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

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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.

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 deals with children with ?mathematical? defects. Dyscalculia and other are usually defects in communication between the child and surrounding world. The goal is to teach these children mathematics on the level they are able to understand. The thesis is divided into four parts. In the first two parts it deals with the dyscalculia. In the second part it deals with ?reeducational? technics. In the third and fourth parts you can find worksheets that have been created by me. The work of children with dyscalculia is valued there by me afterwards. I put focus on work of pupils, e.g. how they?ve found the work with the worksheets and if they brought some value and benefits while working with them. The thesis shows that we use the most common methods and technics that have to be proved by children. This should be a usefull publication for teachers who are working with children with the dyscalculia. In general, it should bring a usefull hand for a better orientation in the problems of dyscalculia and explain it.

Dyskalkyli (specifika räknesvårigheter) är en av flera orsaker till matematiksvårigheter. Studier har påvisat samband mellan dyskalkyli och dyslexi och att personer med dyskalkyli har svårt att klara skolmatematiken. Två skilda synsätt förklarar orsaken till dyskalkyli: systemteorin och modulärteorin. Dyscalculia Screener är ett screeningverktyg som bygger på modulärteorin och att dyskalkyli beror på svårigheter med grundläggande antalsuppfattning och ska urskilja personer med dyskalkyli från de som är dåliga på matematik av andra orsaker. Testet innehåller delar som testar reaktionstid (Simple Reaction Time), antalsuppfattning (Dot Enumeration och Numerical Stroop) och aritmetik (Addition och Multiplication). Denna studie undersökte hur svenska barn i årskurs 5 och 6 presterade på testet, för att ge referensdata för svenska förhållanden och undersöka hur väl de engelska normerna fungerar. Studien studerade även samband mellan avkodningsförmåga, av riktiga ord och non-ord (med testet LäSt) och prestation på Dyscalculia Screener samt samband mellan prestation i skolmatematik och resultat på respektive test. Studien innefattade 66 barn, 36 i årskurs 5 och 30 i årskurs 6. Svenska barns resultat skiljde sig till viss del från de engelska normvärdena. De presterade lägre än normvärdena på deltesten Simple Reaction Time och Multiplication. På Dot Enumeration och Numerical Stroop presterade barnen högre. På Addition låg barnen inom normvärdena. Samband mellan avkodningsförmåga och räkneförmåga kunde påvisas, framförallt för avkodning av non-ord. En skillnad i resultat fanns på deltesten Numerical Stroop, Addition och Multiplication mellan de som uppnådde målen i matematik och de som var tveksamma att uppnå eller inte uppnådde målen. / Dyscalculia (specific mathematics disorder) is one, among other causes of mathematical difficulties. Studies have indicated a correlation between dyscalculia and dyslexia and people with dyscalculia have problems managing school mathematics. Two different theories explain the cause of for dyscalculia: the system theory and the modular theory. Dyscalculia Screener is a screening tool based on the modular theory and that dyscalculia is caused by difficulties in basal number sense and should discriminate people with dyscalculia from those who are bad at mathematics for other reasons. The test includes parts that test reaction time (Simple Reaction Time), number sense (Dot Enumeration and Numerical Stroop) and arithmetics (Addition and Multiplication). This study investigated how Swedish children, in year 5 and 6, scored on the test, to get reference data for Swedish relations and see whether the normes from England could be used. The study also investigated correlations between decoding, of real words and non-words (with the test LäSt) and score on Dyscalculia Screener and correlations between ability to manage school mathematics and score on each test. The study included 66 children, 36 in year 5 and 30 in year 6. Swedish children scored different in some ways from the English norms. They scored lower than the norms on the testparts Simple Reaction Time and Multiplication. On Dot Enumeration and Numerical Stroop they scored higher. On Addition, they scored within the norms. A correlation between decoding and counting ability was found, especially for decoding of non-word. A difference in score was seen on the testparts Numerical Stroop, Addition och Multiplication between children that achieved the goals in mathematics and those who were unsure to achieve them or did not.

The learning of mathematics covers a variety of skills, such as comparing quantities, counting the number of items in a set, dealing with the numerical systems (i.e., writing and reading numbers), performing simple and complex calculations, or solving word problems. Typically, a majority of children are able to master these abilities, but an appreciable percentage of them does not and are then referenced as having developmental dyscalculia. It is clear that not being able to count efficiently, to understand the meaning of numbers, or to calculate as other children do, rapidly becomes a handicap during the development, not only at school but also in society in general, in the same way as not being able to read is. Despite the growing interest observed over these last few years, research on developmental dyscalculia or more general mathematical disability is actually much less advanced than research on dyslexia. It could be due to the complexity of the mathematics field. Several hypotheses have been proposed to account for this learning deficit, but the origin(s) of developmental dyscalculia remain(s) unclear. Research first focused on the role of the auxiliary cognitive functions not directly related to number processing. In particular, the different components of the working memory were extensively measured in children with mathematical difficulties. Other theories are based on potential weak spatial abilities, low speed of processing, or difficulties in retrieving information from long-term memory. More recently, Butterworth (1999b) proposes that humans are born with a capacity specialised for recognising and mentally manipulating numerosities. Unlike the previous hypotheses, he argues for “a highly selective and specific deficit of a very basic capacity for understanding numbers, which leads to a range of difficulties in learning about number and arithmetic”. In the same vein, Dehaene (1997) speaks about the “number sense” as the ability to represent and manipulate number magnitude nonverbally that could be impaired in developmental dyscalculia. In this thesis, we have focused on four main questions with respect to number development. First, we wanted to test whether or not difficulties encountered by mathematically disabled children are specific to the numerical domain. Children with mathematical disabilities manifesting poor calculation abilities were compared to control children of the same age during various tasks of retrieving information from long-term memory (Experiment 1). The second aim was to examine the integrity of the number magnitude representation in dyscalculia. We analysed potential differences in the slope of the numerical distance effect, which reflects the nature of analog magnitudes, in children with or without mathematical disabilities when they had to select the larger of two quantities presented in different formats (Experiment 2). These experiments are presented in Chapters 4 and 5. The two other questions are dedicated to the analysis of brain areas involved in number development using functional magnetic resonance imaging (fMRI). Our third objective was to examine age-related changes in frontal and parietal regions between children and adults during number comparison (Experiment 3). Finally, we conducted a second neuroimaging study to explore the potential neural correlates of dyscalculia. Cerebral activity of both children with pure dyscalculia and control children was analysed during a numerical and a non-numerical comparison tasks (Experiment 4). We also investigated whether or not these differences in brain activation were specific to number processing. These experiments are reported in Chapters 6 and 7.

According to some researchers, dyscalculia is at least as prevalent as dyslexia. Somewhere between 3.6-6 % of all pupils have specific mathematics difficulties named dyslexia. If this be true, it should present the most complex special education predicament by far in schools today. Despite the statistics, dyscalculia is still a rather unknown concept. The cause of dyscalculia is not yet fully analyzed. There are several theories and many researchers see similarities between dyscalculia and the special educational problem of reading and writing, dyslexia. The most important factor for pupils to be able to develop mathematical skills is adequate assistance at the earliest possible stage. It is probable that this adequate assistance is achieved if the pupil is diagnosed with dyscalculia and therefore gets access to a special educational resources. In this essay, I want to analyze the concept of dyscalculia and how recognized it is today. To this end, I have undertaken several interviews with the objective of seeing how educationalists relate to dyscalculia. In order to see how the diagnosis is performed, and what it means to be diagnosed, I have followed the work process from a pupil suspected of having dyscalculia to a possible diagnosis. I have also personally undergone a dyscalculia investigation at an authorized speech therapist in order to achieve a profound insight into the diagnosis process. My study shows that the concept of dyscalculia is not widely recognized, but that the knowledge around dyscalculia is increasing. Research is currently undertaken in the field even though it is not to the same extent as dyslexia.

Dyscalculia is a specific learning disability that affects an individual’s core skills in mathematics, including calculation, recall of number facts, and approximating/comparing number. Research into the origins and aetiology of dyscalculia have suggested the presence of two different networks in the brain used for mathematics; one for verbal (symbolic) tasks such as recalling number facts, and one for non-verbal (non-symbolic) tasks such as approximation and number comparison. While these networks are located in different brain areas, they are often used together on calculation tasks, they are known to impact each other over the course of development, and they both appear to be impacted in dyscalculia. The current study used entertaining computer assisted instruction software, “Timez Attack”, to target the symbolic network, i.e. to improve the fluency of multiplication fact recall in three 9 and 10 year old children who were performing below the expected level on multiplication. An ABA (applied behaviour analysis) multiple-baseline across subject design was used to track participants’ performance on multiplication, addition, and number comparison over the course of the intervention. Results showed improved fluency of multiplication fact recall in all three participants; however this improvement did not generalise to addition or number comparison. This finding suggests that the symbolic and non-symbolic brain networks involved in mathematics are largely independent from each other by middle childhood, and that training targeting one network does not affect the other.