O estudo e observação de Sistemas Químicos Oscilantes vêm se destacando como importante campo de pesquisa da ciência química contemporânea. Tais sistemas têm como comportamento notório principal a variação periódica da concentração de um intermediário de reação química. Sua compreensão vem estimulando debates que transcendem o escopo químico e estabelecem relações com outras disciplinas científicas, e mais marcadamente, o estudo de sistemas complexos em geral. O ensino de sistemas químicos oscilantes, em específico, e de sistemas complexos, em geral, se apresenta na atualidade como desafio necessário e estimulante. Neste trabalho optou-se por tentar contribuir neste esforço, utilizando-se da noção de obstáculos epistemológicos inicialmente estabelecida pelo filósofo francês Gastón Bachelard. O conceito de obstáculos epistemológicos apresentou-se nas últimas décadas como importante ferramenta na abordagem das relações de ensino-aprendizagem de conceitos das ciências contemporâneas. Existem diferentes tipos de obstáculos epistemológicos, entre eles: experiência primeira, conhecimento geral, obstáculo verbal, conhecimento unitário e pragmático e obstáculo animista. Neste trabalho surge a proposta de utilizar a noção de obstáculo epistemológico voltada ao ensino de conceitos da complexidade pertinentes aos Sistemas Químicos Oscilantes. Foram analisadas as presenças de obstáculos epistemológicos em textos didáticos de ensino de sistemas químicos oscilantes. Os textos didáticos escolhidos foram artigos científicos da área de ensino de química voltados ao ensino de sistemas químicos oscilantes, livros didáticos usados em cursos de graduação e livros de divulgação científica. Foram analisados os conteúdos integrais de sete artigos científicos da área de ensino de química voltados ao tema reações químicas oscilantes. Foram também analisadas as seções referentes a reações químicas oscilantes de quatro livros didáticos utilizados em cursos de graduação da USP devotadas ao ensino de sistemas caóticos. Foram também analisadas as seções referentes a reações químicas oscilantes de quatro livros de divulgação científica que abordaram o tema sistemas químicos oscilantes. Foram encontrados grande número de obstáculos da experiência primeira e obstáculos animistas em livros didáticos e um grande número de obstáculos verbais em livros de divulgação científica. Todos os tipos de obstáculos epistemológicos listados foram identificados ao menos uma vez em algum dos textos. Demonstrou-se a viabilidade de aplicação do conceito de obstáculos epistemológicos em textos didáticos de ensino de sistemas químicos oscilantes. / The study and observation of Oscillating Chemical Systems have been highlighted as an important research field of chemical science contemporary. Such systems are notorious behavior as the main periodic variation of the concentration of an intermediate chemical reaction. Your understanding is stimulating debates that transcend the scope of chemical and establish relationships with other scientific disciplines, and most notably, the study of complex systems in general. The teaching of chemical oscillating systems, in particular, and complex systems in general, is presented nowadays as necessary and stimulating challenge. In this work it was decided to try to contribute in this effort, using the notion of epistemological obstacles initially established by the philosopher Gaston Bachelard. The concept of epistemological obstacle presented itself in recent decades as an important tool in addressing the relationships of teaching and learning of contemporary science concepts. There are different kinds of epistemological obstacles, among them: first experience, geral knowledge, verbal obstacle, pragmatic and unitary knowledge and animist obstacle . This work comes propose to use the notion of epistemological obstacle to teach the complexity of concepts relevant to oscillating chemical system .We analyzed the presence of epistemological obstacles in textbooks that have teaching oscillating chemical systems. The selected texts were scientific articles in the area of chemical education aimed at teaching oscillating chemical systems, books used in undergraduate and some popular science books. We analyzed the entire contents of seven papers in the area of chemical education geared to the theme oscillating chemical reactions. We also analyzed the sections pertaining to oscillating chemical reactions of four textbooks used in undergraduate courses devoted to teaching the chaotic systems at USP . We also analyzed the sections pertaining to oscillating chemical reactions of four popular science books that addressed the issue of oscillating chemical systems. We found many first experiences and animists obstacles in textbooks and a large number of verbal obstacles in popular science books. All kinds of epistemological obstacles identified were listed at least once at some of the texts. The results confirm the feasibility of applying the concept of epistemological obstacles in textbooks teaching oscillating chemical systems.

O estudo e observação de Sistemas Químicos Oscilantes vêm se destacando como importante campo de pesquisa da ciência química contemporânea. Tais sistemas têm como comportamento notório principal a variação periódica da concentração de um intermediário de reação química. Sua compreensão vem estimulando debates que transcendem o escopo químico e estabelecem relações com outras disciplinas científicas, e mais marcadamente, o estudo de sistemas complexos em geral. O ensino de sistemas químicos oscilantes, em específico, e de sistemas complexos, em geral, se apresenta na atualidade como desafio necessário e estimulante. Neste trabalho optou-se por tentar contribuir neste esforço, utilizando-se da noção de obstáculos epistemológicos inicialmente estabelecida pelo filósofo francês Gastón Bachelard. O conceito de obstáculos epistemológicos apresentou-se nas últimas décadas como importante ferramenta na abordagem das relações de ensino-aprendizagem de conceitos das ciências contemporâneas. Existem diferentes tipos de obstáculos epistemológicos, entre eles: experiência primeira, conhecimento geral, obstáculo verbal, conhecimento unitário e pragmático e obstáculo animista. Neste trabalho surge a proposta de utilizar a noção de obstáculo epistemológico voltada ao ensino de conceitos da complexidade pertinentes aos Sistemas Químicos Oscilantes. Foram analisadas as presenças de obstáculos epistemológicos em textos didáticos de ensino de sistemas químicos oscilantes. Os textos didáticos escolhidos foram artigos científicos da área de ensino de química voltados ao ensino de sistemas químicos oscilantes, livros didáticos usados em cursos de graduação e livros de divulgação científica. Foram analisados os conteúdos integrais de sete artigos científicos da área de ensino de química voltados ao tema reações químicas oscilantes. Foram também analisadas as seções referentes a reações químicas oscilantes de quatro livros didáticos utilizados em cursos de graduação da USP devotadas ao ensino de sistemas caóticos. Foram também analisadas as seções referentes a reações químicas oscilantes de quatro livros de divulgação científica que abordaram o tema sistemas químicos oscilantes. Foram encontrados grande número de obstáculos da experiência primeira e obstáculos animistas em livros didáticos e um grande número de obstáculos verbais em livros de divulgação científica. Todos os tipos de obstáculos epistemológicos listados foram identificados ao menos uma vez em algum dos textos. Demonstrou-se a viabilidade de aplicação do conceito de obstáculos epistemológicos em textos didáticos de ensino de sistemas químicos oscilantes. / The study and observation of Oscillating Chemical Systems have been highlighted as an important research field of chemical science contemporary. Such systems are notorious behavior as the main periodic variation of the concentration of an intermediate chemical reaction. Your understanding is stimulating debates that transcend the scope of chemical and establish relationships with other scientific disciplines, and most notably, the study of complex systems in general. The teaching of chemical oscillating systems, in particular, and complex systems in general, is presented nowadays as necessary and stimulating challenge. In this work it was decided to try to contribute in this effort, using the notion of epistemological obstacles initially established by the philosopher Gaston Bachelard. The concept of epistemological obstacle presented itself in recent decades as an important tool in addressing the relationships of teaching and learning of contemporary science concepts. There are different kinds of epistemological obstacles, among them: first experience, geral knowledge, verbal obstacle, pragmatic and unitary knowledge and animist obstacle . This work comes propose to use the notion of epistemological obstacle to teach the complexity of concepts relevant to oscillating chemical system .We analyzed the presence of epistemological obstacles in textbooks that have teaching oscillating chemical systems. The selected texts were scientific articles in the area of chemical education aimed at teaching oscillating chemical systems, books used in undergraduate and some popular science books. We analyzed the entire contents of seven papers in the area of chemical education geared to the theme oscillating chemical reactions. We also analyzed the sections pertaining to oscillating chemical reactions of four textbooks used in undergraduate courses devoted to teaching the chaotic systems at USP . We also analyzed the sections pertaining to oscillating chemical reactions of four popular science books that addressed the issue of oscillating chemical systems. We found many first experiences and animists obstacles in textbooks and a large number of verbal obstacles in popular science books. All kinds of epistemological obstacles identified were listed at least once at some of the texts. The results confirm the feasibility of applying the concept of epistemological obstacles in textbooks teaching oscillating chemical systems.

Philosophiae Doctor - PhD / The purpose of this study was to investigate the epistemological obstacles that mathematics students at undergraduate level encounter in coming to understand the limit concept. The role played by language and symbolism in understanding the limit concept was also investigated. A group of mathematics students at undergraduate level at the National University of Lesotho (NUL) was used as the sample for the study. Empirical data were collected by using interviews and questionnaires. These data were analysed using both the APOS framework and a semiotic perspective. Within the APOS framework, the pieces of knowledge that have to be constructed in coming to understand the limit concept are actions, processes and objects. Actions are interiorised into processes and processes are encapsulated into objects. The conceptual structure is called a schema. In investigating the idea of limit within the context of a function some main epistemological obstacles that were encountered when actions were interiorised into processes are over-generalising and taking the limit value as the function value. For example, in finding the limit value L for./{x) as x tends to 0, 46 subjects out of 251 subjects said that they would calculate ./{O) as the limit value. This method is Within the context of a sequence everyday language acted as an epistemological obstacle in interiorising actions into processes. For example, in finding lim (_1)n ,the majority of x~oo n the subjects obtained the correct answer O. It was however revealed that such an answer was obtained by using an inappropriate method. The subjects substituted one big value for n in the formula. The result obtained was the number close to O. Then 0 was taken as the limit value because the subjects interpreted the word 'approaches' as meaning 'nearer to'. Other subjects rounded off the result. In everyday life when one object approaches another, we might say that they are nearer to each other. It seems that in this case the appropriate for calculating the limit values for continuous functions. However, in this case, the method is generalised to all the functions. When these subjects encounter situations in which the functional value is equal to the limit value, they take the two to be the same. However, the two are different entities conceptually. Within the context of a sequence everyday language acted as an epistemological obstacle in interiorising actions into processes. For example, in finding lim (_1)n ,the majority of x~oo n the subjects obtained the correct answer O. It was however revealed that such an answer was obtained by using an inappropriate method. The subjects substituted one big value for n in the formula. The result obtained was the number close to O. Then 0 was taken as the limit value because the subjects interpreted the word 'approaches' as meaning 'nearer to'. Other subjects rounded off the result. In everyday life when one object approaches another, we might say that they are nearer to each other. It seems that in this case the subjects used this meaning to get 0 as the limit value. We also round off numbers to the nearest unit, tenth, etc. The limit value is however a unique value that is found by using the limiting process of 'tending to' or 'approaching' which requires infinite values to be considered. Some are computed and others are contemplated. In constructing the coordinated process schema, f(x) ~ L as x ~ a, over-generalisation and everyday language were still epistemological obstacles. Subjects still perceived the limit value to exist where the function is defined. The limit was also taken as a bound, lower or upper bound. In a case where the function was represented in a tabular form, the first and the seemingly last functional value that appeared in the table of values were chosen as the limit values. Limit values were also approximated. In constructing the coordinated process an ~ L as n ~ 00, representation, generalisation and everyday language also acted as epistemological obstacles. An alternating sequence was perceived as not one but two sequences. Since the subjects will have met situations where convergence means meeting at a point, as in the case of rays of light, a sequence was said to converge to a number that did not change in the given decimal digits. For example, the limit of the sequence {3.1, 3.14, 3.141, 3.1415, ... } was taken to be 3 or 3.1 as these are the digits that are the same in all the terms. In encapsulating processes into objects, everyday language also acted as an epistemological obstacle. When subjects were asked what they understood the limit to be, they said that the limit is a boundary, an endpoint, an interval, or a restriction. Though these interpretations are correct they are however, inappropriate if used in the technical context such as the mathematical context. While some subjects referred to the limit as a noun to show that they refer to it as an object, other subjects described the limit in terms of the processes that give rise to it. That is, it was described in terms of either the domain process or the range process. This is an indication that full encapsulation of processes into objects was not achieved by the subjects. The role of language and symbolism has been identified in making different connections in building the concept of limit as: representation of mathematical objects, translation between modes of representation, communication of mathematical ideas, manipulation of surface or syntactic structures and the overcoming of epistemological obstacles. In representation some subjects were aware of what idea some symbolism signified while other subjects were not. For example, in the context of limit of a sequence, most subjects took the symbolism that represented an alternating sequence, an = (-lr, to represent two sequences. The first sequence was seen as {I, I, 1, 1,... } and the second as {-I, -1, - 1, -1, ... }.This occurred in all modes of representation. In translating from one mode of representation to another, the obscurity of the symbol lim/ex) = L was problematic to the students. This symbol could not be related to its X~a equivalent form lex) ~ L as x ~ a. The equal sign, '=', joining the part lex) and L does not reflect the process ofj{x) tending to L, rather it appears as if it is the functional value that is equal to L. Hence, instead of looking for the value that is approached the subjects chose one of the given functional values. The part of the symbol lim was a x~a source of difficulty in translating the algebraic form to the verbal or descriptive. The subjects saw this part to mean "the limit of x tends to a" rather than seeing the whole symbolism as the limit of j{x) as x tends to a. Some subjects actually wrote some formulae in the place of L because of this structure, e.g., lim/ex) = 2x. These subjects x~a seemed to have concentrated on the part lex) = .... This is probably because they are used to situations where this symbolism is used in representing functions algebraically. In communicating mathematical ideas the same word carried different meanings for the researcher and for the subjects in some cases. For example, when the subjects were asked what it means to say a sequence diverges, one of the interpretations given was that divergence means tending to infinity. So, over-generalisation here acted as an epistemological obstacle. Though a sequence that tends to infinity diverges, this is not the only case of divergence that exists and therefore cannot be generalised in that way. The manipulation of the surface structures was done instrumentally by some subjects. For 1 . ti di 1·.J x 2 examp e, m in mg im +29 - 3 ,urdmugri the mam.pu 1ati.on some subjiects 0 bttaaime d x.... o x 2 part of the expressions such as ~ by rationalising or .:;- by using L'Hospital's rule 2x x which needed to be simplified. Instead of simplifying the expressions further at this stage, the substitution of 0 was done. So, .o2. = 0 was obtained as the answer. This shows that neither the reasons for performing the manipulations, nor the process of rationalising for example was understood. The result was still an indeterminate form of limit. The numerator was also not yet in a rational form. In using language to overcome epistemological obstacles, subjects were exposed to a piece of knowledge that falsified the knowledge they had so that they could rethink replacing the old with the new. In some cases, this was successful but in others, the subjects did not surrender these old pieces of knowledge. For example, when asked what they understood the 'rate of change' to mean, the majority of the subjects associated the rate of change with time only. However, when referred to a situation that required them to find the rate of change of an area with respect to radius, some subjects changed their minds but others did not. Those who did not change their minds probably did not make any connections between ideas under discussion. The implications for practice of the findings include: In teaching one should discuss explicitly how answers to tasks concerning limits are obtained. The idea of the limit value as a unique value can only be recognized if the process by which it is obtained is discussed. It should not be taken for granted that students who respond correctly understand the answers. It is evident from the study that even when correct answers are given, improper methods may have been used. Hence, in investigating epistemological obstacles attention should also be paid to correct answers. Also beyond this, students should be exposed to different kinds of representation of the limit concept using simple functions and using a variety of examples of sequences. Words with dual or multiple meaning should also be discussed in mathematics classrooms so that students may be aware of the meanings they carry in the mathematical context. Different forms of indeterminate states of limit should be given attention. Relations should also be made between the surface structures and the deeper structures.

Este trabalho tem como objetivo contribuir para uma melhor aprendizagem dos alunos da educação básica sobre o conceito dos números inteiros, em particular, a reta numérica. A metodologia utilizada é a pesquisa bibliográfica. Observamos que os documentos oficiais orientam para o uso da história como um elemento que contribui para a aprendizagem, nesse sentido, nos baseamos na ideia de sentidos contrários, dos comerciantes medievais, para entender os sentidos contrários na reta numérica dos números inteiros. Elaboramos uma sequência de atividades para o ensino, inicialmente, da reta dos números naturais que evidenciam seus elementos constitutivos: (a) sua origem, (b) seus sentidos e (c) seus deslocamentos, considerando as várias possibilidades de posição da reta, horizontal, vertical e inclinada. A esses elementos foi possível acrescentar a necessidade da expansão da reta dos números naturais, criando um novo lugar, que necessita de um novo número, os números negativos. Essa nova reta, a dos números inteiros, tem seus elementos constitutivos a partir da reta dos naturais, portanto, é uma expansão dela. Finalizamos com a sugestão de dois materiais didáticos manipuláveis que podem ser propostos como uma complementação da sequência de atividades, visando facilitar o processo de ensino e aprendizagem a fim de diminuir as dificuldades dos alunos nesse campo numérico. / This work aims to contribute to a better learning for students of basic education on the whole numbers, in particular, the numerical line. The methodology used is the bibliographical research. We note that the official documents guide to the use of history as an element that contributes to the learning, in this sense, this work is based on the idea of contrary senses, of medieval traders, to understand the opposite directions in the numerical line of whole numbers. We draw up a sequence of activities for teaching, initially, of the line of the natural numbers that evince its constituent elements: (a) its origin, (b) its directions and (c) its displacements, considering the various possibilities of position of the line, horizontal, vertical and slanted. To these elements it was possible to add the need for the expansion of the line of natural numbers, creating a new place, which needs new numbers, the negative ones. This new line, that of the whole numbers, has its constituent elements from the line of the natural ones, so it is an expansion of it. We conclude with the suggestion of two manipulatable didactic materials that can be proposed as a complement of the sequence of activities, aiming to facilitate the process of teaching and learning, in order to reduce the students a difficulties in this numerical field.

Por meio da análise de versões de textos redigidas por um mesmo sujeito ao longo de um período de onze anos, o quanto podemos compreender a respeito das vicissitudes envolvidas na aprendizagem da escrita do texto acadêmico? Essa pergunta norteou a investigação que deu origem à presente tese cujo objeto voltou-se ao percurso de escrita de um pesquisador em formação. Seu objetivo geral foi, a partir da análise de marcas de reformulação textual em versões de texto, discutir as particularidades do papel da escrita na formação de um pesquisador, papel esse intrinsicamente relacionado com a própria formação em curso. Tomando a psicanálise de orientação lacaniana como nosso principal arcabouço teórico, procuramos dar a ver como o pesquisador estabeleceu relação entre sua palavra e a palavra do outro, nas versões que escreveu para os textos que vieram a ser dois relatórios de iniciação científica, uma dissertação de mestrado e uma tese de doutorado. Com isso, quisemos dar a ver quais foram os pontos de virada pelos quais o pesquisador passou, em diferentes momentos de sua formação, para conseguir construir um lugar próprio para enunciar (RIOLFI; ALAMINOS, 2007). Nossa tese é aquela segundo a qual, por meio da análise das marcas visíveis e invisíveis de formulação textual (GRÉSILLON, 2007), podemos empreender construções em análise (FREUD, 1937) que nos permitem calcular, em nível cognitivo, como o pesquisador está superando os obstáculos epistemológicos que entravam sua reconstrução do conhecimento da modalidade científica (BACHELARD, 1996) e, em nível subjetivo, como, por meio das operações de alienação e separação (LACAN, 1964), colocou-se, emocionalmente, em posição de poder a vir construir novo conhecimento. Com relação aos objetivos específicos tivemos: 1) Analisar as marcas de reformulação textual em versões de texto redigidas por um pesquisador em formação; 2) Analisar, em versões de texto redigidos por um pesquisador em formação, a dinâmica do ultrapassamento de obstáculos epistemológicos em momentos que podem ser qualificados de pontos de virada (RIOLFI; ALAMINOS, 2007); e 3) Estudar a influência que as intervenções realizadas por terceiros (o orientador e colegas de grupo de pesquisa) em versões de texto têm no processo de escrita de textos acadêmicos. A análise de versões de textos permitiu concluir que o ultrapassamento dos obstáculos epistemológicos está ligado à possibilidade de o pesquisador em formação alterar a relação que estabelece com o conhecimento. Para tanto, ele precisa submeter suas impressões iniciais a uma rede simbólica, reformulando o que escreveu. / By means of the analysis of text versions written by the same person over eleven years, what can be comprehended about the vicissitudes related to the learning of the academic text writing? This question directed the investigation that resulted in this thesis which focus is the writing path of a researcher in training. Its general objective was, through the analysis of marks of textual revision in text versions, discuss the particularities of writing in the training of a researcher, being writing intrinsically related to the training ongoing. Taking Lacanian psychoanalysis as our main theoretical framework, we attempted to demonstrate how the researcher stablished a relationship between his own words and the others in the text versions that became two undergraduate research reports, a master dissertation and a PhD thesis. Thus, we intended to demonstrate the turning points by which the researcher passed though in different moments of his training in order to construct a proper place to express himself (RIOLFI; ALAMINOS, 2007). Our thesis is that though the analysis of the visible and the invisible signs of textual formulation (GRÉSILLON, 2007) it is possible to undertake constructions in analysis (FREUD, 1937) that allow us to calculate, cognitively, how the researcher is overcoming the epistemological obstacles that impede his knowledge reconstruction of the scientific modality (BACHELARD, 1996) and, subjectively, how, through the operations of alienation and separation (LACAN, 1964), the researcher put himself, emotionally, in order to be able to construct new knowledge. With regard to the specific objectives, we had: 1) Analyze the marks of textual revision in text versions written by a training researcher; 2) Analyze, in text versions written by a training researcher, the dynamic of overcoming the epistemological obstacles in moments that can be considered turning points (RIOLFI; ALAMINOS, 2007); and 3) Study the influence the interventions made by others (the supervisor and research group colleagues) in text versions had in the writing process of academic texts. The analysis of text versions allowed us to conclude that the surpassing of the epistemological obstacles is related to the possibility of the training researcher changing the relation he stablishes with knowledge. In order to do so, he needs to submit his initial impressions to a symbolic net, reformulating what had written.

Por meio da análise de versões de textos redigidas por um mesmo sujeito ao longo de um período de onze anos, o quanto podemos compreender a respeito das vicissitudes envolvidas na aprendizagem da escrita do texto acadêmico? Essa pergunta norteou a investigação que deu origem à presente tese cujo objeto voltou-se ao percurso de escrita de um pesquisador em formação. Seu objetivo geral foi, a partir da análise de marcas de reformulação textual em versões de texto, discutir as particularidades do papel da escrita na formação de um pesquisador, papel esse intrinsicamente relacionado com a própria formação em curso. Tomando a psicanálise de orientação lacaniana como nosso principal arcabouço teórico, procuramos dar a ver como o pesquisador estabeleceu relação entre sua palavra e a palavra do outro, nas versões que escreveu para os textos que vieram a ser dois relatórios de iniciação científica, uma dissertação de mestrado e uma tese de doutorado. Com isso, quisemos dar a ver quais foram os pontos de virada pelos quais o pesquisador passou, em diferentes momentos de sua formação, para conseguir construir um lugar próprio para enunciar (RIOLFI; ALAMINOS, 2007). Nossa tese é aquela segundo a qual, por meio da análise das marcas visíveis e invisíveis de formulação textual (GRÉSILLON, 2007), podemos empreender construções em análise (FREUD, 1937) que nos permitem calcular, em nível cognitivo, como o pesquisador está superando os obstáculos epistemológicos que entravam sua reconstrução do conhecimento da modalidade científica (BACHELARD, 1996) e, em nível subjetivo, como, por meio das operações de alienação e separação (LACAN, 1964), colocou-se, emocionalmente, em posição de poder a vir construir novo conhecimento. Com relação aos objetivos específicos tivemos: 1) Analisar as marcas de reformulação textual em versões de texto redigidas por um pesquisador em formação; 2) Analisar, em versões de texto redigidos por um pesquisador em formação, a dinâmica do ultrapassamento de obstáculos epistemológicos em momentos que podem ser qualificados de pontos de virada (RIOLFI; ALAMINOS, 2007); e 3) Estudar a influência que as intervenções realizadas por terceiros (o orientador e colegas de grupo de pesquisa) em versões de texto têm no processo de escrita de textos acadêmicos. A análise de versões de textos permitiu concluir que o ultrapassamento dos obstáculos epistemológicos está ligado à possibilidade de o pesquisador em formação alterar a relação que estabelece com o conhecimento. Para tanto, ele precisa submeter suas impressões iniciais a uma rede simbólica, reformulando o que escreveu. / By means of the analysis of text versions written by the same person over eleven years, what can be comprehended about the vicissitudes related to the learning of the academic text writing? This question directed the investigation that resulted in this thesis which focus is the writing path of a researcher in training. Its general objective was, through the analysis of marks of textual revision in text versions, discuss the particularities of writing in the training of a researcher, being writing intrinsically related to the training ongoing. Taking Lacanian psychoanalysis as our main theoretical framework, we attempted to demonstrate how the researcher stablished a relationship between his own words and the others in the text versions that became two undergraduate research reports, a master dissertation and a PhD thesis. Thus, we intended to demonstrate the turning points by which the researcher passed though in different moments of his training in order to construct a proper place to express himself (RIOLFI; ALAMINOS, 2007). Our thesis is that though the analysis of the visible and the invisible signs of textual formulation (GRÉSILLON, 2007) it is possible to undertake constructions in analysis (FREUD, 1937) that allow us to calculate, cognitively, how the researcher is overcoming the epistemological obstacles that impede his knowledge reconstruction of the scientific modality (BACHELARD, 1996) and, subjectively, how, through the operations of alienation and separation (LACAN, 1964), the researcher put himself, emotionally, in order to be able to construct new knowledge. With regard to the specific objectives, we had: 1) Analyze the marks of textual revision in text versions written by a training researcher; 2) Analyze, in text versions written by a training researcher, the dynamic of overcoming the epistemological obstacles in moments that can be considered turning points (RIOLFI; ALAMINOS, 2007); and 3) Study the influence the interventions made by others (the supervisor and research group colleagues) in text versions had in the writing process of academic texts. The analysis of text versions allowed us to conclude that the surpassing of the epistemological obstacles is related to the possibility of the training researcher changing the relation he stablishes with knowledge. In order to do so, he needs to submit his initial impressions to a symbolic net, reformulating what had written.

Este trabalho tem como objetivo contribuir para uma melhor aprendizagem dos alunos da educação básica sobre o conceito dos números inteiros, em particular, a reta numérica. A metodologia utilizada é a pesquisa bibliográfica. Observamos que os documentos oficiais orientam para o uso da história como um elemento que contribui para a aprendizagem, nesse sentido, nos baseamos na ideia de sentidos contrários, dos comerciantes medievais, para entender os sentidos contrários na reta numérica dos números inteiros. Elaboramos uma sequência de atividades para o ensino, inicialmente, da reta dos números naturais que evidenciam seus elementos constitutivos: (a) sua origem, (b) seus sentidos e (c) seus deslocamentos, considerando as várias possibilidades de posição da reta, horizontal, vertical e inclinada. A esses elementos foi possível acrescentar a necessidade da expansão da reta dos números naturais, criando um novo lugar, que necessita de um novo número, os números negativos. Essa nova reta, a dos números inteiros, tem seus elementos constitutivos a partir da reta dos naturais, portanto, é uma expansão dela. Finalizamos com a sugestão de dois materiais didáticos manipuláveis que podem ser propostos como uma complementação da sequência de atividades, visando facilitar o processo de ensino e aprendizagem a fim de diminuir as dificuldades dos alunos nesse campo numérico. / This work aims to contribute to a better learning for students of basic education on the whole numbers, in particular, the numerical line. The methodology used is the bibliographical research. We note that the official documents guide to the use of history as an element that contributes to the learning, in this sense, this work is based on the idea of contrary senses, of medieval traders, to understand the opposite directions in the numerical line of whole numbers. We draw up a sequence of activities for teaching, initially, of the line of the natural numbers that evince its constituent elements: (a) its origin, (b) its directions and (c) its displacements, considering the various possibilities of position of the line, horizontal, vertical and slanted. To these elements it was possible to add the need for the expansion of the line of natural numbers, creating a new place, which needs new numbers, the negative ones. This new line, that of the whole numbers, has its constituent elements from the line of the natural ones, so it is an expansion of it. We conclude with the suggestion of two manipulatable didactic materials that can be proposed as a complement of the sequence of activities, aiming to facilitate the process of teaching and learning, in order to reduce the students a difficulties in this numerical field.

Made available in DSpace on 2014-06-11T19:24:18Z (GMT). No. of bitstreams: 0 Previous issue date: 2010-08-03Bitstream added on 2014-06-13T20:12:26Z : No. of bitstreams: 1 bocanegra_ch_me_rcla.pdf: 669995 bytes, checksum: 85084cdd66592ae6df44ca61d0b149a8 (MD5) / Neste trabalho, foram analisados os aspectos conceituais e epistemológicos do tema Eletroquímica contidos nos livros didáticos de Química aprovados pelo Programa Nacional do Livro Didático para o Ensino Médio (PNLEM) em 2007. Essa análise foi efetuada tendo em conta a correção das estruturas conceituais que compõem esse tópico e os obstáculos epistemológicos bachelardianos aí presentes. Foram consideradas quatro categorias de obstáculos, a saber: animistas, realistas, substancialistas e verbais. Os procedimentos de coleta e análise de dados foram baseados em abordagens de natureza qualitativa. Os principais resultados obtidos indicam a presença de algumas distorções conceituais relacionadas, principalmente, com o conceito de potencial ou diferença de potencial do eletrodo e, também, com as descrições realistas relacionadas à previsão das reações redox em processos eletrolíticos. Em particular, o conceito de potencial e seus contornos teóricos merecem maior atenção por parte dos autores dos livros didáticos. Neste caso, observamos que, em pelo menos um manual, o equívoco conceitual cometido comprometeu a compreensão dos sequenciamentos teóricos ulteriores elaborados. Quanto à previsão das reações redox, observamos que metade dos manuais didáticos analisados a abordou, considerando o desenvolvimento de regras e tabelas práticas com o propósito de mostrar ao estudante a influência de diferentes fatores sobre os processos eletrolíticos mais complexos. No entanto, este procedimento engendrou generalizações precipitadas sobre as causas que determinaram a deposição de certo metal sobre um eletrodo ou a tendência de descarga de uma espécie química sobre uma outra. O uso deste procedimento pedagógico também favoreceu interpretações equivocadas quanto à previsão de ocorrência de certos processos eletrolíticos, além de conduzir o leitor a um... / In this work, we analyzed the epistemological and conceptual aspects of the topic electrochemistry contained in textbooks of chemistry approved by the National Textbook Program for high school (PNLEM) in 2007. This analysis was performed taking into account the correction of the conceptual structures that make up these topics and the Bachelardian epistemological obstacles present in these structures. We considered four categories of obstacles, namely: animist, realistic, substancialistic and verbal. The procedures to collect and analyze data were based on qualitative approaches. The main results indicate the presence of some conceptual distortions mainly related to the concept of potential or difference of potential of the electrode and also to the realistic descriptions related to forecast of redox reactions in the electrolytic process. In particular, the concept of potential and its theoretical field deserve more attention by the authors of the textbooks. In this case, we observed that in at least one textbook the conceptual mistake made affected the understanding of the theoretical issue order further developed. We observed that in half of the analyzed teaching materials the forecast of redox reactions was reported considering the development of practical rules and tables in order to show students the influence of different factors on the more complex electrolytic processes. However, this procedure engendered hasty generalizations about the causes that led to the deposition of some metal on an electrode or a preference for the disposal of a chemical species on another one. In this case, the use of this procedure favored misinterpretations in relation to predict the occurrence of certain electrolytic processes, and lead the reader to a distorted understanding of the production process of scientific knowledge. In summary, we found a significant amount of conceptual distortions... (Complete abstract click electronic access below)

Made available in DSpace on 2014-12-17T14:36:24Z (GMT). No. of bitstreams: 1 MerciaOP_TESE.pdf: 1133404 bytes, checksum: 81953bfb8e7bacc94a6b29fea8929367 (MD5) Previous issue date: 2010-12-22 / Coordena??o de Aperfei?oamento de Pessoal de N?vel Superior / In Mathematics literature some records highlight the difficulties encountered in the teaching-learning process of integers. In the past, and for a long time, many mathematicians have experienced and overcome such difficulties, which become epistemological obstacles imposed on the students and teachers nowadays. The present work comprises the results of a research conducted in the city of Natal, Brazil, in the first half of 2010, at a state school and at a federal university. It involved a total of 45 students: 20 middle high, 9 high school and 16 university students. The central aim of this study was to identify, on the one hand, which approach used for the justification of the multiplication between integers is better understood by the students and, on the other hand, the elements present in the justifications which contribute to surmount the epistemological obstacles in the processes of teaching and learning of integers. To that end, we tried to detect to which extent the epistemological obstacles faced by the students in the learning of integers get closer to the difficulties experienced by mathematicians throughout human history. Given the nature of our object of study, we have based the theoretical foundation of our research on works related to the daily life of Mathematics teaching, as well as on theorists who analyze the process of knowledge building. We conceived two research tools with the purpose of apprehending the following information about our subjects: school life; the diagnosis on the knowledge of integers and their operations, particularly the multiplication of two negative integers; the understanding of four different justifications, as elaborated by mathematicians, for the rule of signs in multiplication. Regarding the types of approach used to explain the rule of signs arithmetic, geometric, algebraic and axiomatic , we have identified in the fieldwork that, when multiplying two negative numbers, the students could better understand the arithmetic approach. Our findings indicate that the approach of the rule of signs which is considered by the majority of students to be the easiest one can be used to help understand the notion of unification of the number line, an obstacle widely known nowadays in the process of teaching-learning / Na literatura especializada na ?rea de Matem?tica, existem registros que ressaltam as dificuldades enfrentadas no processo de ensino/aprendizagem de n?meros inteiros. Tais dificuldades, vivenciadas e superadas pelos matem?ticos do passado por um longo per?odo, tornam-se obst?culos epistemol?gicos que se imp?em a alunos e professores na atualidade. Este trabalho cont?m os resultados de uma pesquisa desenvolvida na cidade de Natal (RN) no decorrer no primeiro semestre de 2010, em uma escola p?blica estadual de educa??o b?sica e em uma universidade p?blica federal e envolveu 45 alunos assim discriminados: 20 do ensino fundamental, 9 do ensino m?dio e 16 do ensino superior. Teve-se como objetivo central identificar, de um lado, a abordagem da justificativa da multiplica??o entre n?meros inteiros que ? mais bem compreendida pelos alunos e de outro, os elementos presentes nas justificativas que contribuem para a supera??o dos obst?culos epistemol?gicos nos processos de ensino e aprendizagem de n?meros inteiros. Para tanto, procurou-se determinar em que medida os obst?culos epistemol?gicos enfrentados pelos alunos na aprendizagem de n?meros inteiros aproximam-se das dificuldades vivenciadas pelos matem?ticos ao longo da hist?ria da humanidade. Em decorr?ncia da natureza do objeto de pesquisa buscaram-se, no referencial te?rico, os estudos relativos ao cotidiano do ensino de Matem?tica e os te?ricos que se dedicam ao processo de constru??o do conhecimento. Foram elaborados dois instrumentos de pesquisa com a finalidade de apreender as seguintes informa??es sobre os sujeitos pesquisados: vida estudantil; diagn?stico dos conhecimentos de n?meros inteiros e suas opera??es, em especial da multiplica??o de dois n?meros inteiros negativos; compreens?o de quatro justificativas diferentes elaboradas pelos matem?ticos para a regra dos sinais na multiplica??o. No trabalho de campo identificou-se, dentre as abordagens aritm?tica, geom?trica, alg?brica e axiom?tica dadas ao produto de dois n?meros negativos, que os alunos compreendiam melhor a que usava argumentos aritm?ticos. Os resultados obtidos indicam que a justificativa para a regra de sinais que ? considerada de mais f?cil compreens?o pela maioria dos alunos dos ensinos fundamental, m?dio e superior pode ser usada para facilitar a compreens?o da unifica??o da reta num?rica, um obst?culo amplamente identificado no processo de ensino/aprendizagem na atualidade

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No. of bitstreams: 1 DISSERTACAO-HerminiaMarques-PDF.pdf: 3490839 bytes, checksum: d445f240e85398ed58ede8a6ad243ff2 (MD5) Previous issue date: 2017-11-29 / FAPEAM - Fundação de Amparo à Pesquisa do Estado do Amazonas / In analyzing the learning of scientific concepts in the light of the Science Philosophy according to Gaston Bachelard, it is proposed to understand the obstacles to the development of scientific ideas. The present research had as objective to study the learning difficulties of High School students about the scientific concepts related to the qualitative aspects of the chemical transformations, such as the evidence of formation of new materials, production of gas and light, seeking to evidence the presence of epistemological obstacles the first experience, the premature generalization, the realistic and substantialist obstacle that are hindrances in the signification and resignification of scientific chemical concepts in the school knowledge. The research was carried out in a public state school in the city of Manaus with students from the 1st grade of High School, based on a didactic sequence with teaching methodologies and investigative learning. The research methodology was ethnographic, such as content analysis. The results showed that the epistemological obstacles with the highest number of frequency contained in the students' comprehension were first experience, followed by the substantialist obstacle, the premature generalization and the realistic obstacle, and that the students' interpretations were based from naive realism, explaining their understandings through of naive realism or of concrete knowledge, in the apparent reality presented to the senses, without considering a greater ponderation, not meaning that all students who participated had identical behaviors. It is concluded that the investigative approach contributed in several aspects to the formation of students in a conceptual, procedural and attitudinal way, reflecting on the teaching-learning process, pointing to the need to work with investigative methodologies that make it possible to question the origin of knowledge, being always important to look for methods aligned with the process of reflection about the construction of scientific concepts, which denote the need for reflection in the light of the science philosophy. / Ao analisar a aprendizagem de conceitos científicos à luz da Filosofia da Ciência pautada em Gaston Bachelard, propõe-se entender os obstáculos ao desenvolvimento das ideias científicas. A presente pesquisa teve como objetivo estudar as dificuldades de aprendizagem de alunos do Ensino Médio sobre os conceitos científicos relacionados aos aspectos qualitativos das transformações químicas, como a evidência de formação de novos materiais, produção de gás e luz, buscando evidenciar a presença dos obstáculos epistemológicos a experiência primeira, a generalização prematura, o obstáculo realista e substancialista que são entraves na significação e ressignificação de conceitos científicos químicos nos saberes escolares. A pesquisa foi realizada numa escola estadual pública do município de Manaus com alunos da 1ª série do Ensino Médio, a partir de uma sequência didática com metodologias de ensino e aprendizagem investigativa. A metodologia de pesquisa foi embasada com características do tipo estudo etnográfico, dando ênfase a observação participante, com análise de conteúdo. Os resultados mostraram que os obstáculos epistemológicos com maior número de frequência contidos nas compreensões dos alunos foram experiência primeira, seguida do obstáculo substancialista, da generalização prematura e obstáculo realista e que as interpretações dos mesmos foram embasadas a partir do senso comum, explicando suas compreensões por meio do realismo ingênuo ou ainda no conhecimento concreto, no real aparente que lhes é apresentado aos sentidos, sem que houvesse uma ponderação maior, não significando que todos alunos que participantes tiveram comportamentos idênticos. Conclui-se que a abordagem das dificuldades de aprendizagem a partir dos obstáculos bachelardianos com a utilização da experimentação investigativa contribuiu em vários aspectos para a formação dos alunos de maneira conceitual, procedimental e atitudinal, refletindo sobre o processo de ensino-aprendizagem, apontando para a necessidade de trabalhar com metodologias investigativas que possibilitem questionar a origem dos conhecimentos, sendo sempre importante procurar métodos alinhados ao processo de reflexão a cercar da construção dos conceitos científicos, que denotem a necessidade de reflexão a luz da filosofia da ciência.