A ausência do Cálculo Diferencial e Integral no currículo do Ensino Médio no Brasil, diferentemente do que acontece em outros países, constituiu-se na motivação original para este trabalho. Considerando as finalidades mais gerais da escola básica apresentadas nos documentos oficiais, mostramos o aporte que o ensino de Cálculo pode conduzir à formação de nossos jovens, favorecendo uma visão mais integrada das disciplinas e o desenvolvimento da capacidade de compreender e interpretar fenômenos. Trazer o estudo do Cálculo para a escola básica, porém, não pode significar uma antecipação do que é feito nos cursos universitários, como acontecia no Brasil há algumas décadas. Pelo contrário, a abordagem deve se basear nas ideias fundamentais do Cálculo, como variação, aproximação e proporcionalidade, que já estão presentes no programa da escola básica. Para tanto, apresentamos o raciocínio covariacional, definido como o conjunto de atividades cognitivas envolvidas na análise coordenada das variações de duas grandezas interdependentes. Construindo uma trajetória que começa nas séries iniciais, chega às grandezas proporcionais, perpassa todo o estudo das funções e se estende até o final do Ensino Médio, mostramos que o modelo representado pelo raciocínio covariacional pode nortear o processo de fortalecimento das ideias do Cálculo no currículo da escola básica. Para ter uma noção do cenário atual, avaliamos o nível de raciocínio covariacional de 66 alunos recém-formados no Ensino Médio brasileiro, aprovados em um competitivo exame seletivo para ingresso na universidade. A enorme dispersão dos resultados indicou a pouca consistência do atual programa de nossa escola básica em relação ao desenvolvimento do raciocínio covariacional. Aproveitando o estudo realizado, extrapolamos o contexto da escola básica para avaliar a relação entre o nível inicial de raciocínio covariacional dos alunos e seu desempenho na disciplina de Cálculo na universidade. Os resultados sinalizam para o efeito positivo que um trabalho mais efetivo com o raciocínio covariacional pode ter no enfrentamento das dificuldades vividas por alunos e professores nas disciplinas de Cálculo do ensino superior. / The absence of Differential and Integral Calculus in Brazilian high school syllabus, differently from what happens in other countries, has been the main motivation to develop this thesis. Considering the most general objectives of the K-12 education presented in the official documents, we hereby demonstrate the robust contribution of teaching Calculus to the secondary school students, by offering an integrated discipline overview, and the development of the ability of understanding and interpreting phenomena. However, the introduction of the study of Calculus to secondary school should not be an anticipation of what is developed in the university courses, as it used to be some decades ago in Brazil. The approach, on the other hand, should be based on the Calculus fundamental ideas, such as: variation, approximation and proportionality, which are already present in the K-12 curriculum. Therefore, we described the covariational reasoning, which is defined as the cognitive activities involved in the coordinated analysis of two interdependent quantities variations. We have designed a track using a covariation framework, starting in elementary school, which then achieves the study of proportionality and functions, and extends up to the end of high school, resulting in the strengthening of the Calculus ideas in the curriculum. In order to have a general view of the current scenario, we evaluated the covariational reasoning level of 66 recent graduated high school students in Brazil, who were approved in a high competitive exam in order to enter university. As a result, we detected an impressive lack of consistency regarding the development of covariational reasoning in the secondary school curriculum. Moreover, we could evaluate the relation between the initial students covariational reasoning level and their understanding of Calculus in the university. Our results indicate that fostering covariational reasoning may effectively lead to a positive influence, when dealing with difficulties faced by students and faculty in Calculus courses at the university level.

Analysis is typically the first of the higher functions listed in taxonomies of higher order thinking. Academics consider these upper categories extremely worthwhile, but they are hard to teach and we are apt to ignore them. Today higher education is being criticized for “dumbing down” curriculum or lowering standards. To rectify this, many policies at the state or national level are requiring higher education institutions to change. In K‐12 education, Race to the Top and Common Core requirements are placing new demands on K‐12 teacher preparation, which include evaluation of the analysis skills of pre‐service teachers. But professors do not always view their disciplines as the proper place for teaching analytical skills. Others become frustrated when trying to teach analysis. But if we do not teach these skills, our teacher candidates will be poorly prepared for successful teaching, a problem which will cascade throughout our society, rendering our citizens less educated. In this paper, we describe our efforts to teach analysis in two courses from widely differing subject areas, literacy and mathematics education. We are now requiring pre‐service teachers to analyze simulated or actual samples of student work. We have developed a sequenced process of analysis education that we designate with the acronym CODE. It includes Compilation of information, Organization of data, Determination of patterns, and Explanation of understanding. We believe this technique can be generalized to many courses in where students’ ability to analyze poses a problem.

Underserved students attending under-resourced schools experience limited opportunities to engage in advanced science. An exploration into the influence a supplemental science program has on underserved students’ acquisition of science knowledge and skills to increase their pursuit of science was conducted to help explain science identity formation in students. The proliferation of supplemental science programs have emerged as a result of limited exposure and resources in science for underserved students, thus prompting further investigation into the influence supplemental science programs have on underserved students interest and motivation in science, attainment of science knowledge and skills, and confidence in science to promote science identities in students. Using a phenomenological qualitative approach, this study examined science identity formation in high school students participating in a university supplemental environmental health science program. The study explored high school students’ perceptions of their lived experiences in science supplemental activities, research, and field experiences and the influences these experiences have in relation to their science identity development. The university supplemental science program was an eight-week summer program in which students interacted with a diverse group of peers from various high schools, through engaging in environmental health science rotations, field experiences, and research with faculty advisors and graduate student mentors. Data collection included existing program evaluation data including, weekly journals and exit interviews, as well as follow-up interviews conducted several months after the program concluded. The study findings from a three step coding process of the follow-up interview transcripts provided six emerging themes as follows: (1) promoting interest and motivation to pursue new areas of science, (2) mechanisms in the acquisition of science knowledge and skills in scientific practice, (3) confidence in science knowledge and abilities, (4) understanding and applying science in the world, (5) emerging relationships with peers and mentors in science, and (6) aspirations to be a science person in the scientific community. This research study informs other supplemental science programs, has implications for improved science curricula and instruction in K12 schools, as well as explains how exposure to science experiences can help students gain identities in science.

Cette thèse, réalisée dans le cadre d’une cotutelle entre l’Université Fédérale de Rio Grande do Sul, Brésil, et l’Université Paris Nanterre, France, examine les relations entre corps et objet à partir de l’exercice du théâtre de formes animées dans le contexte brésilien de formation des enseignants en Licence de Pédagogie. A cet égard, elle utilise la notion métaphorique de surmarionnette d’Edward Gordon Craig et ses expérimentations sur le mouvement du corps et sur l’espace scénique. L’étude part du constat d’une double absence concernant les futur.e.s pédagogues: celle de références artistiques et celle de l’indivisibilité du théâtre de formes animées. A cela s’ajoute (pour ces étudiant.e.s) une perception superficielle et caricaturale de ce langage théâtral, au détriment de sa puissance comme objet d’art, de philosophie et d’histoire.Le questionnement de cette thèse peut être ainsi défini: comment penser les possibilités pour le corps dans la formation des enseignants en Pédagogie à partir de la proposition de la Surmarionnette d’Edward Gordon Craig? A cet effet, ont été réalisés des ateliers de théâtre de formes animées avec onze groupes d’étudiant.e.s du cursus de Licence en Pédagogie de huit universités de Rio Grande do Sul, Brésil. Ces ateliers ont été annotés et enregistrés sur des vidéos, constituant des dossiers qui, postérieurement, ont été analysés. Le fondement théorique s’inspire de l’œuvre foucaldienne, tout particulièrement, des notions de corps docile, fonction-auteur, hétérotopie, corps utopique et dans l’exercice de penser d’autres manières à partir de son archéogénéalogie. Cet exercice est nourri de la notion d’expérience de Larrosa (2015), de celle de formation-expérience de Dias (2012) et de la culture de la présence de Gumbrecht (2010). On envisage le théâtre de formes animées selon ses potentialités de formation dans les déplacements : de la conception d’un processus de formation calquée sur la modélisation, surla transmission et la répétition de contenus vers une formation-expérience; de la formation textocentrique vers l’indéfinition de la situation créative; des vérités pédagogisantes vers l’incertitude. Nous concluons sur une proposition pédagogique qui s’oppose à des formules prédertimées et qui considère que le processus de construction de la connaissance est plus complexe et se révèle par le biais de l’action, et, donc, par celui du corps. / This dissertation, developed in a joint degree agreement between Universidade Federal do Rio Grande do Sul, Brazil and Université Paris Nanterre, France, investigates the relations between body and object from a theater of animated forms exercise in the Brazilian context of teacher training in Pedagogy. For this purpose, Edward Gordon Craig’s metaphoric notion of Übermarionnette and the experiments with movement and forms of the scenic space are used. The study departs from the verification of the deficit of artistic references on part of the future pedagogues, as well as the invisibility of theater of animated forms in this context, often seen in a superficial and grotesque way in detriment of its potency as object of art, philosophy and history. The theoretical basis is inspired by the Foucauldian work, especially the notions of docile body, author function, heterotopia, utopian body and the exercise of thinking in distinct ways from his archeogenealogy. Such exercise is interwoven with Larrosa’s notion of experience (2015), Dias’ training-experience (2012) and Gumbrecht’s presence experience (2010). It is understood that what the theater of animated forms has as formative is its possibility of fostering shifts: from the conception of training based on content modeling, transmission and repetition to training-experience; from text-centered training to the lack of definition of the creative situation; and from pedagogizing truths to uncertainty. It is concluded that it is a pedagogic proposal that opposes to formulas and considers that the process of knowledge construction is more complex and happens through action, therefore through the body. / Esta tese, realizada em convênio de cotutela entre a Universidade Federal do Rio Grande do Sul, Brasil, e a Université Paris Nanterre, na França, investiga as relações entre corpo e objeto a partir do exercício de teatro de formas animadas no contexto brasileiro da formação docente em cursos de gradução em Pedagogia. Para tanto, toma a noção metafórica da Übermarionnette de Edward Gordon Craig e as experimentações com o movimento e as formas do espaço cênico. O estudo parte da constatação do déficit de referências artísticas das futuras pedagogas e, também, da invisibilidade do teatro de formas animadas nesse contexto, frequentemente visto de forma superficial e caricata em detrimento de sua potência como objeto de arte, de filosofia e de história. A questão desta tese pode ser assim definida: como pensar as possibilidades para o corpo na formação docente em Pedagogia a partir da proposta da Übermarionette de Edward Gordon Craig? Para tanto, foram realizadas oficinas de teatro de formas animadas com onze grupos de alunas de cursos de graduação em Pedagogia de oito universidades do Rio Grande do Sul, Brasil. Essas oficinas foram anotadas e registradas em vídeos, produzindo-se dossiês que, posteriormente, foram analisados. A base teórica é constituída a partir da inspiração na obra foucaultiana, em especial, as noções de corpo dócil, função autor, heterotopia, corpo utópico e no exercício de pensar de outros modos a partir da sua arqueogenealogia. Tal exercício é entretecido com a noção de experiência de Larrosa (2015), de formação-experiência de Dias (2012) e de cultura da presença de Gumbrecht (2010). Entende-se que o que o teatro de formas animadas possui de formativo é a sua possibilidade de promover deslocamentos: da concepção de um processo de formação calcada na modelização, transmissão e repetição de conteúdos para uma formação-experiência; da formação textocêntrica para a indefinição da situação criativa; e das verdades pedagogizantes para a incerteza. Conclui-se que é uma proposta pedagógica que se opõe à formulas e considera que o processo de construção do conhecimento é mais complexo e se dá por intermédio da ação e, portanto, do corpo.

Auditory graphs and active point estimation provide an inexpensive, accessible alternative for low vision and blind K-12 students using number lines and coordinate graphs. In the first phase of this research program, a series of four psychophysics studies demonstrated an interactive auditory number line that enables blind, low vision, and sighted people to find small targets with a laptop, headphones, and a mouse or a keyboard. The Fitts' Law studies showed that, given appropriate auditory feedback, blind people can use a mouse. In addition, auditory feedback can generate target response patterns similar to when people use visual feedback. Phase two introduced SQUARE, a novel method for building accessible alternatives to existing education technologies. The standards-driven and teacher-directed approach generated 17 graphing standards for sixth grade mathematics, all of which emphasized point estimation. It also showed that how only few basic behavioral components are necessary for these graphing problems. The third phase evaluated active point estimation tools in terms of training, classroom situations, and a testing situation. This work shows that students can learn to graph in K-12 environments, regardless of their visual impairment. It also provides several technologies used for graphing, and methods to further develop education accessibility research.

Since Minnesota passed the first charter school law in 1991, charter schools have become one of the most prominent school reforms in the U.S. While charter schools educate a small portion of public school enrollments, their existence has prompted various responses from traditional public school districts. For example, districts may change expenditure patterns or work to increase test scores in an effort to retain enrollments. In this sense, a charter school’s most significant impact on public school students may work indirectly through the traditional public school reactions they invoke. This dissertation explores education finance implications for charter schools and their encompassing public school districts. Using a dataset comprised of U.S. public school districts over sixteen years, I examine the local school district’s revenue response to the establishment of a charter school. Following a description of the multi-level policy environment in which charter schools operate, this dissertation includes a summary of the literature examining student achievement and expenditure responses of public school districts to the presence of charter schools. Next, I develop a conceptual model outlining the reasons that a school district may experience a change in revenue when charter schools locate within or nearby. Before testing the public school district response to charter schools, I had to accurately measure charter school locations across the U.S. To do this, I used geographic information system (GIS) software to improve upon alternative charter location databases maintained by the federal government and national charter school organizations. With charter school locations accurately mapped, I estimated the traditional public school district revenue response to the various measures of charter school presence. Findings from this estimation suggest that, on average traditional public school districts experienced changes in per-pupil revenues when charter schools located closer to the district. Specifically, revenues from local sources decreased as charter schools moved nearer, but revenues from federal sources increased. This relationship changed over time, however. As charter schools were authorized in more districts and states, per-pupil revenues began increasing as charter schools moved closer to school districts.

Informed by institutional ethnography, and taking the problematic from disjunctures in teacher/participants’ experience between actual practice and official policy, this study is an intertextual analysis of print/electronic documents pertaining to students ‘at risk.’ It unpacks the Student Success Strategy in Ontario secondary schools as organized around discourses on risk and safety. Discriminatory classing and racializing processes construct students ‘at risk’ in ways that reproduce socio-economic inequities through premature streaming into pathways geared to post-secondary destinations: university, college, apprenticeship and work. This study questions the accounting logic that reduces education to skills training in workplace literacy/numeracy, and contradicts the official ‘success’ story that promotes Ontario as a model of large-scale educational change. The follow-up intertextual analyses reveal ideological circles that promote ‘evidence-based research’ and ‘evidence-informed practice,’ while actually gearing education to improving ‘results’ on large-scale standardized tests and manufacturing consent for government policies. Questions arise about the lack of transparency and selective use of educational research. A web of behind-the-scenes activities are made visible at public policy think-tanks (e.g. Canadian Council on Learning; Canadian Language and Literacy Research Network), and two little-researched bodies in educational governance — the Council of Ministers of Education Canada (CMEC) and OECD. Although invisible to teachers, the infrastructure for the Student Success Strategy is the Ontario School Information System (OnSIS); this web-enabled data-management technology has built-in capacity to profile students ‘at risk’ and to instigate accountability and surveillance over teachers’ work, with implications for re-regulating teaching practice towards test scores and aggregate statistics. With the intention of transforming education towards genuine equity, and linking the re-organization of social relations in large-scale reform locally, nationally and globally, this study contributes to critical scholarship on the effects of reform policies on people’s lives and extends knowledge of how translocal text-mediated ruling relations operate in education.

Informed by institutional ethnography, and taking the problematic from disjunctures in teacher/participants’ experience between actual practice and official policy, this study is an intertextual analysis of print/electronic documents pertaining to students ‘at risk.’ It unpacks the Student Success Strategy in Ontario secondary schools as organized around discourses on risk and safety. Discriminatory classing and racializing processes construct students ‘at risk’ in ways that reproduce socio-economic inequities through premature streaming into pathways geared to post-secondary destinations: university, college, apprenticeship and work. This study questions the accounting logic that reduces education to skills training in workplace literacy/numeracy, and contradicts the official ‘success’ story that promotes Ontario as a model of large-scale educational change. The follow-up intertextual analyses reveal ideological circles that promote ‘evidence-based research’ and ‘evidence-informed practice,’ while actually gearing education to improving ‘results’ on large-scale standardized tests and manufacturing consent for government policies. Questions arise about the lack of transparency and selective use of educational research. A web of behind-the-scenes activities are made visible at public policy think-tanks (e.g. Canadian Council on Learning; Canadian Language and Literacy Research Network), and two little-researched bodies in educational governance — the Council of Ministers of Education Canada (CMEC) and OECD. Although invisible to teachers, the infrastructure for the Student Success Strategy is the Ontario School Information System (OnSIS); this web-enabled data-management technology has built-in capacity to profile students ‘at risk’ and to instigate accountability and surveillance over teachers’ work, with implications for re-regulating teaching practice towards test scores and aggregate statistics. With the intention of transforming education towards genuine equity, and linking the re-organization of social relations in large-scale reform locally, nationally and globally, this study contributes to critical scholarship on the effects of reform policies on people’s lives and extends knowledge of how translocal text-mediated ruling relations operate in education.

Cette thèse, réalisée dans le cadre d’une cotutelle entre l’Université Fédérale de Rio Grande do Sul, Brésil, et l’Université Paris Nanterre, France,examineles relations entre corps et objet à partir de l’exercice du théâtre de formes animées dans le contexte brésilien de formation des enseignants en Licence de Pédagogie. A cet égard, elle utilise la notion métaphorique de surmarionnette d’Edward Gordon Craig etses expérimentations sur le mouvement du corps et sur l’espace scénique. L’étude part du constat d’une double absence concernant les futur.e.s pédagogues : celle de références artistiques et celle de l’indivisibilité du théâtre de formes animées. A cela s’ajoute (pour ces étudiant.e.s) une perception superficielle et caricaturale de ce langage théâtral, au détriment de sa puissance comme objet d’art, de philosophie et d’histoire. Le questionnement de cette thèse peut être ainsi défini: comment penser les possibilités pour le corps dans la formation des enseignants en Pédagogie à partir de la proposition de la Surmarionnette d’Edward Gordon Craig? A cet effet, ont été réalisés des ateliers de théâtre de formes animées avec onze groupes d’étudiant.e.s du cursus de Licence en Pédagogie de huit universités de Rio Grande do Sul, Brésil Ces ateliers ont été annotés et enregistrés sur des vidéos, constituant des dossiers qui, postérieurement, ont été analysés. Le fondement théorique s’inspire de l’oeuvre foucaldienne, tout particulièrement, des notions de corps docile, fonction-auteur, hétérotopie, corps utopique et dans l’exercice de penser d’autres manières à partir de son archéogénéalogie. Cet exercice est nourri de la notion d’expérience de Larrosa (2015), de celle de formation-expérience de Dias (2012) et de la culture de la présence de Gumbrecht (2010). On envisage le théâtre de formes animées selon ses potentialités de formation dans les déplacements : de la conception d’un processus de formation calquée sur la modélisation, sur la transmission et la répétition de contenus vers une formation-expérience; de la formation textocentrique vers l’indéfinition de la situation créative; des vérités pédagogisantes vers l’incertitude. Nous concluons sur une proposition pédagogique qui s’oppose à des formules prédertimées et qui considère que le processus de construction dela connaissance est plus complexe et se révèlepar le biais de l’action, et, donc, par celui du corps. / Esta tese, realizada em convênio de cotutela entre a Universidade Federal do Rio Grande do Sul, Brasil, e a Université Paris Nanterre, na França, investiga as relações entre corpo e objeto a partir do exercício de teatro de formas animadas no contexto brasileiro da formação docente em Pedagogia. Para tanto, toma a noção metafórica da Übermarionnette de Edward Gordon Craig e as experimentações com o movimento e as formas do espaço cênico. O estudo parte da constatação do déficit de referências artísticas das futuras pedagogas e, também, da invisibilidade do teatro de formas animadas nesse contexto, frequentemente visto de forma superficial e caricata em detrimento de sua potência como objeto de arte, de filosofia e de história. A questão desta tese pode ser assim definida: como pensar as possibilidades para o corpo na formação docente em Pedagogia a partir da proposta da Übermarionnette de Edward Gordon Craig? Para tanto, foram realizadas oficinas de teatro de formas animadas com onze grupos de alunas de cursos de gradução em Pedagogia do Rio Grande do Sul, Brasil. Essas oficinas foram anotadas e registradas em vídeos, produzindo-se dossiês que, posteriormente, foram analisados A base teórica é constituída a partir da inspiração na obra foucaultiana, em especial, as noções de corpo dócil, função autor, heterotopia, corpo utópico e no exercício de pensar de outros modos a partir da sua arqueogenealogia. Tal exercício é entretecido com a noção de experiência de Larrosa (2015), de formação-experiência de Dias (2012) e de cultura da presença de Gumbrecht (2010). Entende-se que o que o teatro de formas animadas possui de formativo é a sua possibilidade de promover deslocamentos: da concepção de um processo de formação calcada na modelização, transmissão e repetição de conteúdos para uma formação-experiência; da formação textocêntrica para a indefinição da situação criativa; e das verdades pedagogizantes para a incerteza. Conclui-se que é uma proposta pedagógica que se opõe à formulas e considera que o processo de construção do conhecimento é mais complexo e se dá por intermédio da ação e, portanto, do corpo. / This dissertation, developed in a joint degree agreement between Universidade Federal do Rio Grande do Sul, Brazil, and Université Paris Nanterre, France, investigates the relations between body and object grounded on a theater of animated forms exercise in the Brazilian context of teacher training in Pedagogy. For such, Edward Gordon Craig’s metaphoric notion of Übermarionnette and the experiments with movement and forms of the performing space are used. The study starts from the verification of the deficit of artistic references on part of future pedagogues, as well as the invisibility of theater of animated within this context, which is often considered in a superficial and grotesque way in detriment of its potency as object of art, philosophy and history. The question of this dissertation is: how to think the possibilities for the body in teacher training in Pedagogy, based on Edward Gordon Craig’s Übermarionnette proposal? For this purpose, eleven groups of students from undergraduate Pedagogy courses from Rio Grande do Sul state, Brazil took part in theater of animated forms workshops. These workshops were registered in writing and recorded in video, having been produced dossiers which were later examined The theoretical basis is inspired by Foucault’s work, especially the notions of docile body, author function, heterotopia, utopian body and the exercise of thinking in distinct ways from his archeogenealogy. Such exercise is interwoven with Larrosa’s notion of experience (2015), Dias’ training-experience (2012) and Gumbrecht’s culture of presence (2010). It is understood that what the theater of animated forms has as formativeis its possibility to foster shifts: from the conception of a training process based on content modeling, transmission and repetition of contents to training-experience; from text-centered training to the imprecisionof the creative situation; and from pedagogizing truths to uncertainty. It is concluded that it is a pedagogical proposal that opposes to the formulas and considers that the process of knowledge construction is more complex and happens by means of action, therefore by means of the body.

A ausência do Cálculo Diferencial e Integral no currículo do Ensino Médio no Brasil, diferentemente do que acontece em outros países, constituiu-se na motivação original para este trabalho. Considerando as finalidades mais gerais da escola básica apresentadas nos documentos oficiais, mostramos o aporte que o ensino de Cálculo pode conduzir à formação de nossos jovens, favorecendo uma visão mais integrada das disciplinas e o desenvolvimento da capacidade de compreender e interpretar fenômenos. Trazer o estudo do Cálculo para a escola básica, porém, não pode significar uma antecipação do que é feito nos cursos universitários, como acontecia no Brasil há algumas décadas. Pelo contrário, a abordagem deve se basear nas ideias fundamentais do Cálculo, como variação, aproximação e proporcionalidade, que já estão presentes no programa da escola básica. Para tanto, apresentamos o raciocínio covariacional, definido como o conjunto de atividades cognitivas envolvidas na análise coordenada das variações de duas grandezas interdependentes. Construindo uma trajetória que começa nas séries iniciais, chega às grandezas proporcionais, perpassa todo o estudo das funções e se estende até o final do Ensino Médio, mostramos que o modelo representado pelo raciocínio covariacional pode nortear o processo de fortalecimento das ideias do Cálculo no currículo da escola básica. Para ter uma noção do cenário atual, avaliamos o nível de raciocínio covariacional de 66 alunos recém-formados no Ensino Médio brasileiro, aprovados em um competitivo exame seletivo para ingresso na universidade. A enorme dispersão dos resultados indicou a pouca consistência do atual programa de nossa escola básica em relação ao desenvolvimento do raciocínio covariacional. Aproveitando o estudo realizado, extrapolamos o contexto da escola básica para avaliar a relação entre o nível inicial de raciocínio covariacional dos alunos e seu desempenho na disciplina de Cálculo na universidade. Os resultados sinalizam para o efeito positivo que um trabalho mais efetivo com o raciocínio covariacional pode ter no enfrentamento das dificuldades vividas por alunos e professores nas disciplinas de Cálculo do ensino superior. / The absence of Differential and Integral Calculus in Brazilian high school syllabus, differently from what happens in other countries, has been the main motivation to develop this thesis. Considering the most general objectives of the K-12 education presented in the official documents, we hereby demonstrate the robust contribution of teaching Calculus to the secondary school students, by offering an integrated discipline overview, and the development of the ability of understanding and interpreting phenomena. However, the introduction of the study of Calculus to secondary school should not be an anticipation of what is developed in the university courses, as it used to be some decades ago in Brazil. The approach, on the other hand, should be based on the Calculus fundamental ideas, such as: variation, approximation and proportionality, which are already present in the K-12 curriculum. Therefore, we described the covariational reasoning, which is defined as the cognitive activities involved in the coordinated analysis of two interdependent quantities variations. We have designed a track using a covariation framework, starting in elementary school, which then achieves the study of proportionality and functions, and extends up to the end of high school, resulting in the strengthening of the Calculus ideas in the curriculum. In order to have a general view of the current scenario, we evaluated the covariational reasoning level of 66 recent graduated high school students in Brazil, who were approved in a high competitive exam in order to enter university. As a result, we detected an impressive lack of consistency regarding the development of covariational reasoning in the secondary school curriculum. Moreover, we could evaluate the relation between the initial students covariational reasoning level and their understanding of Calculus in the university. Our results indicate that fostering covariational reasoning may effectively lead to a positive influence, when dealing with difficulties faced by students and faculty in Calculus courses at the university level.