Submitted by Renata Lopes (renatasil82@gmail.com) on 2018-06-28T15:35:21Z No. of bitstreams: 1 thamyresribeiromediros.pdf: 18325340 bytes, checksum: e6dce0c28e760e26f0d2f203653b0636 (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2018-09-03T16:08:17Z (GMT) No. of bitstreams: 1 thamyresribeiromediros.pdf: 18325340 bytes, checksum: e6dce0c28e760e26f0d2f203653b0636 (MD5) / Made available in DSpace on 2018-09-03T16:08:17Z (GMT). No. of bitstreams: 1 thamyresribeiromediros.pdf: 18325340 bytes, checksum: e6dce0c28e760e26f0d2f203653b0636 (MD5) Previous issue date: 2018-04-03 / CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / O presente trabalho tem por objetivo desenvolver uma proposta de ensino em matemática para alunos do ensino médio. O conteúdo abordado na proposta são gráficos de funções, em especial, o gráfico da função quadrática: a parábola. A necessidade de um maior rigor matemático na explicação da justificativa do gráfico da função quadrática ser uma parábola fez com que desenvolvêssemos uma proposta de roteiro de aula com explicações e definições matemáticas mais rigorosas em relação as que são apresentadas atualmente nos livros didáticos. Utilizamos de cálculos algébricos para as demonstrações e também fizemos uso de um material prático, um quadro branco onde nele temos acoplado um esquadro, e com uso de pinos, barbante e pincel para quadro branco conseguimos traçar a parábola levando em conta sua propriedade. O material prático auxilia na explicação bem como exemplifica visualmente o que queremos mostrar com os cálculos algébricos. A proposta foi apresentada aos alunos de duas escolas, uma pública estadual e outra privada, que leciono no município de Viçosa - MG e também foi apresentada a seis professores de matemática, colegas de trabalho, sendo cinco destes professores de escolas públicas estaduais, municipais e privadas do município de Viçosa - MG e um professor de escola pública estadual do município de Teixeiras - MG. / The present work aims to develop a teaching proposal in mathematics for high school students. The content addressed in the proposal are graphs of functions, especially the graph of the quadratic function: the parabola. The need for greater mathematical rigor in explaining the justification of the quadratic function graph to be a parable has led us to develop a lesson plan proposal with more rigorous mathematical explanations and definitions than are currently presented in textbooks. We used algebraic calculations for the demonstrations and also made use of a practical material, a white board where we have attached a square, and with the use of pins, string and whiteboard brush we can draw the parable taking into account its property. The practical material helps in the explanation as well as visually exemplifies what we want to show with the algebraic calculations. The proposal was presented to the students of two schools, one state public and the other private, which I teach in the city of Viçosa - MG and was also presented to six mathematics teachers, co-workers, five of these teachers from state, municipal and state public schools. private schools of the municipality of Viçosa - MG and a teacher of a state public school in the municipality of Teixeiras - MG.

Neural networks play an important role in the execution of goal-oriented paradigms. They offer flexibility, adaptability and versatility, so that a variety of approaches may be used to meet a specific goal, depending upon the circumstances and the requirements of the design specifications. Development of higher-order neural units with higher-order synaptic operations will open a new window for some complex problems such as control of aerospace vehicles, pattern recognition, and image processing. The neural models described in this thesis consider the behavior of a single neuron as the basic computing unit in neural information processing operations. Each computing unit in the network is based on the concept of an idealized neuron in the central nervous system (CNS). Most recent mathematical models and their architectures for neuro-control systems have generated many theoretical and industrial interests. Recent advances in static and dynamic neural networks have created a profound impact in the field of neuro-control. Neural networks consisting of several layers of neurons, with linear synaptic operation, have been extensively used in different applications such as pattern recognition, system identification and control of complex systems such as flexible structures, and intelligent robotic systems. The conventional linear neural models are highly simplified models of the biological neuron. Using this model, many neural morphologies, usually referred to as multilayer feedforward neural networks (MFNNs), have been reported in the literature. The performance of the neurons is greatly affected when a layer of neurons are implemented for system identification, pattern recognition and control problems. Through simulation studies of the XOR logic it was concluded that the neurons with linear synaptic operation are limited to only linearly separable forms of pattern distribution. However, they perform a variety of complex mathematical operations when they are implemented in the form of a network structure. These networks suffer from various limitations such as computational efficiency and learning capabilities and moreover, these models ignore many salient features of the biological neurons such as time delays, cross and self correlations, and feedback paths which are otherwise very important in the neural activity. In this thesis an effort is made to develop new mathematical models of neurons that belong to the class of higher-order neural units (HONUs) with higher-order synaptic operations such as quadratic and cubic synaptic operations. The advantage of using this type of neural unit is associated with performance of the neurons but the performance comes at the cost of exponential increase in parameters that hinders the speed of the training process. In this context, a novel method of representation of weight parameters without sacrificing the neural performance has been introduced. A generalised representation of the higher-order synaptic operation for these neural structures was proposed. It was shown that many existing neural structures can be derived from this generalized representation of the higher-order synaptic operation. In the late 1960s, McCulloch and Pitts modeled the stimulation-response of the primitive neuron using the threshold logic. Since then, it has become a practice to implement the logic circuits using neural structures. In this research, realization of the logic circuits such as OR, AND, and XOR were implemented using the proposed neural structures. These neural structures were also implemented as neuro-controllers for the control problems such as satellite attitude control and model reference adaptive control. A comparative study of the performance of these neural structures compared to that of the conventional linear controllers has been presented. The simulation results obtained in this research were applicable only for the simplified model presented in the simulation studies.

Neural networks play an important role in the execution of goal-oriented paradigms. They offer flexibility, adaptability and versatility, so that a variety of approaches may be used to meet a specific goal, depending upon the circumstances and the requirements of the design specifications. Development of higher-order neural units with higher-order synaptic operations will open a new window for some complex problems such as control of aerospace vehicles, pattern recognition, and image processing. The neural models described in this thesis consider the behavior of a single neuron as the basic computing unit in neural information processing operations. Each computing unit in the network is based on the concept of an idealized neuron in the central nervous system (CNS). Most recent mathematical models and their architectures for neuro-control systems have generated many theoretical and industrial interests. Recent advances in static and dynamic neural networks have created a profound impact in the field of neuro-control. Neural networks consisting of several layers of neurons, with linear synaptic operation, have been extensively used in different applications such as pattern recognition, system identification and control of complex systems such as flexible structures, and intelligent robotic systems. The conventional linear neural models are highly simplified models of the biological neuron. Using this model, many neural morphologies, usually referred to as multilayer feedforward neural networks (MFNNs), have been reported in the literature. The performance of the neurons is greatly affected when a layer of neurons are implemented for system identification, pattern recognition and control problems. Through simulation studies of the XOR logic it was concluded that the neurons with linear synaptic operation are limited to only linearly separable forms of pattern distribution. However, they perform a variety of complex mathematical operations when they are implemented in the form of a network structure. These networks suffer from various limitations such as computational efficiency and learning capabilities and moreover, these models ignore many salient features of the biological neurons such as time delays, cross and self correlations, and feedback paths which are otherwise very important in the neural activity. In this thesis an effort is made to develop new mathematical models of neurons that belong to the class of higher-order neural units (HONUs) with higher-order synaptic operations such as quadratic and cubic synaptic operations. The advantage of using this type of neural unit is associated with performance of the neurons but the performance comes at the cost of exponential increase in parameters that hinders the speed of the training process. In this context, a novel method of representation of weight parameters without sacrificing the neural performance has been introduced. A generalised representation of the higher-order synaptic operation for these neural structures was proposed. It was shown that many existing neural structures can be derived from this generalized representation of the higher-order synaptic operation. In the late 1960s, McCulloch and Pitts modeled the stimulation-response of the primitive neuron using the threshold logic. Since then, it has become a practice to implement the logic circuits using neural structures. In this research, realization of the logic circuits such as OR, AND, and XOR were implemented using the proposed neural structures. These neural structures were also implemented as neuro-controllers for the control problems such as satellite attitude control and model reference adaptive control. A comparative study of the performance of these neural structures compared to that of the conventional linear controllers has been presented. The simulation results obtained in this research were applicable only for the simplified model presented in the simulation studies.

In my thesis I deal with quadratic equation, inequality and quadratic function and their teaching with using computer and interactive whiteboard. The thesis is devided into two parts, theoretical one and practical one. In the theoretical part I deal with motivation to learning, constructivism, rating the teaching materials and interactivity in the school surrounding. I state my conclusions from lessons, where I used the prepaired worksheets with secondary vocational school students. The practical part includes my own created worksheets for teaching with interactive whiteboard and their use in teaching on a secondary vocational school.

Submitted by ANA KARLA PEREIRA RODRIGUES (anakarla_@hotmail.com) on 2017-09-08T13:29:12Z No. of bitstreams: 1 arquivototal.pdf: 8624212 bytes, checksum: 8123f6eb13506d5865b46a957bfa1ae6 (MD5) / Approved for entry into archive by ANA KARLA PEREIRA RODRIGUES (anakarla_@hotmail.com) on 2017-09-08T13:51:23Z (GMT) No. of bitstreams: 1 arquivototal.pdf: 8624212 bytes, checksum: 8123f6eb13506d5865b46a957bfa1ae6 (MD5) / Made available in DSpace on 2017-09-08T13:51:23Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 8624212 bytes, checksum: 8123f6eb13506d5865b46a957bfa1ae6 (MD5) Previous issue date: 2016-07-22 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / The use of technologies as teaching tool is a reality experienced by a significant portion of the student body in Brazil. However, there is still considerable demand for educational projects involving the teaching of mathematics with the technologies offered by computer programs. This work will address - through the Delta Project the usage of electronic spreadsheets as a tool for analysis and resolution of func- tional and polynomial equations, establishing links between the mathematical and computational knowledge. / A utilização das tecnologias como ferramentas didaticas ja é uma realidade vivida por uma parte significativa do alunado no Brasil. No entanto, o ritmo vertiginoso do avanço dessas tecnologias não é acompanhado pela devida adaptação e aplicação a realidade das escolas e, sobretudo, a realidade dos alunos. Diante deste descom- passo faz-se necessário ampliar as ofertas de trabalhos acadêmicos que utilizem as tecnologias oferecidas na forma de aplicativos, softwares ou programas específicos da area de educação, para auxiliar o professor na difícil tarefa de ensinar a matema- tica. Essa dissertação pretende contribuir exatamente nesse sentido. Através de um projeto didatico aplicado em sala de aula - o Projeto Delta - que tem como prin- cipal objetivo ampliar e aprofundar os conceitos de função quadratica, resolução de equações polinomiais, divisão de polinômios e cálculo de áreas e volumes de sólidos geométricos utilizando para tanto a planilha eletrônica como ferramenta didática e link entre os saberes das áreas de matemática e programação. Por meio de exemplos práticos da utilização da planilha eletrônica na criação de programas pelos alunos que participaram do Projeto Delta, e da devida fundamentação teórica, esse tra- balho acadêmico pretende mostrar que no processo de criar programas na planilha eletrônica para auxiliar a resolução de problemas matemáticos o aluno tem como subproduto positivo um aprofundamento do entendimento desses saberes matema- ticos e, mais ainda, uma postura analítica e protagonista diante dos conhecimentos dessa matéria em oposição a postura passiva e pouco reflexiva que, infelizmente, ainda é assumida por grande parte dos nossos alunos.

Made available in DSpace on 2016-08-17T16:54:33Z (GMT). No. of bitstreams: 1 Tese Cristiane Cristina.pdf: 4404224 bytes, checksum: a68e5757bedc2d3d341a5937f100fe1f (MD5) Previous issue date: 2013-07-19 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / In adaptive filtering many adaptive filter are based on the mean square error method (MSE). These filters were developed to improve convergence spedd with a lower misadjustment. The least mean square (LMS) and the recursive least square (RLS) algorithms have been the hallmark of adaptive filtering. In this work we develop adaptive algorithms based on the even powers of the error inspired in the recursive lest square (RLS) algorithm. Namely recursive nom quadratic (RNQ) algorithm. The ideas is based on Widrow s least mean square fourth (LMF) algorithm. Fisrt we derive equations based on a singal even power of the error in order to obtain criterions that guarantee convergence. We also determine equations that measure the misadjustment and the time constant of the adaptive process of the RNQ algorithm. We work also, toward making the algorithm less sensitive to the size of the error in na alternative direction, by proposing a cost function which is a sum of the even powers of the error. This second approach bring the error explicitly to the RLS algorithm formulation by proposing a new cost function that preserves the measnsquare-error (MSE) solution, but allows for the exploitation of higher order moments of the error to speedup the converge of the algorithm. The main goal this work is to create form first principles (new cost functions ) a mechanism to include instantaneous error information in the RLS algorithm, make it track better, and allow for the design of the forgetting factor. As we will see the key aspecto of our approach is to include the error in the Kalman gain that effectively controls the speed of adaptation of the RLS algorithm. / Em filtragem adaptativa, vários filtros são baseados no método do erro quadrático médio (do inglês, MSE- mean squared error ) e muitos desses foram desenvolvidos para obter uma convergência rápida com um menos desajuste. Os algoritmos mínimos quadrático médio (do inglês, LMS- least mean square ) e mínimos quadrados recursivos (do inglês, RLS- recursive least square ) foram um marco em filtragem adaptativa. Nesse trabalho apresentamos o desenvolvimento de uma família de algoritmos adaptativos baseados nas potências pares do erro, inspirado na dedução do algoritmo RLS padrão. Chamaremos esses novos algoritmos de recursivo não-quadrático (RNQ). A ideia básica é baseada na função de custo apresentada por Widrow no algoritmo mínimo quarto médio ( do inglês, LMF least mean square fourth). Inicialmente derivamos equações baseados em uma potência par do erro para obter critérios que garantam a convergência. Determinamos também, equações que definem o desajuste e o tempo de aprendizagem do processo de adaptação do algoritmo RNQ baseado em potência para arbitrária. Trabalhamos também, no sentido de tornar o algoritmo menos sensível ao tamanho do erro numa direção alternativa, propondo uma função de custo baseado na soma das potências pares do erro. Essa segunda abordagem torna explícito o papel do erro na formulação do RLS ao propor uma nova função de custo que preserve a solução MSE, mas permite a utilização dos momentos de alta ordem do erro para aumentar a velocidade de convergência do algoritmo. O principal objetivo do nosso trabalho é criar a partir dos primeiros princípios (novas funções de custo) um mecanismo para incluir informações de erro instantâneo no algoritmo RLS e torná-lo um seguidor melhor. Assim, o aspecto-chave dessa nova abordagem é incluir o erro no ganho de Kalman que controla efetivamente a velocidade de adaptação do algoritmo de RLS.

Submitted by Izabel Franco (izabel-franco@ufscar.br) on 2016-09-09T20:53:36Z No. of bitstreams: 1 DissRAS.pdf: 3203822 bytes, checksum: 3e82df6fb3d591caeebed3490f816c55 (MD5) / Approved for entry into archive by Marina Freitas (marinapf@ufscar.br) on 2016-09-12T18:20:56Z (GMT) No. of bitstreams: 1 DissRAS.pdf: 3203822 bytes, checksum: 3e82df6fb3d591caeebed3490f816c55 (MD5) / Approved for entry into archive by Marina Freitas (marinapf@ufscar.br) on 2016-09-12T18:21:03Z (GMT) No. of bitstreams: 1 DissRAS.pdf: 3203822 bytes, checksum: 3e82df6fb3d591caeebed3490f816c55 (MD5) / Made available in DSpace on 2016-09-12T18:21:12Z (GMT). No. of bitstreams: 1 DissRAS.pdf: 3203822 bytes, checksum: 3e82df6fb3d591caeebed3490f816c55 (MD5) Previous issue date: 2014-09-25 / Não recebi financiamento / After a careful evaluatation of my students, my principal investigator and I decided that students with difficulties in higher learning will be chosen, in this case, the first year of High School students in the three cities Jaboticabal, Monte Alto and Pontal. The math content to be worked upon was chosen from the assessment of difficulty students had learning first and second degree functions, as well as the importance the subject has when applied to other disciplines, such as Physics. To facilitate learning of these subjects, four activity sheets were composed to help improve text comprehension and reasoning, and consequently subject knowledge in such a way that the student builds the foundation concepts as to derive the affine and quadratic functions. Interactive exercises of multiple difficulties were prepared to inspire curiosity between students when solving problems. The exercises were designed to allow the students as much autonomy to finding solutions. The students were expected to develop: regularity identification, table-algebraic-graphic conversions, develop a problem situation without a previous explanation; relationship with the concept of affine function, justifying its proportionality; relationship with the concept of quadratic function; graphic analysis of quadratic functions; maximums and minimums; problems treatments on numeric fields and assay for algebraic fields; enthusiasm developing the activities; participation on activities discussion; the ability developing a problem situation with connection to different contexts; that the student had as much autonomy as possible on exercises solution; that the students build strategies and knowledge, given structure and organization to their thoughts, reaching a higher level of abstraction. Students were organized into pairs and encouraged to discuss while working on the activity sheet and review with each other in other classes the methods employed to solve the problems before the solutions were provided. / Após observar, estudar e avaliar o desenvolvimento do corpo discente para o qual leciono, meu orientador e eu decidimos que as turmas “escolhidas” para a aplicação do trabalho seriam as que apresentavam maior dificuldade de aprendizagem, no caso, o primeiro ano do Ensino Médio e ocorreria em três cidades: Jaboticabal, Monte Alto e Pontal. O conteúdo matemático escolhido para ser trabalhado surgiu das dificuldades destes estudantes com o tema funções afim e quadrática, bem como da importância destes temas quando aplicados na disciplina de Física, por exemplo. Nas escolas em questão, o conteúdo de função afim e função quadrática é revisto no terceiro ano do Ensino Médio e é notório que a dificuldade persiste. Para tentar facilitar e colaborar com o ensino desse conteúdo, foram confeccionadas quatro Folhas de Atividades para trabalhar a interpretação de texto, o raciocínio e, por consequência, o conhecimento sobre o assunto, de modo que o estudante construísse o conceito de função afim e função quadrática. Foram preparadas atividades de níveis fácil e médio que exigissem uma boa interpretação de texto, que despertassem a curiosidade e proporcionassem, durante a resolução, a interação entre os estudantes, dos quais se esperava: identificar regularidades; converter dados tabulares algébricos em gráficos, desenvolver uma situação problema sem explicação anterior; relacionar situações com o conceito de função afim, usando proporcionalidade; relacionar situações com o conceito de função quadrática; analisar graficamente a função quadrática; usar máximos e mínimos; tratar os problemas no campo numérico e fazer alguns ensaios no campo algébrico; ter entusiasmo no desenvolvimento da atividade; participar na discussão da atividade; procurar desenvolver a situação problema com ligação a diferentes contextos; ter autonomia na resolução dos exercícios; criar estratégias e construir conhecimento, dando estrutura e ordem aos seus pensamentos, chegando a atingir um nível de abstração mais elevado. Tudo foi observado na ação da maioria dos estudantes. Organizaram-se em duplas para a resolução das Folhas de Atividades e debateram as dúvidas durante a resolução. Antes mesmo que comentasse sobre os resultados, em uma próxima aula, eles já comentavam entre si o método que cada um havia utilizado e em qual resultado haviam chegado.

Submitted by Viviane Lima da Cunha (viviane@biblioteca.ufpb.br) on 2015-10-20T11:59:28Z No. of bitstreams: 2 arquivototal.pdf: 2975294 bytes, checksum: 8e1df00fddd8f1b9f26e991bf1868338 (MD5) license_rdf: 22190 bytes, checksum: 19e8a2b57ef43c09f4d7071d2153c97d (MD5) / Approved for entry into archive by Viviane Lima da Cunha (viviane@biblioteca.ufpb.br) on 2015-10-20T11:59:51Z (GMT) No. of bitstreams: 2 arquivototal.pdf: 2975294 bytes, checksum: 8e1df00fddd8f1b9f26e991bf1868338 (MD5) license_rdf: 22190 bytes, checksum: 19e8a2b57ef43c09f4d7071d2153c97d (MD5) / Made available in DSpace on 2015-10-20T11:59:51Z (GMT). No. of bitstreams: 2 arquivototal.pdf: 2975294 bytes, checksum: 8e1df00fddd8f1b9f26e991bf1868338 (MD5) license_rdf: 22190 bytes, checksum: 19e8a2b57ef43c09f4d7071d2153c97d (MD5) Previous issue date: 2014-08-26 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / This paper presents a new way of discussing concepts involving function, a ne function and quadratic function. Through simple activities with the use of blocks of cubes, and the multiplane software such as GeoGebra, students will move from a passive position, as simple listener, the active member of the teaching-learning process, enabling them to acquire a broader notion the concept of function and apply it later in solving problems in school and in their daily lives. Besides these diversi ed activities, topics that are usually not given prominence in most books of high school such that the analysis of the canonical form of the quadratic function and the theorem of characterization of a ne function will play an important role in developing what is expected of students about this important area of mathematics. All activities were conducted with 1st grade students of high school Natalicia Maria Figueiroa da Silva, located in the city of Surubim, in the state of Pernambuco. / Este trabalho apresenta uma nova maneira de se discutir conceitos envolvendo função, função a m e função quadrática. Através de atividades simples com uso dos blocos de cubos, do multiplano e de softwares como o Geogebra, o aluno passará de uma posição passiva, como simples ouvinte, a integrante ativo do processo de ensino-aprendizagem, possibilitando ao mesmo adquirir uma noção mais ampla do conceito de função e aplicá- lo posteriormente na resolução de problemas na escola e em sua vida cotidiana. Além dessas atividades diversi cadas, tópicos que geralmente não são colocados em destaque na maioria dos livros de ensino médio tais quais a análise da forma canônica da função quadrática e o Teorema de caracterização da função a m terão um importante papel no desenvolvimento que se espera dos estudantes a respeito dessa importante área da Matemática. Todas as atividades foram desenvolvidas com alunos da 1a série do ensino médio da Escola Estadual Natalícia Maria Figueiroa da Silva, localizada na cidade de Surubim no Estado de Pernambuco.

Made available in DSpace on 2015-03-03T15:36:08Z (GMT). No. of bitstreams: 1 JobsonHSS_DISSERT.pdf: 1416900 bytes, checksum: 677228c50dc507b009762057a3ac8330 (MD5) Previous issue date: 2013-03-15 / In general, the study of quadratic functions is based on an excessive amount formulas, all content is approached without justification. Here is the quadratic function and its properties from problems involving quadratic equations and the technique of completing the square. Based on the definitions we will show that the graph of the quadratic function is the parabola and finished our studies finding that several properties of the function can be read from the simple observation of your chart. Thus, we built the whole matter justifying each step, abandoning the use of decorated formulas and valuing the reasoning / Em geral, o estudo de fun??es quadr?ticas ? baseado numa quantidade excessiva de f?rmulas, todo conte?do ? abordado sem justificativas. Apresentamos a fun??o quadr?tica e suas propriedades a partir de problemas envolvendo equa??es do segundo grau e da t?cnica de completar quadrado. Partindo das defini??es mostraremos que o gr?fico da fun??o quadr?tica ? a par?bola e terminamos nosso estudos verificando que v?rias propriedades da fun??o podem ser lidas a partir da simples observa??o do seu gr?fico. Dessa forma, constru?mos todo o assunto justificando cada passo, abandonando o uso de f?rmulas decoradas e prezando pelo racioc?nio

The object of mathematical study titled function is present in several everyday situations, being used by several areas of knowledge. In this way, the acquisition of its concept becomes fundamental for the development of the individual’s cognitive that is in contact with the mathematics in and out of school. Thus, with the work presented here, it was aimed to analyze the mathematical representations mobilized by the students of the 1st year of high school from Colégio de Aplicação of the Universidade Federal de Sergipe (CODAP/UFS) during the teaching of affine and quadratic function. For this purpose, this study was based on Duval's theory of the registers of semiotic representation (2003, 2009, 2011) as well as the guidelines of the Parâmetros Curriculares Nacionais (BRASIL, 1999, 2002, 2006). In addition to that, it was taken as source the textbook Matemática: Contexto & Aplicações (DANTE, 2010), adopted by the participant groups of the research, as well as photocopies of the four (4) participating students' notebooks and 51 (fifty-one) protocols from a sequence of activities composed of 04 (four) problems that were developed with the students themselves. Among the obtained results, it was pointed out that, as in the 499 (four hundred and ninety-nine) activities categorized in the textbook as in the 108 (one hundred and eight) categorized in the students' notebooks, it was required the semiotic transformation of conversion in the majority of them, this is: 446 (four hundred and forty-six) activities, 89.38%, and 83 (eighty-three), 76.85%, respectively. In addition, the activities proposed by the textbook and those contained in the students' notebooks did not prioritize the back and forth feature of the registers among the conversions, disrupting, according to DUVAL (2003, 2009, 2011), the process of acquiring the concept of function. Moreover, in both research instruments it was noticed that, in conversions in which the graphic records were necessary, they were practically not presented, causing important losses in the process of acquisition of the concept of function. Therefore, among the main results obtained with this sequence of activities, it was highlighted that the vast majority of the individuals used in the research used algorithmization processes to perform most conversions. Finally, many of the students used case-by-case analysis and demonstrated that they were not able to identify and use the relevant visual variables to perform the conversions. / O objeto de estudo matemático intitulado função está presente em várias situações do cotidiano, sendo o mesmo utilizado por diversas áreas do conhecimento. Dessa forma, a aquisição de seu conceito torna-se algo fundamental para o desenvolvimento do cognitivo do indivíduo que esteja em contato com a matemática dentro e fora da escola. Assim, com o trabalho ora apresentado, objetivou-se analisar as representações matemáticas mobilizadas pelos alunos do 1º ano do ensino médio do Colégio de Aplicação da Universidade Federal de Sergipe (CODAP/UFS) durante o ensino de função afim e quadrática. Para tal efeito, o estudo embasou-se na teoria dos registros de representação semiótica de Duval (2003, 2009, 2011) bem como nas orientações dos Parâmetros Curriculares Nacionais (BRASIL, 1999, 2002, 2006). Além disso, tomou-se como fonte o livro didático Matemática: Contexto & Aplicações (DANTE, 2010), adotado nas turmas participantes da pesquisa bem como fotocópias dos cadernos de 04 (quatro) alunos participantes e 51 (cinquenta e um) protocolos de uma sequência de atividades compostas por 04 (quatro) problemas as quais foram desenvolvidas com os próprios alunos. Entre os resultados obtidos, destacou-se que tanto nas 499 (quatrocentas e noventa e nove) atividades categorizadas no livro didático quanto nas 108 (cento e oito) categorizadas nos cadernos dos alunos foram requeridas nelas, majoritariamente, a transformação semiótica de conversão, a saber: 446 (quatrocentas e quarenta e seis) atividades, 89,38%, e 83 (oitenta e três), 76,85%, respectivamente. Somado a isso, as atividades propostas pelo livro didático e as contidas nos cadernos dos alunos não priorizavam a característica de ida e volta de registros entre as conversões, prejudicando, segundo DUVAL (2003, 2009, 2011), o processo de aquisição do conceito de função. Ademais, em ambos os instrumentos de pesquisa notou-se que, em conversões em que eram necessários os registros gráficos, praticamente não foram apresentadas, proporcionando importantes perdas no processo de aquisição do conceito de função. Dessa forma, entre os principais resultados obtidos com essa sequência de atividades destacou-se que a grande maioria dos sujeitos usados na pesquisa recorreu a processos de algoritimização para executar a maioria das conversões realizadas. Por fim, muitos dos alunos usaram análise pontual e demonstraram não saber identificar e usar as variáveis visuais pertinentes para realizar as conversões. / São Cristóvão, SE