The present thesis investigates the hypothesis according to which the arithmetic retrieval deficits observed in children with math disabilities (MD) would be due to an inhibition deficit. In the first chapter, two experiments showed that children with MD (with or without reading disabilities), compared to normally-achieving children, do not present impairments in three inhibition functions (filtering, suppression, and blocking). The second chapter focused on interference in arithmetic tasks. Experiment 3 revealed that, in a multiplication verification task, children with MD were not more sensitive to interference than control children (of the same age or of the same math skills). In contrast, Experiment 4 showed that children with poor math skills were more sensitive to multiplication-related interference (i.e., the negative effect of multiplications on additions) than children with good math skills. Nevertheless, the third chapter established that the arithmetic retrieval deficits of children with MD (as well as the results of Experiment 4) can be accounted for without the recourse to inhibition. Indeed, Experiment 5 demonstrated that children with MD have poor memory representations of difficult single-digit multiplications (i.e., weak and incorrect problem-answer associations), which is sufficient to account for their retrieval deficits. Finally, in the last chapter, we considered the possibility that sensitivity to interference is involved in MD but during the development of arithmetic facts representations (not during their retrieval) and could lead to the poor representations observed in children with MD. In experiment 6, we found that counting to solve an addition might interfere with the memorization of the addition's addends (hence, with the development of problem-answer associations) but there was no evidence that children with MD are more sensitive to this interference than control children. Altogether, these data provide converging evidence against the inhibition-deficit hypothesis and suggest that poor arithmetic representations represent a better candidate as a causal factor of MD. / Le but de cette thèse est d'investiguer l'hypothèse d'un rôle causal des processus d'inhibition dans les Troubles d'Apprentissage de l'Arithmétique (TAA). Selon cette hypothèse, les difficultés de récupération des faits arithmétiques (p.ex., les tables de multiplications) observés dans les TAA seraient dues à des déficits d'inhibition. Le premier chapitre présente deux expériences dans lesquelles nous avons testé trois fonctions d'inhibition (filtrage, suppression et blocage) chez des enfants avec TAA global (avec et sans troubles de lecture associés) et avec troubles spécifiques de récupération de faits arithmétiques (Expériences 1 et 2). Les résultats de ces études n'ont pas mis en évidence de trouble d'inhibition chez ces enfants. Le second chapitre s'est focalisé sur les effets d'interférence classiquement observés dans des tâches arithmétiques. Dans l'expérience 3, nous avons mis en évidence un effet de confusion associative (p.ex., 3 x 7 est plus difficile à rejeter que 3 x 7 = 26) significatif chez des enfants avec troubles de récupération de faits arithmétiques. Néanmoins, cet effet était équivalent à celui observé chez des enfants contrôle. En revanche, dans l'expérience 4, nous avons observé que l'effet interférent de la multiplication sur l'addition était plus important chez des enfants avec faibles capacités de récupération de faits arithmétiques que des enfants avec fortes capacités de récupération. Toutefois, dans le troisième chapitre, nous démontrons que ces derniers résultats, et plus globalement, les troubles de récupération de faits arithmétiques, peuvent être interprétés à la lumière de modèles théoriques qui n'incluent pas de processus d'inhibition. En effet, l'expérience 5 révèle que chez des enfants avec de tels troubles de récupération (en comparaison d'enfants contrôle), les multiplications difficiles (p.ex., 6 x 7) étaient plus faiblement associées à leurs réponses correctes et associées à de réponses incorrectes, ce qui, selon certains modèles théoriques, était suffisant pour rendre compte de déficits de récupération. Ces résultats vont à l'encontre de l'hypothèse de déficits d'inhibition comme facteur causal des troubles de récupération arithmétique dans les TAA. Cependant, dans le dernier chapitre, nous considérons la possibilité que la sensibilité à l'interférence jouait un rôle important dans le développement des représentations arithmétiques (et non dans leur récupération). Dans l'expérience 6, notre hypothèse était que compter pour résoudre une addition pouvait interférer avec la mémorisation des opérandes de cette addition et donc, avec la formation des associations entre problème et réponse correcte. Si les résultats obtenus allaient dans ce sens, nous n'avons trouvé aucune évidence indiquant que cet effet interférent était plus important chez des enfants avec troubles de récupération de faits arithmétiques que chez des enfants contrôle. En conclusion, il semble que de pauvres représentations des faits arithmétiques, plutôt que des déficits d'inhibition, soient à l'origine des troubles de récupération de ces faits dans les TAA.

The present thesis investigates the hypothesis according to which the arithmetic retrieval deficits observed in children with math disabilities (MD) would be due to an inhibition deficit. In the first chapter, two experiments showed that children with MD (with or without reading disabilities), compared to normally-achieving children, do not present impairments in three inhibition functions (filtering, suppression, and blocking). The second chapter focused on interference in arithmetic tasks. Experiment 3 revealed that, in a multiplication verification task, children with MD were not more sensitive to interference than control children (of the same age or of the same math skills). In contrast, Experiment 4 showed that children with poor math skills were more sensitive to multiplication-related interference (i.e., the negative effect of multiplications on additions) than children with good math skills. Nevertheless, the third chapter established that the arithmetic retrieval deficits of children with MD (as well as the results of Experiment 4) can be accounted for without the recourse to inhibition. Indeed, Experiment 5 demonstrated that children with MD have poor memory representations of difficult single-digit multiplications (i.e., weak and incorrect problem-answer associations), which is sufficient to account for their retrieval deficits. Finally, in the last chapter, we considered the possibility that sensitivity to interference is involved in MD but during the development of arithmetic facts representations (not during their retrieval) and could lead to the poor representations observed in children with MD. In experiment 6, we found that counting to solve an addition might interfere with the memorization of the addition's addends (hence, with the development of problem-answer associations) but there was no evidence that children with MD are more sensitive to this interference than control children. Altogether, these data provide converging evidence against the inhibition-deficit hypothesis and suggest that poor arithmetic representations represent a better candidate as a causal factor of MD. / Le but de cette thèse est d'investiguer l'hypothèse d'un rôle causal des processus d'inhibition dans les Troubles d'Apprentissage de l'Arithmétique (TAA). Selon cette hypothèse, les difficultés de récupération des faits arithmétiques (p.ex., les tables de multiplications) observés dans les TAA seraient dues à des déficits d'inhibition. Le premier chapitre présente deux expériences dans lesquelles nous avons testé trois fonctions d'inhibition (filtrage, suppression et blocage) chez des enfants avec TAA global (avec et sans troubles de lecture associés) et avec troubles spécifiques de récupération de faits arithmétiques (Expériences 1 et 2). Les résultats de ces études n'ont pas mis en évidence de trouble d'inhibition chez ces enfants. Le second chapitre s'est focalisé sur les effets d'interférence classiquement observés dans des tâches arithmétiques. Dans l'expérience 3, nous avons mis en évidence un effet de confusion associative (p.ex., 3 x 7 est plus difficile à rejeter que 3 x 7 = 26) significatif chez des enfants avec troubles de récupération de faits arithmétiques. Néanmoins, cet effet était équivalent à celui observé chez des enfants contrôle. En revanche, dans l'expérience 4, nous avons observé que l'effet interférent de la multiplication sur l'addition était plus important chez des enfants avec faibles capacités de récupération de faits arithmétiques que des enfants avec fortes capacités de récupération. Toutefois, dans le troisième chapitre, nous démontrons que ces derniers résultats, et plus globalement, les troubles de récupération de faits arithmétiques, peuvent être interprétés à la lumière de modèles théoriques qui n'incluent pas de processus d'inhibition. En effet, l'expérience 5 révèle que chez des enfants avec de tels troubles de récupération (en comparaison d'enfants contrôle), les multiplications difficiles (p.ex., 6 x 7) étaient plus faiblement associées à leurs réponses correctes et associées à de réponses incorrectes, ce qui, selon certains modèles théoriques, était suffisant pour rendre compte de déficits de récupération. Ces résultats vont à l'encontre de l'hypothèse de déficits d'inhibition comme facteur causal des troubles de récupération arithmétique dans les TAA. Cependant, dans le dernier chapitre, nous considérons la possibilité que la sensibilité à l'interférence jouait un rôle important dans le développement des représentations arithmétiques (et non dans leur récupération). Dans l'expérience 6, notre hypothèse était que compter pour résoudre une addition pouvait interférer avec la mémorisation des opérandes de cette addition et donc, avec la formation des associations entre problème et réponse correcte. Si les résultats obtenus allaient dans ce sens, nous n'avons trouvé aucune évidence indiquant que cet effet interférent était plus important chez des enfants avec troubles de récupération de faits arithmétiques que chez des enfants contrôle. En conclusion, il semble que de pauvres représentations des faits arithmétiques, plutôt que des déficits d'inhibition, soient à l'origine des troubles de récupération de ces faits dans les TAA.

Magister Artium (Psychology) - MA(Psych) / Background: The acquisition of numerical competency is imperative for individuals in society for quality of life and economic well-being. Many children have significant mathematical learning difficulties, this is known as dyscalculia. The prevalence rate for dyscalculia ranges between 3.5%–6.5% of the school-age population. Primary studies report on interventions for children presenting with dyscalculia, however it is difficult to compare these studies without a systematic approach to an evaluation for methodological rigor. Aim: To systematically review available literature of interventions for children presenting with dyscalculia in primary schools in order to provide an evidence base of filtered information assessed for methodological rigor and coherence. Method: The study evaluated literature from 2004 to 2014 that report on interventions for primary school children presenting with dyscalculia. Studies that were included in the review were only full-text, English articles published within the specified timeframe reporting on the focus of the study. University of Western Cape databases were accessed for literature for inclusion in the study. The studies were assessed at title, abstract and full text levels for quality based on the inclusion and exclusion criteria. Meta-synthesis of included texts was conducted incorporating it with the RE-AIM framework. Permission to conduct the proposed study was obtained from relevant Ethics Committee at the University of the Western Cape. Plagiarism was avoided by acknowledging other people's work and collaboration was taken into consideration as the review entailed working with paired reviewers. Findings: The findings in the studies provide a base of effective interventions that can be used in the school setting in different domains and levels such as individually, holistically or through various instructions for children presenting with dyscalculia / Government of Botswana, Department of Tertiary Education and Finance

Syftet med detta arbete är att undersöka aktuell forskningslitteratur för att se hur dyskalkyli framställs för att som pedagog kunna upptäcka och stötta dessa elever i tid. Det syftas också till att få reda på en ungefärlig omfattning av dyskalkyli bland elever i grundskoleålder. För att få fram ett urval av litteratur till denna studie avgränsades sökningen till att beröra forskning om dyskalkyli, inte om att undervisa elever med dyskalkyli. Forskning från år 2000 och framåt har använts för att få så aktuella ståndpunkter som möjligt. Resultatet i denna studie har visat att dyskalkyli är ett omstritt begrepp som idag saknar en allmänt accepterad definition. Trots att en entydig definition saknas föreslår flera studier att dyskalkyli bland annat kan innebära brister i taluppfattningen. På grund av avsaknad av definition av begreppet dyskalkyli är det mycket oenigheter kring diagnosfrågan. Detta då det förekommer flera olika instrument för att mäta det. Ändå har flera studier gjorts där dyskalkylins omfattning bland elever i grundskoleålder är bedömd. Det uppskattas att ungefär 5-6 procent av alla elever i grundskolan har dyskalkyli.

Developmental dyscalculia (DD) is a learning disability that is characterized by severe difficulties with acquiring age-appropriate mathematical skills that cannot be attributed to insufficient education, language skills, or motivation. The prevalence rate is estimated at 3-6%, meaning that a substantial portion of the population struggles to learn mathematics to such a large degree that it affects overall well-being and academic prospects. However, our understanding of the etiology of DD is incomplete and there are competing hypotheses regarding the characteristics of DD and its underlying causal factors. The purpose of the current thesis is to contribute to our understanding of DD from the perspective of cognitive psychology and cognitive neuroscience. To this end, we identify children with DD to identify the cognitive determinants of DD that hamper their ability to learn basic mathematics. It is believed that human beings are endowed with an innate ability to represent numerosities, an ability phylogenetically shared with other species. We investigate whether the purported innate number system plays a role in children with DD insofar as  failures in this system may undermine the acquisition of symbolic representations of number. Although some researchers believe DD is a monolithic learning disability that is genetic and neurobiological in origin, the empirical support for various hypotheses suggests that DD may be shaped by heterogeneous characteristics and underlying causes. The present thesis, and the studies presented therein, provides support for the notion that DD is indeed heterogeneous. We identify at least two subtypes of DD that are characterized by specific deficits in number processing, and one subtype that could more aptly be labelled as a mathematical learning disability, the causal factors of which are likely limited to deficits in non-numerical abilities. In addition, we locate candidate neurocognitive correlates that may be dysfunctional in DD. / Dyskalkyli är en specifik inlärningssvårighet som karaktäriseras av stora svårigheter med att tillgodogöra sig matematikkunskaper som inte kan härledas till bristande undervisningsmöjligheter, språkfärdigheter, eller motivation. Prevalensen av dyskalkyli uppskattas till 3-6%, vilket innebär att en ansenlig andel av populationen har sådana besvär att lära sig matematik att det påverkar deras allmänna välbefinnande och akademiska möjligheter. Förståelsen för dyskalkyli är emellertid knapphändig, men ett flertal konkurrerande hypoteser har föreslagits avseende dess karaktäristika och kausala faktorer. Syftet med denna avhandling är att öka vår förståelse av dyskalkyli utifrån ett kognitionspsykologiskt perspektiv och utifrån kognitiv neurovetenskap. Följaktligen identifierade vi skolbarn med specifika och stora matematiksvårigheter för att sedermera undersöka vilka kognitiva faktorer som underminerar deras förmåga att förvärva grundläggande matematikfärdigheter. Rådande uppfattning är att människan är utrustad med en medfödd förmåga att uppfatta och representera antal, vilket är en förmåga som vi fylogenetiskt delar med andra arter. Vi undersöker huruvida detta medfödda antalsuppfattningssystem är involverat vid utvecklandet av dyskalkyli hos barn, där ett dysfunktionellt antalsuppfattningssystem kan underminera förmågan att tillgodogöra sig symboliska representationer av antal. Gängse uppfattning gör gällande att dyskalkyli är en enhetlig och homogen inlärningssvårighet som genetiskt och neurobiologiskt betingad. Dock har ett flertal hypoteser angående orsaken till dyskalkyli fått empiriskt stöd, vilket möjliggör tolkningen att dyskalkyli snarare är en heterogen inlärningssvårighet med olika kausala faktorer och egenskaper. Föreliggande avhandling ger stöd för denna senare tolkning. Vi identifierar åtminstone två  subtyper av dyskalkyli, som vardera karaktäriseras av specifika svårigheter med numeriska färdigheter, samt en subtyp som mer korrekt bör benämnas som matematiska inlärningssvårigheter där bidragande faktorer sannolikt kan härledas till icke-numeriska förmågor. Vidare så identifierar vi potentiella neurokognitiva korrelat som är dysfunktionella vid dyskalkyli.

Computer-assisted interventions designed to remediate low numeracy and developmental dyscalculia (mathematical learning disability) have been utilised in preschools and kindergartens with some efficacy for over thirty years (Clements, 2002). A recent development in this field is ‘adaptive game’ technology, which adapts task difficulty online as children learn. The Number Race is the first such package for mathematics. Previous efficacy studies suggest its use results in an improvement in core measures of early numeracy, such as speed at enumerating 1-3 objects (subitizing) and comparison of numerals and groups of objects. The present study tested the efficacy of a new version of The Number Race (version 3.0) using New Zealand English and incorporating new instructional factors, in a younger population than most previously tested. Participants were twelve 5-to-7-year-old children and a typically developing control group matched on age and sex (n = 12). Following pre-testing using standardised tests and a computerised battery, children in the intervention group used The Number Race for twenty minutes each school night, for one month. Post-testing results showed that there was a significant improvement in counting and subitizing speed for the intervention group. Participants also became faster and more accurate at comparing numerals. There were no significant changes in standardised mathematics scores. The mental number line task did not show any significant differences before and after intervention but a wide variety of patterns and possible use of strategies were revealed. Overall, this new version of The Number Race seems to have modest effects in this population.

Syftet med vårt arbete var att få en uppfattning om pedagogers kunskaper och erfarenheter kring dyskalkyli samt hur de stödjer elever som har eller misstänks ha diagnosen i sin undervisning. Vi har utgått från två frågeställningar. Den första är: Vilka kunskaper har matematiklärare, specialpedagoger och speciallärare om diagnosen dyskalkyli? och den andra är: Hur arbetar de för att hjälpa elever med konstaterad eller misstänkt dyskalkyli?  Vi har i vår studie utgått från det sociokulturella perspektivet på lärande, något som framkommer genom vår analys och diskussion. Vi har utfört en enkätundersökning och en semistrukturerad intervjustudie. Utifrån våra slutsatser kom vi bland annat fram till att det fanns kunskaper om dyskalkyli i de verksamheter som de deltagande tillhörde, men i väldigt olika utsträckning. Det fanns även kunskaper om olika stödinsatser för att hjälpa elever med diagnosen. Vi fick också fram att pedagogerna tyckte att det fanns för lite kunskaper om dyskalkyli i verksamheterna och att det är något som efterfrågas.

This thesis systematically examined the link between developmental dyscalculia, a specific learning difficulty of mathematics, and mathematics anxiety, a negative emotional reaction to mathematics tasks. The link between these maths learning issues was examined by measuring their prevalence in large samples of English primary (N = 1004; N= 830) and secondary school (N = 927) students. Gender differences were also explored. Systematically varying diagnostic criteria for dyscalculia revealed that its prevalence ranged between 0.89-17.23 percent. When absolute performance thresholds were used, there was no gender difference in dyscalculia prevalence. The association of mathematics performance with other cognitive skills and mathematics anxiety was investigated longitudinally in subsamples of children with dyscalculia (n =10), typical mathematics performance (n=10) and high maths ability (n = 11). 80 percent of the children in the dyscalculia group still met the criteria for diagnosis at the final time point. Mathematics performance was positively associated with working memory performance and negatively associated with mathematics anxiety. Furthermore, children with dyscalculia had higher maths anxiety than the other two groups. The relationship between dyscalculia and high maths anxiety was estimated in a larger sample (N = 1757). Relatively few children with dyscalculia had high maths anxiety and the majority of students with high maths anxiety in fact had mathematics performance within or above the average range. Girls had higher maths anxiety than boys, and more girls had both dyscalculia and maths anxiety than boys. There was an expected negative correlation between maths anxiety and maths performance in the total sample, but this correlation was negligible in the children with dyscalculia. Collectively, these results suggest that cognitive and emotional mathematics problems are dissociable, and indicate that children with dyscalculia and maths anxiety likely require different types of intervention. Furthermore there appears to be no gender difference in maths performance or in the prevalence of dyscalculia. However, girls have higher maths anxiety than boys, and are more likely to be affected by maths anxiety alongside developmental dyscalculia. Maths anxiety may be a potential explanation for the underrepresentation of females in careers involving mathematics.

Dyskalkyli, eller specifik räknesvårighet, är en specifik inlärningsstörning som innebärstora svårigheter att handskas med siffror. Detta är en kvalitativ intervjustudie medföräldrar till ungdomar med dyskalkyli, där frågor kring skolgång, insatser och känslorkring diagnosen samt relationen mellan förälder och ungdom berörs. Åtta föräldrar, allamödrar till ungdomar med dyskalkyli som är mellan 12 och 19 år intervjuades.Analysen som gjordes är en så kallad tematisk analys. De åtta teman som studienresulterade i är: Från upptäckt till utredning, Hur påverkar diagnosen?, Livet utanförskolan, Skolans hantering av svårigheter och dyskalkyli, Föräldrars insatser, Relationentill skolan, Vilka insatser önskas? och Hur dyskalkylin påverkar idag och framtiden.Föräldrar upplevde skolgången som en jobbig tid för både dem och deras barn och imånga fall har kommunikationen mellan skola och hem brustit. Kunskapen omdyskalkyli upplevdes som otillräcklig i de berörda skolorna, vilket påverkadeungdomarna negativt. Föräldrar efterfrågade också tidigare identifikation och utredningav svårigheterna. Studien kom fram till att kunskapen om dyskalkyli i skolorna behöverförbättras för att dessa elever ska kunna bemötas på ett tillfredsställande sätt, derassvårigheter kunna identifieras tidigare samt för att kunna erbjuda tidigare insatser. / Developmental dyscalculia is a specific learning disability that involves greatdifficulties in dealing with numbers. This is a qualitative interview study with parents ofadolescents who have dyscalculia, which raises questions about schooling, interventionand feelings concerning the diagnosis as well as the relationship between adolescent andparent. Eight parents, all mothers of children between the ages of 12 and 19 wereinterviewed. The analysis made is a so called thematic analysis. The eight themes thatresulted from the study were: From discovery to assessment, The effect of the diagnosis,Life outside of school, The schools way of dealing with the difficulties, Parentscontributions, The relationship with the school, What types of interventions arerequested by the parents?, How dyscalculia affects today and in the future. Parents feltthe schooling was tough for them and their children and in many cases thecommunication between the school and the home had fallen short. The knowledge aboutdyscalculia in the schools was perceived as insufficient, which affected the youthsnegatively. The parents also requested earlier identification and assessment of thedifficulties. The study concludes that the knowledge about dyscalculia needsimprovement in the schools in order to give these students a better schooling, to be ableto identify their difficulties earlier and provide earlier intervention.