Interventions for Children with Developmental Dyscalculia PDF

Chapter 5 Interventions for children with developmental dyscalculia Parents, teachers and neuropsychologists working together Flávia Heloísa Santos Proactive attitudes towards children with developmental dyscalculia This chapter will be based on systematic reviews that indicate efficient ways to hel...

Chapter 5 Interventions for children with developmental dyscalculia Parents, teachers and neuropsychologists working together Flávia Heloísa Santos Proactive attitudes towards children with developmental dyscalculia This chapter will be based on systematic reviews that indicate efficient ways to help children with developmental dyscalculia. It will mention the successful strategies and ways to avoid misconduct while managing children’s learning process. It will be focused on three target readers: parents, teachers and neuropsychologists who must work jointly towards children’s development. Recommendations to deal with behavioural aspects such as mathematics anxiety will also be outlined. Copyright © 2020. Taylor & Francis Group. All rights reserved. Relevant aspects for intervention Taken in isolation, the Greek-Latin word “dyscalculia” represents a symptom. Originally, it meant “blindness for numbers” which is expressed by difficulty in calculating. This symptom can be observed in various clinical conditions with clearly established aetiologies, as in some forms of epilepsy, and some genetic disorders, such as Turner syndrome. Dyscalculia can be congenital, as a consequence of cerebral palsy or acquired,1 e.g. as a consequence of a traumatic brain injury – in this sense, it can arise in adolescence or even in adulthood (Santos, 2017a). However, the symptom “dyscalculia” is different from the learning disability developmental dyscalculia. It is rare to think that the knowledge of quantities precedes the acquisition of language and mainly school experience. However, Lucangeli, D. (Ed.). (2020). Understanding dyscalculia : A guide to symptoms, management and treatment. Taylor & Francis Group. Created from bibliovirtualuide-ebooks on 2024-02-14 19:08:17. Copyright © 2020. Taylor & Francis Group. All rights reserved. 66 Flávia Heloísa Santos there is evidence that newborns can perceive quantity changes in emitted sounds (Schleger et al., 2014). Babies at six months are already able to calculate small amounts like 1 + 1 or 2 – 1 (Wynn, 1992). However, if we are already born with a genetic predisposition to perceiving quantities and manipulating them, it does not make sense to think that: 1 a genuine difficulty with the quantic system would arise only in the school period and, 2 this genuine ability cannot be stimulated by strategic procedures. The first question is crucial for the differential diagnosis of developmental dyscalculia and the second for the delineation of interventions for these children. “Mathematical difficulties” refers to inefficient learning in this school discipline, such as low grades, mistakes in homework or during classroom activities. However, this expression encompasses multiple determinants of difficulties: sensorial, intellectual, emotional, pedagogical failures, as well as socio-economic and interpersonal factors. On the one hand, this expression helps to detect all those who need some form of remediation in mathematics; on the other hand, it does not discriminate as to what type of assistance is convenient in each case. For this reason, before thinking about remediation strategies and recommendations for parents, teachers and neuropsychologists, it is necessary to identify the two main groups that present difficulties in mathematics observed in the school context. The first and largest group are children with low attainment in mathematics.2 Their deficits are mild to moderate (≥11 percentile3 ≤25), generally transient and even susceptible to spontaneous recovery or responsive to conventional scholar reinforcements. The cause of these deficits is essentially extrinsic, e.g. students who do not study in their native language, are frequently absent from classes, lack socio-economic resources, present a disease that indirectly affects their learning (by tired, sleepy, feeble states) or, in addition, by shortage of pedagogical resources, such as access to teaching technologies and stimulation for learning. The developmental dyscalculia, also known as mathematical learning disabilities, is the second and smallest group, with prevalence of between 3 and 6.5 per cent of cases (Devine, Soltész, Nobes, Goswami, & Szücs, 2013). It has an intrinsic origin,4 the deficits in numerical cognition are severe (≤10th percentile) and persistent over the years (e.g. Shalev, Manor, Auerbach, & GrossTsur, 1998). Unlike low attainment in mathematics, developmental Lucangeli, D. (Ed.). (2020). Understanding dyscalculia : A guide to symptoms, management and treatment. Taylor & Francis Group. Created from bibliovirtualuide-ebooks on 2024-02-14 19:08:17. Children with developmental dyscalculia 67 dyscalculia does not arise during the school period, although it is usually diagnosed after literacy. Actually, the difficulties in manipulating quantities and magnitudes are expressed early, for instance during kindergarten; they are not restricted to academic activities and in fact can be observed in how the child plays or in daily tasks at home. Once the developmental dyscalculia can be detected already in pre-school, it is essential to develop early tracking tools of quantitative competences, preferably focused on the number sense (Box 5.1). Copyright © 2020. Taylor & Francis Group. All rights reserved. Box 5.1 sense Characteristics of a number The term “number sense” generates much confusion since “number” in this concept is a misnomer, because the quantic system is innate and independent of language acquisition and of symbolic quantity system. Several animals, such as rats, pigeons, dolphins, monkeys, parrots and chimpanzees, among others (Dehaene, Dehaene-Lambertz, & Cohen, 1998) are endowed with a “quantity accumulator”, also observed in babies and isolated indigenous tribes. In contrast, the numerical system itself is slowly acquired by the child’s exposure to words representing quantities (“two” kittens, “many” flowers, I am the “first”, etc.) and its equivalence with numerals in Arabic form. In spite of being able to recite “one, two, three, four” easily, the objective understanding that these words refer as specific quantity of units occurs gradually between two and five years of age, as long as the child acquires the principles of cardinality (Sella, Berteletti, Lucangeli, & Zorzi, 2017). Essentially, the number sense is the analogical representation of quantities. It implies in both capacities to identify, without counting, the precise quantity of items of a given set (subitization; from subitus), and to estimate, also without counting, two sets of quantities in which one there are more units. Briefly, developmental dyscalculia is expressed as a dysfunction of the number sense and this understanding is consistent when we refer to the exact calculations of small Lucangeli, D. (Ed.). (2020). Understanding dyscalculia : A guide to symptoms, management and treatment. Taylor & Francis Group. Created from bibliovirtualuide-ebooks on 2024-02-14 19:08:17. 68 Flávia Heloísa Santos Copyright © 2020. Taylor & Francis Group. All rights reserved. quantities (Feigenson, Dehaene, & Spelke, 2004). However, the approximate calculation of large quantities (Halberda & Feigenson, 2008) also seems to use this mechanism,5 but in this case, the estimation is possible only if the individual has acquired other knowledge of more complex quantities from formal education, such as the mental number line, an internal metric system that ordinarily organizes numerical information (Dehaene, Piazza, Pinel, & Cohen, 2003). The transition from a cardinal system to the ordinal system apparently occurs in a continuum as a function of increasing age, schooling and environmental stimulation (Kucian & Kaufmann, 2009). These intermediate skills such as counting in a direct and inverse order and comparing magnitudes acquired during the systems transition called early competences or preparatory skills, are predictors of later arithmetic skills (Praet & Desoete, 2014). There is no consensus among researchers whether the number sense includes the early competences or whether they would already be part of an ordinal system. It is important to consider that the definitions of the low attainment in mathematics and developmental dyscalculia groups in this chapter have an essentially didactic nature. Although the existence of these two groups is well established, the characteristics defining them have demanded intense and intricate discussions among specialists such as physicians, psychologists, pedagogues and others, and the distinction is much more complex than merely dichotomous between a medical condition versus a pedagogical failure. In fact, it requires deep knowledge, as the distinction between these groups crosses the diagnostic criteria, evaluation instruments adopted (screening, achievement and diagnosis tools) and their respective and arbitrary cut-offs, which define the nomenclature. In addition, even if a child has biological factors in the genesis of their number deficits, an unfavourable environment can intensify them. On the other hand, the inadequate teaching does not seem sufficient to cause a learning disorder. Differences between low attainment in mathematics and developmental dyscalculia go beyond quantitative aspects (such as Lucangeli, D. (Ed.). (2020). Understanding dyscalculia : A guide to symptoms, management and treatment. Taylor & Francis Group. Created from bibliovirtualuide-ebooks on 2024-02-14 19:08:17. Copyright © 2020. Taylor & Francis Group. All rights reserved. Children with developmental dyscalculia 69 percentile, standard deviation and years of scholar delay), as according to follow-up studies there are also qualitative differences between these groups. The curve analyses of the numerical cognition performance from pre-school to the third year of school (Murphy, Mazzocco, Hanich, & Early, 2007) reveal that American children with developmental dyscalculia present substantially lower scores on pre-school, with inexpressive increases in the course of successive school years and this pattern tends to plateau, or may even decrease in some cases. By contrast, although children with low attainment in mathematics present scores below children with typical development and above those with developmental dyscalculia, their curve ascends throughout school years and tends to approach children not presenting difficulties in mathematics. In another study, Belgian children were evaluated twice, in pre-school and the second school year (Desoete, Ceulemans, De Weerdt, & Pieters, 2012). In the pre-school phase, children with low attainment in mathematics exhibited slight difficulties in the task of comparing non-symbolic magnitudes, whereas the lack of precision in symbolic processing prevailed in children with developmental dyscalculia in both assessments. In another trajectory study, American children were evaluated from pre-school to the third year (Geary et al., 2009). The performance curves in high and medium groups were ascending, parallel and equivalent to 20-point gains over the four successive school years, while low attainment in mathematics and developmental dyscalculia groups obtained gains of between 6 and 7 points in the same period. Other analyses within the sample outlined the role of working memory on numerical cognition development (Geary et al., 2007); in fact, deficits in intellectual level and working memory were associated with worse scores in numerical processing tasks. In addition, children with low attainment in mathematics were able to use the decomposition strategy (for example: 17 + 6 is the same as 17 + 3 + 3) more often than children with developmental dyscalculia. As low attainment in mathematics is an exogenous condition, it does not appear in medical manuals, while developmental dyscalculia, which is endogenous, was recognized in the medical manuals as F81.2 Specific disorder of arithmetical skills (ICD-10; WHO, 1992) or 315.1 Specific learning disorder with impairment in mathematics (DSM-V, APA, 2013) with these criteria: 1 A set of specific symptoms is present (deficits in number sense, memorization of arithmetic facts, fluency and precision in mathematical calculation and Lucangeli, D. (Ed.). (2020). Understanding dyscalculia : A guide to symptoms, management and treatment. Taylor & Francis Group. Created from bibliovirtualuide-ebooks on 2024-02-14 19:08:17. Copyright © 2020. Taylor & Francis Group. All rights reserved. 70 Flávia Heloísa Santos reasoning), 2 The symptoms are observed for at least six months, 3 Performance is below that observed in normative data, 4 It has an early onset and tendency to persist until adulthood, 5 Absence of specific aetiologies and 6 Does not respond satisfactorily to conventional interventions. Although medical manuals tend to converge in their classifications, there are certain discrepancies between them. For instance, the discrepancy criterion between age and intelligence was abolished by DSM-V (APA, 2013), considering its lack of discriminant validity to identify the ideal discrepancy in the case of children with intelligence above or below the mean (Murphy et al., 2007). Moreover, discrepancy loses stability over time as well as the reliability to compare children during the initial phases of learning (Mazzocco & Myers, 2003), in which both the child with typical development and the child with developmental dyscalculia have not yet expressed all their potential to perform arithmetic, as well as reading and writing. The ICD-11 (WHO, 2018) restores the discrepancy between intellectual functioning and mathematics performance. It is important to emphasize that persistent does not mean immutable; as the child has a set of cognitive skills and environmental stimulation, it is natural to develop his or her own strategies or others taught in the school context that aid in overcoming some difficulties. In the same way that trajectory of the deficits in groups support the understanding of this neurodevelopmental disorder, monitoring cases clinically is also indicated, in order to adapt the assistance to the changes that may occur in the functioning of the individual. Besides, because persistence of symptoms in successive evaluations and resistance to interventions are diagnostic criteria, the family and neuropsychologist must deal with the possibility that diagnosis in some cases cannot be conclusive in a single evaluation. Therefore, the first evaluation may be important to initiate remediation, and after an interval of at least six months a follow-up and possibly confirmatory evaluation of the diagnostic hypothesis can be performed (Kaufmann et al., 2013). Numeracy deficits may arise isolated or accompanied by deficits in other cognitive functions, among which executive functions and visuospatial abilities or in comorbidity with other neurodevelopmental disorders, particularly reading disability (e. g., Geary et al., 2007). In the latter, the term F81.3 Mixed disorder of school skills can be adopted, for instance, to describe the comorbidity between dyslexia and dyscalculia which is quite frequent Lucangeli, D. (Ed.). (2020). Understanding dyscalculia : A guide to symptoms, management and treatment. Taylor & Francis Group. Created from bibliovirtualuide-ebooks on 2024-02-14 19:08:17. Copyright © 2020. Taylor & Francis Group. All rights reserved. Children with developmental dyscalculia 71 (Butterworth & Kovas, 2013). For some authors, developmental dyscalculia would be a continuum of developmental dyslexia, once the coexistence of reading and mathematics dysfunctions is higher than each isolated prevalence. One explanation for this superposition comes from genetic studies contrasting pairs of monozygotic and dizygotic twins or parent skills, and raised evidence for the hereditary nature of the deficits (Shalev et al., 2001; Kovas et al., 2007). Another argument is the presence of semantic components in both disorders (Geary, 1993). This overlapping within disorders is in accordance with the new categorization of the DSM-V (APA, 2013) that proposes a single disability – specific learning disorder – expressed by specific symptoms. This view is also corroborated by a brain functional study that observed similar activation for both clinical groups while performing mathematical tasks in contrast to controls (Peters, Bulthé, Daniels, Op de Beeck, & De Smedt, 2018). In summary, this information indicates that interventions should consider: 1 the different determinants of deficits, 2 the presence of deficits in other cognitive functions, 3 the presence of comorbid neurodevelopmental disorders, 4 changes in the characteristics of the disorder over time, 5 stimulation versus remediation of numerical cognition, and 6 confounding results from interventions may be due to mixed groups (developmental dyscalculia and low attainment in mathematics, as interchangeable). Regarding treatment, due to the lack of diagnosis, both developmental dyscalculia and low attainment in mathematics groups commonly receive similar educational interventions (after-school tutoring, school tutorials or resource room). The low response of several children to these supports leads the child to a specialized evaluation and then a delayed treatment by an intervention focused on their learning disability. General characteristics of the interventions “Intervention is defined as a specific instruction for a certain period of time to teach a particular domain of the mathematics curriculum” (Kroesbergen & van Luit, 2003, p. 97). The goal of intervention is to improve mathematical skills and knowledge, according to its principles (Box 5.2). Based on systematic review studies and particularly meta-analysis, the most effective interventions can be identified for children with numeracy dysfunctions. Lucangeli, D. (Ed.). (2020). Understanding dyscalculia : A guide to symptoms, management and treatment. Taylor & Francis Group. Created from bibliovirtualuide-ebooks on 2024-02-14 19:08:17. 72 Flávia Heloísa Santos Box 5.2 Principles for effective intervention According to Fuchs et al. (2008), there are seven principles that contribute to the development of effective learning of children with developmental dyscalculia in intensive intervention programmes. These principles can be followed by parents and teachers and professionals who interact with children who present numerical cognition dysfunctions: 1 2 3 4 Copyright © 2020. Taylor & Francis Group. All rights reserved. 5 6 7 Explicit instructions. Provide step-by-step information of what should be done instead of soliciting the child to guess the pathway from a few known elements. Minimize errors during learning. The errorless strategy is to anticipate or eliminate equivocal interpretations of step by step, aiming to automate a precise procedure. Emphasis on conceptual bases. In both classroom activities and in interventions, it is important that the child understands why such procedures are performed, i.e. the theoretical basis. Repetition and memorization. The repetition is crucial for the automation of procedures, fixation of the semantic components and acquisition of fluency in the performance of exercises. Cumulative revision. Each session must always resume what was learned in the previous as a way of consolidating learning and ensuring correct sequencing of knowledge. The child must get used to revising his or her own work after each exercise. Motivational processes. The child’s effort must be rewarded and every step achieved throughout the learning process must be recognized. Self-regulatory processes. Strategies that help to control emotional stress in the face of difficulties must be implemented. The careful handling of the pauses, as well as the choice of the appropriate time and environment for the intervention, helps to maintain the focal attention. Lucangeli, D. (Ed.). (2020). Understanding dyscalculia : A guide to symptoms, management and treatment. Taylor & Francis Group. Created from bibliovirtualuide-ebooks on 2024-02-14 19:08:17. Copyright © 2020. Taylor & Francis Group. All rights reserved. Children with developmental dyscalculia 73 Kroesbergen and van Luit (2003) carried out meta-analysis focused on instruction in mathematical learning. They selected 58 prospective or case-control studies regarding supporting programmes for children with difficulties in mathematics up to the sixth school year. Results indicated that short interventions are more efficient than those lasting 12 months or more, possibly as they focus on fewer components unlike more complex programmes. According to Cohen-Kadosh et al. (2013)’s systematic review, which was based on ten cognitive, educational and neuroscience studies, caution is still needed regarding interventions for developmental dyscalculia. As there are still few studies carried out in the field of neurosciences, on the other, this field is still incipient. In general, each study addresses a different technique, for example, computer games, non-invasive brain stimulation and interventions based on pedagogical groups. In fact, a few interventions were replicated to confirm that the findings were not random. From the methodological point of view, there are still many single case6 studies or convenience samples, without randomization, some of which lack control group or adopt passive control groups which allows studying the effect of a technique but not the superiority of that compared to another. In addition it restricts discrimination of the placebo effect, since “a certain attention is always better than none”. Once all these limitations are considered, it can be affirmed that some interventions seem effective in the short and medium terms. However, little is known about the mechanisms that justify such findings. A way to study the mechanisms by which interventions produce cognitive and behavioural effects is to understand brain-related changes on morphology. Neuroimaging studies show the plasticity processes obtained through the intervention. In general, neuroplasticity can be predicted by functional and structural changes of the individual in response to remediation (Iuculano et al., 2015). Hypothetically, there are two possible processes in response to an intervention; on the one hand, compensatory mechanisms could occur, i.e. other brain areas not crucial for calculation could be recruited; on the other hand, canonical areas of the quantic system previously hypoactive could become more functional, i.e. normalization. However, a few studies were able to demonstrate the association between cognitive and behavioural gains with changes in brain Lucangeli, D. (Ed.). (2020). Understanding dyscalculia : A guide to symptoms, management and treatment. Taylor & Francis Group. Created from bibliovirtualuide-ebooks on 2024-02-14 19:08:17. Copyright © 2020. Taylor & Francis Group. All rights reserved. 74 Flávia Heloísa Santos function. Knowing how intervention modifies brain architecture is also a way to broaden understanding of the neurocognitive mechanisms involved in numerical learning, which in turn would help researchers design more appropriate remediation methodologies. Interventional studies methodologically characterized by randomized and controlled trials (RCTs) and those prospective studies that accumulate different sources of evidence of beneficial effect, that is, cognitive, behavioural and encephalic changes in post-training, are the most reliable. Participants are evaluated by instruments in at least two time points. Researchers calculate relative learning gain (post-test – pre-test/pre-test) or at least the absolute learning gain (post-test minus pre-test) and interpret these values in terms of learning transfer: near transfer, when the training produces gains in abilities similar to those trained, or far transfer – gains in untrained skills (Santos, 2017a). However, one must bear in mind that there is no single intervention suitable once the developmental dyscalculia profiles are very heterogeneous (Dowker, 2005). Currently according to the protocol for systematic review of Furlong, McLoughlin, McGilloway, and Geary (2016), we have essentially five modalities of interventions for developmental dyscalculia: 1 focused on mathematics; 2 psychological and behavioural approaches; 3 noninvasive brain stimulation technologies; 4 pharmacological and 5 multi-components (involve combinations of these treatments). Interventions focused on mathematics can have a pedagogical or cognitive approach. In the pedagogical one, the tutor carries out explicit trainings, based on processes, through concrete materials and offers feedback on the execution. The prototypical example is the Numerical Cognition Tutorial that stimulates counting strategies and the mental number line (Iuculano et al., 2015). In the cognitive approach, implicit trainings, based on strategies, prevail by means of adaptive computerized materials (for example, The Number Race)7 that objectively control the time of exposure and the degree of complexity as well as the use of behavioural reinforcers. The most prominent example is the Calcularis (Santos, 2017b). The psychological and behavioural approaches act indirectly in the treatment of developmental dyscalculia for children who present school phobia, mathematics anxiety and low self-efficacy. In this sense psychotherapy can stimulate academic facilitators, which are motivation, commitment, social skills and behavioural measures of academic competence. As for the behavioural approach, the child can be helped to develop academic competence (prepare for Lucangeli, D. (Ed.). (2020). Understanding dyscalculia : A guide to symptoms, management and treatment. Taylor & Francis Group. Created from bibliovirtualuide-ebooks on 2024-02-14 19:08:17. Copyright © 2020. Taylor & Francis Group. All rights reserved. Children with developmental dyscalculia 75 class, meet deadlines, follow directions, do homework, appropriate school behaviour). For more details, see Furlong et al. (2016)’s protocol. The use of non-invasive brain stimulation technologies such as neurofeedback and direct current transcranial stimulation (tDCS) seems promising, although the long-term effects of such interventions in brain functioning remain unknown. In comparison with sham condition, boys treated by the neurofeedback (20 sessions of 30 minutes each) on post-test showed a decrease of attention deficits and improvements in mathematical performance; besides, the effects were persistent after one year (Hashemian & Hashemian, 2015). Studies of the effects of tDCS on children are scarce, since this field is still in development. However, in adults with developmental dyscalculia treated with tDCS, improvements in basic numerical skills, arithmetic reasoning and automaticity were observed. There was also a long-term transfer effect in the cerebral regions of the intraparietal sulcus and the dorsolateral prefrontal cortex, which are core areas for calculation and working memory (Cohen-Kadosh, Soskic, Iuculano, Kanai, & Walsh, 2010). As for pharmacological interventions, it is important to emphasize that there is no pharmacological treatment for dyscalculia per se. However, children with developmental dyscalculia who have comorbidities with other neurodevelopmental disorders, such as depression, anxiety and attention deficit hyperactivity disorder, may eventually benefit from drug treatment for these specific conditions (Cohen-Kadosh et al., 2013). In other words, the pharmacological improvement of the comorbidities would indirectly favour higher performance in mathematics classes. Chodura, Kuhn, and Holling (2015) recently conducted a metaanalysis with 35 prospective studies of interventions. All selected studies included a control group and samples of ten or more participants in each. In this study, it was possible to confirm that mathematical interventions are effective, for example, problem-solving training for children with low attainment in mathematics (Fuchs, Fuchs, Hamlett, & Appleton, 2002). Among the strategies used, it was verified that direct or assisted instructions, mainly of basic competences are preferable. Moreover, individual interventions seem more promising than groups. Regarding computer-assisted interventions (CAI), they were more useful for children with low attainment in mathematics than for those with developmental dyscalculia, even in non-adaptive training, i.e non-progressive increase Lucangeli, D. (Ed.). (2020). Understanding dyscalculia : A guide to symptoms, management and treatment. Taylor & Francis Group. Created from bibliovirtualuide-ebooks on 2024-02-14 19:08:17. 76 Flávia Heloísa Santos the degree of complexity of the exercises. Besides, instruction by the CAI was as effective as a face-to-face tutor. Next, we will address four intervention areas for children with numerical cognition dysfunctions; the first two which refer to activities predominantly performed by clinicians, are intervention programmes focused on the cognitive and emotional aspects of children with developmental dyscalculia or low attainment in mathematics. Then a few alternative approaches will be mentioned. Finally, as regards the school context, we will present activities that can be developed by teachers during the teaching of mathematics. Interventions of cognitive, emotional and educational aspects Copyright © 2020. Taylor & Francis Group. All rights reserved. Numerical cognition Systematic reviews consistently indicate that most interventions are focused on basic arithmetic skills, i.e. reducing the response time in non-symbolic item counting tasks, increasing precision in number estimation on a number line and transcoding. It also seems more effective to focus on the dysfunctional components of a particular child than to offer the same programme to all children with numerical cognition dysfunction (Cohen-Kadosh et al., 2013). The term “problem solving” is still a challenge for many students of mathematics and is one of the weaknesses of children with low attainment in mathematics and developmental dyscalculia. In recent years, more interventions have been developed in this field. The success of the programme relies on metacognition combining both instructions: schematic (conceptualizing the problem) and cognitive strategies (rewriting the question, creating a bar model, formulating hypothetical results and checking the response). A set of single cases of nine-to-ten-year-old children were treated by this combined approach daily for eight weeks, for 25–40 minutes after class, revealing that students were able to develop metacognition and objectively improve performance in problem solving (Morin et al., 2017). In this line of face-to-face training, the numerical cognition tutorial is a pedagogical programme administered in individual sessions (child and tutor) for eight weeks, in which 22 lessons were carried out lasting 40–50 minutes each, combining non-accelerated (learning a new strategy step-by-step) and accelerated (applying Lucangeli, D. (Ed.). (2020). Understanding dyscalculia : A guide to symptoms, management and treatment. Taylor & Francis Group. Created from bibliovirtualuide-ebooks on 2024-02-14 19:08:17. Copyright © 2020. Taylor & Francis Group. All rights reserved. Children with developmental dyscalculia 77 the learned strategy) practices. In the evaluation of mathematical skills, the control and experimental groups became equivalent in post-training. Regarding the functional neuroimaging study, in pretraining it was possible to distinguish between the brain functioning of children with developmental dyscalculia and that of the control children with 83 per cent of certainty. However, in post-training children with developmental dyscalculia started to activate the same brain areas as the controls making groups morphologically indiscriminate; in other words, the tutorial promoted normalization of brain function (Iuculano et al., 2015). Early numerical competences are reliable predictors of later mathematical academic achievement (Booth & Siegler, 2006). Thus, the training of the mental number line in the pre-school phase, by means of a three-dimensional board, which allows spatially visualizing a linear trajectory, favours the acquisition of new numerical knowledge precisely, enables comparison of magnitudes and number line estimation and also leads to more correct responses in arithmetic tasks. Moreover, the linear board game was more efficient than the circular one (Siegler & Ramani, 2009). CAIs are among the procedures to develop early competences, and programmes are generally focused on a specific numerical cognition skill, e.g. to develop the mental number line. In this sense, Rescue Calcularis is the first study covering the three parameters of evidence – cognitive, behavioural and neuroimaging in children with developmental dyscalculia. The computerized training programme consisted of daily 15-minute sessions, five days per week, for five consecutive weeks. In this programme, the player is invited to pilot a spaceship, use a joystick, look for a certain exact location in a horizontal number line, with numbers oriented from left to right, from zero to 100, having a figure indicated in Arabic form as a coordinate, by points, or by the result of an addition or subtraction. Each success is rewarded with fuel for new trips, assigned after completing the mission (75 calculations progressively increasing complexity). Following training, there was improvement in the performance of numerical cognition tasks. The functional neuroimaging study revealed recruitment of new areas to boost the function, suggesting compensatory processes. An important aspect is that the improvement in this task is suggestive of improvement in the mental numerical line itself; however, gains require the training of symbolic and non-symbolic magnitudes (Kucian et al., 2011). Lucangeli, D. (Ed.). (2020). Understanding dyscalculia : A guide to symptoms, management and treatment. Taylor & Francis Group. Created from bibliovirtualuide-ebooks on 2024-02-14 19:08:17. 78 Flávia Heloísa Santos The programme was recently expanded and modernized, including three-dimensional stimuli and 17 computerized games to be used three to four times a week for approximately 20 minutes with progressive degrees of complexity (numerals 0–10, 0–20, 0–100 and 0–1,000). This software is known as Calcularis, suitable for children from 7 to 13 years old; in children with low attainment in mathematics, it has produced a more precise and agile performance in additions and subtractions (Käser et al., 2013). Copyright © 2020. Taylor & Francis Group. All rights reserved. Mathematics anxiety Mathematics anxiety can be present in any child, even among those without any learning difficulties; it appears to have an increased trajectory from childhood to adolescence and be influenced, in part, by gender stereotypes or by anxious teachers (cf. review by Dowker, Sarkar, & Looi, 2016). In addition, a child may not sleep the night before a test and experience trembling, sweating and heart palpitations in the classroom, although performance on the test itself may be satisfactory. It is also observed that, although there are more reports of anxious symptoms in girls (with or without developmental dyscalculia), their performance in tasks of numerical cognition is equivalent to boys (Devine et al., 2013). However, mathematics anxiety is a characteristic observed in some children with developmental dyscalculia (Wu, Willcutt, Escovar, & Menon, 2014). Wu, Willcutt, Escovar, and Menon (2014) studied 366 children with an association of behavioural problems and low performance in mathematics. Children with developmental dyscalculia from the second and third school years exhibited more social and attentional problems than those with typical development. The most frequent problems were non-compliance and aggressive behaviours suggesting that this group may be at risk of these more severe externalizing behavioural problems. In general, these results suggest that children with developmental dyscalculia may have an increased risk of having social problems and comorbidities such as ADHD and oppositional defiant disorder. There were no significant associations between performance in mathematics and mastery of internalizing behaviours, which included trait anxiety, depression, abstinence and somatic complaints. The developmental dyscalculia and low attainment in mathematics groups showed higher levels of mathematics anxiety than controls; this negative association between anxiety to mathematics and school achievement remained Lucangeli, D. (Ed.). (2020). Understanding dyscalculia : A guide to symptoms, management and treatment. Taylor & Francis Group. Created from bibliovirtualuide-ebooks on 2024-02-14 19:08:17. Copyright © 2020. Taylor & Francis Group. All rights reserved. Children with developmental dyscalculia 79 significant, even when the intellectual level, general anxiety and depression were controlled. According to Passolunghi et al. (2016), the combination of deficits in working memory and numerical cognition are risk factors for mathematics anxiety; its presence affects the functioning of the attention system and reduces attentional control in tasks related to this discipline. For some children, doing mathematical exercises is simply a challenge of specific knowledge, but for those anxious about the subject, they are actually thinking of their real knowledge of the discipline while performing the task, wondering what their teachers, family and colleagues will think of them if they do not provide the correct answer. Thus, its mnemonic capacity, which should be focused on the calculation, is diverted towards these concerns, which consequently reduces the likelihood of success in the exercises, since sufficient concentration is lacking. For example, a sample of sixth- and eighth-grade students who did not present general anxiety, matched in terms of age, gender and vocabulary, was evaluated by a scale on mathematics anxiety, as well as phonological memory tasks. The students were divided into two groups: with high or low anxiety to mathematics. The groups did not differ in tasks related to literacy. However, children with high mathematics anxiety showed difficulties in the mathematical tasks, except in one of approximate calculation; in addition, they exhibited difficulties in phonological memory tasks. Therefore, this is evidence of the negative relationship between mathematics anxiety, verbal working memory and mathematical performance (Passolunghi et al., 2016). To broaden the understanding of the cognitive mechanisms underlying mathematics anxiety, Mammarella, Caviola, Giofrè, and Borella (2017) evaluated three clinical groups (children with mathematics anxiety, children with developmental dyscalculia and children with concurrence of both) compared to a group control, in measures of inhibitory control: resistance to proactive interference and inhibition of the prepotent response and in phonological working memory. The results indicated deficits in working memory were selective in children with developmental dyscalculia, i.e. in the absence of general anxiety or mathematics anxiety. On the other hand, children with the latter were more susceptible to proactive interference compared to co-occurrence group or just developmental dyscalculia. No differences were found between the groups regarding the inhibition of prepotent response. Therefore, this study Lucangeli, D. (Ed.). (2020). Understanding dyscalculia : A guide to symptoms, management and treatment. Taylor & Francis Group. Created from bibliovirtualuide-ebooks on 2024-02-14 19:08:17. 80 Flávia Heloísa Santos confirms the association between working memory and inhibitory deficits in children with mathematics anxiety. As regards mathematics anxiety prevention, teachers and family should have a proactive attitude towards the subject (Box 5.3), controlling their own expectations and gender Copyright © 2020. Taylor & Francis Group. All rights reserved. Box 5.3 Proactive actions to the learning of children with developmental dyscalculia According to Santos (2017a), there are some proactive attitudes that can be taken by family and teachers of children with numerical cognition dysfunctions, in order to encourage and facilitate their experience with mathematics: Always encourage the children to try, in order to develop self-confidence in themselves. Explain the subject by means of concrete objects and everyday situations. Show the utility of mathematical knowledge in nonacademic contexts and in professions. Read the arithmetic problem out loud at least twice so the children can pick up the details. Always use several synonyms for words applied to mathematics. Instead of pushing for faster response in class, offer a reduced number of exercises. Avoid suddenly asking the children to respond to arithmetic exercises aloud or on the board. Avoid associating the correction of their mistakes in school activities with punishment. Avoid making destructive comments, especially about their performance and slowness. Avoid exposing the children’s test scores in front of others. Avoid comparing children’s performance. Identify environmental distractors and competing interests, etc. that disrupt performance. Organize an evaluation system in which the children can identify their progress. Lucangeli, D. (Ed.). (2020). Understanding dyscalculia : A guide to symptoms, management and treatment. Taylor & Francis Group. Created from bibliovirtualuide-ebooks on 2024-02-14 19:08:17. Children with developmental dyscalculia 81 Copyright © 2020. Taylor & Francis Group. All rights reserved. stereotypes (Dowker et al., 2016). Besides, intervention for numerical c­ognition sometimes reduces mathematics anxiety (e.g. Arias-Rodriguez, Nascimento, Voigt, & Santos, 2019; Ribeiro & ­Santos, 2017; Käser et al., 2013). In the school setting, teachers can reduce student anxiety about the subject by easing the pressure of the test, allowing students the chance to talk about their concerns regarding the exam or even write down negative thoughts and feelings. The idea is to transfer ruminant sensations from the mind to paper; in fact, the more detailed the stories, the more efficient the therapeutic writing (Ramirez & Beilock, 2011). Supekar, Iuculano, Chen, and Menon (2015) offered an eight-week tutorial programme for seven–nine-year-old children with mathematics anxiety. After three sessions per week of intensive tutorial, children presented lower levels of mathematics anxiety, and the functional neuroimaging study pre- and post-test comparison indicated changes in brain circuitry on the basolateral amygdala nucleus while performing a mathematical task in students with high mathematics anxiety. Passolunghi and Pellizzoni (2018) conducted the first clinical study for mathematics anxiety intervention in children contrasting two proposals with eight sessions of one hour per week for children in the fourth year. The first was focused on developing numeracy and the second on regulatory strategies to cope with anxiety. Both strategies reduced mathematics anxiety; however, only the group stimulated in terms of numeracy presented a better mathematical performance on post-test. This is evidence that improving numerical cognition reduces mathematics anxiety; however, reducing this anxiety alone appears insufficient to improve learning. Other cognitive functions and musical skills Neuropsychological remediation was effective in the treatment of eight–nine-year-old Iranian girls with developmental dyscalculia (Faramarzi & Sadri, 2014). This study involved a programme of ten sessions of two hours each, twice a week, including activities to reinforce attention, planning and organization, working memory, language and visuospatial processing. The analysis of covariance, taking pre-training as a covariate, indicated expressive gains for basic concepts, operations and applications for the treated group compared to a control group. There are also other interventions that focus on a particular cognitive ability, according to the following examples. Lucangeli, D. (Ed.). (2020). Understanding dyscalculia : A guide to symptoms, management and treatment. Taylor & Francis Group. Created from bibliovirtualuide-ebooks on 2024-02-14 19:08:17. Copyright © 2020. Taylor & Francis Group. All rights reserved. 82 Flávia Heloísa Santos In an RCT study, pre-school children of low socio-economic status and with difficulties in mathematics received intervention in this subject (Barnes et al., 2016). One-third of the children were treated with mathematical tutorial in small groups, the Pre-K Mathematics Tutorial, complementary to curricular activity; another third in addition to the tutorial received attention training; and the last third just attended regular classes. After 30 activities with concrete materials related to numbers, arithmetic, space, geometry and measurements, the two groups treated showed better scores in the school achievement test in mathematics compared to the control. However in the numerical cognition battery, the differences in the post-test were subtle and restricted to the group that only performed the tutorial. The attention gains in attention measures were significant but minimal. Barnes et al. (2016) concluded that attention training did not moderate the learning of mathematics, since the tutorial plus attentional training did not produce transfer of learning in measures of school achievement and numerical cognition. Children with developmental dyscalculia do not have an automatization of arithmetic facts, particularly basic additions and multiplications such as 6 + 7 or 2 x 3; consequently, they depend on some strategy, e.g. using their fingers to count, which slows down their response compared to controls (Gersten, Jordan, & Flojo, 2005). These deficits are due to lower mnemonic capacity. There are at least two mnemonic systems considered crucial for the functioning of quantic and numerical systems, semantic memory and working memory, also from the neural point of view (Fias, Menon, & Szücs, 2013). The acquisition of mnemonic strategies seems to feed the learning processes, for example, repeat, reintegrate, group information (Santos, 2017b). Semantic memory supports estimation and the acquisition of fluency for arithmetic fact and contributes to calculus and algebraic knowledge of fractions (Geary, Hoard, Nugent, & Rouder, 2015). It can be stimulated at an early age by using manipulatives that facilitate the knowledge of non-symbolic arithmetic, and later by algorithmic strategies that reinforce arithmetic facts to prepare for mental calculation (Sherman & Bisanz, 2009). Correlational studies evidence that different components of working memory – executive, visuospatial and phonological) contribute to the performance of numerical cognition tasks, throughout school years in children with typical development (Ribeiro, Silva, & Santos, 2016). Deficits in working memory components Lucangeli, D. (Ed.). (2020). Understanding dyscalculia : A guide to symptoms, management and treatment. Taylor & Francis Group. Created from bibliovirtualuide-ebooks on 2024-02-14 19:08:17. Copyright © 2020. Taylor & Francis Group. All rights reserved. Children with developmental dyscalculia 83 are observed in children with developmental dyscalculia, especially in those who have the co-occurrence of deficits in reading (Szücs, 2016). In this sense, working memory training could be an effective resource to improve quantitative skills. Layes, Lalonde, Bouakkaz, and Rebai (2017) conducted a prospective study in 28 children with developmental dyscalculia from the fourth school year, divided into a control and experimental group. The latter performed an adaptive training for eight weeks, taking three sessions of 45 minutes per week. Successful responses were reinforced with stars and the activities were carried out face-to-face, between the tutor and the child. The stimulated components were number sense, digits span, comparison of numerals and visual and auditory memory for numbers. At the beginning of each new session, a brief practice of the previous session content was performed. When children did not reach the 70 per cent success rate, the extension of the sequences was reduced. There was near transfer, i.e. improvement in working memory tasks, as well as far transfer as they improved in mathematics compared to the control group. Musical training is an interesting approach that puts all children on an equal footing as they perform fun, collective activities not directly related to academic content. The stimulation of musical abilities seems to produce cognitive gains. For example, the Numeracy Musical Training (Silva, Baldin, & Santos, 2017; Arias-­ Rodriguez et al., 2019), based on the neurodevelopmental model of the numerical cognition of von Aster and Shalev (2007), was developed as a tool for music teachers with the aim of offering a shared musical stimulation for pre-school children in the school. Brazilian pre-schoolers who underwent a prospective, blind and pseudorandomized study with Numeracy Musical Training showed both near and far transfers and improvements in working memory and numerical cognition compared to the control group. Besides, gains were resistant to the false discovery rate. In other non-instrumental musical training, children with developmental dyscalculia and the control group had 14 sessions of melodic and rhythmic activities in group one hour per week. In the pre-training cognitive assessment, the cluster analysis was able to precisely distinguish the groups. In post-training assessment some children with developmental dyscalculia normalized the performance; consequently, in the new cluster analysis, some children no longer belonged to the clinical group but rather were identified in the control group (Ribeiro & Santos, 2017; Ribeiro & Santos, 2020). Lucangeli, D. (Ed.). (2020). Understanding dyscalculia : A guide to symptoms, management and treatment. Taylor & Francis Group. Created from bibliovirtualuide-ebooks on 2024-02-14 19:08:17. 84 Flávia Heloísa Santos According to the meta-analysis by Melby-Lervåg and Hulme (2013) that compared 30 samples in studies with quasi-experimental design or RCT, working memory training should be viewed with caution. On the one hand, near transfer is evident for both new tasks of short-term memory and working memory; nevertheless, these effects were not time-resistant in the verbal modality and were controversial in the visuospatial ability according to followup studies. On the other hand, far transfer after working memory training was not consistent, especially concerning arithmetic. Some recent meta-analysis seems discouraging as regards far transfer effects overall. It is important to restrain overestimation of the benefits claimed by working memory training, chess or even musical training, i.e. these resources indeed seem to remediate cognitive deficits, eventually change behaviour towards learning but apparently do not make someone smarter (Sala & Gobet, 2017). The lack of effects also means that studies need more rigorous design. Based on current evidence, these approaches should not be used in isolation for remediation of developmental dyscalculia. Copyright © 2020. Taylor & Francis Group. All rights reserved. Strategies of teaching and learning with scholar context One effective aspect observed in different intervention programmes is the need for direct instruction by the teacher or the CAI. Nevertheless, as a complement, self-instruction is useful in stimulating the autonomy of the child, especially for problem solving. The components of the effective instructions include organizing content, modelling skills, encouraging explicit practice, controlling the difficulty of the task, highlighting strategies and clues and promoting questioning and elaboration (Zheng, Flynn, & Lee Swanson, 2012). During primary school, the teacher can help the child through differentiation, i.e. an adaptation of the instruction according to the specific educational needs of each child (Prast, Van de WeijerBergsma, Kroesbergen, & Van Luit, 2018). To develop appropriate instructions based on the needs of children with low attainment in mathematics and developmental dyscalculia, teachers must be able to follow the cycle of differentiation: identifying the educational needs of the children with learning disability, setting specific goals for the learning process, developing appropriate instructions for the understanding of the children according to the characteristics of their difficulties, differentiating Lucangeli, D. (Ed.). (2020). Understanding dyscalculia : A guide to symptoms, management and treatment. Taylor & Francis Group. Created from bibliovirtualuide-ebooks on 2024-02-14 19:08:17. Copyright © 2020. Taylor & Francis Group. All rights reserved. Children with developmental dyscalculia 85 regular practice in the classes and evaluating the process and the progress of the children’s learning (Prast et al., 2018). Children with learning disabilities benefit from teachers who have mastery in the four dimensions of adaptive teaching: 1 identifying the sequence in which the children learn such concepts; 2 monitoring progress and identifying educational needs; 3 adopting teaching methods, which vary in terms of the level of abstraction, according to the needs of the students; and 4 organizing collaborative activities among the students during the classes (Vogt & Rogalla, 2009). In the field of learning, the prediction of academic success is the “main objective of psychological and educational research” (Ruffing et al., 2015, p. 8). Academic success is related to indicators of economic prosperity, professional and social success. Since it is a relevant aspect for the individual and society, there is great interest in identifying its predictors. The intellectual level is the most well-established predictor and perhaps the most difficult to change. However, there are other predictors such as learning strategies that can be trained, through psychological and behavioural remediation approaches. The more teachers know about academic success predictors, the more adequately they will stimulate the students. A sample of 461 young adults was assessed in terms of intellectual level and two categories of learning strategies, namely: strategies of resource management (effort, attention, management of learning environment and time) and cognitive strategies (organization, relationships, evaluation, criticism and essay), as well as metacognition. The highest correlations (r>.50) were between attention and effort, metacognition and effort, learning environment and effort, as well as between critical evaluation and relationships. In general, there was a predominance in the use of resource management strategies. However, among all, effort alone was the variable that best explained academic success, adding 12 per cent of variance on intellectual level. By means of the latent variable model, it was possible to identify that men and women do not use learning strategies in the same way. Men focus on critical assessment and relationships, while women exhibit more frequent use of other skills (Ruffing et al., 2015). These learning strategies developed in childhood and adolescence. Effortful control is “the ability to inhibit the dominant response in order to perform the subdominant response, which requires detecting errors, and planning” (Rothbart, 2011, p. 57). Therefore, Lucangeli, D. (Ed.). (2020). Understanding dyscalculia : A guide to symptoms, management and treatment. Taylor & Francis Group. Created from bibliovirtualuide-ebooks on 2024-02-14 19:08:17. Copyright © 2020. Taylor & Francis Group. All rights reserved. 86 Flávia Heloísa Santos the shortest path to develop this type of effort is to stimulate focal attention and inhibitory control. However, a meta-analysis study (Cameron & Pierce, 1994) of 96 experimental studies regarding the effects of reward on intrinsic motivation reveals that children do not always perceive the relationship between effort and subsequent school performance, so the first step for parents and teachers is to stimulate awareness, and the second step is to adopt reinforcing behaviours whenever the child uses the strategy of effort. Most CAIs include explicit reinforcers in games. Teachers can adopt symbolic or abstract reinforcements in class. Family members may use affective reinforcements such as praise, affection and small rewards previously agreed with the child. Therefore, reinforcement can help in the process, if administered with moderation since rewards in excess can inhibit the intrinsic motivation of the child. Planning processes are not usually taught directly in a way that children develop a plan and its execution strategy during classroom exercises. The Planning Facilitation Method (PFM) is an intervention developed in India that can be administered by the teacher in class activities. Objectively, first the students complete a sheet of mathematical exercises for ten minutes. Once the students have worked on the problems, they receive ten minutes of planning facilitation in which the teacher stimulates students’ perception of different ways of responding successfully to the exercises. Consequently, children perform another ten minutes of mathematics where they are able and encouraged to implement and consolidate the strategies learned. A total of 140 children with mathematics disorder were selected, half of whom received the intervention, and the other half who did not perform these strategies. The results indicated an improvement in multiplication skills after intervention (Kumar & Darolia, 2016). Lucangeli, Tressoldi, and DeCandia (2015) developed the “Numeric Intelligence” programme to teach learning strategies related to the curricular content: counting, lexical processes, syntactic processes, oral calculus and written calculation. The Italian programme focuses on cognitive and metacognitive strategies and has four levels: 3–6, 6–8, 9–11 years plus special material for children with developmental dyscalculia. After 17 sessions of 90 minutes, the effectiveness of this programme in pre-school children was more evident for the less stimulated processes in the curriculum (reading, syntax and comparison of numbers). In seven-year-old children, there was improvement Lucangeli, D. (Ed.). (2020). Understanding dyscalculia : A guide to symptoms, management and treatment. Taylor & Francis Group. Created from bibliovirtualuide-ebooks on 2024-02-14 19:08:17. Children with developmental dyscalculia 87 in the calculation with just ten sessions of one hour each. For children diagnosed with developmental dyscalculia, case studies revealed improvements in performance. Therefore, in addition to stimulating the automation of arithmetic facts that is common in classes, teachers must develop students’ metacognitive skills that make them more autonomous. The final example comes from the UK – a non-intensive intervention known as “Catch Up Numeracy” was offered for children with low achievement for 15 minutes twice a week in individual sessions. The intervention was focused on factual, conceptual and procedural knowledge; training was delivered by the classroom assistant. After training, children showed more than two times gain over time than expected on time lapsed (Holmes & Dowker, 2013). Final thought This chapter was based on a systematic review of studies and metaanalyses; a few detailed studies were presented as examples of such approaches. It was not the purpose of this chapter to comprehensively portray the subject but to present its various nuances. Some interventions must be carried out by specialists in learning disabilities, others may be implemented in schools by their teachers and with the help of properly oriented family carers and by proactive attitudes towards learning. One component that should never be neglected in learning is the ludic nature of children. Copyright © 2020. Taylor & Francis Group. All rights reserved. Acknowledgement The author would like to thank Barry Noonan for reviewing this chapter. Notes 1 Some authors named acquired dyscalculia as “acalculia” or “anaritmetia”. 2 This group is also known as “at risk of dyscalculia” or “mathematical learning difficulties”. 3 Some researchers adopt even less strict criterion such as percentile ≤35. 4 A well-established neurobiological finding is the heritability. 5 The “approximate quantity/magnitude system”. 6 This experimental design has a bias: the effect sizes are higher because the training ceases when the criterion of correct responses is achieved. 7 Free download: https://sourceforge.net/projects/numberrace/ Lucangeli, D. (Ed.). (2020). Understanding dyscalculia : A guide to symptoms, management and treatment. Taylor & Francis Group. Created from bibliovirtualuide-ebooks on 2024-02-14 19:08:17. 88 Flávia Heloísa Santos Copyright © 2020. Taylor & Francis Group. All rights reserved. References American Psychiatric Association. (2013). Diagnostic and statistical manual of mental disorders (5th ed.). Washington, DC: American Psychiatric Association. Arias-Rodriguez, Nascimento, J., Voigt, M., & Santos, F. H. (2019). Numeracy musical training for school children with low achievement in mathematics. Anales de Psicología, 35(3), 405–416. Barnes, M. A., Klein, A., Swank, P., Starkey, P., McCandliss, B., Flynn, K.,... Roberts, G. (2016). Effects of tutorial interventions in mathematics and attention for low-performing preschool children. Journal of Research on Educational Effectiveness, 9(4). Booth, J. L., & Siegler, R. S. (2006). Developmental and individual differences in pure numerical estimation. Developmental Psychology, 41, 189–201. Butterworth, B., & Kovas, Y. (2013). Understanding neurocognitive developmental disorders can improve education for all. Science, 340(6130), 300–305. Cameron, J., & Pierce, W. D. (1994). Reinforcement, reward, and intrinsic motivation: A meta-analysis. Review of Educational Research, 64, 363–423. Chodura, S., Kuhn, J. T., & Holling, H. (2015). Interventions for children with mathematical difficulties: A meta-analysis. Zeitschrift für Psychologie, 223(2), 129–144. Cohen-Kadosh, R., Dowker, A., Heine, A., Kaufmann, L., Kucian, K., & von Aster, M. (2013). Interventions for improving numerical abilities: Present and future. Trends in Neuroscience and Education, 2(2), 85–93. Cohen-Kadosh, R., Soskic, S., Iuculano, T., Kanai, R., & Walsh, V. (2010, November 23). Modulating neuronal activity produces specific and long-lasting changes in numerical competence. Current Biology, 20(22), 2016–2020. http://doi.org/10.1016/j.cub.2010.10.007 Dehaene, S., Dehaene-Lambertz, G., & Cohen, L. (1998). Abstract representations of numbers in the animal and human brain. Trends in Neurosciences, 21(8), 355–361. Dehaene, S., Piazza, M., Pinel, P., & Cohen, L. (2003). Three parietal circuits for number processing. Cognitive Neuropsychology, 20(3–6), 487–506. Desoete, A., Ceulemans, A., De Weerdt, F., & Pieters, S. (2012). Can we predict mathematical learning disabilities from symbolic and nonsymbolic comparison tasks in kindergarten? Findings from a longitudinal study. British Journal of Educational Psychology, 82(1), 64–81. Devine, A., Soltész, F., Nobes, A., Goswami, U., & Szücs, D. (2013). Gender differences in developmental dyscalculia depend on diagnostic criteria. Learning and Instruction, 27, 31–39. Lucangeli, D. (Ed.). (2020). Understanding dyscalculia : A guide to symptoms, management and treatment. Taylor & Francis Group. Created from bibliovirtualuide-ebooks on 2024-02-14 19:08:17. Copyright © 2020. Taylor & Francis Group. All rights reserved. Children with developmental dyscalculia 89 Dowker, A. (2005). Individual differences in arithmetic: Implications for psychology, neuroscience and education. New York: Psychology Press. Dowker, A., Sarkar, A., & Looi, C. (2016). Mathematics anxiety: What have we learned in 60 years? Frontiers in Psychology, 7, 508. Faramarzi, S., & Sadri, S. (2014). The effect of basic neuropsychological interventions on performance of students with dyscalculia. Neuropsychiatria i Neuropsychologia, 9(2), 48–54. Feigenson, L., Dehaene, S., & Spelke, E. (2004). Core systems of number. Trends in Cognitive Sciences, 8(7), 307–314. Fias, W., Menon, V., & Szucs, D. (2013). Multiple components of developmental dyscalculia. Trends in Neuroscience and Education, 2(2), 43–47. Fuchs, L. S., Fuchs, D., Hamlett, C. L., & Appleton, A. C. (2002). Explicitly teaching for transfer: Effects on the mathematical problem-solving performance of students with mathematics disabilities. Learning Disabilities Research and Practice, 17, 90–106. Fuchs, L. S., Fuchs, D., Powell, S. R., Seethaler, P. M., Cirino, P. T., & Fletcher, J. M. (2008). Intensive intervention for students with mathematics disabilities: Seven principles of effective practice. Learning Disability Quarterly, 31(2), 79–92. Furlong, M., McLoughlin, F., McGilloway, S., & Geary, D. (2016). Interventions to improve mathematical performance for children with mathematical learning difficulties (MLD) (protocol). Cochrane Database of Systematic Reviews, 4, art. no. CD012130. Geary, D. C. (1993). Mathematical disabilities: Cognitive, neuropsychological, and genetic components. Psychological Bulletin, 114(2), 345–362. Geary, D. C., Bailey, D. H., Littlefield, A., Wood, P., Hoard, M. K., & Nugent, L. (2009). First-grade predictors of mathematical learning disability: A latent class trajectory analysis. Cognitive Development, 24, 411–429. Geary, D. C., Hoard, M. K., Byrd Craven, J., Nugent, L., & Numtee, C. (2007). Cognitive mechanisms underlying achievement deficits in children with mathematical learning disability. Child Development, 78(4), 1343–1359. Geary, D. C., Hoard, M. K., Nugent, L., & Rouder, J. N. (2015). Individual differences in algebraic cognition: Relation to the approximate number and semantic memory systems. Journal of Experimental Child Psychology, 140, 211–227. Gersten, R., Jordan, N. C., & Flojo, J. R. (2005). Early identification and interventions for students with mathematics difficulties. Journal of Learning Disabilities, 293–304. Halberda, J., & Feigenson, L. (2008). Developmental change in the acuity of the “number sense”: The approximate number system in 3-, 4-, 5-, and 6-year-olds and adults. Developmental Psychology, 44(5), 1457. Lucangeli, D. (Ed.). (2020). Understanding dyscalculia : A guide to symptoms, management and treatment. Taylor & Francis Group. Created from bibliovirtualuide-ebooks on 2024-02-14 19:08:17. Copyright © 2020. Taylor & Francis Group. All rights reserved. 90 Flávia Heloísa Santos Hashemian, P., & Hashemian, P. (2015). Effectiveness of neuro-feedback on mathematics disorder. African Journal of Psychiatry, 18, 243. Holmes, W., & Dowker, A. (2013). Catch up numeracy: A targeted intervention for children who are low-attaining in mathematics. Research in Mathematics Education, 15(3). Iuculano, T., Rosenberg-Lee, M., Richardson, J., Tenison, C., Fuchs, L., Supekar, K., & Menon, V. (2015). Cognitive tutoring induces widespread neuroplasticity and remediates brain function in children with mathematical learning disabilities. Nature Communications, 6. Käser, T., Baschera, G. M., Kohn, J., Kucian, K., Richtmann, V., Grond, U.,... von Aster, M. (2013, August 5). Design and evaluation of the computer-based training program Calcularis for enhancing numerical cognition. Frontiers in Psychology, 4, 489. Kaufmann, L., Mazzocco, M., Dowker, A., von Aster, M., Göbel, S. M., Grabner, R. H.,... Rubinsten, O. (2013). Dyscalculia from a developmental and differential perspective. Frontiers in Psychology, 4(516). Kovas, Y., Haworth, C. M. A., Harlaar, N., Petrill, S. A., Dale, P. S., & Plomin, R. (2007). Overlap and specificity of genetic and environmental influences on mathematics and reading disability in 10-year-old twins. Journal of Child Psychology and Psychiatry, 48(9), 914–922. Kroesbergen, E. H., & Van Luit, J. E. H. (2003). Mathematics interventions for children with special educational needs. A Meta-Analysis, 24(2), 97–114. Kucian, K., Grond, U., Rotzer, S., Henzi, B., Schönmann, C., Plangger, F.,... von Aster, M. (2011). Mental number line training in children with developmental dyscalculia. NeuroImage, 57(3), 782–795. Kucian, K., & Kaufmann, L. (2009). A developmental model of number representation. Behavioral and Brain Sciences, 32(3–4), 340–341. Kumar, P., & Darolia, C. R. (2016). Effectiveness of PASS based remedial programs for children with reading, spelling and mathematical deficits. Man in India, 96(4), 1037–1048. Layes, S., Lalonde, R., Bouakkaz, Y., & Rebai, M. (2017). Effectiveness of working memory training among children with dyscalculia: Evidence for transfer effects on mathematical achievement – a pilot study. Cognitive Processing, 19(3). Lucangeli, D., Tressoldi, P., & De Candia, C. (2015). Education and treatment of calculation abilities of low-achieving students and students with dyscalculia: Whole class and individual implementations. Cognition and Learning in Diverse Settings, 199–223. Mammarella, I. C., Caviola, C., Giofrè, D., & Borella, E. (2017). Separating math from anxiety: The role of inhibitory mechanisms. Applied Neuropsychology: Child, 7(4). Mazzocco, M. M., & Myers, G. F. (2003). Complexities in identifying and defining mathematics learning disability in the primary school-age years. Annals of Dyslexia, 53(1), 218–253. Lucangeli, D. (Ed.). (2020). Understanding dyscalculia : A guide to symptoms, management and treatment. Taylor & Francis Group. Created from bibliovirtualuide-ebooks on 2024-02-14 19:08:17. Copyright © 2020. Taylor & Francis Group. All rights reserved. Children with developmental dyscalculia 91 Melby-Levåg, M., & Hulme, C. (2013). Is working memory training effective? A meta-analytic review. Developmental Psychology, 49(2), 270–291. Morin, L. L., Watson, S. M. R., Hester, P., & Raver, S. (2017). The use of a bar model drawing to teach word problem solving to students with mathematics difficulties. Learning Disability Quarterly, 1–14. Murphy, M. M., Mazzocco, M. M., Hanich, L. B., & Early, M. C. (2007). Cognitive characteristics of children with mathematics learning disability (MLD) vary as a function of the cutoff criterion used to define MLD. Journal of Learning Disabilities, 40(5), 458–478. Passolunghi, M. C., Caviola, C., De Agostini, R., Perin, C., & Mammarella, I. C. (2016). Mathematics anxiety, working memory, and mathematics performance in secondary-school children. Frontiers in Psychology, 7. Passolunghi, M. C., & Pellizzoni, S. (2018). Math anxiety and numeracy training in fourth-grade children. 1st Mathematical Cognition and Learning Society Conference, Oxford. Peters, L., Bulthé, J., Daniels, N., Op de Beeck, H., & De Smedt, B. (2018). Dyscalculia and dyslexia: Different behavioral, yet similar brain activity profiles during arithmetic. NeuroImage: Clinical, 18, 663–674. http:// doi.org/10.1016/j.nicl.2018.03.003 Praet, M., & Desoete, A. (2014). Enhancing young children’s arithmetic skills through non-intensive, computerised kindergarten interventions: A randomised controlled study. Teaching and Teacher Education, 39, 56–65. Prast, E. J., Van de Weijer-Bergsma, E., Kroesbergen, E. H., & Van Luit, J. E. H. (2018). Differentiated instruction in primary mathematics: Effects of teacher professional development on student achievement. Learning and Instruction, 54, 22–34. Ramirez, G., & Beilock, S. L. (2011). Writing about testing worries boosts exam performance in the classroom. Science, 331(14). Ribeiro, F. S., & Santos, F. H. (2017). Enhancement of numeric cognition in children with low achievement in mathematic after a non-instrumental musical training. Research in Developmental Disabilities, 62, 26–39. Ribeiro, F. S., & Santos, F. H. (2020). Persistent effects of musical training on mathematical skills of children with developmental dyscalculia. Frontiers in Psychology, 10, http://doi.org/10.3389/fpsyg.2019.02888 Ribeiro, F. S., Silva, P. A. & Santos, F. H. (2016). Padrões de dissociação da memória operacional na Discalculia do Desenvolvimento. Porto Alegre: Artmed. Rothbart, M. K. (2011). Becoming who we are: Temperament and personality in development. New York: Guilford Press. Ruffing, S., Wach, F. S., Spinath, F. M., Brünken, R., & Karbach, J. (2015, August 19). Learning strategies and general cognitive ability as predictors of gender-specific academic achievement. Frontiers in Psychology, 6. Lucangeli, D. (Ed.). (2020). Understanding dyscalculia : A guide to symptoms, management and treatment. Taylor & Francis Group. Created from bibliovirtualuide-ebooks on 2024-02-14 19:08:17. Copyright © 2020. Taylor & Francis Group. All rights reserved. 92 Flávia Heloísa Santos Sala, G., & Gobet, F. (2017). Does far transfer exist? Negative evidence from chess, music, and working memory training. Current Directions in Psychological Science, 26, 1–6. Santos, F. H. (2017a). Discalculia do Desenvolvimento. São Paulo: Pearson Clinical Brasil. Santos, F. H. (2017b). Guia do tutor calcularis. São Paulo: Pearson Clinical Brasil. Schleger, F., Landerl, K., Muenssinger, J., Draganova, R., Reinl, M., Kiefer -Schmidt, I.,... Preissl, H. (2014). Magnetoencephalographic signatures of numerosity discrimination in fetuses and neonates. Developmental Neuropsychology, 39(4), 316–329. Sella, F., Berteletti, I., Lucangeli, D., & Zorzi, M. (2017). Preschool children use space, rather than counting, to infer the numerical magnitude of digits: Evidence for a spatial mapping principle. Cognition, 158, 56–67. Shalev, R. S., Manor, O., Auerbach, J., & Gross-Tsur, V. (1998). Persistence of developmental dyscalculia: What counts? Results from a 3-year prospective follow-up study. The Journal of Pediatrics, 133(3), 358–362. Shalev, R. S., Manor, O., Kerem, B., Ayali, M., Badihi, N., Friedlander, Y., & Gross-Tsur, V. (2001). Familial-genetic facets of developmental dyscalculia. Journal of Learning Disabilities, 34, 59–65. Sherman, J., & Bisanz, J. (2009). Equivalence in symbolic and nonsymbolic contexts: Benefits of solving problems with manipulatives. Journal of Educational Psychology, 101(1), 88–100. Siegler, R. S., & Ramani, G. B. (2009). Playing linear number board games – but not circular ones – improves low-income preschoolers’ numerical understanding. Journal of Educational Psychology, 101(3), 545–560. Silva, E. R., Baldin, M. S., & Santos, F. H. (2017). Cognitive effects of numeracy musical training in Brazilian preschool children: A prospective pilot study. Psychology & Neuroscience, 10(3), 281–296. Supekar, K., Iuculano, T., Chen, L., & Menon, V. (2015). Remediation of childhood math anxiety and associated neural circuits through cognitive tutoring. Journal of Neuroscience, 35, 12574–12583. Szücs, D. (2016). Subtypes and comorbidity in mathematical learning disabilities: Multidimensional study of verbal and visual memory processes is key to understanding. Progress in Brain Research, 227, 277–304. Vogt, F., & Rogalla, M. (2009). Developing adaptive teaching competency through coaching. Teaching and Teacher Education, 25, 1051–1060. von Aster, M., & Shalev, R. S. (2007). Number development and developmental dyscalculia. Developmental Medicine & Child Neurology, 49(11), 868–873. World Health Organization. (1992). The ICD-10 classification of mental and behavioural disorders: Clinical descriptions and diagnostic guidelines. Geneva: World Health Organization. World Health Organization [WHO]. (2018). The ICD-11 classification of mental and behavioural disorders: Diagnostic criteria for research. Geneva: World Health Organization. Lucangeli, D. (Ed.). (2020). Understanding dyscalculia : A guide to symptoms, management and treatment. Taylor & Francis Group. Created from bibliovirtualuide-ebooks on 2024-02-14 19:08:17. Children with developmental dyscalculia 93 Copyright © 2020. Taylor & Francis Group. All rights reserved. Wu, S. S., Willcutt, E. G., Escovar, E., & Menon, V. (2014). Mathematics achievement and anxiety and their relation to internalizing and externalizing behaviors. Journal of Learning Disabilities, 47(6), 503–514. Wynn, K. (1992). Addition and subtraction by human infants. Nature, 358(6389), 749–750. Zheng, X., Flynn, L. J., & Lee Swanson, H. (2012). Experimental intervention studies on word problem solving and math disabilities: A selective analysis of the literature. Learning Disability Quarterly, 36(2), 97–111. http://doi.org/10.1177/0731948712444277 Lucangeli, D. (Ed.). (2020). Understanding dyscalculia : A guide to symptoms, management and treatment. Taylor & Francis Group. Created from bibliovirtualuide-ebooks on 2024-02-14 19:08:17.