Intervention Signs and Symptoms PDF

Chapter 4 Intervention programmes for students with dyscalculia Living with the condition Maria Chiara Fastame Copyright © 2020. Taylor & Francis Group. All rights reserved. Introduction Dyscalculia is a genetically predisposed but heterogeneous specific learning disorder in mathematics (i.e. seriou...

Chapter 4 Intervention programmes for students with dyscalculia Living with the condition Maria Chiara Fastame Copyright © 2020. Taylor & Francis Group. All rights reserved. Introduction Dyscalculia is a genetically predisposed but heterogeneous specific learning disorder in mathematics (i.e. serious impairment of the development of numerical-arithmetical skills) that negatively affects one’s lifespan, since it persists into adulthood (Kaufmann et al., 2013). Despite having normal intellectual skills and lacking environmental deprivation, sensory, developmental, motor and neurological disorders, dyscalculia affects a wide range of daily activities, such as academic achievement and occupational performance (American Psychiatric Association, 2013). These, in turn, predict early school leaving, adult financial status, work productivity and psychological well-being (e.g. Butterworth, 2018; Ritchie & Bates, 2013). Indeed, students with dyscalculia often report emotional distress and can develop mathematics anxiety and school phobia because their mathematical attainment is low. This is even more evident when the persistent mathematics disorder is accompanied by comorbid conditions, such as ADHD or dyslexia (i.e. a specific learning disorder characterized by reading difficulties). In a recent study, Morsanyi and co-workers (2018) applied the DSM-5 diagnostic criteria for the identification of children with a specific learning disorder in mathematics. In agreement with previous research (e.g. Rubinsten & Henik, 2009), the authors found that the prevalence rate of dyscalculia concerns 6 per cent of male students and 5.5 per cent of female students attending primary school (i.e. grades 4–7). However, when the authors used the criterion of 1 standard deviation below the population mean for age on standardized curriculum-based tests assessing mathematics achievement, the prevalence rate of persistent and severe difficulties with Understanding Dyscalculia : A Guide to Symptoms, Management and Treatment, edited by Daniela Lucangeli, Taylor & Francis Group, 2020. ProQuest Ebook Central, http://ebookcentral.proquest.com/lib/bibliovirtualuide-ebooks/detail.action?docID=6 Created from bibliovirtualuide-ebooks on 2024-02-14 17:16:30. 42 Maria Chiara Fastame Copyright © 2020. Taylor & Francis Group. All rights reserved. mathematics was 13.2 per cent, and within this subsample the cooccurrence of ADHD (5.54 per cent), dyslexia (1.33 per cent), communication and interaction (7.17 per cent) and speech and language difficulties (5.27 per cent) was common. Extending this epidemiologic evidence, in their longitudinal study Wong and Chan (2019) concluded that the core problems underlying the persistent mathematical learning disability are a deficit on the mapping between number symbols and magnitude and a deficit in the understanding of the logical structure of the symbolic number system (e.g. number line, magnitude comparison of different number symbols and placevalue correspondence). Even though dyscalculia is not rare, it received much less attention than dyslexia, such that teachers, educators, educational psychologists and policy makers are often unaware of the former and its implications (Butterworth, Varma, & Laurillard, 2011; Butterworth, 2018). This would explain why unlike dyslexic students, children with persistent mathematics disorder often do not receive adequate interventions and are not provided with specific instructions to improve their curriculum-based attainment (Morsanyi, van Bers, McCormack, & McGourty, 2018). Thus, implementing appropriate psychoeducational interventions that are tailored to the specific cognitive profile of the dyscalculic child is crucial. The next section presents an overview of the effectiveness of targeted intervention programmes aimed at contrasting the persistency of dyscalculia and related disorders. Educational intervention programmes for dyscalculic students: state of the art and future perspectives Psychoeducational interventions for the empowerment of mathematics skills Mathematical interventions refer to the pool of “instructional practices and activities designed to enhance the mathematics achievement of students with learning disabilities” (Gersten et al., 2009, p. 1205). The implementation of intervention programmes for dyscalculic students is a complex matter of debate, since the persistency and severity of that specific learning disability can vary across individuals (i.e. interpersonal variability) and the within-person Understanding Dyscalculia : A Guide to Symptoms, Management and Treatment, edited by Daniela Lucangeli, Taylor & Francis Group, 2020. ProQuest Ebook Central, http://ebookcentral.proquest.com/lib/bibliovirtualuide-ebooks/detail.action?docID=6 Created from bibliovirtualuide-ebooks on 2024-02-14 17:16:30. Copyright © 2020. Taylor & Francis Group. All rights reserved. Interventions for dyscalculic students 43 behavioural and cognitive characteristics can change in a ­lifespan (i.e. intra-individual variability). Nonetheless, considering the heterogeneity of dyscalculia profiles, the intervention must be individualized and adapted to the actual educational and psychological needs of the student presenting that specific cognitive, behavioural and affective phenotype, that is to say, the strengths and weaknesses of the learner must be kept in mind (e.g. Gillum, 2014). This implies that mathematical interventions for student with dyscalculia must be driven by an accurate, objective and comprehensive assessment of the psychological characteristics affecting the development and utilizations of mathematical skills and by a clear understanding of the cognitive and metacognitive processes underpinning mathematical achievement (Dowker, 2008; Jitendra, Dupuis, Star, & Rodriguez, 2016). At present, a variety of psychoeducational interventions has been developed to enhance mathematical skills of dyscalculic students and peers displaying some mathematical difficulties – the latter group does not satisfy the criteria for the diagnosis of dyscalculia but could present common features (APA, 2013). According to Kroesbergen and Van Luit (2003), “an intervention is judged effective when the students acquire the knowledge and skills being taught and thus appear to adequately apply this information at, for example, posttest” (p. 99). In other words, to be effective, interventions for dyscalculic students must modify mental functions directly (e.g. problem-solving abilities) or indirectly (e.g. attention, reading, executive functions, visuospatial working memory and metacognition), and they must limit the emotional impact (e.g. anxiety) of the disorder on the daily life. Therefore, it is crucial to assess the effectiveness of interventions in terms of their long-term impact on academic achievement and everyday life. In recent years, several reviews and meta-analyses on the effectiveness of mathematical interventions have been published (e.g. Monei & Pedro, 2017; Szűcs & Myers, 2017). However, they often do not have conclusions regarding the specific impact of the interventions on the dyscalculic learners, because the criteria used to define the disorder vary (e.g. use of mixed groups composed of dyscalculics and students with some mathematical difficulties) and because they often analyze only the short-term effect of the psychoeducational trainings. Mathematical interventions can be classified with respect to the skills enhanced. Thus, there are interventions mainly focused on the Understanding Dyscalculia : A Guide to Symptoms, Management and Treatment, edited by Daniela Lucangeli, Taylor & Francis Group, 2020. ProQuest Ebook Central, http://ebookcentral.proquest.com/lib/bibliovirtualuide-ebooks/detail.action?docID=6 Created from bibliovirtualuide-ebooks on 2024-02-14 17:16:30. Copyright © 2020. Taylor & Francis Group. All rights reserved. 44 Maria Chiara Fastame empowerment of number sense skills, which in turn, are fundamental for the development of Piagetian operations (e.g. classification, seriation and quantity conservation). There are also interventions focused on the automatization of number facts (the four basic operations, that is addition, subtraction, multiplication and division) as well as those designed to enrich problem-solving strategies (that is to promote learning on how and when to apply basic mathematical skills both in well-known and unfamiliar situations). Additionally, these interventions can be combined with strategy instruction interventions, which are aimed at providing “the tools and techniques that they [learners] can use in order to understand and learn new materials or skills” (Monei & Pedro, 2017, p. 285), such as verbal strategies (e.g. underlining) to identify the key information or visual ones based on the use of nonverbal aids (e.g. diagrams) to represent the structure of a problem. Early numeracy interventions are mainly focused on the empowerment of number sense (or Approximate Number System) skills, which refer to a set of early mathematical abilities based on the counting, writing and use of numbers and numerical symbols (Hassinger-Das, Jordan, Glutting, Irwin, & Dyson, 2014). Number sense has also been defined as the ability to understand sense of magnitude representing numerosity in an approximate fashion that allows to discriminate magnitudes (Szűcs & Myers, 2017). Number sense deficits of dyscalculic children implies an evident reduction of understanding of numbers meaning that in turn, is reflected in a low achievement in symbolic (e.g. numerical comparison and approximation) and non-symbolic (e.g. estimation, comparison and approximate addition of dot arrays) tasks. Psychoeducational trainings enhancing number sense include a wide range of activities, such as dot enumeration (i.e. subitizing); numbers reading and writing; magnitude comparison; recognizing the correspondence between quantities (e.g. concrete objects) and Arabic digits visually and auditorily presented; basic addition and subtraction facts; and objects and verbal counting. It is assumed that if these numerical activities are effectively empowered, near and far transfer effects should be found in terms of the enhancement of advanced mathematical skills such as those requested in complex numerical facts (e.g. division) and in the symbolic number processing underlying complex problem-solving tasks. Even though number sense interventions based on the manipulation of concrete items to be counted or to be compared are widely used even in kindergartners, Understanding Dyscalculia : A Guide to Symptoms, Management and Treatment, edited by Daniela Lucangeli, Taylor & Francis Group, 2020. ProQuest Ebook Central, http://ebookcentral.proquest.com/lib/bibliovirtualuide-ebooks/detail.action?docID=6 Created from bibliovirtualuide-ebooks on 2024-02-14 17:16:30. Copyright © 2020. Taylor & Francis Group. All rights reserved. Interventions for dyscalculic students 45 the effectiveness of certain interventions is not always clear. This is because of the great inter-individual variability and the different methodological biases in the studies exploring the empirically based effect of interventions, such as the lack of control groups (e.g. composed of untrained dyscalculic students) to be compared with the trained dyscalculic participants, the paucity of participants and the lack of follow-up measures to investigate the long-term impact of the practices and activities (e.g. Szűcs & Myers, 2017). For instance, Wilson et al. (2006) developed a well-known computerassisted number sense training (i.e., the Number Race) designed to enrich numerical comparison, to foster the link between symbolic representations of numbers and space and to promote the learning of small operation facts (i.e. addition and subtraction) by the approximate estimation of a small range of numbers and processing of concrete quantities representations. The intervention programme is usually proposed in a way that is intensive (i.e. 30 minutes per day, four days a week over a period of five weeks) and adaptive (e.g. modulating the difficulty of the task and speed of response). Although this training successfully enhances basic numerical cognition, transfer effects to arithmetic tasks (e.g. counting), if present, are minimal (Iuculano, 2016). Other intervention programmes have been used to enrich mathematical operations skills in dyscalculic learners, since these students commit more counting and basic fact retrieval errors and rely on less efficient counting strategies. Usually, automaticity in basic arithmetic facts is achieved by the provision of extensive practice activities or the overt teaching of successful strategies. Despite the paucity of studies, dyscalculic students seem to benefit from computerassisted instruction interventions enhancing number combinations retrieval (e.g. Hasselbring et al., 1988) and strategy instruction programmes (i.e. based on a demonstration of the strategy to use to compute the algorithm) focused on number facts retrieval (Tournaki, 2003). In contrast, the transfer effect of rote memorization of basic facts interventions seems to be limited to the set of facts that the students practised (Fuchs et al., 2006). Powell and colleagues (2009) documented the effectiveness of two intensive tutoring fact retrieval interventions aimed at enriching conceptual knowledge and/or procedural computation underpinning double-digit addition and subtraction facts retrieval respectively. Specifically, the authors found that students with mathematical difficulties benefited more than students with reading and mathematical difficulties Understanding Dyscalculia : A Guide to Symptoms, Management and Treatment, edited by Daniela Lucangeli, Taylor & Francis Group, 2020. ProQuest Ebook Central, http://ebookcentral.proquest.com/lib/bibliovirtualuide-ebooks/detail.action?docID=6 Created from bibliovirtualuide-ebooks on 2024-02-14 17:16:30. Copyright © 2020. Taylor & Francis Group. All rights reserved. 46 Maria Chiara Fastame from combined explicit computer-assisted numerical facts retrieval training, ­pencil-and-paper number facts problems intervention and double-digit flash card practice requiring the solution of addition and subtraction operations. However, the intervention was effective only if the students were provided with immediate and corrective feedback via computer or an expert tutor immediately after errors in numerical facts occur. Overall, this emerging evidence suggests that to execute mathematical facts, students with dyscalculia not only need to automatize basic number combinations retrieval, but they also need to understand which strategy applies and how to monitor the performance. This would allow them to develop conceptual understanding related to number facts. Nonetheless, so far, no studies have investigated the long-term and transfer effects of the interventions enhancing numerical facts in dyscalculic students, so future research is needed to determine if dyscalculic students can maintain the benefits of the numerical facts trainings in their daily lives and for their advanced academic achievement (Dennis, Sorrells, & Falcomata, 2016). Further interventions are designed to enhance mathematical word problem-solving skills. Mathematical word problems are verbally presented problems requiring the development of a mental representation of the statements contained in the story, followed by the selection of the arithmetic operations necessary to reach a solution (Zheng, Flynn, & Swanson, 2012). Low achievement in problem-solving tasks of dyscalculic students can be caused by many factors, such as difficulties in problem representation, in selecting the relevant information and in understanding the correct strategy to reach the solution. A type of arithmetic problem-solving intervention is based on the use of “keyword” strategy, such that each algebraic sign and the corresponding operation are associated with a word (i.e. “altogether” indicates addition, “left” corresponds to subtraction, “times” is associated with multiplication and “among” indicates division), so when the student has to solve the problem, the keyword-cue is provided and then the learner understands which operation is necessary to solve the problem. However, this type of training has been criticized (Parmar, Cawley, & Frazita, 1996) because the mathematical behaviour of the students is elicited by the keyword and not by a deep conceptual understanding of the task to be carried out. A further intervention consists of teaching a general four-step heuristic procedure (i.e. read the problem, plan the action, solve and check), but this strategy is not very effective for dyscalculic students Understanding Dyscalculia : A Guide to Symptoms, Management and Treatment, edited by Daniela Lucangeli, Taylor & Francis Group, 2020. ProQuest Ebook Central, http://ebookcentral.proquest.com/lib/bibliovirtualuide-ebooks/detail.action?docID=6 Created from bibliovirtualuide-ebooks on 2024-02-14 17:16:30. Copyright © 2020. Taylor & Francis Group. All rights reserved. Interventions for dyscalculic students 47 because of the previously mentioned difficulties in focusing on the crucial information and selecting the correct strategy. Instead, successful problem-solving interventions for dyscalculic learners rely on the use of schema-based strategy instruction, that is, on the creation of a complete representation of the problem (i.e. that illustrates the mathematical relations among key elements in the problem by a schematic diagram), which, in turn, facilitates the encoding and then the selection of the algorithms to be computed. In other words, schema-based strategy instruction is combined with the previously mentioned general heuristic procedure to enhance conceptual understanding of the problem structure. With this approach, students learn to identify the problem type and to represent it using a schematic diagram, after which they learn to transform the diagram in a sequence of procedures necessary to reach the solution, carry out the operation(s) and finally verify the reasonableness of their answer (Xin, Jitendra, & Deatline-Buchman, 2005). So far, few investigations have been carried out to explore the effectiveness of interventions aimed at enhancing proportional reasoning skills underlying complex problems in dyscalculic learners. Proportional reasoning skills refers to the pool of skills allowing the students to understand the multiplicative relationships between quantities (i.e. ratios) and the “covariance of quantities and invariance of ratios” (Lamon, 2007, p. 638). These skills underpin different complex arithmetic problems, such as scale drawing, linear function, percentages, measurement conversions and discounts. Using a multicomponent intervention based on schema-based instruction combined with explicit instructions given by the teacher, followed by teacher-guided practice and explicit mathematics modeling (e.g. corrective feedbacks), Xin and co-workers (2005) empowered basic multiplicative knowledge (i.e. simple ratio and proportion word problems) in a small group of dyscalculic students and documented the near transfer effect (a few weeks after the end of the training) of the intervention. Similarly, Jitendra, Harwell, Dupuis, and Karl (2017) documented the effectiveness of a schemabased instruction intervention for the enhancement of complex proportional reasoning skills (i.e. ratios and proportional relationships) in seventh graders with mathematical problem-solving difficulties. Specifically, after having identified the type of problem (e.g. by deep-level questions) and building the corresponding diagram, students were encouraged to develop procedural flexibility – by selecting a range of possible problem-solving strategies which they Understanding Dyscalculia : A Guide to Symptoms, Management and Treatment, edited by Daniela Lucangeli, Taylor & Francis Group, 2020. ProQuest Ebook Central, http://ebookcentral.proquest.com/lib/bibliovirtualuide-ebooks/detail.action?docID=6 Created from bibliovirtualuide-ebooks on 2024-02-14 17:16:30. Copyright © 2020. Taylor & Francis Group. All rights reserved. 48 Maria Chiara Fastame know when, how and why to use – and to boost the metacognitive knowledge (i.e. monitoring and reflecting on the problem-solving process) driving the execution of the task. In this regard, Jitendra et al. (2017) highlighted that the combined promotion of deep procedural and metacognitive knowledge is essential for the long-term positive effect of the problem-solving interventions. However, it must be noticed that reading skills are an important factor moderating the effectiveness of problem-solving interventions in dyscalculic students (Zheng et al., 2012). Therefore, when a word problem-solving intervention is implemented for students showing both dyscalculia and dyslexia, specific attention must be paid not only on the contents of the training enhancing problemsolving achievement but also on the role played by reading skills. In this regard, Jitendra et al. (2016) noted the equal effectiveness of an intensive (i.e. about 1,350 minutes dispensed in six weeks) schema-based instruction intervention for the enhancement of proportional problem-solving skills (i.e., ratio, proportion and per cent) and metacognitive processes in students showing only mathematical difficulties or comorbid with reading difficulties. Specifically, at the end of the intervention and after six weeks, students showing comorbidity improved in terms of ratio, proportion and per cent skills, whereas performance of learners with mathematics difficulties improved in per cent tasks only. Nonetheless, as expected (Jitendra, Star, Dupuis, & Rodriguez, 2013), no transfer effect to novel problems having the same mathematical structure as learned problems (ratios) or having a modified problem structure (e.g. probability) was found in the two groups. Altogether, despite some encouraging outcomes about the effectiveness of the psychoeducational trainings enhancing the mathematical skills of dyscalculics, clear evidence about the long-term effects of such interventions is often lacking or inconsistent (e.g. Gillum, 2014). Therefore, future research is needed to clarify this issue and to track the future directions to provide the best intervention tools for the different dyscalculic phenotypes. Interventions to enhance supportive skills and to remediate the negative emotional responses of dyscalculics A broad literature highlighted that numerical competence is strictly related to the efficiency of different supportive cognitive skills such as visuospatial working memory, executive functions (e.g. attention Understanding Dyscalculia : A Guide to Symptoms, Management and Treatment, edited by Daniela Lucangeli, Taylor & Francis Group, 2020. ProQuest Ebook Central, http://ebookcentral.proquest.com/lib/bibliovirtualuide-ebooks/detail.action?docID=6 Created from bibliovirtualuide-ebooks on 2024-02-14 17:16:30. Copyright © 2020. Taylor & Francis Group. All rights reserved. Interventions for dyscalculic students 49 and inhibition) and language. In this regard, there is evidence that mathematical performance of kindergartners can benefit from the empowerment of both visuospatial memory and numerical skills by the presentation of pencil-and-paper and computer-assisted psychoeducational trainings (e.g. Agus et al., 2016). Similarly, the long-term impact (i.e. one year after the end of the training) of a computer-assisted verbal and visuospatial working memory intervention (i.e. Cogmed) has been documented in children attending primary school, since trained students showed significant improvement in reading and mathematical achievement (Söderqvist & Bergman Nutley, 2015). Despite this, there is also evidence that even when the same intervention was provided, long-term transfer (i.e. after 12 and 24 months from the end of the training) of working memory abilities to mathematics and reading comprehension skills in typically developing children is minimal, if present (e.g. Roberts et al., 2016). Similarly, for what concerns the dyscalculic students or those with mathematical difficulties, children’s benefits from working memory trainings and gains in mathematics are often considered limited, short term or even inconsistent (e.g. MelbyLervåg & Hulme, 2013; Ang, Lee, Cheam, Poon, & Koh, 2015). Bearing that in mind, Nelwan, Vissers, and Kroesbergen (2018) found that mathematical skills (i.e. operations and problem-solving competence) of 9–12-year-old students with both attentional and mathematical difficulties significantly improved after the completion of an adaptive and interactive computer-assisted working memory training (i.e. Jungle Memory) requiring the temporary maintenance or processing of verbal and visuospatial stimuli respectively. Specifically, the short- and long-term impact of the working memory training was more evident for the empowerment of visuospatial abilities, whereas the effect of the intervention on verbal working memory was short and quite small. Moreover, the authors highlighted that the positive effect of the working memory training was more evident across the participants. They also noted that the adult coaches provided reinforcement by giving the students continuous feedback about their performance, reducing stress, motivating them and helping them formulate the best strategies to solve each task. It has also been documented that mathematical achievements (i.e. calculation and problem solving) of 10–13-year-old students with specific learning disabilities in reading and mathematics can benefit from an intensive monthly updating working memory training (Zhang, Chang, Chen, Ma, & Zhou, 2018). In short, this intervention is based on a series of verbal and visuospatial tasks Understanding Dyscalculia : A Guide to Symptoms, Management and Treatment, edited by Daniela Lucangeli, Taylor & Francis Group, 2020. ProQuest Ebook Central, http://ebookcentral.proquest.com/lib/bibliovirtualuide-ebooks/detail.action?docID=6 Created from bibliovirtualuide-ebooks on 2024-02-14 17:16:30. Copyright © 2020. Taylor & Francis Group. All rights reserved. 50 Maria Chiara Fastame requiring the monitoring of input serial information and the updating of the corresponding mental trace by the replacement of the stimuli sequence with the last three target ones. The updating tasks are difficult because the students are not previously informed about the sequence length; so first they can only temporarily maintain the whole series of stimuli, then they must select only the target stimuli to be recalled, discharging information which is no longer relevant. Using a similar computer-assisted working memory updating training, after six months from the intervention, Ang and colleagues (2015) found an improvement of updating working memory skills but not of mathematical achievement in seven-year-old students with mathematical difficulties. Recently, Layes and co-workers (2018) provided 10–11-year-old Arabic dyscalculic learners with an eight-week face-to-face working memory intervention aimed at empowering the manipulation and temporary maintenance of arithmetic information (e.g. number sense, number identification and number comparison). The authors found a significant improvement of passive and active verbal immediate serial recall and mathematical skills (i.e. counting backward, mental calculation, numerical dictation, reading numbers and written number comparisons) at the end of the intervention. But despite the evidence about the near transfer effect, information about far transfer effects was lacking. Overall, these investigations suggest that the transfer effect of working memory trainings to mathematical achievements can enhance both the capacity to monitor one’s own memory performance and the ability to temporarily maintain and process information more accurately, which, in turn, boost greater automatization of memory strategies necessary for problem solving and numerical facts. This is in line with a body of studies documenting the importance of empowering visuospatial working memory abilities, since they are crucial for the mental visualization and representation of quantities on the number line, as well as to the representation of quantities in diagrams for the solution of word problems (e.g. see Layes, Lalonde, Bouakkaz, & Rebai, 2018). However, the longterm impact of this type of intervention on mathematical achievement is questionable. Furthermore, one of the rare studies exploring the impact of attentive processes training on the mathematical attainment of learners with some arithmetic difficulties was conducted by Guarnera and D’Amico (2014). Specifically, the authors provided fourth and Understanding Dyscalculia : A Guide to Symptoms, Management and Treatment, edited by Daniela Lucangeli, Taylor & Francis Group, 2020. ProQuest Ebook Central, http://ebookcentral.proquest.com/lib/bibliovirtualuide-ebooks/detail.action?docID=6 Created from bibliovirtualuide-ebooks on 2024-02-14 17:16:30. Copyright © 2020. Taylor & Francis Group. All rights reserved. Interventions for dyscalculic students 51 fifth graders with a four-week intensive computer-assisted intervention aimed at enriching reaction time, attentive shifting, visuospatial and auditory selectivity, inhibition and divided attention skills. Guarnera and D’Amico (2014) found the near far effect of the intervention on numerical system skills (i.e. number dictation, denomination of arithmetic symbols, insertion of symbols “ < ” and “ > ” between two numbers, increasing arrangements of numbers and decreasing arrangements of numbers) and reaction time. Even though the long-term impact of the psychoeducational intervention on mathematical achievement was not reported, this investigation suggests the need to empower attentional processes in order to improve mathematical attainment in learners with low arithmetical functioning. However, the urgency of a combined attentional processes and arithmetical skills intervention is even more evident for dyscalculic students showing comorbidity with ADHD. As reported in previous studies, the comorbidity of dyscalculia and ADHD is not uncommon, and it involves 31–45 per cent of students (DuPaul, Gormley, & Laracy, 2013). Although a tradition of research evaluating the effectiveness of interventions for the population with comorbid diagnoses is lacking, some evidence-based studies point out that the interventions must be carried out at school and at home, that is, they must be based on a strict collaboration between parents and teachers to alleviate ADHD symptoms and enhance academic achievement of the learners with those comorbid disorders. Thus, students showing ADHD and dyscalculia could benefit from peer tutoring, intensive computer-assisted direct and explicit instruction interventions enhancing specific skills, interventions based on the empowerment of organizational skills, as well as consequencesbased interventions requiring behaviourist techniques (e.g. token economy and response cost) after a target behaviour is displayed (Trout, Lienemann, Reid, & Epstein, 2007; DuPaul et al., 2013). For instance, keeping in mind the limited attention span, a short number of concepts should be taught per time and the presentation of procedures/information in chunks should be preferred both at school and at home. Moreover, to enhance self-regulation skills, a highly structured environment with limited distractions and with a well-planned schedule should be provided, especially at school (Soares, Evans, & Patel, 2018). However, future research must investigate more deeply the effectiveness of ADHD and mathematics skills intervention for Understanding Dyscalculia : A Guide to Symptoms, Management and Treatment, edited by Daniela Lucangeli, Taylor & Francis Group, 2020. ProQuest Ebook Central, http://ebookcentral.proquest.com/lib/bibliovirtualuide-ebooks/detail.action?docID=6 Created from bibliovirtualuide-ebooks on 2024-02-14 17:16:30. 52 Maria Chiara Fastame the dyscalculic population, to provide more accurate information about the best practice. Finally, it is known that dyscalculia can occur with further comorbid conditions that have a negative impact on the affective dimension of life (e.g. depression and anxiety). Nonetheless, at present a tradition of studies about the effectiveness of concurrent treatments of psychopathological affective conditions and dyscalculia is lacking. Despite the lack of research specifically addressing interventions for this population, Soares and co-workers (2018) posit that cognitive-behaviour therapy can be successfully used to treat mathematics anxiety, to improve academic achievement and to promote the development of a positive attitude towards mathematics. The authors stress the importance of developing early interventions, since negative emotional responses tend to increase with age and to cause pervasive and adverse effects across different dimensions of the daily lives of dyscalculic students. Although this promising evidence-based approaches to remediate against negative emotional responses are essential, future research is needed for a more thorough understanding of how to develop successful interventions for students with comorbid dyscalculia and affective disorders. Copyright © 2020. Taylor & Francis Group. All rights reserved. The epigenetic effect of interventions on the “dyscalculic” brain Recent but promising evidence suggests the necessity of paying attention to the effect of psychological interventions enhancing numeracy in terms of the functional reorganization of the brain of trained dyscalculic learners. This implies that researchers must investigate more deeply the epigenetic impact of psychological interventions for dyscalculia, highlighting the relationship between good practice enhancing mathematical skills and brain changes. Neurofunctional studies reported that the occurrence of dyscalculia is associated with aberrations in the ventral temporal – occipital cortex (i.e. underlying symbol recognition and numerical judgement of visually presented stimuli) in the medial temporal lobe (i.e. engaged in the retrieval of numerical facts from long-term memory), in the intraparietal sulcus region of the parietal cortex (i.e. responsible for magnitude and quantitative information processing), as well as in the fronto-parietal circuitry (implicated in Understanding Dyscalculia : A Guide to Symptoms, Management and Treatment, edited by Daniela Lucangeli, Taylor & Francis Group, 2020. ProQuest Ebook Central, http://ebookcentral.proquest.com/lib/bibliovirtualuide-ebooks/detail.action?docID=6 Created from bibliovirtualuide-ebooks on 2024-02-14 17:16:30. Copyright © 2020. Taylor & Francis Group. All rights reserved. Interventions for dyscalculic students 53 the temporary maintenance and information processing in working memory and attentional functions) (e.g. Butterworth et al., 2011). Although at present only very few studies have been conducted, emerging evidence pointed out that after training, functional neural plasticity can significantly strengthen mathematical skills of students with dyscalculia. For instance, Kucian and colleagues (2011) conducted a pioneering study to explore the effect of an intensive (i.e. 15 minutes a day, five days a week for five weeks) computerbased training for children with dyscalculia that was aimed at enhancing number representation and automatizing the spatial mental representation of numbers along an internal number line. The authors found that after the intervention, the spatial processing of numbers along the mental number line improved significantly in a group of dyscalculic students and that thanks to the automatization of number processing, a reduction of brain activation – especially in the frontal and parietal lobes which are involved in spatial representation of numerical stimuli – was found immediately after training. More recently, Michels and co-workers (2018) used the same training programme and procedure used by Kucian and colleagues (2011) to investigate the impact of the intervention on brain connections of children with dyscalculia. From a cognitive perspective, the authors found an improvement in the dyscalculic participants in terms of number line performance (i.e. indicating the spatial position of a series of numerical stimuli on a 0–100 number line) and accuracy in carrying out some operations (i.e. additions and subtractions) solved on the number line. Besides Michels, O’Gorman, and Kucian (2018) found that after training, the hyperconnectivity in the parietal, frontal, visual, cerebellar and temporal brain regions of the children with dyscalculia dropped dramatically, becoming like that showed by typically developing controls. The authors hypothesized that the improvement of the functioning of the fibers connecting different neural loci was responsible of the enhancement of number line processing and calculation after training. Moreover, Iuculano and co-workers (2015) proposed that children with dyscalculia undergo an eight-week one-to-one tutoring intervention (i.e. tutors were expert research assistants) promoting the enhancement of numerical problem-solving skills. The authors found that after the intervention, the widespread brain activation of dyscalculic participants was significantly reduced, such that the pattern of neural engagement was like that of typically developing children. Understanding Dyscalculia : A Guide to Symptoms, Management and Treatment, edited by Daniela Lucangeli, Taylor & Francis Group, 2020. ProQuest Ebook Central, http://ebookcentral.proquest.com/lib/bibliovirtualuide-ebooks/detail.action?docID=6 Created from bibliovirtualuide-ebooks on 2024-02-14 17:16:30. 54 Maria Chiara Fastame Altogether, these promising outcomes about the critical role played by neural plasticity for the improvement of numerical performance of dyscalculics encourage further in-depth investigations on the effectiveness of different types of mathematics interventions and their impact on the different brain substrates underpinning distinct numeracy skills. In this regard, future research must clarify whether after effective mathematical interventions, the same neural populations activated in typically developing children are also recruited in the brain of dyscalculics (i.e. neural normalization hypothesis) or whether trained students with dyscalculia engage unusual and additional neural networks (i.e. neural compensation hypothesis) to perform mathematical tasks similarly to control peers (Iuculano et al., 2015). Copyright © 2020. Taylor & Francis Group. All rights reserved. Educational implications of interventions for dyscalculia for classroom practice It is well known that a crucial aspect of the effectiveness of mathematics interventions is related to the type of strategy instruction used to improve the mathematical skills proficiency and how it is used. Usually strategy instruction provides clear and explicit information about the appropriate type of strategy for solving a certain task. Goldman (1989) posited that the type of instructions should vary depending upon the goal of the skill being trained (e.g. instruction for basic and computational mathematical skills versus instructions for problem-solving tasks). Thus, the author distinguished three types of instructions: 1 Direct instructions, which are designed to teach action sequences. They are scripted and structured step-bystep to ensure mastery before the pupil conducts the task. In this case, the instruction provided by the teacher gradually disappears, while practice and repetition are used to avoid information losing. 2 Self-instruction, which are verbal prompts used to remind the learners what they are doing, so they can reflect about why they select one strategy instead of another. Thus, student verbalizations mediate for cognitive and metacognitive operations (e.g. thinking aloud) underpinning the execution of the task. 3 Mediated/assisted performance (or guided learning) that models mathematic performance through guided experience (e.g. computer-assisted). Specifically, starting from the mental representation of the task showed by the student, the teacher models task performance by means of Understanding Dyscalculia : A Guide to Symptoms, Management and Treatment, edited by Daniela Lucangeli, Taylor & Francis Group, 2020. ProQuest Ebook Central, http://ebookcentral.proquest.com/lib/bibliovirtualuide-ebooks/detail.action?docID=6 Created from bibliovirtualuide-ebooks on 2024-02-14 17:16:30. Interventions for dyscalculic students 55 coaching, questioning, fading and providing explanations (i.e. to make the mathematical task explicit, to verify understanding and to encourage mathematical reasoning from the students). In their meta-analyses, Kroesbergen and Van Luit (2003) and Gersten et al. (2009) reported that the use of self-instruction strategies is more effective for accomplishing the development of mathematical skills of students with special educational needs than direct instruction or mediated/assisted instruction. Furthermore, according to Kroesbergen and Van Luit (2003) the effectiveness of instructional strategies given by the teacher is greater than the use of computer-assisted instruction. More recently, Sood and Mackey (2014) posited the effectiveness of the instructional interventions encouraging rote learning of procedural mathematical knowledge (e.g. computation) by the memorization, repetition and application of sequences of procedures in combination with the constructionist trainings, which are mainly based on the enhancement of conceptual knowledge. In this perspective, the conceptual knowledge is actively built by the learners through their interactions with the environment, such that the students reflect and give sense to their experiences, while the teacher supports them in absorbing new information into an already existing mental schema or in modifying the schema to integrate the new strategic knowledge. This suggests that the teacher serves for scaffolding, accompanying the students through the Vygotsky’s zone of proximal development, that is, beyond the level of current competence, favouring the development of their potential skills through guidance (Butterworth, 2018; Nelwan et al., 2018). In this perspective, the combination of the use of digital technologies (i.e. to make practice) and traditional aids and tasks (i.e. with which the teacher supports the dyscalculic students in learning the foundational concepts and principles driving numeracy processing) is crucial to promote academic achievements in dyscalculic learners. From an applied viewpoint, this implies that the teacher 1 provides clear and precise didactic instructions about what the students need to learn to achieve a targeted goal; 2 selects mathematics-related activities which are consistent with the strengths of the students with dyscalculia, to foster successful learning and minimize the risk of avoidance behaviours or emotional distress due to repeated failures (i.e. adapting the successive task to the current level of performance); 3 gradually modulates the complexity of mathematical tasks, first proposing concrete problems (e.g. based on the manipulation of aids such as coins, wooden cubes, Cuisenaire Copyright © 2020. Taylor & Francis Group. All rights reserved.. Understanding Dyscalculia : A Guide to Symptoms, Management and Treatment, edited by Daniela Lucangeli, Taylor & Francis Group, 2020. 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All rights reserved. 56 Maria Chiara Fastame rods and dominoes), then pictorial representations of problems (e.g. visual diagrams) and finally the abstract mathematical symbols; 4 uses schema-based instruction to promote the understanding of the structure of the problem and to find the correct solution; 5 uses a wide range of examples to favour the learning of mathematical processes, especially when the transfer of newly learned skills must be promoted across unfamiliar problems (i.e keeping in mind that one of the most evident difficulties of dyscalculic learners is the inability to generalize); 6 encourages students to think aloud and verbalize their strategies, to avoid the practice of solving the problem impulsively by randomly combining numbers; 7 supports students in regulating their motivation, attention and effort oriented to academic achievements; 8 uses both extrinsic feedbacks about the performance (i.e. tells students if they performed well or not) and intrinsic ones (i.e. gives feedbacks about the appropriateness of the learners’ actions in relation to the goal, such that the students gradually infer what to do to improve their performance without further advice and guidance from the teacher) to foster conceptual learning; 9 monitors ongoing performance progresses showed by the dyscalculic students (e.g. applies curriculum-based measurements), to modify, if necessary, the proposed activities and didactic strategies; 10 provides extra time to perform the mathematical task; and 11 is provided verbal feedbacks and graphic information about student progress in mathematical tasks by school psychologists, in order to understand the developmental trajectories of the dyscalculic students and plan the most appropriate educational activities to enhance their mathematical attainment (e.g. Fuchs et al., 2008; Gersten et al., 2009). Furthermore, Zheng et al. (2012) stress the importance of combining explicit feedbacks to dyscalculic learners (i.e. especially those comorbid with dyslexia) about how they are performing, with explicit practice and instruction, questioning, strategies cues (i.e. to remind students to use specific strategies or procedures), sequencing (i.e. breaking down the task in a sequence of shorter activities) and small-group (i.e. 3–5 students) interactive settings to enhance problem-solving achievement. Finally, it must be kept in mind that communication and mutual collaboration among teachers, school psychologists, parents and students with dyscalculia is essential to work synergistically to promote the present (e.g. school) and future (e.g. work productivity) successful achievements of those learners. The next section discusses the role played by educational and social policies for the promotion Understanding Dyscalculia : A Guide to Symptoms, Management and Treatment, edited by Daniela Lucangeli, Taylor & Francis Group, 2020. ProQuest Ebook Central, http://ebookcentral.proquest.com/lib/bibliovirtualuide-ebooks/detail.action?docID=6 Created from bibliovirtualuide-ebooks on 2024-02-14 17:16:30. Interventions for dyscalculic students 57 of the assessment and interventions enhancing the mathematical skills of dyscalculic students. Copyright © 2020. Taylor & Francis Group. All rights reserved. Educating the community: let dyscalculia be recognized and treated On the one hand, individualized and targeted learning interventions to treat dyscalculia are necessary to prevent the negative impact of this specific disorder on the daily life of the individuals with persistent deficits in mathematics; on the other hand, parallel “systematic knowledge transfer into the community and educational practice is necessary” (Dresler et al., 2018, p. 2) to promote psychological life quality of those learners (WHO, 2002). Overall, knowledge transfer implies that effective communication strategies need to be developed to achieve different goals. First, it is fundamental to the dissemination of scientific knowledge about the neurocognitive phenotypes associated with dyscalculia to correct misconceptions about its symptoms and its neural bases, to highlight the complexity of the subgroups associated with the disorder and therefore to highlight the variability underlying the expression of the disorder. The dissemination of the core characteristics of dyscalculia will prevent the underestimation of the disorder and will foster the diagnosis, since often the disorder seems to be unknown or masked by further disorders (e.g. dyslexia and anxiety). Indeed, as pointed out by Butterworth (2018), dyscalculia is underestimated, whereas more attention and economic resources are destined to the assessment and treatment of further specific learning disabilities, such as dyslexia. Second, it is crucial to provide educators, teachers, educational psychologists and parents with correct information about the adequate tools developed to assess (e.g. validated tests assessing the accuracy and speed in carrying out arithmetic facts) and train (i.e. intervention programmes) numeracy skills in dyscalculic students. This will prevent prejudices about the actual efficacy of targeted psychoeducational interventions confuting the myth of “non-change”, that is, the misconception that although dyscalculia is at least partially genetically determined, this does not mean that it is immune to the effect of cognitive and behavioural interventions (e.g. Kaufmann et al., 2013). From an applied perspective, the realization of the previously mentioned goals depends upon the choices made by policy makers, Understanding Dyscalculia : A Guide to Symptoms, Management and Treatment, edited by Daniela Lucangeli, Taylor & Francis Group, 2020. ProQuest Ebook Central, http://ebookcentral.proquest.com/lib/bibliovirtualuide-ebooks/detail.action?docID=6 Created from bibliovirtualuide-ebooks on 2024-02-14 17:16:30. Copyright © 2020. Taylor & Francis Group. All rights reserved. 58 Maria Chiara Fastame that is, on the economic resources directed: 1 to educate the stakeholders about the neurobiological and cognitive bases associated with dyscalculic profiles; 2 to conduct screening initiatives at school – to assess the efficiency of mathematical functions and the related cognitive processes; 3 to disseminate the best teaching strategies (e.g. use of reinforcement, explicit instructions) selected as a function of the actual educational needs of each dyscalculic student; and 4 to implement effective early psychoeducational interventions to improve school achievements and when appropriate to treat the emotional problems (e.g. anxiety) related to the specific learning disability. Thus, if in the future long-term behavioural and cognitive outcomes and neural functions associated with dyscalculia can be systematically shown using effective psychoeducational trainings, it will be necessary to stress that long-lasting change in dyscalculic profiles can be achieved. From an applied viewpoint, this implies the correct communication about what the experimentally valid effective interventions for dyscalculia are and the dissemination of the know-how about the best practice to empower mathematical skills at school, such as designing targeted interventions tailored to treat the core deficits of each individual learner. Last but not least, the economic benefit of the attitude of paying attention to the early diagnosis and intervention of students with dyscalculia must be considered. Specifically, as pointed out by Butterworth (2018), in the United Kingdom the cost for the assistance of people with dyscalculia is approximately £2.4 billion per year. Nonetheless, “the total cost to society would be lower if more were spent on educational help for the lowest attaining, especially the dyscalculics” (Butterworth, 2018, p. 12). Indeed, it is argued that policy choices providing greater opportunities to increase knowledge of the underlying mechanisms and the heterogeneous symptoms of dyscalculia and offering effective practical protocols to improve dyscalculics’ lives can massively contribute to the reduction of medical (e.g. use of health resources for the occurrence of mental problems, such as anxiety and depression), legal (e.g. being in trouble with law because of deviant behaviours) and additional educational costs (e.g. greater request of psychoeducational support in case of late intervention) for society. This is something that governments must think about, since so far wellestablished good practices for helping dyscalculic learners are not Understanding Dyscalculia : A Guide to Symptoms, Management and Treatment, edited by Daniela Lucangeli, Taylor & Francis Group, 2020. ProQuest Ebook Central, http://ebookcentral.proquest.com/lib/bibliovirtualuide-ebooks/detail.action?docID=6 Created from bibliovirtualuide-ebooks on 2024-02-14 17:16:30. Copyright © 2020. Taylor & Francis Group. All rights reserved. Interventions for dyscalculic students 59 internationally shared. In this regard, in Italy – where a legislative framework to support students with specific learning disabilities was approved only in October 2010 – the Consensus Conference document about the assessment of specific learning disabilities is shared with the educational field (e.g., teachers, school psychologists and educators), but so far, a standardized protocol for the intervention of the different profiles associated with dyscalculia is still lacking. Despite this, in several Italian universities, high-level qualification training opportunities are offered to acquire expertise about the assessment and intervention for specific learning disabilities by postgraduate master courses for experts working in the educational and medical field (e.g. educators, special needs teachers, psychologists and development neuropsychiatrists). Altogether, assuming an international viewpoint and considering the lack of shared good practices for dyscalculic individuals (see for instance Kerins et al., 2018), it is desirable that in the future, government policies will be coherent and planned to allocate resources to develop or propose specific educational opportunities for professional staff in combination with early assessment and the implementation of targeted psychoeducational interventions for the enhancement of numeracy skills in dyscalculic learners. The need for well-known and experimentally robust interventions is even more evident when comorbid conditions occur with dyscalculia. In conclusion, to improve the life quality of dyscalculics with and without further psychological disorders, the starting point of good practice is investing in resources to promote know-how among parents, students, teachers, pediatricians and educational and school psychologists facing dyscalculia. This is essential since the effects of dyscalculia can reverberate even in adulthood, ­negatively affecting different dimensions of life quality (Kaufmann et al., 2013; Ritchie & Bates, 2013). References Agus, M., Mascia, M. L., Fastame, M. C., Napoleone, V., Porru, A. M., Siddu, F., Lucangeli, D., & Penna, M. P. (2016). Comparing the effects of combined numerical and visuospatial psychoeducational trainings conducted by curricular teachers and external trainers. Preliminary evidence across kindergarteners. Journal of Physics: Conference Series, 772. doi:10.1088/1742-6596/772/1/012038 Understanding Dyscalculia : A Guide to Symptoms, Management and Treatment, edited by Daniela Lucangeli, Taylor & Francis Group, 2020. ProQuest Ebook Central, http://ebookcentral.proquest.com/lib/bibliovirtualuide-ebooks/detail.action?docID=6 Created from bibliovirtualuide-ebooks on 2024-02-14 17:16:30. Copyright © 2020. Taylor & Francis Group. All rights reserved. 60 Maria Chiara Fastame American Psychiatric Association. (2013). Diagnostic and statistical manual of mental disorders (5th ed.). Washington, DC: American Psychiatric Association. Ang, S. Y., Lee, K., Cheam, F., Poon, K., & Koh, J. (2015). Updating and working memory training: Immediate improvement, long-term maintenance, and generalisability to non-trained tasks. Journal of Applied Research in Memory and Cognition, 4, 121–128. doi:10.1016/j. jarmac.2015.03.001 Butterworth, B. (2018). The implications for education of an innate numerosity-processing mechanism. Philosophical Transactions of the Royal Society B: Biological Sciences, 373(1740). doi:10.1098/ rstb.2017.0118 Butterworth, B., Varma, S., & Laurillard, D. (2011). Dyscalculia: From brain to education. Science, 332, 1049–1053. doi:10.1126/science.1201536 Dennis, M. S., Sorrells, A. M., & Falcomata, T. S. (2016). Effects of two interventions on solving basic fact problems by second graders with mathematics learning disabilities. Learning Disability Quarterly, 39, 95–112. doi:10.1177/0731948715595943 Dowker, A. (Ed.). (2008). Mathematical difficulties: Psychology and intervention. London: Academic Press. Dresler, T., Bugden, S., Gouet, C., Lallier, M., Oliveira, D. G., PinheiroChagas, P.,... Weissheimer, J. (2018). A translational framework of educational neuroscience in learning disorders. Frontiers in Integrative Neuroscience, 12, 25. doi:10.3389/fnint.2018.00025 DuPaul, G. J., Gormley, M. J., & Laracy, S. D. (2013). Comorbidity of LD and ADHD: Implications of DSM-5 for assessment and treatment. Journal of Learning Disabilities, 46, 43–51. doi:10.1177/ 0022219412464351 Fuchs, L. S., Fuchs, D., Compton, D. L., Powell, S. R., Seethaler, P. M., Capizzi, A. M., & Fletcher, J. M. (2006). The cognitive correlates of third-grade skill in arithmetic, algorithmic computation, and arithmetic word problems. Journal of Educational Psychology, 98, 29–43. doi:10.1037/0022-0663.98.1.29 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, 79–92. doi:10.2307/20528819 Gersten, R., Chard, D. J., Jayanthi, M., Baker, S. K., Morphy, P., & Flojo, J. R. (2009). Mathematics instruction for students with learning disabilities: A meta-analysis of instructional components. Review of Educational Research, 79, 1202–1242. doi:10.3102/0034654309334431 Gillum, J. (2014). Assessment with children who experience difficulty in mathematics. Support for Learning, 29, 275–291. doi:10.1111/1467-9604. 12061 Understanding Dyscalculia : A Guide to Symptoms, Management and Treatment, edited by Daniela Lucangeli, Taylor & Francis Group, 2020. ProQuest Ebook Central, http://ebookcentral.proquest.com/lib/bibliovirtualuide-ebooks/detail.action?docID=6 Created from bibliovirtualuide-ebooks on 2024-02-14 17:16:30. Copyright © 2020. Taylor & Francis Group. All rights reserved. Interventions for dyscalculic students 61 Goldman, S. R. (1989). Strategy instruction in mathematics. Learning Disability Quarterly, 12, 43–55. doi:10.2307/1510251 Guarnera, M., & D’Amico, A. (2014). Training of attention in children with low arithmetical achievement. Europe’s Journal of Psychology, 10, 277–290. doi:10.5964/ejop.v10i2.744 Hassinger-Das, B., Jordan, N. C., Glutting, J., Irwin, C., & Dyson, N. (2014). Domain-general mediators of the relation between kindergarten number sense and first-grade mathematics achievement. Journal of Experimental Child Psychology, 118, 78–92. doi:10.1016/j. jecp.2013.09.008 Hasselbring, T. S., Goin, L. I., & Bransford, J. D. (1988). Developing math automatically in learning handicapped children: The role of computerized drill and practice. Focus on Exceptional Children, 20(6), 1–7. Iuculano, T. (2016). Neurocognitive accounts of developmental dyscalculia and its remediation. Progress in Brain Research, 227, 305–333. doi:10.1016/bs.pbr.2016.04.024 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, 8453. doi:10.1038/ncomms9453 Jitendra, A. K., Dupuis, D. N., Star, J. R., & Rodriguez, M. C. (2016). The effects of schema-based instruction on the proportional thinking of students with mathematics difficulties with and without reading difficulties. Journal of Learning Disabilities, 49, 354–367. doi:10.1177/ 0022219414554228 Jitendra, A. K., Harwell, M. R., Dupuis, D. N., & Karl, S. R. (2017). A randomized trial of the effects of schema-based instruction on proportional problem solving for students with mathematics problemsolving difficulties. Journal of Learning Disabilities, 50, 322–336. doi:10.1177/0022219416629646 Jitendra, A. K., Star, J. R., Dupuis, D. N., & Rodriguez, M. (2013). Effectiveness of schema-based instruction for improving seventh-grade students’ proportional reasoning: A randomized experiment. Journal of Research on Educational Effectiveness, 6, 114–136. doi:10.1080/1934 5747.2012.725804 Kaufmann, L., Mazzocco, M. M., Dowker, A., von Aster, M., Goebel, S., Grabner, R.,... Rubinsten, O. (2013). Dyscalculia from a developmental and differential perspective. Frontiers in Psychology, 4(516), 1–5. doi:10.3389/fpsyg.2013.00516 Kerins, P., Casserly, A. M., Deacy, E., Harvey, D., McDonagh, D., & Tiernan, B. (2018). The professional development needs of special needs assistants in Irish post-primary schools. European Journal of Special Needs Education, 33, 31–46. doi:10.1080/08856257.2017.1297572 Understanding Dyscalculia : A Guide to Symptoms, Management and Treatment, edited by Daniela Lucangeli, Taylor & Francis Group, 2020. ProQuest Ebook Central, http://ebookcentral.proquest.com/lib/bibliovirtualuide-ebooks/detail.action?docID=6 Created from bibliovirtualuide-ebooks on 2024-02-14 17:16:30. Copyright © 2020. Taylor & Francis Group. All rights reserved. 62 Maria Chiara Fastame Kroesbergen, E. H., & Van Luit, J. E. (2003). Mathematics interventions for children with special educational needs: A meta-analysis. Remedial and Special Education, 24(2), 97–114. doi:10.1177/07419325030240020501 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, 782–795. doi:10.1016/j. neuroimage.2011.01.070 Lamon, S. J. (2007). Rational numbers and proportional reasoning: Toward a theoretical framework for research. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 629–667). Charlotte, NC: Information Age. Layes, S., Lalonde, R., Bouakkaz, Y., & Rebai, M. (2018). Effectiveness of working memory training among children with dyscalculia: Evidence for transfer effects on mathematical achievement – a pilot study. Cognitive Processing, 19, 375–385. doi:10.1007/s10339-017-0853-2 Melby-Lervåg, M., & Hulme, C. (2013). Is working memory training effective? A meta-analytic review. Developmental Psychology, 49, 270–291. doi:10.1037/a0028228 Michels, L., O’Gorman, R., & Kucian, K. (2018). Functional hyperconnectivity vanishes in children with developmental dyscalculia after numerical intervention. Developmental Cognitive Neuroscience, 30, 291–303. doi:10.1016/j.dcn.2017.03.005 Monei, T., & Pedro, A. (2017). A systematic review of interventions for children presenting with dyscalculia in primary schools. Educational Psychology in Practice, 33(3), 277–293. doi:10.1080/02667363.2017. 1289076 Morsanyi, K., van Bers, B. M. C. W., McCormack, T., & McGourty, J. (2018). The prevalence of specific learning disorder in mathematics and comorbidity with other developmental disorders in primary school-age children. British Journal of Psychology, 109(4), 917–940. doi:10.1111/ bjop.12322 Nelwan, M., Vissers, C., & Kroesbergen, E. H. (2018). Coaching positively influences the effects of working memory training on visual working memory as well as mathematical ability. Neuropsychologia, 113, 140–149. doi:10.1016/j.neuropsychologia.2018.04.002 Parmar, R. S., Cawley, J. F., & Frazita, R. R. (1996). Word problem-solving by students with and without mild disabilities. Exceptional Children, 62, 415–429. doi:10.1177/001440299606200503 Powell, S. R., Fuchs, L. S., Fuchs, D., Cirino, P. T., & Fletcher, J. M. (2009). Effects of fact retrieval tutoring on third-grade students with math difficulties with and without reading difficulties. Learning Disabilities Research & Practice, 24, 1–11. doi:10.1111/j.1540-5826. 2008.01272.x Understanding Dyscalculia : A Guide to Symptoms, Management and Treatment, edited by Daniela Lucangeli, Taylor & Francis Group, 2020. ProQuest Ebook Central, http://ebookcentral.proquest.com/lib/bibliovirtualuide-ebooks/detail.action?docID=6 Created from bibliovirtualuide-ebooks on 2024-02-14 17:16:30. Copyright © 2020. Taylor & Francis Group. All rights reserved. Interventions for dyscalculic students 63 Ritchie, S. J., & Bates, T. C. (2013). Enduring links from childhood mathematics and reading achievement to adult socioeconomic status. Psychological Science, 24, 1301–1308. doi:10.1177/0956797612466268 Roberts, G., Quach, J., Spencer-Smith, M., Anderson, P. J., Gathercole, S., Gold, L.,... Wake, M. (2016). Academic outcomes 2 years after working memory training for children with low working memory: A randomized clinical trial. JAMA Pediatrics, 170, e154568–e154568. doi:10.1001/ jamapediatrics.2015.4568 Rubinsten, O., & Henik, A. (2009). Developmental dyscalculia: Heterogeneity might not mean different mechanisms. Trends in Cognitive Sciences, 13, 92–99. doi:10.1016/j.tics.2008.11.002 Soares, N., Evans, T., & Patel, D. R. (2018). Specific learning disability in mathematics: A comprehensive review. Translational Pediatrics, 7, 48–62. doi:10.21037/tp.2017.08.03 Söderqvist, S., & Bergman Nutley, S. (2015). Working memory training is associated with long term attainments in math and reading. Frontiers in Psychology, 6, 1711. doi:10.3389/fpsyg.2015.01711 Sood, S., & Mackey, M. (2014). Number sense instruction: A comprehensive literature review. World Journal of Education, 4, 58–67. doi:10.5430/wje.v4n5p58 Szűcs, D., & Myers, T. (2017). A critical analysis of design, facts, bias and inference in the approximate number system training literature: A systematic review. Trends in Neuroscience and Education, 6, 187–203. doi:10.1016/j.tine.2016.11.002 Tournaki, N. (2003). The differential effects of teaching addition through strategy instruction versus drill and practice to students with and without learning disabilities. Journal of Learning Disabilities, 36, 449–458. doi:10.1177/00222194030360050601 Trout, A. L., Lienemann, T. O., Reid, R., & Epstein, M. H. (2007). A review of non-medication interventions to improve the academic performance of children and youth with ADHD. Remedial and Special Education, 28, 207–226. Wilson, A., Dehaene, S., Pinel, P., Revkin, S., Cohen, L., & Cohen, D. (2006). Principles underlying the design of “the number race”, an adaptive computer game for remediation of dyscalculia. Behavioral and Brain Functions, 2, 20. doi:10.1186/1744-9081-2-19 Wong, T. T. Y., & Chan, W. W. L. (2019). Identifying children with persistent low math achievement: The role of number-magnitude mapping and symbolic numerical processing. Learning and Instruction, 60, 29–40. doi:10.1016/j.learninstruc.2018.11.006 World Health Organization. (2002). The world health report 2002: Reducing risks, promoting healthy life. Geneva: World Health Organization. Xin, Y. P., Jitendra, A. K., & Deatline-Buchman, A. (2005). Effects of mathematical word Problem – Solving instruction on middle school students Understanding Dyscalculia : A Guide to Symptoms, Management and Treatment, edited by Daniela Lucangeli, Taylor & Francis Group, 2020. ProQuest Ebook Central, http://ebookcentral.proquest.com/lib/bibliovirtualuide-ebooks/detail.action?docID=6 Created from bibliovirtualuide-ebooks on 2024-02-14 17:16:30. 64 Maria Chiara Fastame Copyright © 2020. Taylor & Francis Group. All rights reserved. with learning problems. The Journal of Special Education, 39, 181–192. doi:10.1177/00224669050390030501 Zhang, H., Chang, L., Chen, X., Ma, L., & Zhou, R. (2018). Working memory updating training improves mathematics performance in middle school students with learning difficulties. Frontiers in Human Neuroscience, 12, 154. doi:10.3389/fnhum.2018.00154 Zheng, X., Flynn, L. J., & Swanson, H. L. (2012). Experimental intervention studies on word problem solving and math disabilities: A selective analysis of the literature. Learning Disability Quarterly, 36, 97–111. doi:10.1177/0731948712444277 Understanding Dyscalculia : A Guide to Symptoms, Management and Treatment, edited by Daniela Lucangeli, Taylor & Francis Group, 2020. 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