The Triple Code Model (TCM) of numerical cognition has become one of the most predominantly theories for how humans perceive, manipulate, and communicate numerical information. It builds on the notion that there exist three functionally distinct but neurologically connected codes that handle manipulations of different numerical input (non-symbolic magnitudes, symbolic representations, and verbal number words). In this study, we add a developmental perspective by collecting child data and comparing it to existing adult data. The main question is whether or not children elicit the same neural correlates as adults while performing three different number comparison tasks in line with TCM. Neuroimaging data using fMRI were collected for a total of 20 participants (ten children and ten adults). The results suggest that children rely on more right-lateralized regions and that a developmental shift towards the left hemisphere and associated language areas occur during acquisition of mathematical proficiency. / <p>VG</p>

Menschen teilen mit vielen Spezies die Fähigkeit, aus einer Menge von Objekten deren Numerosität zu extrahieren. Es wird angenommen, dass diese Fähigkeit die Grundlage für die Menschen eigene, symbolisch-mathematische Fertigkeiten bildet. Daher ist ein besseres Verständnis der neuralen Charakteristiken dieser Fähigkeit von großer Bedeutung. Eines der einflussreichsten Modelle (das Triple Code Modell-TCM) nimmt an, dass dieser evolutionär alte Mechanismus in horizontalen Anteil des intraparietalen Sulcus verortet werden kann, der die Bedeutung von Anzahl in einer format- und modalitätsunabhängigen Art und Weise repräsentiert (d.h., Größencode). Zusätzlich wird angenommen, dass Subtraktion auf eben dieser Fähigkeit aufbaut, wohingegen Multiplikation stärker auf phonologischen Verarbeitungsmechanismen beruht (d.h., verbaler Code). Elektrophysiologische Untersuchungen beim Affen deuten auf einen gewissen Grad an Abstraktion von semantischer Größeninformation im parietalen Kortex hin. Jedoch wurde dies bisher nur für kleine Numerositäten ( / Humans as well as other animals are endowed with the capacity to extract the numerosity (i.e., the number of items) of a given set of objects. This capacity is thought to form the basis of human specific symbolic mathematical abilities. Hence, understanding its nature is of importance. One of the most influential models (The Triple Code Model) suggests that this evolutionarily ancient mechanism resides on the horizontal aspect of the intraparietal sulcus and represents number semantics in a format and modality independent fashion (i.e., magnitude code). In addition, subtraction is thought to rely more on this mechanism whereas multiplication relies more on phonological circuits (i.e., verbal code). Although there is evidence from non-human primate electrophysiology suggesting a certain degree of abstraction for number semantics in the parietal cortex, this was only found for small numerosities (

Le modèle du triple code a été proposé par Dehaene (1992 ; Dehaene & Cohen, 2000)sur la base d’arguments neuro-anatomiques et neuropsychologiques pour rendre compte du traitement des nombres et des quantités. Le modèle postule l’existence de trois types de représentations correspondant chacune à un format de l’information numérique : une représentation analogique approximative préverbale, et deux représentations symboliques,l’une verbale, l’autre arabe. Si des études ont pu être mettre en évidence les caractéristiques de la dimension analogique tant chez le nouveau-né que chez l’adulte, la question de la« greffe » chez l’enfant des représentations symboliques sur la représentation analogique reste posée. L’objectif de cette thèse est de rechercher en suivant le développement comment s’effectue cette mise en relation. Nous avons élaboré un ensemble d’épreuves de comparaisons testant chacune une des représentations du modèle du triple code afin de déterminer chez des enfants dès 4 ans des indices de cette mise en relation. Si le lien entre dimensions analogique et symbolique est présent, un effet de rapport, « signature » de ce lien est attendu tant avec les comparaisons analogiques que symboliques. Cinq expérimentations ont été menées : avec des adultes, des enfants de 4 et 5 ans tout-venant, des enfants prématurés et des enfants atteints du syndrome de Down. Les résultats montrent que, dans toutes les populations, l’effet de rapport est présent avec la dimension analogique. Ensuite,entre 4 et 5 ans, avec l’acquisition du code verbal et indo-arabe la représentation symbolique change de nature. Enfin, les populations qui présentent des troubles du traitement du nombre sont affectées essentiellement sur la dimension verbale. Ces résultats sont discutés en regard de deux conceptions alternatives. / The triple code model was proposed by Dehaene (1992 ; Dehaene & Cohen, 2000) onthe basis of neuro anatomical and neuropsychological arguments in order to account for number and quantity processing. This model postulates the existence of three types of representations, a preverbal and approximate analogical representation, and an Arabic and verbal symbolic representations. If researchers have extendedly studied the characteristics of the analogic dimension in the new born as well as the grown up, the issue of the « graft » ofsymbolic representations for the child on analogical representation remains an open debate inthe current literature. The aim of this thesis is to explore how this connection operates with regard to development. We set out a series of comparing tests to try each representation of the triple code model in order to find signs of this connection in children as young as four years old. If a relation ship between the analogical and symbolical dimensions is found then, asignature of this connection is expected to be found in the analogical comparisons as well as in the symbolical. Five different experiments were carried out on adults and four-five year-oldchildren from all walks of life, including prematured and Down Syndrom children. The results show that in all the samples, a ratio effect is found in the analogical dimension. Then between four and five years old, the acquisition of the Indo Arabic and verbal code, the nature of the symbolic representation changes. Finally, populations showing troubles with numbers are mainly affected on the verbal dimension. These results are assessed with regard to two alternative conceptions.

Reading difficulties is the most common learning difficulty in the western world and it is common that people with reading disabilities also exhibit arithmetic difficulties. Different theories about the cause of the relationship exists, one theory describes the importance of good phonological ability in reading as well as in arithmetic, while another theory describes the importance of a reliable number system and that only a subgroup of students with reading disabilities also have difficulties with arithmetic. The purpose of this study is to investigate how students with reading difficulties (RD), without any known mathematical difficulties, perform on mathematical tasks relative to a control group. The study was theoretically grounded on the Triple code model (Dehaene, 1992), which is a model for numerical information processing that describes how various numerical and arithmetic tasks are processed through three distinct representation systems in the brain, a verbal and a visual representation system and a quantity system. Reading skills, phonological skills, arithmetic skills and number processing skills were examined in 61 students through a variety of tests. After examination of reading ability, the participants were split into two groups, students with RD and a control group. Statistical comparisons were calculated by one-way analysis of variance between the two groups on each task, and for some tasks one-way analysis of covariance were used. The results provided partial support for the present hypotheses. The main findings showed that students with RD have difficulties within the verbal and visual representation system but exhibit an intact quantity system. Within the verbal representation system, students with RD performed significantly worse in retrieval of arithmetic facts (addition, subtraction and multiplication), they retrieved fewer established answers from long-term memory on all of the three arithmetic operations compared to the control group. The students with RD also made more errors regarding subtraction and multiplication and within the visual representation system they had significantly fewer answers that were correct on written arithmetic calculation and was significantly slower in symbolic number comparison, compared with the control group. It is discussed whether a connection difficulty, namely difficulties in linking a particular symbol with a semantic content, is the cause of the exhibited arithmetic difficulties in students with RD. / Lässvårigheter är den vanligaste inlärningssvårigheten i västvärlden och det är vanligt att personer med lässvårigheter även uppvisar aritmetiska svårigheter. Skilda teorier kring orsaken till sambandet finns och en teori beskriver vikten av god fonologisk förmåga vid läsning såväl som vid räkning. En annan teori beskriver vikten av ett tillförlitligt antalsystem och att endast en undergrupp av elever med lässvårigheter också har svårigheter med aritmetik. Syftet med föreliggande studie är att undersöka hur elever med lässvårigheter (LS) utan kända matematiksvårigheter presterar på matematiska uppgifter i förhållande till en kontrollgrupp. Studiens teoretiska utgångspunkt är Trippel-kod-modellen (Dehaene, 1992), vilket är en modell för numerisk informationsbearbetning som beskriver hur olika numeriska och aritmetiska uppgifter antas bearbetas genom tre representationssystem i hjärnan, det vill säga verbalt och visuellt representationssystem samt kvantitetssystem. Läsfärdighet, fonologisk förmåga, aritmetisk färdighet samt antalsuppfattning undersöktes hos 61 elever genom ett flertal test. Efter undersökning av läsfärdighet delades deltagarna upp i två grupper, elever med LS och en kontrollgrupp. Statistiska jämförelser beräknades genom envägs variansanalys mellan grupperna på respektive uppgift och för vissa uppgifter beräknades även envägs kovariansanalys. Resultatet gav delvis stöd för de uppsatta hypoteserna då huvudfyndet visade att elever med LS har svårigheter inom både verbalt och visuellt representationssystem men uppvisar ett intakt kvantitetssystem. Inom verbalt representationssystem presterade eleverna med LS signifikant sämre än kontrollgruppen på uppgiften framplockning av aritmetiska talfakta inom addition, subtraktion och multiplikation då de hade färre svar att plocka fram från minnet på alla tre räknesätt. Eleverna med LS hade också fler fel gällande subtraktion och multiplikation. Inom visuellt representationssystem uppvisade de signifikant färre rätt på skriftlig aritmetisk kalkylering samt var signifikant långsammare gällande symbolisk antalsuppfattning jämfört med kontrollgruppen. Utifrån resultaten diskuteras huruvida en kopplingsproblematik, det vill säga svårigheter att koppla en bestämd symbol med ett semantiskt innehåll, ligger till grund för de uppvisade aritmetiska svårigheterna hos elever med LS.