Clinical Practice Guideline
The Diagnosis and Treatment of Dyscalculia
Background: 3–7% of all children, adolescents, and adults suffer from dyscalculia. Severe, persistent difficulty performing arithmetical calculations leads to marked impairment in school, at work, and in everyday life and elevates the risk of comorbid mental disorders. The state of the evidence underlying various methods of diagnosing and treating this condition is unclear.
Methods: Systematic literature searches were carried out from April 2015 to June 2016 in the PsycInfo, PSYNDEX, MEDLINE, ProQuest, ERIC, Cochrane Library, ICTRP, and MathEduc databases. The main search terms on dyscalculia were the German terms “Rechenstörung,” “Rechenschwäche,” and “Dyskalkulie” and the English terms “dyscalculia,” “math disorder, and “math disability.” The data from the retrieved studies were evaluated in a meta-analysis, and corresponding recommendations on the diagnosis and treatment of dyscalculia were jointly issued by the 20 societies and associations that participated in the creation of this guideline.
Results: The diagnosis of dyscalculia should only be made if the person in question displays below-average mathematical performance when seen in the context of relevant information from the individual history, test findings, clinical examination, and further psychosocial assessment. The treatment should be directed toward the individual mathematical problem areas. The mean effect size found across all intervention trials was 0.52 (95% confidence interval [0.42; 0.62]). Treatment should be initiated early on in the primary-school years and carried out by trained specialists in an individual setting; comorbid symptoms and disorders should also receive attention. Persons with dyscalculia are at elevated risk of having dyslexia as well (odds ratio [OR]: 12.25); the same holds for attention deficit/hyperactivity disorder and for other mental disorders, both internalizing (such as anxiety and depression) and externalizing (e.g., disorders characterized by aggression and rule-breaking).
Conclusion: Symptom-specific interventions involving the training of specific mathematical content yield the best results. There is still a need for high-quality intervention trials and for suitable tests and learning programs for older adolescents and adults.
Three to seven percent of all children, adolescents, and adults suffer from dyscalculia. This figure corresponds to some 84 000 to 195 750 primary-school pupils in Germany (1–3). The significance of dyscalculia is still underappreciated. Poor mathematical ability places a major burden on society and on the affected individual (4). A large-scale cohort study in England revealed that poor mathematical ability is associated with major psychosocial and economic risks: 70–90% of the affected persons ended their schooling prematurely at age 16; at age 30, very few of them were employed full-time. Their probability of being unemployed and of developing depressive symptoms was twice as high as that of persons without dyscalculia (5). The costs arising from severe impairment of mathematical ability in Great Britain have been estimated at £2.4 billion per year (6).
Persons with dyscalculia have marked, persistent problems in applying the basic methods of arithmetic and in knowledge of math facts (the multiplication table); according to the ICD-10 definition of the disorder (code F81.2), these problems are not merely due to low intelligence or inadequate schooling. These problems are often associated with impaired basic processing of numbers and quantities (7–10) (Box). The sex ratio of sufferers is approximately even, with a trend toward a higher prevalence among girls (11).
When dyscalculia is not recognized as such (as often happens), negative school experiences and repeated lack of success in mathematical tasks generate fears of failure as well as diminished self-esteem. The affected children and adolescents develop diverse mental symptoms and disorders (12). Symptoms are common (ca. 10–40%), both of the externalizing type (such as aggressiveness and agitation) and of the internalizing type (such as anxiety and depressed mood) (13–15). Dyscalculia also displays high comorbidity with reading and/or spelling disorder (dyslexia; ca. 30–40%) as well as with attention deficit/hyperactivity disorder (ADHD; ca. 10–20%) (1, 2, 16, 17). Without specific intervention, dyscalculia often leads to scholastic failure and school absenteeism (12, 18).
The past two decades have seen markedly increased interest in dyscalculia, both among specialists studying the problem and among the general public (11, 19). Nonetheless, the new knowledge gained during this time has not been systematically integrated into medical, psychological, learning-therapeutic, and educational practice. A variety of procedures, criteria, and tests are used in the diagnostic evaluation of dyscalculia (7). Although a broad spectrum of therapeutic and learning programs is available, their effectiveness has generally not been studied or else remains unclear (20). Moreover, the classification of dyscalculia in the ICD-10, which is based exclusively on deficits in carrying out basic arithmetical tasks, must be questioned on the basis of recently acquired scientific knowledge.
The above considerations indicate the need for a guideline in which the current state of research in the field is systematically assessed and the participating scientific and professional organizations, working in collaboration, jointly issue clear and empirically well-grounded recommendations for the uniform and valid diagnostic evaluation and effective treatment of this condition. Twenty societies and associations under the leadership of the German Society of Child and Adolescent Psychiatry, Psychosomatics and Psychotherapy (eBox 1) have now created the world’s first evidence- and consensus-based S3 guideline on the diagnosis and treatment of dyscalculia (guideline No. 028-046 of the Association of the Scientific Medical Societies in Germany, Arbeitsgemeinschaft der Wissenschaftlichen Medizinischen Fachgesellschaften [AWMF]).
This guideline is divided into four sections concerning, respectively, the symptoms, diagnosis, treatment, and comorbidities of dyscalculia. The current state of research in the field was evaluated by systematic literature searches in multiple scientific databases (PsycINFO, Medline, ProQuest, ERIC, Cochrane, ICTRP, PSYNDEX, MathEduc). With regard to tests and learning programs, further searches were carried out for materials issued by relevant specialized publishers. The retrieved publications were selected on the basis of multiple inclusion criteria for each of the four sections of the guideline (eBox 2). The overall procedure and flow charts for the literature search in each of the four areas are shown in eFigures 1 and 2.
The methodological assessment of study quality was performed with the aid of checklists for each relevant study type (e.g., randomized controlled trial, non-randomized controlled trial) (21, 22). On this basis, each study was assigned an evidence grade, according to the scheme of the Oxford Center for Evidence-Based Medicine (OCEBM) (23). The datasets for each of the four areas were meta-analytically evaluated.
The methodological quality of diagnostic tests was evaluated with the aid of a specially developed rank-ordering procedure. For all tests, a rank order was determined on the basis of how well each test fulfilled a set of quality criteria in comparison to the other tests.
Learning programs were only considered if they had been evaluated in at least one trial involving a control group, an intervention group, and a pre–post design. These programs were assessed with respect to the quality of the evaluative trials providing evidence for their efficacy. The main criterion was whether the evaluative trials had been subjected to peer review and displayed a correspondingly high scientific quality, and/or whether they were carried out in persons with dyscalculia and were therefore valid for the purposes of this guideline.
On the basis of the findings of the literature search and evaluation, all of the participating organizations developed and agreed upon the recommendations of the guideline in a consensus conference under the neutral moderation of the AWMF. For each recommendation, the degree of consensus was rated as a strong consensus (>95%), a consensus (76–95%), or majority approval (51–75%).
All recommendations emerging from the consensus conference were strong (i.e., recommendation grade A) and supported by a broad consensus (i.e., at least 76% approval). Moreover, the findings of further studies published after the end of the literature search period and the publication of the guideline were still consistent with the guideline’s recommendations (eBox 3).
Manifestations and diagnosis
Persons with dyscalculia have major difficulties in all areas of arithmetic (basic arithmetic operations, fact retrieval, word problems) (Table 1) and in the processing of numbers and quantities. They need much more time than persons without dyscalculia to solve problems. In addition to these mathematics-specific deficits, they have markedly impaired performance in visuospatial working memory (e.g., remembering the position of dots in a matrix) and in the suppression of distracting stimuli (inhibition).
The diagnosis of dyscalculia involves not only obligatory psychometric (arithmetical) testing, but also a clinical examination, thorough history-taking, and further psychosocial assessment. The medical diagnostic algorithm is shown in the Figure.
The clinical diagnostic evaluation consists of a physical examination (including a neurological examination with testing of vision and hearing) and a standardized intelligence test. The diagnostic criteria for dyscalculia specify that impaired performance on mathematical tasks must not be attributable to low intelligence as defined by the ICD-10 (IQ <70), brain damage, brain disease (e.g., infantile cerebral palsy, epilepsy), or a previously undetected impairment of sight or hearing (24). The effects of neurogenetic disorders (e.g., fragile-X syndrome, 22q11 deletion syndrome) and other factors that can impair performance on mathematical tasks (e.g., premature birth, low birth weight) should also be taken into account in the differential diagnosis (25–27).
History and further psychosocial assessment
The person’s biographical course of development and his or her familial and scholastic situation should be documented systematically, as should the effects of the performance deficits on mental and social development, school integration, and social participation (psychosocial integration).
In the differential diagnosis, other potential causes of difficulty in performing mathematical tasks must be ruled out, e.g.: inadequate schooling (frequent change of teachers or lessons being cancelled), insufficient learning and support opportunities (family conflicts, learning disorders in the family, poverty), prolonged absence from school, or the effects of other disorders on mathematical performance ability, such as anxiety disorders (school phobia).
To assure a correct diagnosis, supportive criteria for the diagnosis of dyscalculia should be applied, including family clustering of dyscalculia (28, 29) or difficulty in developing the concepts of number and quantity in the preschool years (10, 30).
Consideration of multiple risk factors sometimes enables prediction of the course and stability of dyscalculia: comorbid mental disorders, psychosocial stress factors (e.g., unsuccessful integration in school), and low family socioeconomic status should be taken into account, as these can affect the course of the disorder and the efficacy of interventions (16).
Psychometric tests (of mathematical performance) should be used to document, as completely as possible, the overall picture of the deficits. All tests were evaluated for methodological quality and assigned a rank order in a list (eTable 1). The tests at the top of the list are recommended; those in the top half of the list are considered to be of better quality than those in the bottom half. If no test from the top half of the list is suitable for measuring the particular deficits of the person to be tested, a test from the next (i.e., third) quarter of the list can be chosen. This would be the case, for example, if the subject is in the sixth grade and none of the tests in the top half of the list is normed for this level, but one from the third quarter of the list is so normed. The tests in the lowest quarter of the list should not be used. An abbreviated listing of the best tests is given in Table 2.
Establishment of the diagnosis
The diagnosis is established on the basis of information from all three sources (testing, clinical examination, and history, including further psychosocial assessment) (Figure). Whatever test is used for mathematical performance, below-average performance (≤ 16th percentile) in mathematics must be documented, particularly in basic arithmetic operations and numerical and quantitative processing. The threshold value on the test that should be used as a criterion for the diagnosis depends on the degree to which the clinical examination, the history, and the psychosocial assessment support the suspected diagnosis of dyscalculia. If they do not do so, then a strict (low) threshold of 1.5 standard deviations below the age- or grade-appropriate mean is to be used (i.e., ≤ 7th percentile or T-value ≤ 35). On the other hand, if there is already evidence to support the diagnosis of dyscalculia (e.g., preschool difficulties with the concepts of number and quantity), the threshold test value need not be so strict and can be set at 1 standard deviation below the age- or grade-appropriate mean (i.e., ≤ 16th percentile or T-value ≤ 40).
The treatment of dyscalculia
All proposed interventional methods for dyscalculia must be scientifically evaluated with respect to their content and the conceptions of support and treatment that they embody. This is the only way to ensure that any positive effects are independent of other factors (e.g., the therapist–patient relationship). Evidence-based treatments are not yet available for all age groups, and there may thus be deviations in the treatment plan. The areas of mathematical performance that the diagnostic evaluation has shown to be problematic are the main targets of the therapeutic intervention. A meta-analysis on this topic has shown that symptom-specific interventions, in which persons with dyscalculia are mainly given mathematical tasks to practice, yields markedly better improvement in all areas of mathematical performance than no intervention at all or non–symptom-specific interventions that mainly train other skills (e.g., working memory). The mean effect size (Hedges’ g) in all intervention trials was 0.52 (95% confidence interval [0.42; 0.62]) (e14, e35–e59). Performance in numerical and quantitative processing improved by 0.30 [0.08; 0.52], in basic arithmetic operations by 0.44 [0.14; 0.58], and in word problems by 0.47 [0.14; 0.61]. Other clinically relevant symptoms and disorders that might affect mathematical performance should also be taken into account in choosing suitable interventions. If such symptoms/disorders are present, it is important to differentiate whether they are functionally linked to dyscalculia (e.g., math anxiety) or not (e.g., ADHD). In all cases, any comorbid mental disorder must be considered in the design of a suitable treatment plan.
In persons with dyscalculia, mathematical abilities should be reinforced through the application of standardized, disorder-specific interventions whose efficacy has been scientifically demonstrated (eTable 2). These, however, should only be applied if they are appropriate in the context of the individual treatment plan. If the patient, for example, simultaneously suffers from an attention deficit that makes it impossible for him or her to follow a standardized program, then that program cannot be used.
Treatment should be provided only by specialized personnel who have received appropriate pedagogical-therapeutic training in the development of mathematical ability and its disorders, according to the standards established by the relevant specialty associations (the German Dyslexia and Dyscalculia Association [BVL] and the Association for Integrative Learning Therapy [FiL]), or who have undertaken a course of university study centering on learning therapy.
Treatment should be provided in individual sessions of at least 45 minutes’ duration. Treatment was found to have a weaker effect if provided in a group setting (−0.19 [−0.37; −0.01]) or in sessions lasting less than 45 minutes (−0.49 [−1.02; 0.04]).
Preschool children who are held to be at risk for developing dyscalculia should receive supportive treatment as early as possible, as this has been found to have a beneficial effect on the later development of mathematical competence and on scholastic performance (31, 32). The decision when to end treatment depends on the course of the response and on changing individual factors (e.g., the severity of comorbid symptoms). Treatment should thus be continued as long as it is appropriate and necessary in the judgment of the interdisciplinary team caring for the child (e.g., therapist, teacher, and physician). The indication for continued treatment should be reevaluated at least once a year, with disorder-specific follow-up examinations carried out by independent specialists (i.e. not the person conducting therapy) who have the relevant expertise.
Comorbid disorders in persons with dyscalculia
Dyscalculia has high comorbidity with other disorders and symptoms. The prevalences, odds ratios, and relative frequencies were determined in a meta-analysis (eTable 3). The most common comorbidities were found to be dyslexia, symptoms from the ADHD spectrum (mainly attention deficits), and symptoms of either the internalizing type (mainly math anxiety, test anxiety, and school phobia) or the externalizing type (e.g., aggressive behavior). Any individual who is given a diagnosis of dyscalculia should, therefore, undergo diagnostic screening for these potentially comorbid disorders. If a screening test yields the suspicion of a comorbid disorder, then a corresponding diagnostic work-up should be performed, preferably as specified in the relevant guideline (33–37).
The need for action and further research
There is currently a lack of high-quality standardized tests and evidence-based learning programs for children and adolescents with dyscalculia from the fifth grade and up, and also, in particular, for adults. There is likewise a lack, for all age groups, of high-quality randomized controlled trials with multiple follow-up examinations that could inform us about the intermediate- and long-term effects of treatment. Research is also needed on the long-term course of dyscalculia onward into adulthood and on the development of comorbid disorders that interact with dyscalculia (above all, math anxiety and school phobia), which can be major impediments to scholastic achievement and to the success of treatment.
Action is needed, in particular, on the level of social policy, because dyscalculia persists through all age categories, with manifold negative consequences for its sufferers. At present, across Germany, pupils with dyscalculia are not given equal treatment to pupils with dyslexia. For example, supportive measures (e.g., deficit compensation) are available only at the primary-school level, or not at all. Moreover, if learning therapy is needed outside of school, the costs are not borne by the health-insurance carriers; this places a major financial burden on the affected families that can go on for years, often leading to inadequate support and treatment of the affected children and adolescents. Social policy in the areas of education and health thus faces the task of making evidence-based scholastic supportive treatment available to all who need it, and of providing financial support for the costs of treatment. These two aspects are explicitly stressed in the preamble to the guideline, reflecting the consensus of the groups that participated in its creation.
The practical application of the S3 guideline
With the issuance of this guideline on the diagnosis and treatment of dyscalculia, evidence- and consensus-based S3 guidelines are now available that cover the entire area of specific developmental disorders of scholastic skills (ICD F81). This guideline contains relevant information for children, adolescents, and adults suffering from dyscalculia and should be implemented in all areas of its diagnosis and treatment. To enable better implementation of the recommendations, the guideline also includes additional information on their application in school, in learning therapy, and in the treatment of adults with dyscalculia. It also includes case illustrations exemplifying the diagnostic process. Fact sheets on each test that indicate its parameters and the included subtests, as well as lecture slides detailing the contents of the guideline, are available for downloading on the AWMF website.
Conflict of interest statement
The authors state that they have no conflict of interest.
Manuscript submitted on 29 November 2018, revised version accepted on 4 December 2018.
Translated from the original German by Ethan Taub, M.D.
Prof. Dr. med. Gerd Schulte-Körne
Klinik und Poliklinik für Kinder- und Jugendpsychiatrie,
Psychosomatik und Psychotherapie
Klinikum der Universität München
D-80336 Munich, Germany
eTables, eFigures and eBoxes:
Prof. Dr. med. Gerd Schulte-Körne
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