La présente thèse a pour objectif de clarifier la nature de la relation entre les habiletés numériques innées – le Sens du Nombre – et les compétences en arithmétique apprises à l’école. L’originalité de cette recherche consiste en l’attention particulière que je porterai au rôle que jouent les habiletés numériques innées dans les différentes manières de résoudre une addition complexe, telle que 48 + 25, c’est-à-dire les stratégies de résolution. Dans le présent travail, je m’attèlerai à déterminer si la possession de compétences numériques plus développées favorise l’utilisation de procédures de calcul qui tiennent compte des propriétés numériques des opérandes du calcul, et si, inversement, la possession d’habiletés numériques plus imprécises entrave leur application, au profit de stratégies de calcul plus basiques. <p><p>À cette fin, j’axerai la présente thèse en trois volets distincts. Dans un premier volet, je vérifierai que les habiletés numériques sont essentielles à l’implémentation de toutes les stratégies de calcul, malgré le fait qu’elles soient engagées à des degrés d’élaboration différents en fonction de la stratégie exécutée. Ensuite, dans un second volet, je confirmerai que les compétences numériques orientent les préférences stratégiques ;comme je le supposais, les calculateurs possédant les habiletés numériques les plus développées ont davantage recours à des stratégies basées sur la magnitude complète des nombres, alors que ceux qui ont des capacités plus limitées les évitent. Enfin, dans un dernier volet, je mettrai en évidence que l’application de telles stratégies qui impliquent de traiter les numérosités entières engendre au niveau cérébral une activité accrue au sein des régions intrapariétales, aires dédiées au traitement des magnitudes numériques, par rapport aux autres procédures de calcul.<p><p>Les résultats que je rapporte dans la présente thèse mettent ainsi en évidence que les habiletés numériques sont critiques dans la résolution d’additions complexes non seulement au niveau de l’exécution de la stratégie de calcul, mais aussi dans l’établissement à long terme de la préférence stratégique des individus. Outre ces observations, la présente recherche plaide plus généralement en faveur de la prise en considération des stratégies de résolution dans les tâches arithmétiques, car les compétences numériques peuvent y être associées à des degrés différents. Au-delà de la simple performance, s’intéresser plus qualitativement aux stratégies de résolution constitue selon moi une étape cruciale dans la compréhension de la nature du lien entre le Sens du Nombre inné et les compétences en arithmétique.<p><p>/<p><p>The current thesis aims at clarifying the nature of the relationship between innate numerical abilities – the Number Sense – and arithmetic skills acquired at school. I will particularly focus in this research on the role played by these innate numerical abilities in selecting and executing the different procedures that could be used to solve a complex addition such as 48 + 27. In the current thesis, I will attempt to determine whether more elaborated numerical competence favours the utilisation of solving strategies that take into account the numerical properties of the addends, and conversely, whether inaccurate numerical representations discourage from using these strategies, for the benefit of more basic solving strategies.<p><p>In the current thesis, I will more specifically cover three different aspects. First of all, I will demonstrate that numerical abilities are crucial in implementing every solving strategy, but that they are engaged to a different extent as a function of the executed strategy. Secondly, I will show that numerical competence determine strategic preference; as I hypothesized, adults who possess the best numerical abilities would use more frequently solving strategies that are based on the entire numerical magnitude of the addends, whereas adults with more limited abilities would rather avoid them and execute basic procedures. Finally, in the third section, I will emphasize that the use of such elaborated solving strategies do imply at the cerebral level a stronger activity within the intraparietal regions, which are dedicated to the numerical magnitude processing, in comparison to other basic solving strategies.<p><p>The data I report here thus highlight that numerical abilities are essential in solving complex additions, not only in the execution of the solving strategy, but also in the long-term establishment of the preferred strategy. Besides this observation, the current thesis claims more generally in favour of the consideration of solving strategies when assessing arithmetic tasks, because numerical abilities are involved to a distinct extent in these tasks. Over and above regular performance, investigating through a qualitative perspective the solving strategies constitutes, according to me, a fundamental step in understanding the nature of the relationship between the innate Number Sense and arithmetic skills.<p> / Doctorat en Sciences Psychologiques et de l'éducation / info:eu-repo/semantics/nonPublished

Recent research has elucidated the sustained benefits of early mathematics instruction. With growing concern about the performance of South Africa’s senior learners in mathematics, it is imperative to look at long-term solutions within the education process. One such solution may be to focus on improved mathematics instruction as early as preprimary school. However, children at this young age are not typically suited to formal teaching. Alternative methods of mathematics instruction must be considered for maximum and effective impact. The study was conducted to test the notion that not all early methods of mathematics instruction are equal. During the empirical research approximately 200 preprimary school children in three different socio-economic environments (urban higher SES, township and rural) were tested after experiencing a teacher-guided play-based mathematics teaching intervention, or after experiencing a worksheet-based or free-flow play-based curriculum. The test performance of the participants was primarily compared to find relations between teaching methods and early mathematics performance. The study found that a teacher-guided play-based curriculum is superior to other curriculums in the instruction of mathematics in all educational settings, regardless of socioeconomic background. / Psychology of Education / M. Ed. (Psychology of Education)

Numerical cognition has been shown to share many aspects of spatial cognition, both behavioural and neurological. However, it is unclear whether a particular type of spatial cognition, visuospatial mental imagery (VSMI), may play a role in symbolic numerical representation. In this thesis, I first show that mental rotation, a form of VSMI, is related to two measures of basic numerical representation. I then show that number-space synaesthesia (NSS), a rare type of VSMI involving visualised spatial layouts for numbers, does not show an advantage in mental rotation, but shows interference in number line mapping. I next present a study investigating links between NSS and the ability to learn novel numerical symbols. I demonstrate that NSS shows an advantage at learning novel numerals, and that transcranial random noise stimulation, which increases cortical excitability, confers broadly similar advantages that nonetheless differ in subtle ways. I present a study of transcranial alternating current stimulation on the same symbol learning paradigm, which fails to demonstrate effects. Lastly, I present data showing that strength of numerical representation in these newly-learnt symbols is correlated with a measure of mental rotation, and also with visual recognition ability for the symbols after, but not before, training. All together, these findings suggest that VSMI does indeed play a role in numerical cognition, and that it may do so from an early stage of learning symbolic numbers.

Recent research has elucidated the sustained benefits of early mathematics instruction. With growing concern about the performance of South Africa’s senior learners in mathematics, it is imperative to look at long-term solutions within the education process. One such solution may be to focus on improved mathematics instruction as early as preprimary school. However, children at this young age are not typically suited to formal teaching. Alternative methods of mathematics instruction must be considered for maximum and effective impact. The study was conducted to test the notion that not all early methods of mathematics instruction are equal. During the empirical research approximately 200 preprimary school children in three different socio-economic environments (urban higher SES, township and rural) were tested after experiencing a teacher-guided play-based mathematics teaching intervention, or after experiencing a worksheet-based or free-flow play-based curriculum. The test performance of the participants was primarily compared to find relations between teaching methods and early mathematics performance. The study found that a teacher-guided play-based curriculum is superior to other curriculums in the instruction of mathematics in all educational settings, regardless of socioeconomic background. / Psychology of Education / M. Ed. (Psychology of Education)