This dissertation explores the modular learning in artificial neural networks that mainly driven by the inspiration from the neurobiological basis of the human learning. The presented modularization approaches to the neural network design and learning are inspired by the engineering, complexity, psychological and neurobiological aspects. The main theme of this dissertation is to explore the organization and functioning of the brain to discover new structural and learning inspirations that can be subsequently utilized to design artificial neural network. The artificial neural networks are touted to be a neurobiologicaly inspired paradigm that emulate the functioning of the vertebrate brain. The brain is a highly structured entity with localized regions of neurons specialized in performing specific tasks. On the other hand, the mainstream monolithic feed-forward neural networks are generally unstructured black boxes which is their major performance limiting characteristic. The non explicit structure and monolithic nature of the current mainstream artificial neural networks results in lack of the capability of systematic incorporation of functional or task-specific a priori knowledge in the artificial neural network design process. The problem caused by these limitations are discussed in detail in this dissertation and remedial solutions are presented that are driven by the functioning of the brain and its structural organization. Also, this dissertation presents an in depth study of the currently available modular neural network architectures along with highlighting their shortcomings and investigates new modular artificial neural network models in order to overcome pointed out shortcomings. The resulting proposed modular neural network models have greater accuracy, generalization, comprehensible simplified neural structure, ease of training and more user confidence. These benefits are readily obvious for certain problems, depending upon availability and usage of available a priori knowledge about the problems. The modular neural network models presented in this dissertation exploit the capabilities of the principle of divide and conquer in the design and learning of the modular artificial neural networks. The strategy of divide and conquer solves a complex computational problem by dividing it into simpler sub-problems and then combining the individual solutions to the sub-problems into a solution to the original problem. The divisions of a task considered in this dissertation are the automatic decomposition of the mappings to be learned, decompositions of the artificial neural networks to minimize harmful interaction during the learning process, and explicit decomposition of the application task into sub-tasks that are learned separately. The versatility and capabilities of the new proposed modular neural networks are demonstrated by the experimental results. A comparison of the current modular neural network design techniques with the ones introduced in this dissertation, is also presented for reference. The results presented in this dissertation lay a solid foundation for design and learning of the artificial neural networks that have sound neurobiological basis that leads to superior design techniques. Areas of the future research are also presented. / Ph. D.

Map generalization is a traditional cartographical issue which should be particularly considered in today’sinformation age. The aim of this study is to find some characteristics about head/tail breaks which worksas generalization method compared with the well known Topfer’s method. A questionnaire survey wasconducted to let 30 users choose either of the series maps of both methods and the reason(s) for thatchoice. Also to test their understanding of the series maps histograms were added for them to match.Afterwards the sample results were analyzed using both univariate and bivariate analysis approaches. Itshows that the head/tail breaks method was selected by 58%, compared with 38.7% of Topfer’s method,because of its simplicity. By checking the correctness of histogram question it also shows that those whowell understood answers choose the head/tail breaks rather than the Topfer’s method. However in somecases, where the amount of geographical features is relatively small, Topfer’s method is more selectedbecause of its informative characteristic and similar structure to the original map. It was also found that inthe comparison the head/tail breaks is more advantageous in line feature type generalization than in arealfeature type. This is probably because Topfer’s method changes its minority selection rule to half selectionin line feature type, whereas the head/tail breaks keeps the scaling property. Any difference between thetwo tested scales, Finland level and Helsinki level, is not found in this comparison study. However, futurework should explore more regarding this and other issues.

Les enfants atteints d’un trouble du spectre de l’autisme (TSA) présentent souvent des difficultés à généraliser leurs apprentissages à des nouveaux stimuli, contextes et individus (Brown & Bebko, 2012; Happé & Frith, 2006; Lovaas, Koegel, Simmons, & Long, 1973; Plaisted, O'Riordan, & Baron-Cohen, 1998). Pour cette raison, il est important d’utiliser des techniques promouvant la généralisation au sein des programmes d’intervention leur étant destinés. Cette recherche visait à évaluer l’efficacité de deux des techniques les plus fréquemment utilisées dans les programmes d’intervention comportementale intensive (ICI), soit l’enseignement séquentiel et l’enseignement simultané, afin de déterminer si l’une d’elles était systématiquement plus efficace que l’autre pour promouvoir la généralisation des concepts chez les enfants ayant un TSA. Des devis expérimentaux à cas unique ont été utilisés pour évaluer les effets des deux techniques sur la généralisation de quatre enfants ayant un diagnostic de TSA et recevant des services d’ICI en clinique privée. Pour deux participants, la méthode enseignement simultané a démontré une plus grande efficacité quant à la généralisation des concepts enseignés. Pour les deux autres, les deux techniques se sont avérées aussi efficaces. Bien que préliminaires, les résultats suggèrent qu’il serait préférable d’appliquer la méthode enseignement simultané lors de l’enseignement de concepts chez les enfants ayant un TSA en contexte d’ICI. / Children with autism spectrum disorder (ASD) often show difficulties in generalizing what they have learned to new stimuli, contexts or persons (Brown & Bebko, 2012; Happé & Frith, 2006; Lovaas, Koegel, Simmons, & Long, 1973; Plaisted, O'Riordan, & Baron-Cohen, 1998). For this reason, it is important to implement strategies to promote generalization within programs intended for this population. This study aimed to compare the effectiveness of two of the most commonly used strategies in intensive behavioral intervention (IBI), serial training and concurrent teaching, to determine whether one was systematically more effective than the other at promoting generalization in children with ASD? Single-case experimental designs were used to assess the effects of the two strategies with four children with an ASD diagnosis receiving services in a private clinic. For two participants, concurrent teaching was more effective to promote generalisation of the learned concepts. For the remaining two participants, the two strategies were equally effective. Albeit preliminary, the results suggest that it may be preferable to introduce exemplars concurrently when teaching concepts to children with ASD within IBI programs.

Lorsque le système nerveux central est exposé à une nouvelle association visuoproprioceptive, l’adaptation de la carte visuomotrice est nécessaire afin d’exécuter des mouvements précis. L’efficacité de ces processus adaptatifs correspond aussi à la capacité à les transférer dans des contextes différents de l’apprentissage de cette nouvelle association, par exemple dans de nouvelles régions de l’espace extrapersonnel (généralisation spatiale). Comme le contexte exerce une influence considérable sur les processus adaptatifs, les composantes multidimensionnelles de la tâche et de la perturbation pourraient constituer des éléments affectant considérablement l’adaptation et la généralisation spatiale. Ce mémoire présente une étude exploratoire de l’adaptation à une perturbation triaxiale, introduite graduellement, réalisée dans un environnement virtuel tridimensionnel et sa généralisation spatiale. Nos résultats suggèrent que les trois axes de l’espace présentent des différences importantes quant aux processus adaptatifs qui les sous-tendent. L’axe vertical présente à la fois une plus grande variabilité et de plus grandes erreurs spatiales au cours de l’adaptation comparativement à l’axe sagittal et à l’axe horizontal, tandis que l’axe sagittal présente une plus grande variabilité que l’axe horizontal. Ces différences persistent lors de l’effet consécutif, l’axe vertical affichant une désadaptation importante. Le test de généralisation spatiale montre une généralisation à l’ensemble des cibles, cependant, la généralisation semble plus faible le long de l’axe vertical. Ces résultats suggèrent que l’adaptation à une translation tridimensionnelle se généralise à travers l’espace le long des trois axes de l’espace et renforcent l’idée que le système nerveux central utilise une stratégie de décomposition modulaire des composantes de l’espace tridimensionnel. / We explored visuomotor adaptation and spatial generalization in the context of three-dimensional reaching movements performed in a virtual reality environment using a learning paradigm composed of four phases: pre-exposure, baseline, learning, and post-exposure (aftereffect and generalization). Subjects started by performing five reaching movements to six 3D memorized target locations without visual feedback (pre-exposure). Next, subjects performed twelve reaching movements to the learning target with veridical visual feedback (baseline). Immediately after, the 3D visuomotor dissociation (horizontal, vertical and sagittal translations) between actual hand motions and visual feedback of hand motions in the 3D virtual environment was gradually introduced (learning phase). Finally, subjects aimed at the pre-exposure and baseline targets without visual feedback (post-exposure). Although subjects were unaware of the visuomotor perturbation, they showed movement adaptation for each component of the triaxial perturbation, but they displayed reduced adaptation rate along the vertical axis. Subjects persisted in applying the new visuomotor association when the perturbation was removed, but the magnitude of this post-exposure shift was lower along the vertical axis. Similar trends were observed for movement aimed at pre-exposure targets. Furthermore, these post-exposure shifts were, on average, greater along the horizontal and sagittal axes relative to the vertical axis. These results suggest that the visuomotor map may be more adaptable to shifts in the horizontal and sagittal directions, than to shifts in the vertical direction. This finding supports the idea that the brain may employ a modular decomposition strategy during learning to simplify complex multidimensional visuomotor tasks.

Ces dernières années, l'importance cruciale des métriques en apprentissage automatique a mené à un intérêt grandissant pour l'optimisation de distances et de similarités en utilisant l'information contenue dans des données d'apprentissage pour les rendre adaptées au problème traité. Ce domaine de recherche est souvent appelé apprentissage de métriques. En général, les méthodes existantes optimisent les paramètres d'une métrique devant respecter des contraintes locales sur les données d'apprentissage. Les métriques ainsi apprises sont généralement utilisées dans des algorithmes de plus proches voisins ou de clustering.Concernant les données numériques, beaucoup de travaux ont porté sur l'apprentissage de distance de Mahalanobis, paramétrisée par une matrice positive semi-définie. Les méthodes récentes sont capables de traiter des jeux de données de grande taille.Moins de travaux ont été dédiés à l'apprentissage de métriques pour les données structurées (comme les chaînes ou les arbres), car cela implique souvent des procédures plus complexes. La plupart des travaux portent sur l'optimisation d'une notion de distance d'édition, qui mesure (en termes de nombre d'opérations) le coût de transformer un objet en un autre.Au regard de l'état de l'art, nous avons identifié deux limites importantes des approches actuelles. Premièrement, elles permettent d'améliorer la performance d'algorithmes locaux comme les k plus proches voisins, mais l'apprentissage de métriques pour des algorithmes globaux (comme les classifieurs linéaires) n'a pour l'instant pas été beaucoup étudié. Le deuxième point, sans doute le plus important, est que la question de la capacité de généralisation des méthodes d'apprentissage de métriques a été largement ignorée.Dans cette thèse, nous proposons des contributions théoriques et algorithmiques qui répondent à ces limites. Notre première contribution est la construction d'un nouveau noyau construit à partir de probabilités d'édition apprises. A l'inverse d'autres noyaux entre chaînes, sa validité est garantie et il ne comporte aucun paramètre. Notre deuxième contribution est une nouvelle approche d'apprentissage de similarités d'édition pour les chaînes et les arbres inspirée par la théorie des (epsilon,gamma,tau)-bonnes fonctions de similarité et formulée comme un problème d'optimisation convexe. En utilisant la notion de stabilité uniforme, nous établissons des garanties théoriques pour la similarité apprise qui donne une borne sur l'erreur en généralisation d'un classifieur linéaire construit à partir de cette similarité. Dans notre troisième contribution, nous étendons ces principes à l'apprentissage de métriques pour les données numériques en proposant une méthode d'apprentissage de similarité bilinéaire qui optimise efficacement l'(epsilon,gamma,tau)-goodness. La similarité est apprise sous contraintes globales, plus appropriées à la classification linéaire. Nous dérivons des garanties théoriques pour notre approche, qui donnent de meilleurs bornes en généralisation pour le classifieur que dans le cas des données structurées. Notre dernière contribution est un cadre théorique permettant d'établir des bornes en généralisation pour de nombreuses méthodes existantes d'apprentissage de métriques. Ce cadre est basé sur la notion de robustesse algorithmique et permet la dérivation de bornes pour des fonctions de perte et des régulariseurs variés / In recent years, the crucial importance of metrics in machine learningalgorithms has led to an increasing interest in optimizing distanceand similarity functions using knowledge from training data to make them suitable for the problem at hand.This area of research is known as metric learning. Existing methods typically aim at optimizing the parameters of a given metric with respect to some local constraints over the training sample. The learned metrics are generally used in nearest-neighbor and clustering algorithms.When data consist of feature vectors, a large body of work has focused on learning a Mahalanobis distance, which is parameterized by a positive semi-definite matrix. Recent methods offer good scalability to large datasets.Less work has been devoted to metric learning from structured objects (such as strings or trees), because it often involves complex procedures. Most of the work has focused on optimizing a notion of edit distance, which measures (in terms of number of operations) the cost of turning an object into another.We identify two important limitations of current supervised metric learning approaches. First, they allow to improve the performance of local algorithms such as k-nearest neighbors, but metric learning for global algorithms (such as linear classifiers) has not really been studied so far. Second, and perhaps more importantly, the question of the generalization ability of metric learning methods has been largely ignored.In this thesis, we propose theoretical and algorithmic contributions that address these limitations. Our first contribution is the derivation of a new kernel function built from learned edit probabilities. Unlike other string kernels, it is guaranteed to be valid and parameter-free. Our second contribution is a novel framework for learning string and tree edit similarities inspired by the recent theory of (epsilon,gamma,tau)-good similarity functions and formulated as a convex optimization problem. Using uniform stability arguments, we establish theoretical guarantees for the learned similarity that give a bound on the generalization error of a linear classifier built from that similarity. In our third contribution, we extend the same ideas to metric learning from feature vectors by proposing a bilinear similarity learning method that efficiently optimizes the (epsilon,gamma,tau)-goodness. The similarity is learned based on global constraints that are more appropriate to linear classification. Generalization guarantees are derived for our approach, highlighting that our method minimizes a tighter bound on the generalization error of the classifier. Our last contribution is a framework for establishing generalization bounds for a large class of existing metric learning algorithms. It is based on a simple adaptation of the notion of algorithmic robustness and allows the derivation of bounds for various loss functions and regularizers.

Les grammaires de construction postulent l’émergence progressive des structures du langage via l’utilisation de processus cognitifs généraux. Les hypothèses théoriques qui en émanent suggèrent que la complexité et la structure des formes morphosyntaxiques ne peuvent s’expliquer que dans une perspective constructiviste, où l’enfant développe ses nouvelles formes en complexifiant et en généralisant ses propres productions antérieures. Ces hypothèses ont été éprouvées auprès de populations présentant un développement typique du langage (DTL) mais ont peu fait l’objet d’une mise en application auprès d’enfants avec troubles spécifiques du langage (TSL). Or, ces théories offrent de nouvelles perspectives théoriques permettant de mieux appréhender leurs difficultés langagières. Ces enfants présentent un manque de productivité syntaxique ainsi qu’une plus grande dépendance à l’input linguistique, allant dans le sens d’un manque de généralisation des schémas de construction. Nous suggérons que, contrairement aux enfants avec DTL, l’abstraction des schémas de construction des enfants avec TSL serait entravée en raison d’un mécanisme de généralisation qui se mettrait en place plus lentement. Ce travail de thèse a pour objectif de tester cette hypothèse chez les enfants avec TSL, en s’intéressant plus particulièrement au rôle du mapping analogique. Les résultats obtenus sont prometteurs et compatibles avec cette hypothèse. Si l’étude du mapping analogique comme facteur à l’origine des difficultés des enfants avec TSL est particulièrement séduisante, de nombreuses pistes restent à explorer pour appuyer davantage notre hypothèse. / Construction grammars argue that language structures progressively emerge thanks to the use of general cognitive processes. Theoretical hypotheses suggest that complexity and structure of morphosyntactic forms can only be explained in a constructivist perspective in which children develop their new forms by making more complex and generalizing their own prior utterances. These hypotheses have been already tested with children with typical language development (TLD) but few studies were interested in children with specific language impairment (SLI). These hypotheses give new interesting theoretical perspectives for apprehending their language disorders better. Children with SLI present a lack of syntactic productivity and a more important input dependency. These observations are compatible with the hypothesis of a lack of generalization of construction schemas. Consequently, the children’s abstraction of construction schemas would be slowed down compared to children with TLD’s abstraction. The current doctoral thesis studies the hypothesis of a lack of generalization in children with SLI by analyzing more particularly the role of analogical mapping. The results obtained are promising and in agreement with our hypothesis. If studies about the role of analogical mapping as a factor explaining the disorders in children with SLI are attractive, other considerations have still to be explored for strengthening our hypotheses.

O processo de mineração de dados tem como objetivo encontrar o conhecimento implícito em um conjunto de dados para auxiliar a tomada de decisão. Do ponto de vista do usuário, vários problemas podem ser encontrados durante a etapa de pós-processamento e disponibilização do conhecimento extraído, como a enorme quantidade de padrões gerados por alguns algoritmos de extração e a dificuldade na compreensão dos modelos extraídos dos dados. Além do problema da quantidade de regras, os algoritmos tradicionais de regras de associação podem levar à descoberta de conhecimento muito específico. Assim, pode ser realizada a generalização das regras de associação com o intuito de obter um conhecimento mais geral. Neste projeto é proposta uma metodologia interativa que auxilie na avaliação de regras de associação generalizadas, visando melhorar a compreensibilidade e facilitar a identificação de conhecimento interessante. Este auxílio é realizado por meio do uso de técnicas de visualização em conjunto com a aplicação medidas de avaliação objetivas e subjetivas, que estão implementadas no módulo de visualização de regras de associação generalizados denominado RulEE-GARVis, que está integrado ao ambiente de exploração de regras RulEE (Rule Exploration Environment). O ambiente RulEE está sendo desenvolvido no LABIC-ICMC-USP e auxilia a etapa de pós-processamento e disponibilização de conhecimento. Neste contexto, também foi objetivo deste projeto de pesquisa desenvolver o Módulo de Gerenciamento do ambiente de exploração de regras RulEE. Com a realização do estudo dirigido, foi possível verificar que a metodologia proposta realmente facilita a compreensão e a identificação de regras de associação generalizadas interessantes / The data mining process aims at finding implicit knowledge in a data set to aid in a decision-making process. From the users point of view, several problems can be found at the stage of post-processing and provision of the extracted knowledge, such as the huge number of patterns generated by some of the extraction algorithms and the difficulty in understanding the types of the extracted data. Besides the problem of the number of rules, the traditional algorithms of association rules may lead to the discovery of very specific knowledge. Thus, the generalization of association rules can be realized to obtain a more general knowledge. In this project an interactive methodology is proposed to aid in the evaluation of generalized association rules in order to improve the understanding and to facilitate the identification of interesting knowledge. This aid is accomplished through the use of visualization techniques along with the application of objective and subjective evaluation measures, which are implemented in the visualization module of generalized association rules called RulEE-GARVis, which is integrated with the Rule Exploration Environment RulEE. The RulEE environment is being developed at LABIC-ICMC-USP and aids in the post-processing and provision of knowledge. In this context, it was also the objective of this research project to develop the Module Management of the rule exploration environment RulEE. Through this directed study, it was verified that the proposed methodology really facilitates the understanding and identification of interesting generalized association rules

A partir de um levantamento do conceito de conceito na filosofia e da polissemia da noção de generalização em várias áreas do conhecimento, chegamos à conclusão de que a última questão não se encontra problematizada na literatura consultada. Tal fato pode ser reflexo de considerações do senso comum sobre o processo de generalização, fazendo com que não haja \"razão aparente\" para discuti-lo. A grande maioria dos trabalhos tem por generalização o processo indutivo em si ou a conclusão a partir dele. Outros trabalhos, particularmente referentes às obras de Vigotski, associam generalização à descontextualização. Segundo nossa reflexão, tais modos de ver a generalização podem ser encontrados em trabalhos de fundamentação da Teoria do Perfil Conceitual (MORTIMER, 1994a, 1994b, 1995, 1998, 2000). A partir de referenciais teóricos ligados ao materialismo dialético, à psicologia histórico-cultural e à complexidade, discutimos as limitações do modelo de perfil e propomos de que maneira a noção de generalização entendida sob uma abordagem dialético-complexa de ensinoaprendizagem é capaz de trazer nova luz à dinâmica das zonas do perfil e à relação sujeito-objeto. / From an investigation about the concept of concept in philosophy and the polysemy of generalization in several knowledge areas, we have reached the conclusion that the last topic is not problematized in the literature studied. Such a fact may be a reflex of common sense consideration concerning the process of generalization, making people conclude that there is no \"appearant reason\" to discuss it. The vast majority of the works investigated understand generalization as the inductive process per se or the conclusion obtained from it. Other works, particularly referring to Vigotski´s ideas, associate generalization to decontextualization. According to our reflections, such ways to consider generalization have been found in works basing the Conceptual Profile Theory (MORTIMER, 1994a, 1994b, 1995, 1998, 2000). From theoretical frameworks related to dialectic materialism, cultural-historical psychology and complexity, we discuss the limitations of the conceptual profile model and we talk about the way in which generalization, seen under a dialectic-complex approach of the teaching-learning process, is able to shed some light to the dynamics of the conceptual profile zones and to the subject-object relation.

Submitted by Maria Cristina (library@lncc.br) on 2017-04-06T18:25:05Z No. of bitstreams: 1 Klaus_Thesis.pdf: 4909850 bytes, checksum: cd68a30c3bae22dc6ea75b6cb4dc6368 (MD5) / Approved for entry into archive by Maria Cristina (library@lncc.br) on 2017-04-06T18:25:18Z (GMT) No. of bitstreams: 1 Klaus_Thesis.pdf: 4909850 bytes, checksum: cd68a30c3bae22dc6ea75b6cb4dc6368 (MD5) / Made available in DSpace on 2017-04-06T18:25:28Z (GMT). No. of bitstreams: 1 Klaus_Thesis.pdf: 4909850 bytes, checksum: cd68a30c3bae22dc6ea75b6cb4dc6368 (MD5) Previous issue date: 2016-06-22 / Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) / Different graph generalizations have been recently used in an ad hoc manner to represent time-varying complex networks, i.e. networks in which vertices and edges may vary in time. Similar constructions have also been used to represent multilayer networks, i.e. systems formed by distinct interdependent layers where each layer can be seen as a complex network. In this thesis, we introduce the concept of MultiAspect Graph (MAG). We show that a MAG is isomorphic to a directed graph, which is an important theoretical result because this allows the use of the isomorphic directed graph as a tool to analyze both the properties of a MAG and the behavior of dynamic processes over a MAG. In our proposal, the set of vertices, layers, time instants, or any other independent feature of the system being modelled is considered as an aspect of the MAG. For instance, a MAG is able to represent multilayer or time-varying networks, while both concepts can also be combined to represent a multilayer time-varying network. Since the MAG structure admits an arbitrary (finite) number of aspects, it hence introduces a powerful modelling abstraction for networked complex systems. Further, we present algebraic representations and basic algorithms for MAGs, constructed from well-known graph algorithms, such as degree computing, Breadth First Search (BFS), and Depth First Search (DFS). These algorithms adapted to the MAG context can be used as primitives for building other more sophisticated MAG algorithms. Building upon the basic MAG concept, we also present derived applications, such as a MAG-based unifying model for time-varying graphs as well as MAG-based centrality notions. / Recentemente, várias generalizações de grafos têm sido propostas para tratar problemas específicos envolvendo redes complexas variantes no tempo e redes complexas multi-camadas. Essas representações são propostas de maneira adequada para resolver problemas específicos, mas não são adequadas para uso geral e muitas vezes são incompatíveis entre si. Nesta tese apresentamos o conceito de Grafo Multi-Aspectos (MAG), que é uma generalização de grafos capaz de representar redes variantes no tempo, redes multi-camadas e redes simultaneamente multi-camadas e variantes no tempo. Mostramos que todo MAG é isomorfo a um grafo direcionado, o que é um importante resultado teórico. Com base nesse resultado é possível utilizar o conhecimento previamente obtido em teoria de grafos para problemas envolvendo MAGs. Dessa maneira, torna-se possível criar representações algébricas para MAGs com características semelhantes às encontradas nas representações para grafos orientados. Além disso, pode-se construir algoritmos básicos para MAGs através da adaptação de algoritmos conhecidos para grafos. Esses algoritmos básicos podem servir como modelo para criação de outros algoritmos para MAGs, bem como serem utilizados como primitivas para construção de novos algoritmos. Utilizando essas primitivas, introduzimos o conceito de centralidades em MAGs, bem como construimos algoritmos apropriadas para calcular essas centralidades.

Made available in DSpace on 2016-04-27T16:57:17Z (GMT). No. of bitstreams: 1 Juliano de Paula Mineli.pdf: 2480017 bytes, checksum: e6777d50d1d15cbae78249914a247c2f (MD5) Previous issue date: 2012-06-15 / This research aimed to study the formation of skills of elementary school students to solve problems, or more specifically, problems whose solutions can be expressed by 1st order equations. My teaching experience has made me raise a hypothesis that the difficulties that students encountered in the organization of the equation, related to the situations of Generalization of Patterns. From then define the objectives of this research is to: investigate problems related to skills training for the Generalization of Patterns and teaching situations to facilitate the training. For data collection, drafted a sequence containing three Curriculum Activities supported on the elements of Fractal Geometry, with a view to generalization of Standards and their implementation based on the Theory of Didactic Situations of Brousseau - theoretical framework used in this research.This sequence was applied in seven sessions to a class of 7th grade (6th grade) of a private Institution located in the city of Ribeirão Preto.This is a qualitative research study using a methodology supported by the Didactic Engineering. The observations and analyzes showed that: the characteristics of fractal figures provide pattern recognition, pattern recognition encourages students to make generalization, the use of geometric shapes provides better organization of data from a mathematical problem, which favors their resolution; generalization of a given situation helps the development of algebraic thinking as well as their attitudes and autonomy in order to observe, raising conjectures, draw conclusions and justify their answers / Esta pesquisa objetivou estudar formação de habilidades de estudantes do Ensino Fundamental para resolver problemas, ou mais especificamente problemas cujas soluções podem ser expressas por equações do 1º grau. Minha experiência docente me fez levantar uma hipótese de que as dificuldades que os estudantes encontravam, na organização da equação, relacionavam-se à situações de Generalização de Padrões. A partir daí definimos os objetivos desta pesquisa que são: investigar dificuldades relacionadas à formação de habilidades para a Generalização de Padrões e de situações de ensino facilitadoras para essa formação. Para a coleta de dados, elaborei uma Sequência Didática contendo três Atividades apoiadas nos elementos da Geometria Fractal, tendo em vista a Generalização de Padrões e sua aplicação baseada na Teoria das Situações Didáticas de Brousseau referenciais teóricos utilizados nesta pesquisa. Essa Sequência foi aplicada em sete sessões a uma turma do 7° ano (6ª série) de uma instituição privada situada na cidade de Ribeirão Preto. Trata-se de uma pesquisa de caráter qualitativo com metodologia apoiada na Engenharia Didática. Como conclusão podemos apontar que: as características das figuras fractais propiciam o reconhecimento de padrões; o reconhecimento de padrões favorece ao aluno realizar generalização; a utilização de figuras geométricas propicia melhor organização dos dados de um problema matemático, o que favorece sua resolução; a generalização de uma dada situação auxilia o desenvolvimento do pensamento algébrico, bem como suas atitudes e autonomia no sentido de observar, levantar conjecturas, tirar conclusões e justificar suas respostas