (IDEA) in USA recognizes dyscalculia (along with dyslexia). The Office of Special Education and Rehabilitative Services of the USA’s Department of Education requires state and local education authorities to carry out appropriate assessments and to provide appropriate help.

The Office of Special Education Programs (OSEP) funds a large network of technical assistance centers that develop materials and resources to support States, school districts, schools, and teachers to improve the provision of services to children with disabilities, including materials on the use of accommodations … [which refers] to the various components of a free appropriate public education, including special education, related services, supplementary aids and services, and program modifications or supports for school personnel, as well as accommodations for students taking assessments.

(Yudin, 2015)

The problem with this approach is that the authorities may not recognize dyscalculia; and even if they do, the authorities may not provide support, such as provision for additional money to buy in specialized help, or special provision (“accommodations”) in the school.

Here is one example of failure to recognize from the UK Department for Education in 2016. It has dropped all the useful material about dyscalculia that had been there until 2015. However, a previous UK government did have dyscalculia on its website and in its publications. Here is the definition in Guidance to support pupils with dyslexia and dyscalculia published by the Department for Education and Skills in 2001:

Dyscalculia is 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. Even if they produce a correct answer or use a correct method, they may do so mechanically and without confidence.… Purely dyscalculic learners who have difficulties only with number will have cognitive and language abilities in the normal range, and may excel in nonmathematical subjects.

First it describes the actual cognitive differences between the dyscalculic and typically developing peers, and not just that they may be slower and more limited in their acquisition of arithmetical skills. So it is not just that they are worse at arithmetic, which may have many causes. The dyscalculic disability is identified in terms of a particular cognitive deficit – a deficit in understanding simple number concepts and having an intuitive grasp of numbers.

Dyscalculia: it is what professionals think it is

Usually this will mean a special educational needs coordinator or an educational psychologist, but sometimes it can mean a medical doctor or a psychiatrist. These professionals may provide an assessment that recognizes dyscalculia, and indeed, can recommend the help that is needed. These professionals are important because the authorities do not specify what the assessments or the help should be. This is left to the professionals, and professionals will use definitions and criteria provided by professional organisations such as the American Psychiatric Association or the World Health Organisation.

Professional definitions

1. The Diagnostic and Statistical Manual of Mental Disorders, fourth Edition. DSM-IV

This is the “old testament” of categories of disorders devised by the American Psychiatric Association in the USA. It gives the following diagnostic criteria for “Mathematics Disorder” (Section 315.1)

1. Mathematical ability, as measured by individually administered standardized tests, is substantially below that expected given the person’s chronological age, measured intelligence, and age-appropriate education.
2. The disturbance in Criterion A significantly interferes with academic achievement or activities of daily living that require mathematical ability.
3. If a sensory deficit is present, the difficulties in mathematical ability are in excess of those usually associated with it.

The first point to note is that the “standardized test” is not specified. If it is a standardized test of arithmetic, then there will be many reasons why a child may underperform, as we will see, especially in Chapter 3.

The second point to note is that this is a “discrepancy” criterion, which rules out by definition the possibility that someone can have both a mathematics disorder and low general cognitive ability; and it presumably implies that low measured intelligence is sufficient to cause the symptoms of “mathematics disorder”. Indeed, for learners with equivalently poor performance on the standardized test, the one with the higher IQ is more likely to be granted the classification of Mathematics Disorder.

No justification is presented either for the terminology nor the evidential base for this classification. In fact, DSM-IV claims, again without evidence, that the prevalence of Mathematical Disorder is 1%. We will return to this in Chapter 2.

One practical probl...

Table of contents

• Cover
• Half Title
• Title Page
• Copyright Page
• Table of Contents
• Preface
• 1 What is dyscalculia? It’s not just being bad at maths
• 2 Number sense: our intuitive understanding of numbers
• 3 The arithmetic starter kit
• 4 Core deficit in the number module: the cognitive cause of dyscalculia
• 5 Development of arithmetic depends on domain-specific numerical competences
• 6 The dyscalculic brain
• 7 Heritability and the effects of brain damage on numerical abilities
• 8 Society, school, and home
• 9 Assessment: how to identify dyscalculic learners
• 10 Intervention for dyscalculic learners
• 11 Policy: what to do about dyscalculia locally and nationally
• Index