Math anxiety in children with and without mathematical difficulties: the role of gender and genetic factors

Mathematics anxiety is generally defined as feeling tense, fearful and apprehensive about mathematics (Richardson & Suinn, 1972). It is a multi-dimensional construct, characterized by different types of reactions: emotional (i.e., negative feelings); cognitive (e.g., intrusive concerns and thoughts); physiological (e.g., increased arousal, stress and agitation); and behavioural (e.g., avoiding contexts that require the use of mathematical skills, disengagement and off-task behaviours).From a different angle, math anxiety can generate reverse effect than positive factors, such as an interest toward mathematics and self-efficacy (Moore, Rudig & Ashcraft, 2014). Individuals with high levels of math anxiety tend to take fewer mathematics courses; gain lower grades in those they do attend; and avoid, where possible, additional maths classes (Ashcraft, 2002).In addition, highly math-anxious students are also more likely to avoid mathematically-oriented college majors and career paths that require quantitative skills (Ashcraft, Krause, & Hopko, 2007; Ashcraft & Moore, 2009).Math anxiety seems to have serious long-term consequences, adversely influencing an individual’s choice of career, type of occupation, and professional growth in adulthood (Ashcraft & Ridley, 2005; Beasley, Long & Natali, 2001; Hembree, 1990; Ho et al., 2000). Beyond consequences for an individual’s personal life, math anxiety also affects society. For example, in the USA math anxiety may contribute to the shortage of graduates, who want to work in the area of science, technology, engineering and mathematics-for the demands of a technology-dependent society -despite increased emphasis on improving mathematical education (Beilock & Maloney, 2015). Because of its consequences in limiting people’s mastery of mathematics, math anxiety has become a subject of increasing interest in educational, rather than only clinical settings. Many factors are involved in the links between math anxiety and mathematics. For example, these links depend on the nature of mathematics, such as increasing complexity of its contents during the school-years. In the following sections, we summarize previous studies of math anxiety, focusing on gender differences, distinction between mathematics difficulties related to math anxiety vs those related to specific mathematics impairments, and the role of genetic factors

Predictors of mathematics in primary school: Magnitude comparison, verbal and spatial working memory measures.

We determined the relative importance of the so-called approximate number system (ANS), symbolic number comparison (SNC) and verbal and spatial short-term and working memory (WM) capacity for mathematics achievement in 1,254 Grade 2, 4 and 6 children. The large sample size assured high power and low false report probability and allowed us to determine effect sizes precisely. We used reading decoding as a control outcome measure to test whether findings were specific to mathematics. Bayesian analysis allowed us to provide support for both null and alternative hypotheses. We found very weak zero-order correlations between ANS measures and math achievement. These correlations were not specific to mathematics, became non-significant once intelligence was considered and ANS measures were not selected as predictors of math by regression models. In contrast, overall SNC accuracy and spatial WM measures were reliable and mostly specific predictors of math achievement. Verbal short-term and WM and SNC reaction time were predictors of both reading and math achievement. We conclude that ANS tasks are not suitable as measures of math development in school-age populations. In contrast, all other cognitive functions we studied are promising markers of mathematics development

Multidimensional components of (state) mathematics anxiety: Behavioral, cognitive, emotional, and psychophysiological consequences

The present study aimed to analyze the different components of state mathematics anxiety that students experienced while solving calculation problems by manipulating their stress levels. A computerized mathematical task was administered to 165 fifth-graders randomly assigned to three different groups: positive, negative, and control conditions, in which positive, negative, or no feedback during the task was given, respectively. Behavioral (task performance), emotional (negative feelings), cognitive (worrisome thoughts and perceived competence), and psychophysiological responses (skin conductance and vagal withdrawal) were analyzed. Behavioral responses did not differ in the positive and negative conditions, while the latter was associated with children's reportedly negative emotional states, worries, and perceived lack of competence. The stress induced in the negative condition led to an increase in skin conductance and cardiac vagal withdrawal in children. Our data suggest the importance of considering students' interpretation of mathematics-related experiences, which might affect their emotional, cognitive, and psychophysiological responses

Mathematics anxiety, working memory, and mathematics performance in secondary-school children

Mathematics anxiety (MA) has been defined as \u201ca feeling of tension and anxiety that interferes with the manipulation of numbers and the solving of math problems in a wide variety of ordinary life and academic situations\u201d. Previous studies have suggested that a notable proportion of children in primary and secondary school suffer from MA, which is negatively correlated with calculation skills. The processing efficiency and attentional control theories suggest that working memory (WM) also plays an important part in such anxious feelings. The present study aimed to analyze the academic achievement and cognitive profiles of students with high math anxiety (HMA) and low math anxiety (LMA). Specifically, 32 students with HMA and 34 with LMA matched for age, gender, generalized anxiety, and vocabulary attending sixth to eighth grades were selected from a larger sample. The two groups were tested on reading decoding, reading comprehension, mathematics achievement, and on verbal short-term memory and WM. Our findings showed that HMA students were weak in several measures of mathematics achievement, but not in reading and writing skills, and that students with HMA reported lower scores on short-term memory and WM performances (with associated difficulties in inhibiting irrelevant information) than children with LMA. In addition, a logistic regression showed that weaknesses in inhibitory control and fact retrieval were the strongest variables for classifying children as having HMA or LMA

The underlying structure of visuospatial working memory in children with mathematical learning disability.

This study examined visual, spatial-sequential, and spatial-simultaneous working memory (WM) performance in children with mathematical learning disability (MLD) and low mathematics achievement (LMA) compared with typically developing (TD) children. Groups were matched on reading decoding performance and verbal intelligence. Besides statistical significance testing, we used bootstrap confidence interval estimation and computed effect sizes. Children were individually tested with six computerized tasks, two for each visuospatial WM subcomponent. We found that both MLD and LMA children had low visuospatial WM function in both spatial-simultaneous and spatial-sequential WM tasks. The WM deficit was most expressed in MLD children and less in LMA children. This suggests that WM scores are distributed along a continuum with TD children achieving top scores and MLD children achieving low scores. The theoretical and practical significance of findings is discussed. Statement of Contribution What is already known on this subject? Working memory plays an important role in mathematical achievement. Children with mathematical learning disability (MLD) usually have low working memory resources. Conflicting results have been reported concerning the role of VSWM in individuals with MLD. What the present study adds? Children with different degree of impairment in math achievement and typically developing children were tested. Visual, spatial-sequential, and spatial-simultaneous working memory tasks were examined. Only spatial-sequential and spatial-simultaneous working memory tasks discriminated the two impairments groups

Maths anxiety in primary and secondary school students: Gender differences, developmental changes and anxiety specificity

Maths anxiety (MA) is a debilitating negative emotional reaction towardsmathematics.However,MA research in primary and early secondary school is surprisingly sparse and inconsistent. Here we tested primary and secondary students' maths and reading performance and their maths and general anxiety (GA). We examined gender differences, developmental changes regarding the MA/maths performance link and investigated whether MA is linked to other academic domains (reading) and/or to other anxiety-types (GA). Results revealed that girls exhibited higherMA than boys at both educational levels.Whilst there was a reliable negative correlation between MA and secondary students' arithmetic performance, no such relationship was revealed in primary students. Finally, MA was moderately correlated with GA and, when GA was partialled out, MA remained significantly correlated with secondary students' arithmetic performance. MA was not related to reading performance when GA was controlled. It was concluded that the negative MA/maths performance link surfaces later in the educational timeline and MA appears to be both exclusively related to maths and independent of GA

Stress, Time Pressure, Strategy Selection and Math Anxiety in Mathematics: A Review of the Literature.

We review how stress induction, time pressure manipulations and math anxiety can interfere with or modulate selection of problem-solving strategies (henceforth "strategy selection") in arithmetical tasks. Nineteen relevant articles were identified, which contain references to strategy selection and time limit (or time manipulations), with some also discussing emotional aspects in mathematical outcomes. Few of these take cognitive processes such as working memory or executive functions into consideration. We conclude that due to the sparsity of available literature our questions can only be partially answered and currently there is not much evidence of clear associations. We identify major gaps in knowledge and raise a series of open questions to guide further research

Anxiety profiles and protective factors: A latent profile analysis in children

The current study investigated the presence of different anxiety profiles in schoolchildren in order to understand whether Mathematics and Test Anxiety are a manifestation of a general form of anxiety, or the expression of specific forms of anxiety. Moreover, we also examined the influence of personal protective factors. The results of a latent profile analysis, conducted on 664 children attending grades 3 to 6, clearly identified three different profiles distinguished on the basis of the level of general, test and mathematics anxiety. Protective factors, such as self-concept and resilience, were differently related to anxiety: the former was clearly lower when the risk profile was higher, whereas students were able to maintain a certain level of resilience up to an average risk of developing forms of anxiety. The implications of these findings may lead to the development of specific intervention programs aimed at reducing students’ anxiety and fostering self-concept and resilience. © 2017 Elsevier Lt

Why mental calculation is so complicated? The contribution of working memory components in children with typical development and learning disabilities

Many studies support that working memory (WM Baddeley, 1986) is related to mental calculation in general but also confirm that this relationship is more complex than previously described. Although increasing numbers of recent studies have investigated these relationships, the involvement of various WM subcomponents in mental addition problems remains unclear, and empirical evidence of how one’s WM tackles problems is sparse. A theoretical framework that is particularly appropriate for studying WM involvement in mental addition is the multi-component WM model developed by Baddeley and Hitch (1974; Baddeley, 1986), which comprises three distinct components: a central executive and two slave systems, a verbal and a visuo-spatial WM components. Even though central executive involvement in mental calculations seems clear, the roles of the other two WM components in calculations are still not fully understood, especially in children. For this reason, the present study focuses only on the involvement of both verbal and visuo-spatial WM in children’s mental calculations. Thus, the main objective of this PhD dissertation is to increase the current understanding of the role of WM subcomponents in the execution of simple and complex mental addition problems in: i) typically developing children (Study I – Experiment 1-3), and in ii) children with a diagnosis of learning disabilities (Study II – Experiment 4-5). A number of studies stated that the role of WM in multi-digit calculation seems to depend on several factors, such as the type of presentation format, the type of algorithm required (e.g. additions or subtractions), the presence of carrying/borrowing or the nature of computation expected (Ashcraft & Kirk, 2001; DeStefano & LeFevre, 2004; Fürst & Hitch 2000; Imbo & LeFevre, 2010; Raghubar, Barnes, & Hecht, 2010; Trbovich & LeFevre, 2003). Previous research analyzing WM involvement in mental calculation mainly used the dual task paradigm. In particular, participants perform a primary task (a mental calculation problem) in combination with a secondary task, which involves one WM component. The paradigm assumed that, if the primary and secondary tasks use overlapping cognitive resources, then performance on the primary task will worsen as the secondary task becomes more demanding. This approach has been widely used with typically achieving adults, but only rarely extended to children (McKenzie, Bull, & Gray, 2003; Imbo & Vandierendonck, 2007) – Study 1, and never used with children with learning disabilities – Study II. Based on literature outlines, Study I has been carried out to examine as the presentation of a verbal or visuo-spatial WM task damages the execution of a mental calculation in children attending 3rd and 4th grade of primary school. Specifically, three different experiments were conducted to analyze potential computation impairment (exact vs. approximate), the specific role of WM sub-components (i.e., letters recall vs. positions recall), manipulating both the presentation format of the operations (i.e., operations presented horizontally vs. operations presented vertically) and the complexity of operations themselves (presence vs. absence of carrying). In Experiment 1, children were presented with exact and approximate addition problems with carrying, in Experiment 2 with exact and approximate addition problems without carrying, while in Experiment 3 approximate addition problems with and without carrying were directly compared. The findings provide information about the specific involvement of WM components in children’s mental addition operations, and suggest that WM components are deeply involved when calculation processes become more challenging and complex. In Experiment 1, analysis showed that horizontally presented problems were generally more impaired than vertically presented problems by verbal WM load, and, vice versa, vertical problems were more affected than horizontal one by visuo-spatial WM load. Moreover, this result was stronger for approximate than for exact calculation. Differently from adult literature, results revealed that children generally found approximate calculation more difficult than exact calculation. In particular, in Experiment 2, where pupils had to compare exact and approximate calculations without carrying, children seemed to use the same strategy for both exact and approximate calculation in single tasks. Finally, in Experiment 3, in which children were asked to solve approximate addition problems only, the specific effect of verbal and visuo-spatial load emerged specifically in addition problems requiring a carrying procedure. Therefore, we assume that carrying is crucial to determine the specific involvement of different WM subcomponents in the solution process. The association of learning disabilities with WM impairments has been demonstrated in a number of studies (Schuchardt, Maehler, & Hasselhorn, 2008; Swanson, 2006). The content of Study II was to extend the dual task paradigm to two different clinical samples: children diagnosed with developmental dyscalculia (DD – Experiment 4) and with non-verbal learning disability (NLD – Experiment 5). Developmental Dyscalculia (DD), also called mathematical learning disability, is characterized by severe impairments in the acquisition of mathematical skills. Traditional classification systems (e.g. DSM-IV-TR; APA, 2000)state that the child must substantially underachieve on a standardized mathematical test relative to the level expected on the basis of his/her age, education, and intelligence and must experience disruption to academic achievement or daily living in order to receive a diagnosis of DD. In particular, there must be a considerable discrepancy between the child’s general intellectual ability and the child’s academic achievement. Non-verbal learning disability (NLD) children are chiefly characterized by intact verbal abilities, but impaired visuospatial skills, showing a discrepancy between Verbal and Performance IQ, and major problems in areas of visuo-spatial working memory, psychomotor, visuo-constructive skills and mathematics, within a context of well-developed psycholinguistic skills. Although, this disorder is not included in any clinical classification systems, it is possible delineate some specific criteria for diagnosing children with NLD: a marked discrepancy between verbal and visuo-spatial intelligence associated with a specific pattern in academic achievement, characterized by major learning difficulties in arithmetic, geometry and science (Mammarella, Lucangeli & Cornoldi, 2010). In both Experiment 4 and 5, it has been decide to present only exact addition problems with carrying. In fact, previous results of Study I showed that TD children do not spontaneously and easily use the most functional strategies employed by adults. In each Experiment, clinical sample performance has been compared to a control group, formed by typically developing children (TD) matched for age, schooling and socio-economic status, with no reported school difficulties. Finding of Study II shown that the dual task paradigm applied to children with learning disabilities revealed that their performances did not completely overlap those observed in TD children. In particular, children with DD performed poorly when addition problems were presented in horizontal format and associated with verbal information, revealing that verbal weaknesses are critical in the majority of children with DD. Conversely, NLD results are perfectly in line with those emerged in Study I with TD children for approximate calculation, revealing as the presence of carrying procedure makes the primary task sufficiently highly demanding on WM resources to produce a selective interference between presentation format and secondary task in NLD children Taken as a whole, the results of the present study offer a general picture on how children meet with mental addition request and put forward important clinical and educational implications, further confirming that mathematical deficits could depend on poor WM resources. These findings are noteworthy not only in order to deepen the understanding of the relationship between memory processes and calculation, but also to provide scientific evidence to plan functional and specific intervention for learning disability treatments, based on the actual processes involved in the solution phase.Gli studi a sostegno del coinvolgimento della memoria di lavoro (ML, Baddeley, 1986) nell’esecuzione del calcolo a mente sono numerosi, ma allo stesso tempo confermano quanto complessa sia questa relazione. Nonostante l’interesse crescente per quest’ambito, il ruolo delle diverse componenti della ML nello svolgimento di addizioni a mente rimane ancora poco chiaro e le evidenze a riguardo sono spesso incoerenti. Secondo il modello multi-componenziale di Baddeley (1986) sia l’esecutivo centrale, che il loop fonologico ed il taccuino visuo-spaziale sono coinvolti, a vari livelli, nell’esecuzione di calcoli a mente. Sulla base di tale modello sono stati effettuati diversi studi che, se da un lato permettono di confermare il coinvolgimento della ML, dall’altro non sempre hanno portato a risultati univoci e coerenti su come le diverse componenti entrino in gioco, ad esempio, nonostante il ruolo dell’esecutivo centrale sembri ampiamente riconosciuto, il ruolo delle altre sotto-componenti appare ancora molto confuso, soprattutto nei bambini. Per questa ragione, gli studi descritti in questa tesi si sono focalizzati nell’analisi del coinvolgimento specifico delle sole componenti verbale e visuo-spaziale della ML nell’esecuzione di calcoli a mente in bambini frequentanti la scuola primaria. La presente tesi di Dottorato mira pertanto ad indagare il ruolo della ML, nello specifico le sue componenti verbale e visuo-spaziale, nella soluzione di operazioni di addizione, con o senza riporto, in i) bambini di età scolare a sviluppo tipico (Studio 1 – Esperimenti 1-3), e in ii) bambini con diagnosi di disturbo specifico dell’apprendimento (Studio 2 – Esperimenti 4-5). Ricerche recenti hanno messo in luce come l’esecuzione del calcolo possa coinvolgere domini diversi e quindi diversi aspetti della ML, in relazione a quelli che sono le caratteristiche stesse del compito aritmetico o la complessità dell’algoritmo presentato (DeStefano & LeFevre, 2004; Raghubar, Barnes, & Hecht, 2010). Il ruolo della ML nella soluzione di calcoli a mente a più cifre sembra dunque dipendere da diversi fattori, come ad esempio il tipo di formato di presentazione (Trbovich & LeFevre, 2003), il tipo di algoritmo coinvolto (Imbo & LeFevre, 2010), oppure la complessità del calcolo (Fürst & Hitch 2000; Ashcraft & Kirk, 2001). Kalaman e LeFevre (2007) hanno inoltre analizzato come l’influenza della ML possa variare in relazione alla tipologia di stima richiesta: addizioni in condizione di calcolo esatto o approssimato. La metodologia utilizzata con maggior frequenza per analizzare il ruolo della ML nel calcolo a mente è il paradigma del doppio compito. Tale paradigma richiede ai partecipanti di svolgere il compito principale (un calcolo a mente) in combinazione con uno specifico compito secondario, che coinvolge selettivamente una specifica componente della ML (ad es. dominio verbale vs. visuo-spaziale). Il paradigma assume che, se compito primario e secondario vanno ad attingere alle stesse risorse cognitive, la prestazione al compito primario sarà destinata a peggiorare. Questo approccio è stato ampiamente utilizzato con partecipanti adulti, ma solo raramente esteso a bambini a sviluppo tipico (McKenzie, Bull, & Gray, 2003; Imbo & Vandierendonck, 2007) – Studio I, e mai proposto a bambini con diagnosi di disturbo specifico dell’apprendimento – Studio II. Sulla base dei risultati emersi dalla letteratura, attraverso il primo Studio si è voluto andare ad indagare come la presentazione di un compito di ML, verbale o visuo-spaziale, che precede l’esecuzione del calcolo a mente, possa compromettere o meno l’esecuzione di quest’ultimo in bambini frequentanti le classi 3^ e 4^ della scuola primaria. In modo specifico, tre diversi esperimenti hanno preso in esame l’eventuale compromissione del calcolo (esatto vs. approssimato) e la tipologia di compito di ML associato (ricordo di lettere vs. ricordo di posizioni) in relazione alla modalità di presentazione (in riga vs. in colonna) e alla complessità (riporto vs. no riporto) delle addizioni stesse. Nell’Esperimento 1 è stato chiesto ai bambini di risolvere delle addizioni con riporto in condizione di calcolo esatto e approssimato, nell’Esperimento 2 di eseguire delle addizioni senza riporto sempre di calcolo esatto e approssimato, infine nell’Esperimento 3 è stata direttamente confrontata la prestazione di addizioni con e senza riporto nella sola condizione di calcolo approssimato. I risultati forniscono inoltre informazioni importanti sullo specifico coinvolgimento del dominio verbale e visuo-spaziale nell’esecuzione delle addizioni, evidenziando come il ruolo di tali componenti diventi maggiormente esplicito a mano a mano che i processi di calcolo divengono sempre più impegnativi e complessi. Nell'esperimento 1, in cui è stato chiesto ai bambini di risolvere le operazioni di calcolo esatto e approssimato con il riporto, le analisi hanno mostrato come le addizioni presentate in riga fossero generalmente più compromesse di quelle presentate in colonna dalla presenza di un carico verbale, e, viceversa, come i problemi presentati in colonna fossero invece più danneggiati da un carico di natura visuo-spaziali rispetto a quelli presentati in riga. Questo effetto è emerso con maggior chiarezza nella condizione approssimata. Diversamente da quanto emerge per gli adulti, le analisi rilevano che i bambini trovano più complessa l’esecuzione di calcoli approssimati piuttosto che di calcoli esatti. Nell'esperimento 2, in cui è stato chiesto ai bambini di risolvere i problemi senza il riporto, i bambini sembravano utilizzare la stessa strategia di soluzione sia per i calcoli esatti che per i calcoli approssimati. Infine, nell’esperimento 3, in cui è stato chiesto ai bambini di risolvere addizioni con e senza riporto solamente in condizione di calcolo approssimato, l'effetto specifico di carico verbale e visuo-spaziale è emerso in particolare nelle addizioni che richiedevano l’esecuzione della procedura di riporto, confermando come la complessità del calcolo sia una caratteristica cruciale per discriminare il ruolo delle diverse componenti della ML all’interno del processo di soluzione del calcolo. L’importante legame tra disturbi d’apprendimento e deficit a livello di ML è stato ampiamente dimostrato in un vasto numero di studi (Schuchardt, Maehler, & Hasselhorn, 2008; Swanson, 2006). Nel secondo Studio, il paradigma descritto in precedenza è stato applicato per analizzare il coinvolgimento della ML nell’esecuzione di addizioni in due differenti gruppi clinici: bambini con diagnosi di discalculia evolutiva (Developmental Dyscalculia, DD – Esperimento 4), e con diagnosi di disturbo dell’apprendimento non-verbale (Non-verbal Learning Disability, NLD – Esperimento 5). La discalculia evolutiva (DD) è caratterizzata da disturbi nell'acquisizione di competenze matematiche. Sistemi di classificazione tradizionali (ad esempio, DSM-IV-TR; APA, 2000) affermano che un bambino per ricevere diagnosi di DD non deve raggiungere i normali livelli di competenza attesi in base a livello di età, di istruzione e di intelligenza ad un test standardizzato di matematica. In altre parole, ci deve essere una discrepanza notevole tra le capacità intellettive generali ed il rendimento scolastico in matematica. Il disturbo dell’apprendimento non-verbale (NLD) si caratterizza invece per una difficoltà di carattere generale nell’elaborazione di informazioni visive e spaziali, all’interno di un profilo cognitivo in norma, in cui le abilità verbali sono preservate. Nonostante tale disturbo non trovi ancora spazio nei principali manuali diagnostici è possibile delineare alcuni chiari criteri per la diagnosi, quali ad esempio difficoltà cognitive specifiche di natura visuo-spaziale (ad esempio, discrepanza tra quoziente intellettivo verbale e di performance di almeno di 15 punti) associate ad un profilo di apprendimenti scolastici con cadute nell’area della matematica o in altre discipline che sottendono il coinvolgimento di abilità visuo-spaziali e grafo-motorie (Mammarella, Lucangeli & Cornoldi, 2010). In entrambi gli esperimenti, è stato scelto di sottoporre ai bambini solo la condizione di calcolo esatto. Tale scelta è stata guidata dai risultati emersi dai precedenti esperimenti dello Studio I, che mostrano come bambini a sviluppo tipico non sappiano ancora spontaneamente usare strategie di arrotondamento che rendono, per gli adulti, i processi di stima veloci ed efficaci. In ciascuno dei due esperimenti, la prestazione dei gruppi clinici è stata inoltre confrontata con un gruppo di controllo formato da bambini a sviluppo tipico appaiati per genere età e livello socio-culturale. I risultati di questo secondo Studio hanno portato in luce come le diverse componenti della ML siano diversamente coinvolte nell’esecuzione di calcoli a mente rispetto a quanto emerso analizzando le prestazioni dei bambini con sviluppo tipico (Studio I). In particolare, per quanto riguarda i bambini con DD il diverso coinvolgimento delle componenti della ML nell’esecuzione di operazioni di addizione sembra tradursi in una richiesta di risorse prevalentemente di natura verbale, indipendentemente dal formato di presentazione, diversamente da quanto emerso per il gruppo di controllo. Invece, per quanto riguarda il gruppo con NLD, il pattern che emerge sembra sostanzialmente coerente con i risultati dello Studio I riferiti al solo calcolo approssimato. Tali risultati evidenziano come la presenza della procedura di riporto renda l’esecuzione del calcolo altamente richiestiva per le risorse di ML possedute da questi bambini, tanto da determinare un’interferenza selettiva tra il formato di presentazione dell’operazione stessa e la natura del compito secondario. In sintesi, i risultati dei presenti Studi offrono nel loro complesso un quadro generale piuttosto articolato di come i bambini affrontano e gestiscono le richieste cognitive derivate dall’esecuzione di addizioni a mente. Presi nel loro complesso, entrambi gli studi, offrono lo spunto per trarre delle importanti implicazioni, sia in ambito educativo che clinico, dimostrando come le difficoltà che i bambini incontrano nel risolvere calcoli a mente siano collegate a limitate risorse di ML. Tali evidenze risultano infatti significative non solo allo scopo di approfondire la comprensione della relazione che intercorre tra processi di memoria e di calcolo, ma anche per fornire evidenze scientifiche utili a impostare materiali per il trattamento delle difficoltà di apprendimento, capaci di tenere in considerazione gli effettivi processi attivati nella fase di soluzione

Lights and shadows of mental arithmetic: Analysis of cognitive processes in typical and atypical development

Arithmetical learning is not only a fundamental part of children\u2019s education but it is also central in several daily activities. The focus of this chapter is to analyse how children at different ages use limited mental resources to manage complex mental calculation from a developmental perspective. Moreover, some sections will deal with the processes in children\u2019s minds when they are solving arithmetic problems, paying particular attention to the strategies applied