La compréhension du développement des habiletés numériques est un enjeu majeur pour guider les pratiques éducatives et rééducatives des jeunes enfants. Les résultats des enquêtes nationales et internationales sont unanimes à cet égard : le niveau moyen des élèves en mathématiques a chuté depuis 2003 (PISA, 2012). L’hypothèse la plus avancée à l’heure actuelle est celle d’un déficit des correspondances entre les codes numériques et le « sens des nombres » (Dehaene, 1997). Le « sens du nombre » est contenu dans la représentation analogique et non verbale des nombres. Dans le présent travail, nous cherchons à démontrer que l’estimation numérique permet ainsi d’exercer les correspondances entre les codes afin de donner du sens aux représentations symboliques écrites et orales. Malgré l’importance accordée aujourd’hui au processus d’estimation, son rôle dans les apprentissages doit encore être précisé afin d’orienter et de mieux guider les pratiques (ré)éducatives (Dehaene et Cohen, 2001 ; Von Aster et Shalev 2007). A travers trois études expérimentales, nous explorons ainsi le rôle de l’estimation numérique dans les apprentissages d’un point de vue éducatif (auprès d’enfants scolarisés en CP) et d’un point de vue rééducatif (dans le syndrome génétique de la trisomie 21). L’acquisition des différentes représentations et des relations complexes qui s’établissent entre-elles est également analysée et discutée pour mieux préciser les modèles de traitements du nombres et du calcul actuels. Les résultats obtenus corroborent ainsi une hypothèse de spiralité des apprentissages symboliques. / Understanding the development of numerical abilities is a major issue to guide educative and reeducative practices in mathematics in young children. National and international investigations has demonstrated that the mathematical skills of students has decrease since 2003 (PISA, 2012). Nowadays, weak capacities to map numerical representations and therefore a defective « number sense » (Dehaene, 1997 ; 2001) is the most supported hypothesis. The « number sense » is contained into the analogical and non-verbal representation of number. In this work, we consider that numerical estimation is a good way to exercise this mapping and give sense to verbal and written numerical symbols. Indeed, the role of numerical estimation needs to be specified in order to lead the (re)educative practices (Dehaene, 1997 ; 2001 ; Von Aster et Shalev). During three experimental studies, we explore the role of numerical estimation, in an educative and reeducative way in children in first year and children with down’s syndrom. The acquisition of numerical representations and the complex relations they have are also explored and discussed through a spirality hypothesis in order to better specify actual models of number treatment.

The diploma thesis deals with sequencing methods and genome assembly methods including usage of numerical representations. The theoretical part of thesis describes the history of DNA research, generations of sequencing methods, the assembly methods themselves and definiton of numerical representations. Numerical represenatations serve to convert character form of DNA to numerical form and so allow to use digital signal processing methods. There is an algorithm for genome assembly using numerical represenatation proposed in thesis, which is later tested at sequence data.

Modern methods of processing genomic data yield good results, however they are often redeemed by time consummation. This is mainly the reason why this thesis deals with numerical methods of bacterial genome processing which could be a suitable alternative for current methods, both in terms of quality and computational demands. This thesis presents the current methods used for processing of genomes in silico and proposes suitable numerical presentations for the whole genome analysis. Some of these methods are programmed and used for processing further in this diploma thesis. In it, various mathematical and statistical methods are being tested, ones that could lead to successful species delineation of bacteria by numerical presentations of their genomes.

Most methods for analysis of genomic data work with symbolic sequences. Numerically represented genomic sequences can be analyzed by signal processing methods. A new method of numerical representation of DNA sequences, nucleotide density vectors, is proposed in this thesis. Usability of this method for purposes of molecular species identification is tested on DNA barcoding sequences. DNA barcoding is modern and popular methodology based on comparison of short mitochondrial DNA sequences. Beside species identification by proposed method based on nucleotide density vectors, higher taxa rank identification (e.g. families) was also tested. Furthermore, dendrograms were constructed from standardly used evolutionary distances and distances between nucleotide density vectors and the dendrograms were compared.