Dyscalculia Signs & Symptoms PDF

Chapter 3 Developmental dyscalculia Signs and symptoms Nicoletta Perini, Francesco Sella, Emma Blakey Developmental dyscalculia affects between 3.5 percent and 6.5 percent of children, with similar prevalence rates to dyslexia and ADHD (Gross-Tsur, Manor, & Shalev, 1996; Morsyani, van Bers, O’Connor...

Chapter 3 Developmental dyscalculia Signs and symptoms Nicoletta Perini, Francesco Sella, Emma Blakey Developmental dyscalculia affects between 3.5 percent and 6.5 percent of children, with similar prevalence rates to dyslexia and ADHD (Gross-Tsur, Manor, & Shalev, 1996; Morsyani, van Bers, O’Connor, & McCormack, 2018). Developmental dyscalculia is characterized by persistent difficulties in understanding mathematical concepts, counting and fluent arithmetic in the absence of low IQ or sensory difficulties (Butterworth, 2005; Geary, 2006). Two classification systems, the International Classification of Diseases of the World Health Organization (ICD 10, World Health Organization, 2004) and the Diagnostic and Statistical Manual of Mental Disorders (American Psychiatric Association, 2013) suggest three core deficits in dyscalculia: Copyright © 2020. Taylor & Francis Group. All rights reserved. 1 2 3 The acquisition of mathematical skills is compromised. These problems are not consequences of lack of opportunity to learn or low general cognitive abilities (i.e. low IQ) or motor and neurological disorders. Difficulties cannot be accounted for by brain trauma or disease. The difficulties involve several domains of mathematical learning. The deficit persists after a period of training. Mathematical skills are an essential component of everyday life – from telling the time to managing finances to understanding health statistics – and therefore, it is perhaps not surprising that dyscalculia can affect education, employment and well-being (Kucian & von Aster, 2015; Shalev, Auerbach, Manor, & Gross-Tsur, 2000). Early diagnosis of dyscalculia is crucial for supporting children who are struggling before difficulties have time to embed and affect later outcomes (Kucian & von Aster, 2015). This is particularly important in dyscalculia as mathematics is a cumulative subject, 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 17:13:52. 24 Perini, Sella, Blakey where early skills lay a foundation for more advanced mathematical learning (Melhuish, 2013). In support of this, early foundational mathematical skills are known to predict overall academic success (Duncan et al., 2007). In this chapter, we present three clinical cases that highlight the characteristics of developmental dyscalculia and its impact on students’ school life. The cases describe the cognitive profiles of children with mathematical difficulties. We hope that they will help guide educators and educational psychologists in identifying signs of developmental dyscalculia in children and give a broader picture for researchers on how varied this developmental condition can be. In addition, we provide examples that distinguish between developmental dyscalculia and mathematical difficulties. In the last paragraph, we introduce the characteristics of mathematics anxiety, which represents the more prevalent negative emotion related to mathematical learning. Mathematics anxiety is very common among children who display difficulties in mathematics. Often support for children focuses on improving their numbers or calculation skills directly, but it is also important for educators to recognize if the children have anxiety and address the issue. Here we identify factors that may contribute to the development of mathematics anxiety and present strategies on how to support students cope with their condition. Copyright © 2020. Taylor & Francis Group. All rights reserved. A clinical case of developmental dyscalculia: Fabio Fabio was eight years old and attending the third year of primary school when his parents brought him to the neuropsychiatric unit for a psychological evaluation. He had been struggling with mathematics since the beginning of the primary school. According to his teachers, Fabio’s mathematical achievement was evidently lower compared to his peers. Not surprisingly, his parents were concerned about his scholastic achievement and were afraid he could develop a bad attitude towards mathematics or, more broadly, towards school and learning. Fabio appeared as a regular eight-year-old boy, even though his body movements and walking were somewhat clumsy. He completed several tests to evaluate his cognitive and learning skills. He demonstrated a good fluency in reading, even though he showed some limitations in reading comprehension. He also followed grammatical rules when writing, even though his 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 17:13:52. Developmental dyscalculia 25 Copyright © 2020. Taylor & Francis Group. All rights reserved. handwriting was not clear and he often wrote outside the sheet margins. Fabio displayed poor mathematical skills. He could choose the larger between two digits, but he made several errors when asked to put in ascending or descending order large numbers entailing hundreds and thousands. He could slowly perform simple arithmetic calculations by counting with his fingers, even in the case of basic additions and subtractions problems which at his age should have been memorized as arithmetic facts (e.g. 3 + 2 = 5). He could perform some written calculations, mainly additions and subtractions, but frequently misplaced numbers or wrote wrong arithmetic signs (e.g. + instead of -). He did not know the procedures to perform written multiplications and divisions. Moreover, he made several errors when writing numbers under dictation, especially in case of numbers with hundreds and thousands (e.g. “one-thousand and three”  10003; “one-hundred and thirteen”  10013). Fabio’s intelligence, as assessed with a standardized test, was average for his age. However, he displayed poor visuospatial skills, as indexed by an extremely low performance in a cubes reconstruction task. Fabio’s cognitive assessment revealed the presence of significant and persistent difficulties in a wide range of mathematical skills, which could not be attributed to intellectual disability or sensory deficit. Moreover, he displayed poor visuospatial memory associated with mathematical difficulties. Does Fabio meet the criteria for a diagnosis of developmental dyscalculia? To answer this question, we need to outline the criteria for a diagnosis proposed by two widely adopted international manuals, the Diagnostic and Statistical Manual of Mental Disorders (DSM-V) and the International Table 3.1 Fabio’s strengths and weaknesses in mathematics Fabio’s strengths Fabio’s weaknesses Written calculation: additions and subtractions Writing numbers with tens and units Discrimination of quantities with two numbers Mental calculations with fingers Written calculation: multiplication and division Writing numbers with hundreds and thousands Sorting of quantities with four numbers Recovery of numerical facts Recovery of the reverse number sequence from memory 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 17:13:52. Copyright © 2020. Taylor & Francis Group. All rights reserved. 26 Perini, Sella, Blakey Classification of Diseases (ICD-10). Finally, we present the Italian guidelines for the diagnosis in case of learning disability proposed by the Associazione Italiana per la Ricerca e l’Intervento nella Psicopatologia dell’Apprendimento (AIRIPA) and Associazione Italiana Dislessia (AID) (AIRIPA and AID, Agreement document, 2012). The DSM-V proposed a single category for learning disability, whereby difficulties can be related to different areas, including reading, written expression and mathematics. Concerning the latter, the difficulties can be related to the concept of number, memorization of numerical facts, calculation and mathematical reasoning. Difficulties in one or more of these areas must be present for at least six months and persist after dedicated intervention. The performance in mathematical skills must be inferior to that expected according to the chronological age and manifested in the early school years. Importantly, the observed difficulties could not be explained as a consequence of intellectual disability, impaired visual or auditory acuity, other mental or neurological disorder, psychosocial adversity, linguistic deficit or inadequate schooling. Finally, the condition can be classified as mild, moderate or severe according to the level of impairment displayed by a child. The ICD-10 describes the specific disorder of arithmetic skills, within the category of specific developmental disorders of scholastic skills, as a condition characterized by the specific impairment of arithmetical skills that is not solely explainable on the basis of general intellectual disability or inadequate schooling. This disorder involves deficit in mastering basic arithmetic skills, such as addition, subtraction, multiplication and division, and rather than mathematical reasoning abilities involved in algebra, trigonometry and geometry (ICD-10, 1992). According to the Italian guidelines (Istituto Superiore di Sanitá; AIRIPA-AID), a diagnosis of developmental dyscalculia would be made with the presence of low scores in at least half of the subtests from a large mathematical ability scale, which accurately assesses different numerical skills, such as number representation, calculation and mathematical problem solving. The scores should be equal or inferior to the 5th percentile or two standard deviations below the mean compared to those expected according to the chronological age. The mathematical difficulties must be persistent and have a detrimental effect on scholastic achievement. Importantly, the mathematical difficulties must persist after the implementation of adequate training to improve the compromised mathematical components. 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 17:13:52. Developmental dyscalculia 27 Persistent difficulties in a wide range of mathematical skills measured through standardized tests: basic processes of numerical intelligence; ability to solve addition, subtraction, multiplication and division problems; ability to employ more abstract mathematical reasoning skills involved in algebra, trigonometry and geometry, etc. This problem does not improve, even after specialized training. It leads to severe adaptive consequences in areas such as well-being and day-to-day functioning. It emerges early on in development. This problem cannot be explained by other conditions, including intellectual disability, sensory difficulties, socio-cultural disadvantage, etc. It is often accompanied by other difficulties in skills that underpin mathematical learning, such as memory and visuospatial skills. Copyright © 2020. Taylor & Francis Group. All rights reserved. Figure 3.1 Characteristics of developmental dyscalculia Fabio displayed generalized difficulties in mathematics, which were present since the beginning of the primary school and significantly interfered with his well-being. These difficulties could not be explained by other neurodevelopmental disorders or sensory deficits. However, before determining a diagnosis of developmental dyscalculia, it was necessary to implement a specific clinical intervention on compromised components to ensure that those are resistant to intervention. Fabio underwent three interventions under the supervision of a clinical psychologist who specialized in learning disability. The interventions specifically targeted those numerical skills that were especially compromised. First, he was trained in associating numerical quantities (i.e. sets of elements) with the corresponding number words and Arabic numbers to reinforce the understanding of the numerical magnitude associated with numerical symbols. This activity involved comparison tasks (e.g. choose the larger set, larger number), enumeration task (e.g. quickly enumerate sets of objects) and estimation task (e.g. try to guess the numerosity of a set without counting). Fabio also showed a poor knowledge of the counting sequence. Therefore, he was trained in reciting the counting sequence forward and backward. Fabio always relied on his fingers when performing calculation. The intervention involved the gradual memorization of arithmetic facts with a reduction in finger 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 17:13:52. 28 Perini, Sella, Blakey support. He was also trained in better understanding the place value of the Arabic symbolic system and the lexical rules regulating the transcoding between number words and Arabic numbers. For instance Fabio struggled in understanding the meaning of the terms “unit”, “decade”, “hundred”, “thousand”, etc. In the final stages of the intervention, Fabio was also trained in recognizing the different elements of a mathematical problem and in selecting the right arithmetic operation to solve it. After thirty sessions of training across two years, his abilities only marginally improved. His ability to discriminate between symbolic and non-symbolic numerical quantities improved. However, he only memorized few arithmetic facts, and he kept using his fingers as support for calculation. He could solve mathematical problems only when they were related to concrete examples that he could easily visualize. Fabio met all the criteria of a diagnosis of developmental dyscalculia. Accordingly, he presented a performance that was below the 5th percentile in at least half of the subtests composing the larger test to assess numerical skills. The mathematical difficulties were present at the beginning of schooling and they were resistant to intervention. Furthermore, the low performance could not be explained by deficits in general intellectual abilities or sensory systems, nor by cultural or scholastic disadvantage. Copyright © 2020. Taylor & Francis Group. All rights reserved. A case of mathematical difficulties but not developmental dyscalculia: Aurora Aurora was brought to the neuropsychiatric unit by her parents when she was eight years old. According to her teachers, she had been showing some difficulties in mathematical learning. Aurora had been seeing a speech and language therapist as she had displayed a delay in the acquisition of language when she was younger. Accordingly, she had displayed reading and writing difficulties, which mostly disappeared thanks to the speech therapy. During the assessment, Aurora was talkative and talked about herself and her interests. She reported she enjoyed going to school and had a good relationship with the teachers. However, she said that most of the time she was not interested in listening to the teachers in class. The teachers reported that Aurora did not ask for extra help when she was not able to solve a problem but rather stayed quiet, embarrassed and left the task unsolved. 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 17:13:52. Copyright © 2020. Taylor & Francis Group. All rights reserved. Developmental dyscalculia 29 A complete assessment of Aurora revealed some difficulties related to mathematical achievement. In particular, she displayed a poor understanding of the place value of digits in the Arabic system, she had not memorized enough arithmetic facts for her age and she also showed a poor performance when counting backwards and solving mathematical problems. She also made some errors when writing under dictation (spelling errors) and in reading comprehension, while her fluency and accuracy in reading was perfectly in line with that expected for the third grade. On the one hand, Aurora displayed difficulties in understanding the meaning of large numbers entailing hundreds and thousands, memorizing numerical facts and solving mathematical problems. When presented with a mathematical problem, she failed to recognize the main question of the problem and the relevant data. She blindly chose some numbers in the problem and performed some arithmetical operation without really realizing the meaning of what she was doing. On the other hand, Aurora was confident in calculations when she could use her fingers and she clearly had learnt the procedures to solve written calculation. Her general intellectual abilities were average, while her verbal working memory (the ability to maintain and process verbal information) was below that expected for her age. Aurora completed a specific mathematical training programme under the supervision of a clinical psychologist specialized in learning disabilities. The training involved mental calculation and early numeracy exercises. Teachers were also informed about the results of Aurora’s psychological evaluation and participated in the training programme as they were requested to implement some activities to facilitate Aurora’s learning during mathematics classes. After the implementation of the brief intervention, Aurora completed a second evaluation of her mathematical skills. She Table 3.2 Aurora’s strengths and weaknesses in mathematics Aurora’s strengths Aurora’s weaknesses Mental calculation Written calculation Syntactic aspects of number Recovery of numerical facts Recovering the sequence of inverse numbers from the memory Solving mathematical problems 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 17:13:52. Copyright © 2020. Taylor & Francis Group. All rights reserved. 30 Perini, Sella, Blakey performed the mental calculation correctly, even though she kept using immature strategies such as counting with her fingers instead of retrieving the answer from the long-term memory. The use of fingers when solving simple arithmetic problems slowed down her performance but it did mean that most of the answers were correct. Aurora showed a better understanding of place values and the numerical meaning of hundreds and thousands. However, she still displayed a poor comprehension of decimal numbers. She also displayed a better ability to represent the information of word problems and selecting the appropriate arithmetic operation, even though she sometimes failed when executing the calculation, which ultimately led to a wrong answer. Overall, the improvement observed in Aurora’s mathematical achievement ruled out the diagnosis of developmental dyscalculia. Her difficulties in mathematics were modified after a brief intervention and remained circumscribed to specific mathematical components rather than being generalized. Aurora most likely had poor working memory and some linguistic difficulties, which had a detrimental effect on her mathematical learning rather than a specific learning disability. After the first intervention, she kept improving her mathematical learning displayed a more positive attitude towards the subject and, more broadly, towards attending school. The training provided Aurora with more efficient strategies that she could use which allowed her to not just rely on her limited working memory. Fabio and Aurora are two clinical cases that clearly reflect the difference between a severe case of developmental dyscalculia (Fabio) and a less severe case of mathematical learning difficulty (Aurora). What differences can be found between the two prototypical profiles of Fabio and Aurora? Fabio presented severe difficulties in mathematical learning: he displayed a compromised understanding of the numerical meaning of numbers, extremely poor calculation and word problem-solving skills. Aurora, instead, displayed a good understanding of number meaning but still had some difficulties with place-value understanding and the memorization of arithmetic facts. Fabio showed a specific deficit in visuospatial abilities, while Aurora did 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 17:13:52. Developmental dyscalculia 31 Table 3.3 What is the difference between difficulties in mathematics and developmental dyscalculia? Difficulties in mathematics Developmental dyscalculia Circumscribed difficulties Profile modifiable Wide range of difficulties Presence of visuospatial difficulties Poor modifiability of the profile The implementation of an intervention slightly improved Fabio’s condition, whereas Aurora largely benefitted from it and kept showing signs of continuous improvements afterwards. Table 3.3 presents the main differences between a profile of difficulties in mathematics and one of developmental dyscalculia. Copyright © 2020. Taylor & Francis Group. All rights reserved. A case of developmental dyscalculia in secondary school: Giorgio Giorgio was 15 years old when his parents brought him to the neuropsychiatric unit for a psychological evaluation. They reported that he had been struggling with mathematical learning since the beginning of primary school. Throughout his schooling, Giorgio was supported by a home tutor who supervised him when completing home assignments, especially in mathematics. Nevertheless, Giorgio’s mathematical learning was constantly low compared to other students, whereas his achievement in other subjects was above average. He inevitably had developed a negative attitude towards mathematics to the point that, during the evaluation, he reported to have experienced anxiety when completing mathematical tasks. From the evaluation, it emerged that Giorgio had severe difficulties in mental calculation and recovery of numerical facts, in problem solving and in understanding the basic principles of algebra and geometry. Most of his errors were related to poor visuospatial skills. Despite the mathematical difficulties, Giorgio was extremely fluent in reading and could perfectly understand the meaning of the read text. His writing skills were excellent as indexed by a rich vocabulary and correct spelling. In line with this scenario, Giorgio showed good verbal skills, while his visuospatial skills were weak as well as his overall working memory and speed of processing. 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 17:13:52. 32 Perini, Sella, Blakey Table 3.4 Giorgio’s strengths and weaknesses in mathematics Giorgio’s strengths Giorgio’s weaknesses Copyright © 2020. Taylor & Francis Group. All rights reserved. Mental calculation Recovery of numerical facts Poor knowledge of algebra and geometry Arithmetic Solving mathematical problems Tasks of visuospatial nature Several points emerged from Giorgio’s psychological evaluation. First, he displayed extremely a low performance in different numerical skills rather than a circumscribed condition. Second, the compromised mathematical learning not only had a negative impact on his scholastic achievement but also on his well-being, as indexed by the presence of mathematics anxiety. Third, the mathematical difficulties could not be related to other causes such as sensory deficits, different neurological or psychiatric conditions or lack of appropriate education. Fourth, Giorgio has experienced such mathematical difficulties for a long period ranging from primary to secondary school. Finally, there was an evident discrepancy between Giorgio’s mathematical and visuospatial skills compared to his verbal abilities. Giorgio seemed to present a cognitive profile compatible with a diagnosis of developmental dyscalculia. As recommended earlier, to ensure the presence of specific learning disorder, it is good practice to assess whether a specific intervention can or cannot significantly improve mathematical difficulties. However, it was clear that Giorgio had been receiving constant tailored support for years, but this did not lead to any improvement in his mathematical skills. Moreover, in the case of older children at the end of high school, an intervention could represent a burden in terms of time and resources while providing limited advantages to his future scholastic career. In line with this reasoning, Giorgio was diagnosed with developmental dyscalculia and the teachers were invited to support him during the last months of secondary school. The presence of a formal diagnosis helped teachers understand that Giorgio’s difficulties were not due to lack of motivation but the result of a specific condition. Accordingly, teachers developed a personalized and simplified study programme for Giorgio. Parents also regained trust 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 17:13:52. Developmental dyscalculia 33 in teachers and in the school, and Giorgio had a better attitude towards school. What and how to observe the development of a student’s mathematical learning In the previous paragraphs, we described the characteristics of mathematical learning disorder by taking a psychological perspective. However, parents, teachers and educators should be empowered to recognize when a child does not meet the learning goals that are expected in a given age with the aim to identify those situations in which a child needs further support in mathematics. The earlier the support is given, the more effective it is likely to be. It is vital to recognize early signs of struggling to implement appropriate educational interventions and, if this arises, conduct a detailed investigation of the child’s cognitive and mathematical skills. In Tables 3.5–3.8, we report some questions to ask regarding mathematical learning for different school grades. These questions can lead the exploration of a student’s mathematical learning across school years and help in identifying when expected goals are not achieved. Copyright © 2020. Taylor & Francis Group. All rights reserved. Table 3.5 How to observe mathematical learning at kindergarten Process Useful questions Semantic processes Can the student compare two sets of objects and say where there is more? Can the student compare two numbers and say which one is the biggest? Does the student recognize some numbers written in Arabic code? Can the student write some numbers if they are dictated? Does the student understand that a set can be formed of different elements? E.g. A necklace is made up of many pearls. Can the student count collections of a few elements? Otherwise: Does the student know the sequence of numbers? (stable order) Can the student pair two objects? (biunivocal correspondence) After counting, use the last word-number to define the number of the whole? (principle of cardinality) Lexical processes Pre-syntactic processes Count 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 17:13:52. 34 Perini, Sella, Blakey Table 3.6 Obser ving mathematical learning at the beginning of primary school Process Useful questions Semantic processes Does the student struggle to sort numbers by size? Does the student handle the Arabic code well? Does the student know the place of unity and tens? Does the student handle zero well within numbers? Can the student count the sets of objects? Can the student use your fingers to perform simple calculations? Can the student line up? Does the student remember the + and – procedure? Are the intermediate calculations right? Lexical processes Syntactic processes Count Calculation in mind Written calculation Table 3.7 Observing mathematical learning at the end of primary school Process Useful questions Semantic processes Does the student struggle to sort numbers by size? Does the student handle the Arabic code well? Does the student know the place of unity, tens, hundreds, thousands? Does the student handle zero well within numbers? Does the student know the comma? Does the student use functional mental calculation strategies, does the student use fingers or does the student represent the numbers in the column? Can the student line up? Does the student remember the + and – procedure? Are the intermediate calculations right? Does the student know the tables? Does the student have any automatic number combinations (e.g. 50 + 50)? Lexical processes Copyright © 2020. Taylor & Francis Group. All rights reserved. Syntactic processes Calculation in mind Written calculation automation 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 17:13:52. Developmental dyscalculia 35 Table 3.8 Ho w to observe mathematical learning during problem solving at the end of primary school Process Useful questions Problem solving Does the student understand the text of the problem and know how to identify the important information for the solution? Can the student represent the data and their relationship in a simple way? Does the student know any solution schemes and can the student recover them when it is time to solve the problem? Can the student plan the steps to solve the problem? Can the student perform the calculations? Can the student control what they did? The Consensus Conference (2011) proposes to observe as critical the profiles of the children who, by the middle of the first year of primary school, present: Difficulty in recognizing small quantities; Difficulty in reading and/or writing numbers from 1 to 10; Difficulty in the oral calculation with numbers between 1 and 10 with concrete support. Copyright © 2020. Taylor & Francis Group. All rights reserved. Mathematics anxiety Mathematics is probably the main scholastic subject that can generate a feeling of fear and stress in students (i.e. mathematics anxiety). When dealing with numbers and situations related to mathematics, some people experience anxiety, which can have a negative impact on their performance (Punaro & Reeve, 2012). The anxiety experienced is very specific to situations that involve mathematics or numbers, which differentiates it from a more general test anxiety or trait anxiety (i.e. a stable condition). Not surprisingly, mathematics anxiety often occurs in people who also have low performance in mathematics. The relationship between mathematics anxiety and performance seems to be bi-directional: poor performance can trigger feelings of anxiety and the emotional reaction can further reduce 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 17:13:52. 36 Perini, Sella, Blakey their performance, in a negative spiral (Carey, Hill, Devine, & Szücs, 2016; Suarez-Pelliccioni, Núñez-Peña, & Colomé, 2016). Such relation between mathematics anxiety and low performance can have negative long-term consequences on future academic and career path (Carey et al., 2016; Suarez-Pelliccioni et al., 2016). It seems that mathematics anxiety emerges very early and is already present in primary school children. Which factors contribute to its development and maintenance? Factors related to the environment Copyright © 2020. Taylor & Francis Group. All rights reserved. Negative experiences related to mathematics (e.g. embarrassing experiences in front of peers) seem to be closely related to the origin of mathematics anxiety (Ashcraft, 2002). In particular, the role of teachers seems to be very important: teachers who require a high level of performance by giving little support to students might generate mathematics anxiety in their students (Turner, 2003). Moreover, teachers’ mathematics anxiety can have a negative impact on their effectiveness when teaching the subject (Swars, Daane, & Giesen, 2006). Parents and caregivers can also exert an influence on mathematics anxiety. For instance, parents’ negative attitude towards mathematics might lead to the same feeling in their children. However, parents can also have a positive impact. Their support when children complete home assignments seems to reduce children’s anxiety (Goetz, Bieg, Lüdtke, Pekrun, & Hall, 2013). In addition to the role of people, two domain general cognitive skills have been related to children’s mathematical anxiety. Low spatial skills Some studies have shown that poor spatial skills can be linked to the onset of mathematics anxiety. This could be because individuals with poor spatial skills are more likely to display a low mathematical achievement, which in turn could lead to mathematics anxiety (Eden, Heine, & Jacobs, 2013). Mathematics anxiety in children with high working memory capacity Some studies have suggested that children who rely heavily on working memory are more likely to display a negative impact of mathematics anxiety on their mathematical performance. When solving arithmetic problems, these children implement sophisticated solution 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 17:13:52. Developmental dyscalculia 37 strategies, which depend greatly on working memory resources. Mathematics anxiety disrupts working memory capacity and, therefore, compromises the performance (Ashcraft & Kirk, 2001). Sensitivity to error Individuals with high levels of mathematics anxiety show a higher emotional reaction when they make mistakes in a number-related task compared to a neutral task (Suárez-Pellicioni, Núñez-Peña, & Colomé, 2013). What can we do? Suggestions for teachers and educators (according to Suarez-Pelliccioni et al., 2016): Copyright © 2020. Taylor & Francis Group. All rights reserved. Do not embarrass students with mathematical difficulties. In particular, avoid highlighting errors when the student is among peers or in a group and these peers are within earshot. Avoid situations in which frustration could arise by carefully implementing gradual and flexible targets for children to aim towards. Emphasize the students’ successes and highlight that errors are learning opportunities. Stress the importance of commitment, practice and motivation. Monitor those students with high levels of mathematics anxiety. Mathematics anxiety can easily emerge in timed activities. Consider placing less emphasis on speed and give students more time to complete a task if necessary. Students with mathematics anxiety show greater physiological activation during mathematics evaluations (Faust, 1992). Such bodily reactions are normal during an examination but can have a detrimental effect on performance if they are interpreted negatively (e.g. I am panicking). Teachers can inform students that these reactions are a normal bodily response when facing a complex task. Suggestions for parents: Be aware that your own mathematics anxiety or negative attitude towards mathematics can be “transmitted” to your child. For instance, statements such as “I have never been good at math”, “you are like me, I couldn’t do math either” most likely reinforce the idea that mathematical abilities are fixed and cannot be learned. 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 17:13:52. 38 Perini, Sella, Blakey Build in time for mathematical games, both formally and informally, and highlight the importance of mathematics and numerosity in everyday life. If necessary, provide support in mathematics homework. Copyright © 2020. Taylor & Francis Group. All rights reserved. Conclusions Children with a low performance in mathematics (bottom 25 per cent) are usually considered having a mathematical learning disorder. The diagnosis of developmental dyscalculia is restricted to more severe cases, usually in children with a mathematical performance in the 5–10 per cent bottom of the distribution. Children with developmental dyscalculia usually have visuospatial difficulties too. We believe that resistance to training should be considered the gold standard to ensure that the child has a severe condition that could not be better explained by other factors (e.g. educational disadvantages). In this vein, resistance to appropriate training can differentiate between a child with a learning disability (i.e. dyscalculia) and a child with less severe difficulties. Both groups of children would benefit from effective didactic strategies, even though in case of developmental dyscalculia, additional supports at school (e.g. the use of calculator) might be required. That said, all children with low mathematical achievement would benefit from appropriate educational and teaching strategies. It is therefore important that teachers, educators and practitioners implement such strategies while recognizing the children’s broader cognitive and emotional profiles. Keeping this broader picture in mind will ensure that interventions are tailored to children’s specific needs and that they are able to engage to the best of their ability. References AIRIPA and AID, Agreement document (2012). Diagnosis of dyscalculia. American Psychiatric Association. (2013). Diagnostic and statistical manual of mental disorders (5th ed.). Washington, DC: American Psychiatric Association. Ashcraft, M. H. (2002). Math anxiety: Personal, educational, and cognitive consequences. Current Directions in Psychological Science, 11(5), 181–185. Ashcraft, M. H., & Kirk, E. P. (2001). The relationships among working memory, math anxiety, and performance. Journal of Experimental Psychology: General, 130(2), 224. 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 17:13:52. Copyright © 2020. Taylor & Francis Group. All rights reserved. Developmental dyscalculia 39 Butterworth, B. (2005). The development of arithmetical abilities. Journal of Child Psychology and Psychiatry, 46(1), 3–18. Carey, E., Hill, F., Devine, A., & Szücs, D. (2016). The chicken or the egg? Mathematics anxiety and mathematics performance. Frontiers in Psychology, 6, 1987. Consensus Conference, Istituto Superiore di Sanità. (2011). I Disturbi Specifici dell’Apprendimento (DSA): Cosa sono e come si affrontano. Retrieved from http://snlg-iss.it/cc_disturbi_specifici_apprendimento Duncan, G. J., Dowsett, C. J., Claessens, A., Magnuson, K., Huston, A. C., Klebanov, P.,... Sexton, H. (2007). School readiness and later achievement. Developmental Psychology, 43(6), 1428. Eden, C., Heine, A., & Jacobs, A. M. (2013). Mathematics anxiety and its development in the course of formal schooling—A review. Psychology, 4(6), 27. Faust, M. W. (1992). Analysis of physiological reactivity in mathematics anxiety (Unpublished doctoral dissertation). Bowling Green State University, Ohio. Geary, D. C. (2006). Dyscalculia at an early age: Characteristics and potential influence on socio-emotional development. Encyclopedia on Early Childhood Development, 15, 1–4. Goetz, T., Bieg, M., Lüdtke, O., Pekrun, R., & Hall, N. C. (2013). Le ragazze provano davvero più ansia in matematica? Scienze psicologiche, 24(10), 2079–2087. Gross-Tsur, V., Manor, O., & Shalev, R. S. (1996). Developmental dyscalculia: Prevalence and demographic features. Developmental Medicine & Child Neurology, 38(1), 25–33. Kucian, K., & von Aster, M. (2015). Developmental dyscalculia. European Journal of Pediatrics, 174(1), 1–13. Melhuish, E. (2013). Longer-term effects of early childhood education & care: Evidence and policy. Cadernos de Pesquisa, 43(148), 124–149. Morsanyi, K., van Bers, B. M. C. W., O’Connor, P. A., & McCormack, T. (2018). Developmental dyscalculia is characterized by order processing deficits: Evidence from numerical and non-numerical ordering tasks. Developmental Neuropsychology, 43(7), 595–621. Punaro, L., & Reeve, R. (2012). Relationships between 9-year-olds’ math and literacy worries and academic abilities. Child Development Research, 2012. http://dx.doi.org/10.1155/2012/359089 Shalev, R. S., Auerbach, J., Manor, O., & Gross-Tsur, V. (2000). Developmental dyscalculia: Prevalence and prognosis. European Child & Adolescent Psychiatry, 9, S58–S64. Suárez-Pellicioni, M., Núñez-Peña, M. I., & Colomé, À. (2013). Abnormal error monitoring in math-anxious individuals: Evidence from errorrelated brain potentials. PLoS One, 8(11), e81143. Suárez-Pellicioni, M., Núñez-Peña, M. I., & Colomé, À. (2016). Math anxiety: A review of its cognitive consequences, psychophysiological 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 17:13:52. 40 Perini, Sella, Blakey Copyright © 2020. Taylor & Francis Group. All rights reserved. correlates, and brain bases. Cognitive, Affective, & Behavioral Neuroscience, 16(1), 3–22. Swars, S. L., Daane, C. J., & Giesen, J. (2006). Mathematics anxiety and mathematics teacher efficacy: What is the relationship in elementary preservice teachers? School Science and Mathematics, 106(7), 306–315. Turner, J. C., Meyer, D. K., Midgley, C., & Patrick, H. (2003). Teacher discourse and sixth graders’ reported affect and achievement behaviors in two high-mastery/high-performance mathematics classrooms. The Elementary School Journal, 103(4), 357–382. World Health Organization. (1992). ICD-10: International statistical classification of disease and related health problems (vol. 1, 10th ed.). Geneva: World Health Organization. World Health Organization. (2004). ICD-10: International statistical classification of diseases and related health problems: Tenth revision (2nd ed.). Geneva: World Health Organization. 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 17:13:52.