Dyscalculia: A unifying concept in understanding mathematics learning disabilities

Abstract

Individuals display a mathematics disability when their performance on standardized calculation tests or on numerical reasoning tasks is comparatively low, given their age, education and intellectual reasoning ability. Low performance due to cerebral trauma Is called acquired dyscalculia. Mathematical learning difficulties with similar features but without evidence of cerebral trauma are referred to as developmental dyscalculia. This review identifies types of developmental dyscalculia, the neuropsychological processes that are linked with them and procedures for Identifying dyscalculia.     

Predictors of primary school teachers’ knowledge about developmental dyscalculia

Developmental dyscalculia is a specific learning disability that is described as a heterogeneous and persistent cognitive disorder. Given the need to detect and intervene as early as possible to minimise its effects, teachers’ knowledge about symptoms, characteristics and effective intervention strategies in dyscalculia is essential. Given the lack of research about this topic and measures to evaluate teachers’ knowledge, this study aims to present a literature-based measure to evaluate knowledge about developmental dyscalculia and to investigate the predictors of this type of knowledge. Data were collected from a sample of 175 primary school teachers. The measure presented adequate psychometric properties. Teachers’ personal characteristics such as age and gender did not predict their knowledge about dyscalculia. Being a Special Education teacher predicted a higher knowledge of intervention strategies in dyscalculia and having heard about dyscalculia predicted higher knowledge about not only intervention strategies but also dyscalculia characteristics. The data are discussed, and suggestions for further studies are presented.     

发展性计算障碍的诊断与矫治

发展性计算障碍的发生率大约为 5 % - 6% ,有些国家甚至更高。患有发展性计算障碍的儿童在学习、生活和以后的工作中都会遇到很多的困难 ,关于发展性计算障碍的研究应该引起人们的重视。本文从诊断、矫治两个方面对已有研究进行了综述。发展性计算障碍的诊断是进行此类研究需要首先解决的问题 ,矫正障碍则是这方面研究的最终目的 ,本文对发展性计算障碍的矫正进行了初步探讨。     

Naming speed in dyslexia and dyscalculia

In four carefully selected samples of 8- to 10-year old children with dyslexia (but age adequate arithmetic skills), dyscalculia (but age adequate reading skills), dyslexia/dyscalculia and controls a domain-general deficit in rapid automatized naming (RAN) was found for both dyslexia groups. Dyscalculic children exhibited a domain-specific deficit in rapid naming of quantities. This finding is in line with recent assumptions that dyscalculia is associated with a neurobiological deficit in the processing of numerosities. In the dyslexia/dyscalculia group, RAN deficits were additive, that is, the dyslexia/dyscalculia group exhibited the sum of the deficits found in the dyslexia only and dyscalculia only groups. This finding suggests that the cognitive bases of dyslexia and dyscalculia are independent from each other. Within the naming speed paradigm no differential impact of special demands on the executive functions inhibition and shifting was found for any of the four groups.     

A systematic review of interventions for children presenting with dyscalculia in primary schools

The acquisition of numerical competency is regarded as imperative for quality of life and economic well-being. Many children have significant mathematical learning difficulties known as dyscalculia. The aim of this research was to systematically review the available literature for interventions with children presenting with dyscalculia in primary schools, in order to provide an evidence base of filtered information assessed for methodological rigour and coherence. The study evaluated literature from 2004 to 2014 that reported on interventions for primary school children presenting with dyscalculia. Specific databases were accessed to highlight literature for inclusion in the study. The studies were assessed at title, abstract and full text levels for quality based on the inclusion and exclusion criteria. The findings provide a base of effective interventions that can be used in the school setting for individual development with a holistic focus and present various methods of instruction for children presenting with dyscalculia.     

ADHD and dyscalculia: Evidence for independent familial transmission

The familial relationship between dyscalculia and attention-deficit/hyperactivity disorder (ADHD) was assessed. We conducted a familial risk analysis using probands with and without ADHD of both genders and their first-degree relatives. Participants were assessed with structured diagnostic interviews and a cognitive test battery. We found elevated rates of ADHD in relatives of both ADHD proband groups, regardless of dyscalculia status, and elevated rates of dyscalculia in relatives of probands with dyscalculia, irrespective of ADHD status. There was no evidence for cosegregation or assortative mating. Our findings support the hypothesis that ADHD and dyscalculia are independently transmitted in families and are etiologically distinct. These results reinforce the current nosological approach to these disorders and underscore the need for separate identification and treatment strategies for children with both conditions.     

Identifying Children with Persistent Developmental Dyscalculia from a 2‐min Test of Symbolic and Nonsymbolic Numerical Magnitude Processing

Developmental dyscalculia (DD) is a mathematical learning disability that occurs in around 5%–7% of the population. At present, there are only a handful of screening tools to identify children that might be at risk of developing DD. The present study evaluated the classification accuracy of one such tool: The Numeracy Screener, a 2‐min test of symbolic (Arabic numerals) and nonsymbolic (dot arrays) discrimination ability. A sample of 222 children who demonstrated persistent deficits (n = 55), inconsistent deficits (n = 51), or typical performance (n = 116) on standardized tests of math achievement over multiple observations was tested. The Numeracy Screener correctly classified children in all three groups. Notably, the symbolic condition has greater sensitivity in discriminating children with persistent DD from the other two groups. Screening tools that assess early numeracy skills may be promising for identifying children at risk for developing severe mathematical difficulties.     

The design and development of a dyscalculia checklist based on a focus group interview

This article aims to explore the symptoms and characteristics of dyscalculia. This is a qualitative study. Five experts in the field of special education took part in a focus group interview. Each expert had more than ten years of experience in their area of expertise. To determine the content validity of the protocol, three experts in special education, language and qualitative research evaluated each of the eight items. Cohen's kappa analysis was used to assess inter-rater reliability. The findings of this study indicate that 59 items have been developed, based on six constructs in the dyscalculia checklist. The six constructs were subitising, estimating, Arabic numerals, verbal numbers, arithmetic facts and calculating processes. Following the focus group interview, a new construct emerged: math anxiety. The study implies that teachers might utilise this checklist to carry out early detection of students with dyscalculia in primary schools. This will enable appropriate intervention, resulting in significant benefits for the Ministry of Education, for educators and teachers, and for the students themselves. Although this study was based in Malaysia, the results have wider implications because dyscalculia is present everywhere.     

Emotional and behavioral characteristics over a six-year period in youths with persistent and nonpersistent dyscalculia

The authors examined behavior problems in a matched sample of 58 youths with persistent dyscalculia (PD) and nonpersistent dyscalculia (NPD). Participants were classified as having dyscalculia at age 10-11 years. Parents completed the Child Behavior Checklist for their children at ages 10-11, 13-14, and 16-17 years, while the youths did so at the last two age periods. Only at age 16-17 years were there significantly more problems, particularly attention problems and externalizing problems, reported by parents for PD youths compared to NPD youths. A higher percentage in the PD group than in the NPD group received scores in the clinical range for externalizing problems. However, the mean levels of behavior problems at this age and the earlier ages were within the normal range for both groups. For youth-reported problems, the only significant difference was for attention problems at 16-17 years. Therapeutic interventions should focus on the academic domain and improving and altering behavioral patterns.     

发展性计算障碍研究述评

发展性计算障碍研究越来越受到研究者的关注,已有研究发展性计算障碍的诊断、病因及其与工作记忆之间的关系等方面取得了丰硕的成果.但是,已有研究在被试的同质性、被试的代表性、控制组的设置问题以及数字加工和计算能力的测量等问题上还存在着一定的问题,需要进一步改进.     

Case study of language and numerical disability: A sequential processing deficit?

We report a case study of Christine, an intelligent 30-year-old woman with a developmental learning disability. Psychometric evaluation and extensive interviews revealed several findings: most notably, evidence of anomia, auditory processing problems, difficulty acquiring reading and spelling skills, and an extremely poor sense of number. In addition, Christine showed all four of the Gerstmann symptoms (left-right confusion, finger agnosia, dysgraphia, and dyscalculia). We suggest that most, if not all, of these impairments may be explained in terms of a sequential processing deficit (e.g., Bakker 1967; Tallal 1980). In Christine’s case, difficulty perceiving serial order appears to have resulted in a major conceptual impairment involving number. HD—To me four is a number that comes after three and before five. It means twice two … C—To me four is a picture. This paper is dedicated to the memory of Professor Victor Lotter.     

How to Choose the Best

This chapter deals with a crucial component of our position, the presumption that there are objective grounds for preferring one thing to another within the various cultural institutions we deal with, that there are better or worse symphonies, soufflés and theories of the atom. The task of showing this is more urgent for some institutions than others. While philosophers can doubt anything, most people are persuaded of the objectivity of our efforts to comprehend the physical world and to weigh, count and measure accurately in many areas of human activity. Again, when we are faced with a choice among functional objects or processes, most people will admit that we can ground a preference for a knife or an exercise routine on objectively established facts: sharpness, or measurable increase in strength. Here, certainly, various conflicting desiderata may enter and make actual decisions more difficult — the sharpest knife may also be the most expensive; we may need to worry about its safety features; it may be ugly; and so on. But many will doubt that our judgements of comparative worth for non-functional objects such as paintings or sonatas can claim a similarly objective basis. We shall, therefore, concentrate our efforts on the most doubted areas, but will begin with the less contentious, where we think it is useful to draw attention to the genuine problems some philosophers have stressed, to show in fact that what we believe to be popular unconcern deserves to be somewhat ruffled.     

A reply to M. Marangudakis

In his reply to our paper Marangudakis raises important points regarding: (1) the measurement of environmental values; and (2) potential risks of deep ecological views to human welfare. We definitely agree that a more rigorous approach to the measurement of environmental values is needed. While the extent of belief in deep ecology remains an open question, we believe Marangudakis may be overly simplifying deep ecology and, for that matter, Christian world views.     

Phonological working memory, phonological awareness and language in literacy difficulties in Brazilian children

One of the most usual flaws that lead to literacy disability regards cognitive difficulties and alterations some children present in the literacy process. Many studies have found alterations in phonological processing, more specifically in phonological working memory (PWM) and phonological awareness (PA). Therefore, our aim was to identify alterations in skills of phonological working memory, phonological awareness and language (semantic, syntactic and phonological aspects) of Brazilian children with literacy disabilities (age 7–8). They were divided into two groups: (1) Group of Normal Literacy (NL); and (2) Group With Literacy Disabilities (LD). The evaluation comprised tests that assessed general cognitive functions and the skills at stake. The LD presented a poorer performance than the NL in the skills of PWM, PA and language aspects. The factor analysis showed that these skills prevailed in differentiating the groups. Thus, children with literacy disabilities presented deficits in phonological processing and language. These deficits seem to be a result of alterations of the phonological representations and poor language skills that are prior to the literacy period. Consequently, we believe that the early identification of these alterations can be very useful for the prevention of future literacy problems.     

国外发展性计算障碍儿童大脑神经机制的研究进展

有关发展性计算障碍儿童大脑神经机制的研究是近些年才逐渐发展起来的.研究发现,发展性计算障碍与脑结构功能失调有关,主要表现在顶叶和额叶上.但从整体上看,发展性计算障碍儿童加工过程中的神经机制和正常儿童是类似的,只是皮层的激活程度要弱一些;为了弥补加工困难,有些皮层会表现出补偿性机制,如角回、前扣带皮层等;一些皮层的作用还...     

Beyond the far too incessant schism: special education and the social model of disability

Special education critics' vigorous appraisals of the social model of disability, along with their analysis of its implications for special education, provide a valuable forum for meaningful dialogue about how educators are to understand the nature of disability. In this article, we offer our response to their recent articles. As advocates of the social model, we find their critiques intriguing, at moments a bit provocative, but more importantly we find in their work an opportunity to advance beyond the far too incessant schism between those who support the medical model of disability and those who endorse its alternatives.     

Evaluation of a numeracy intervention program focusing on basic numerical knowledge and conceptual knowledge: a pilot study

The preliminary results of this study suggested that children with developmental dyscalculia benefit from a numeracy intervention program that focuses on basic numerical knowledge and conceptual knowledge. All children in the experimental group showed considerable and partly significant performance increases on all calculation components. Six children with developmental dyscalculia were trained individually and in small-group settings for a relatively short duration (one school semester). We argue that the positive intervention effects to a large extent are attributable to the explicit teaching of numerical domains that often have been found to be neglected in school mathematics.     

Working memory deficits in children with specific learning disorders

This article examines working memory functioning in children with specific developmental disorders of scholastic skills as defined by ICD-10. Ninety-seven second to fourth graders with a minimum IQ of 80 are compared using a 2 x 2 factorial (dyscalculia vs. no dyscalculia; dyslexia vs. no dyslexia) design. An extensive test battery assesses the three subcomponents of working memory described by Baddeley (1986): phonological loop, visual-spatial sketchpad, and central executive. Children with dyscalculia show deficits in visual-spatial memory; children with dyslexia show deficits in phonological and central executive functioning. When controlling for the influence of the phonological loop on the performance of the central executive, however, the effect is no longer significant. Although children with both reading and arithmetic disorders are consistently outperformed by all other groups, there is no significant interaction between the factors dyscalculia and dyslexia.     

Disability,Dependency and Indebtedness?

What does dependency reveal about human learning? All humans are dependent, largely because we are variously vulnerable and disabled at more than one stage in our lives. In this paper the subject of dependency is approached largely in the context of our vulnerable and disabled states, including in particular, states of profound disability. The primary contention is that our dependent states should feature in accounts of how we learn, and of relations between learner and teacher, in ways that compare with the attention given to personal autonomy and independence.     

A program for excellence in physics and physical science teaching

Conclusion It seems reasonable to conclude that the impact of these projects has been extensive and that we have met our basic objectives regarding the improvement of science education for the target teachers and students. The long-term goal of improved scientific literacy of at least a part of the citizens of this country and world can only be assessed by some form of longitudinal study that is beyond the scope and funding for these projects. But our assessment of what has been accomplished in the short term efforts seems to indicate very positive gains in those areas of knowledge, confidence, and pedagogical capability that we believe will enable the participants to make contributions to the improvement of scientific literacy for the students with whom they work. In short, we believe we have had two successful and worthwhile programs that have been useful and effective.