Academic literature on the topic 'Differential and integral calculus teaching'
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Journal articles on the topic "Differential and integral calculus teaching"
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Gray, Allan B., and Charles G. Moore. "Sharing Teaching Ideas: Integral Cubics." Mathematics Teacher 83, no. 5 (May 1990): 370–71. http://dx.doi.org/10.5951/mt.83.5.0370.
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The teacher of differential calculus needs to be able to draw from a store of problems that have neat answers, solutions that are integers. These problems furnish valid items for quizzes or short tests because fundamental concepts involved in the problem can be tested without the student's becoming ensnared in peripheral details.
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Pereira, Breno De Faria Arnaut, Fabiane Mondini, and Luciane Ferreira Mocrosky. "Expondo os índices de permanência e continuidade na disciplina de Cálculo Diferencial e Integral I em cursos de engenharia na UNESP– Câmpus de Guaratinguetá." Revista Brasileira de Educação em Ciências e Educação Matemática 3, no. 3 (December 28, 2019): 841. http://dx.doi.org/10.33238/rebecem.2019.v.3.n.3.23755.
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Resumo: Este texto apresenta resultados de uma pesquisa cujo objetivo foi estudar como se mostram os índices de permanência e continuidade, na disciplina de Cálculo Diferencial e Integral I, na Universidade Estadual Júlio de Mesquita Filho, UNESP – Câmpus de Guaratinguetá. Justificamos a escolha do tema por sua relevância e pelos altos índices de reprovação e evasão que comumente ocorrem nessa disciplina. Os dados foram constituídos entre os anos de 2013 e 2016. Orientados pela interrogação “como estão os índices de permanência e continuidade na disciplina de CDI - I nos cursos de engenharia da FEG/UNESP?, nossa intenção é expor os dados e nossas considerações de modo a subsidiar futuras pesquisas ou ações voltadas para o ensino da disciplina, não se registrindo a este contexto em que a investigação se desenvolve, mas avançando para outros contextos mais abrangentes, permitindo um pensar sobre novas metodologias e abordagens de ensino que sejam capazes de romper o status quo do ensino de Cálculo Diferencial e Integral.Palavras-chave: Cálculo Diferencial e Integral; Educação Matemática; Ensino Superior; Índices de Permanência e Continuidade. A study on permanence and continuity indices in Differential and Integral Calculation I in engineering courses at UNESP - Guaratinguetá CampusAbstract: This paper presents results of a research whose objective was to study how to show the indices of permanence and continuity in the discipline of differential and integral calculus I, at Unesp - Campus de Guaratinguetá. We justify the choice of the theme for its relevance and the high rates of retention and dropout that commonly occur in this discipline. The data were constituted between 2013 and 2016. uided by the question “how are the indices of permanence and continuity in the discipline of CDI - I in engineering courses at FEG / UNESP?”, our intention is to expose the data and considerations in order to support future research or actions aimed at teaching this discipline, not restricting itself to this context in which research develops, but advancing to a broader context, allowing one to think about new teaching methodologies and approaches that are able to break the status quo of differential and integral calculus teaching.Keywords: Differential and integral calculus; Mathematics education; University education; Permanence and Continuity Indices.
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Bigotte de Almeida, Maria Emília, Araceli Queiruga-Dios, and María José Cáceres. "Differential and Integral Calculus in First-Year Engineering Students: A Diagnosis to Understand the Failure." Mathematics 9, no. 1 (December 29, 2020): 61. http://dx.doi.org/10.3390/math9010061.
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Difficulties in the curricular units (CU) of the mathematical science area, particularly those related to differential and integral calculus (DIC), are often found among students of engineering degrees, leading to high failure rates. A research work was developed with the objective of finding the reasons that lead the students to fail in the CU of DIC (CU-DIC) taught in the 1st year of the engineering undergraduate degrees at the Coimbra Engineering Institute (ISEC), in Portugal. Applying a case study methodology, this article will present a current diagnosis with the objective to establish relationships between teaching methods and students’ learning strategies, and besides, we propose to build learning environments that lead to higher success. The analysis of collected data allows us to conclude that the CU-DIC in the ISEC maintain an identical distribution in the hourly load in several engineering degrees, where contents are adjusted to each context taking into account the CUs of each degree. The data analysis found better results in the academic year that includes two examination moments without any relationship between class attendance, dropout and pass rates. We propose some different teaching/learning strategies in CU-DIC and new learning environments that enhance freshmen students’ engagement and participation in their own learning process.
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Vorontsova, Ol’ga R., and Tat’yana A. Chebun’kina. "Assessment of students' psychoemotional state in the process of teaching higher mathematics using colour matrix." Vestnik of Kostroma State University. Series: Pedagogy. Psychology. Sociokinetics 26, no. 4 (February 24, 2021): 196–202. http://dx.doi.org/10.34216/2073-1426-2020-26-4-196-202.
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The article deals with the psychoemotional state of students when studying the modules "Integral calculus" and "Differential equations" in the course of higher mathematics. The factors that affect the degree of assimilation of educational material by first-year students are described, and the causes of emotional (psychological) stress are noted. The study is confirmed by an empirical description, which was conducted using the "colour painting" technique, first used to assess the psychoemotional state of first-year students when studying sections of the higher mathematics course. The proposed method makes it possible to "see" the mood of students on each topic of the module, to track the dynamics of emotional states in the team on the topics of each module and the overall picture of the mood of each individual in the student group. Colour matrix allows recording the emotional response to events (for the authors of the article, these are modules of the course) and finding out how it was perceived by students, who of them is experiencing difficulties. The study of the psychoemotional state of respondents was conducted by means of a questionnaire, where the authors were interested in how the study materials on the topic "Integral calculus" and "Differential equations"affect the students' health/mood. Based on the analysis, the most difficult topics for learning modules were identified, and recommendations were given on their possible forms and methods of teaching.
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Grattan-Guinness, I. "On proving certain optimisation theorems in plane geometry." Mathematical Gazette 97, no. 538 (March 2013): 75–80. http://dx.doi.org/10.1017/s0025557200005441.
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A pleasurable aspect of mathematics and its teaching is to review the diversity of ways in which theorems are proved. Especially in elementary branches, there are various kinds of proof: using (or avoiding) spatial geometry, analytic or coordinate geometry, common algebra, vectors, abstract algebras, matrices, determinants, the differential and integral calculus, and maybe mixtures thereof. Further, sometimes a proof of one kind is elegant while another is clumsy, or one proof of a theorem suggests why it follows while another proof is not perspicuous. There is also the question of whether a proof is direct or indirect (for example, proofby contradiction).
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Lema Carrera, Miguel. "Empleo de simulaciones dinámicas en matlab como parte del proceso de enseñanza-aprendizaje de las matemáticas con aplicación al cálculo diferencial e integral." Revista Científica y Tecnológica UPSE 5, no. 1 (June 20, 2018): 36–41. http://dx.doi.org/10.26423/rctu.v5i1.306.
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La matemática en todos los tiempos ha tenido como principal fuente de inspiración la visualización, jugando un papel importante en el desarrollo de conceptos, nociones e ideas básicas del cálculo diferencial e integral. El presente trabajo proporciona herramientas y métodos básicos de uso relativamente sencillo, desarrollados en el paquete computacional MATLAB, trabajando temas como la definición geométrica de derivada, la integral definida y cálculo de volúmenes de revolución utilizando el método de discos, que permite obtener resultados muy poderosos en simulaciones dinámicas “animadas” que sirvan de soporte y recurso didáctico facilitador en el proceso de enseñanza-aprendizaje del cálculo. Modificando y renovando en una primera instancia la forma tradicional de enseñanza de esta asignatura en los primeros años del ciclo básico universitario en esta institución y porque no del país, además, se espera que este trabajo, permita desterrar el paradigma entorno a la comunidad estudiantil, que ha relacionado al cálculo matemático con una idea pura y completamente algebraizada, estática y memorística.
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The mathematics of all time has had as the main source of inspiration the visualization, playing an important role in the development of concepts, notions and basic ideas of the differential and integral calculus. The present work provides tools and basic methods of use relatively simple, developed in the computational package Matlab, working topics such as the geometric definition of derivative, the definite integral and calculation of volumes of revolution using the disk method, which allows to obtain very powerful results in "animated" dynamic simulations that serve as support and facilitating didactic resource in the teaching-learning process of calculus. Modifying and renewing in the first instance the traditional way of teaching this subject in the first years of the basic university cycle in this institution and why not in the country, in addition, it is expected that this work, to banish the paradigm around the student community, that has related to the calculus with a pure and completely algebraic, static and rote idea.
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Lopes, Vanessa Rodrigues, and Suely Scherer. "Cálculo Diferencial e Integral e o Uso de Tecnologias Digitais de Informação e Comunicação: uma Discussão de Pesquisas nos Últimos Onze Anos." Jornal Internacional de Estudos em Educação Matemática 11, no. 2 (September 11, 2018): 145. http://dx.doi.org/10.17921/2176-5634.2018v11n2p145-159.
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Os conceitos de Cálculo Diferencial e Integral são estudados em diversos cursos do Ensino Superior, como por exemplo, Engenharias, Química, Ciência da Computação, Administração, Biologia, Física, Matemática, dentre outros. Nos últimos onze anos, diversas pesquisas foram realizadas com foco nos processos de ensino e/ou de aprendizagem de Cálculo e em muitas se anuncia que foram motivadas pelos índices de reprovação nesta disciplina. Neste artigo, o objetivo é apresentar e analisar pesquisas desenvolvidas nos últimos onze anos, cujo objeto de investigação é o ensino e/ou a aprendizagem de Cálculo em espaço presencial e/ou virtual, no Ensino Superior, com uso de Tecnologias Digitais de Informação e Comunicação (TDIC) e refletir sobre a problemática do ensino e da aprendizagem de Cálculo com uso de TDIC, em especial com momentos à distância, a partir do cenário evidenciado por essas pesquisas. O estudo foi realizado a partir de uma busca no banco de teses e dissertações da Capes e na Biblioteca Digital Brasileira de teses e dissertações, tendo como resultado final vinte pesquisas sobre o tema, que foram analisadas nesse artigo. Esse cenário de pesquisas evidencia que o uso de tecnologias digitais pode ser um caminho para a superação de algumas dificuldades na aprendizagem do Cálculo. E um desafio para pesquisas sobre essa temática/problemática é considerar a possibilidade da aprendizagem móvel, ou M-learning, da aprendizagem ubíqua, ou u-learning, afinal os alunos do Ensino Superior estão cada vez mais com a tecnologia digital em suas mãos, acessível a qualquer momento, em vários espaços.Palavras-chave: Cálculo Diferencial e Integral I. Tecnologia Digital de Informação e Comunicação. Espaço Presencial. Espaço Virtual.AbstractThe concepts of Differential and Integral Calculus are studied in several courses of Higher Education, such as in Engineering, Chemistry,Computer Science, Administration, Biology, Physics, Mathematics, among others. In the last eleven years, several researches have beenconducted focusing on the teaching and / or learning process of Calculus, and in many, it is announced that they were motivated by the failurerates in this discipline. In this article the objective is to present and analyze researches developed in the last eleven years whose object ofresearch is the teaching and / or learning of Calculus in presence and / or virtual space in higher education, using Digital Information andCommunication Technologies ( TDIC), and to reflect on the teaching and learning of Calculus using TDIC, especially with moments at adistance, based on the scenario evidenced by these studies. The study was carried out from a search of the thesis and dissertation bank ofCapes and the Brazilian Digital Library of theses and dissertations, with the result of twenty researches on the subject, which were analyzed inthis article. This research scenario shows that the use of digital technologies can be a way to overcome some difficulties in learning Calculus.And a challenge for research on this issue / problem is to consider the possibility of mobile learning, or M-learning, ubiquitous learning, oru-learning, after all Higher Education students are increasingly with digital technology at their fingertips, Accessible at any time, in variousspaces.Keywords: Differential and Integral Calculus I. Digital Information and Communication Technology. Face-to-Face Space. Virtual Space.
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Oliveira, Júlia, Leonardo Panontim, Vitor Hugo Fonseca, Pedro Gonçalves, Diovana Napoleão, and Marco Alcântara. "Project-Based Learning." International Journal for Innovation Education and Research 9, no. 7 (July 1, 2021): 224–37. http://dx.doi.org/10.31686/ijier.vol9.iss7.3244.
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One of the problems that concerns engineering courses in Brazil is the students low level of motivation in regarding the type of teaching and, as a consequence, low academic performance. This article encourages the introduction of active methods in Engineering teaching, emphasizing the methodologies of Project Based Learning. The approach used was proposing a project for students to analyze important aspects in the production of cylindrical cans. The students applied calculus concepts and developed a model for the optimal dimensions of the cylinder and the utilization of the plates used. Characteristics of two materials used in the manufacture of these cans (tinplate and aluminum) were also gotten. Such aspects are relevant for both environmental sustainability and production costs. Concepts of application of derivatives and Fermat's theorem were used, learned in the discipline of Differential and Integral Calculus, in order to obtain the maximum and minimum values of an established function which relates the dimensions of the can and the amount of material needed. The dimensions obtained theoretically proved to be close to the real values found in cans available on the market. After analyzing the resistance to corrosion, the cost, the decomposition time and the mechanical resistance, it was concluded that the most appropriate material for the production of cans was the tinplate. In this context, teaching with Project Based Learning methodologies may contribute to innovative teaching practices in the training of engineering professionals, overcoming the limitations of traditional teaching methods.
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Trevisan, André Luis, and Eliane Maria de Oliveira Araman. "Argumentos Apresentados por Estudantes de Cálculo em uma Tarefa de Natureza ExploratóriaArguments Presented by Students of Calculus in an Exploratory Task." Educação Matemática Pesquisa : Revista do Programa de Estudos Pós-Graduados em Educação Matemática 23, no. 1 (April 11, 2021): 591–612. http://dx.doi.org/10.23925/1983-3156.2021v23i1p591-612.
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ResumoA presente pesquisa tem como objetivo reconhecer conceitos matemáticos que foram utilizados por estudantes de Cálculo Diferencial e Integral na elaboração de argumentos, na resolução de uma tarefa de natureza exploratória envolvendo representações gráficas. Como referencial teórico, recorremos aos estudos relacionados ao raciocínio matemático e à argumentação, aos episódios de resolução de tarefas e à aprendizagem do conceito de função. A pesquisa segue princípios de uma investigação baseada em design. Para produção de dados, utilizamos gravações em áudio e a produção escrita dos estudantes no trabalho com a tarefa, além do diário de campo dos pesquisadores. Apoiados pelo arcabouço teórico, analisamos os argumentos apresentadas por quatro grupos de estudantes durante a discussão da tarefa. Como resultados, destacamos que os estudantes mobilizam alguns processos de raciocínio (identificar padrão, conjecturar, comparar e justificar) ao elaborarem a descrição do gráfico de funções, recorrendo, para tal, a conceitos matemáticos como (de)crescimento de função, variação da taxa de crescimento, concavidade de um gráfico e assíntota horizontal.Palavras-chave: Ensino de matemática. Ensino de cálculo diferencial e integral. Raciocínio matemático. Argumentação.AbstractThis research aims to analyse arguments developed by students of the Differential and Integral Calculus subject of a public university in Paraná when solving an exploratory task. The theoretical framework is formed by studies related to mathematical reasoning and argumentation, episodes of solving tasks, and learning the concept of function. The research follows the principles of design research. The data were audio recordings and the written production of students working on the task, and the researchers’ field diary. Supported by the theoretical framework, we analysed the arguments presented by four groups of students during the discussion of the task. The result show that students mobilise some reasoning processes (identify pattern, conjecture, compare, and justify) when elaborating the function graph description, using mathematical concepts such as function growth and decrease, rate variation of growth, concavity of a graph, and horizontal asymptote.Keywords: Mathematics teaching. Teaching Differential and Integral Calculus. Mathematical reasoning. Argumentation. ResumenEsta investigación tiene como objetivo analizar los argumentos desarrollados por estudiantes de la asignatura Cálculo Diferencial e Integral de una universidad pública de Paraná al momento de resolver una tarea exploratoria. El marco teórico está formado por estudios relacionados con el razonamiento y la argumentación matemática, episodios de resolución de tareas y aprendizaje del concepto de función. La investigación sigue los principios de la investigación basada en diseño. Los datos fueron grabaciones de audio y la producción escrita de los estudiantes trabajando en la tarea y el diario de campo de los investigadores. Apoyados en el marco teórico, analizamos los argumentos presentados por cuatro grupos de estudiantes durante la discusión de la tarea. El resultado muestra que los estudiantes movilizan algunos procesos de razonamiento (identificar patrón, conjeturar, comparar y justificar) al elaborar la descripción del gráfico de funciones, utilizando conceptos matemáticos como crecimiento y disminución de funciones, tasa de variación de crecimiento, concavidad de una gráfica y asíntota horizontal.Palabras clave: Enseñanza de las matemáticas. Enseñanza del cálculo diferencial e integral. Razonamiento matemático. Argumentación.
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Molon, Jaqueline, and Edson Sidney Figueireo. "CÁLCULO NO ENSINO MÉDIO: UMA ABORDAGEM POSSÍVEL E NECESSÁRIA COM AUXÍLIO DO SOFTWARE GEOGEBRA." Ciência e Natura 37 (August 7, 2015): 156. http://dx.doi.org/10.5902/2179460x14523.
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http://dx.doi.org/10.5902/2179460X14523This article is the result of the dissertation of the Professional Masters in Mathematics in National Network, held in March 2013 at the Federal University of Santa Maria (UFSM). The work aimed to verify the possibility of inclusion in high school, the intuitive ideas of the Differential and Integral Calculus: limits of a function, the average rate of change, instantaneous variation and calculation of areas under the graph of positive functions, limited the x-axis and vertical lines, or even between positive functions in a particular area of the same range. To facilitate the understanding of these ideas, activities were developed using the Software GeoGebra as support learning tool. The activities were applied to an experimental group of students from the first year of High School, combined with the study of quadratic functions. It was found that you can open the horizons within the teaching and learning of mathematics in high school, to the intuitive ideas of calculus. In this work, the objectives of this research will be presented, some proposed activities and the results achieved, and propose developments to deepen and apply the issues discussed here.
Dissertations / Theses on the topic "Differential and integral calculus teaching"
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Almeida, Marcio Vieira de. "Material para o ensino do cálculo diferencial e integral: referências de Tall, Gueudet e Trouche." Pontifícia Universidade Católica de São Paulo, 2017. https://tede2.pucsp.br/handle/handle/20263.
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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES
This thesis presents a material for the teaching of Differential and Integral Calculus, composed by seven activities, which were based on theoretical references of Mathematical Education. The concepts of function, continuity, differentiability, solution of a differential equation, integral and limit of sequences were approached in these activities. The intention was to defend that one of the ways to establish the narrowing of the relation of theory and practice in this area of investigation is done through the elaboration of materials for teaching with this goal. The concepts of generic organizer, cognitive root, and Three Worlds of Mathematics by Tall and collaborators and the idea of resource of Documental Genesis of Gueudet and Trouche were used. The use of the computer and the construction of tools on GeoGebra were productive procedures to obtain a material with the planned qualities. The research, which had as a result the material for teaching, followed the methodological orientation of a type of fundamental research, in which the goal is the filling of gaps in knowledge related to the solution of problems through practice. An explanatory, theoretical posture was adopted, the construction of considerations with rigor and logical coherence to validate the obtained results. In the scope of theoretic-methodological references seven activities were elaborated for the teaching of Calculus organized in three components which, compose a resource (mathematics, material and didactics) in the conception of Documental Genesis, incorporating cognitivist ideas of Tall and his associates. Using the components (mathematics, material and didactics) allows that the material may configure itself as an element of the set of resources, according to the Documental Genesis, which a teacher of Calculus can use for the development of a class. As a result it is possible to demonstrate that the way of elaboration proposed for a material for teaching, in which theories of Mathematical Education are elaborated and adequate software is used, may be a powerful way to favor the integration of theory and practice, pursued and necessary for Mathematic Education, besides contributing with learning
Esta tese apresenta um material para o ensino de Cálculo Diferencial e Integral composto por sete atividades que foram embasadas em referenciais teóricos da Educação Matemática. Nelas, foram abordados os conceitos de função, continuidade, diferenciabilidade, solução de uma equação diferencial, integral e limite de sequências. Pretendeu-se defender que uma das formas de se estabelecer o estreitamento da relação teoria e prática nessa área de investigação é feita por meio de elaboração de materiais para o ensino com essa finalidade. Foram utilizadas as noções de organizador genérico, raiz cognitiva e Três Mundos da Matemática de Tall e colaboradores, e a noção de recurso da Gênese Documental de Gueudet e Trouche. O uso do computador e a construção de ferramentas no GeoGebra foram procedimentos férteis para se obter um material com as competências planejadas. A pesquisa, que teve por resultado o material para o ensino, seguiu orientação metodológica de uma do tipo pesquisa fundamental, na qual se objetiva o preenchimento de lacunas no conhecimento relativo à solução de problemas advindos da prática. Adotou-se uma postura teórica exploratória, a da construção de argumentos com rigor e coerência lógica para validar os resultados obtidos. Nesse âmbito de referenciais teórico- metodológicos, foram elaboradas sete atividades para o ensino de Cálculo, organizadas em três componentes, as quais compõem um recurso (matemática, material e didática) na concepção da Gênese Documental, incorporando noções cognitivistas de Tall e seus associados. A utilização das componentes (matemática, material e didática) possibilita que o material possa se configurar em um elemento do conjunto de recursos, conforme a Gênese Documental, de um professor de Cálculo, para o desenvolvimento de uma aula. Como resultado pode-se demonstrar que o modo de elaboração proposto para um material para o ensino, em que se incorporam teorias da Educação Matemática e se utiliza um software adequado, pode ser um meio potente para favorecer a integração teoria e prática, almejada e necessária pela Educação Matemática, além de contribuir com a aprendizagem
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Floret, Rejane Teixeira de Souza. "Uma proposta para introdução de noções de Cálculo no ensino médio." Universidade do Estado do Rio de Janeiro, 2014. http://www.bdtd.uerj.br/tde_busca/arquivo.php?codArquivo=7803.
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Coordenação de Aperfeiçoamento de Pessoal de Nível SuperiorA presente dissertação tem o objetivo de propor a reinclusão de elementos de Cálculo no ensino médio, pois no passado o Cálculo fazia parte do currículo e foi abolido após uma reforma no ensino da matemática. O trabalho apresenta os resultados de um levantamento estatístico sobre os índices de reprovação na disciplina Cálculo Diferencial e Integral I nos períodos mais recentes da Universidade do Estado do Rio de Janeiro (UERJ) e, também, uma pesquisa quantitativa com quarenta professores de matemática com o objetivo de analisar a viabilidade do projeto e os problemas a serem enfrentados. Por fim, a dissertação conta com uma série de atividades comentadas sobre o tema de limites, que é o foco do trabalho. Tais atividades podem ser incluídas já no 1 ano do ensino médio, paralelamente ao conteúdo de funções, e visam proporcionar aos estudantes o contato com elementos de Cálculo em uma linguagem acessível, e orientar o professor nesta tarefa
This dissertation has the objective of proposing the reinclusion of Calculus elements in high school, because in the past Calculus was part of the curriculum and it was abolished after a reform in mathematics teaching. This paper presents the results of a statistical return about the rates of fails in the subject Differential and integral Calculus I in recent terms at Universidade do Estado do Rio de Janeiro (UERJ) and also a quantitative research with forty mathematics teachers, which has the objective of analyzing the viability of the project and the problems to be faced. Finally, the dissertation has a series of discussed activities about the theme of limits, which is the focus of this paper. These activities can be included in the first year of high school, at the same time as functions content. They aim to offer students a contact with Calculus elements in an accessible language and also to orientate the teacher in this task.
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Almeida, Marcio Vieira de. "Um panorama de artigos sobre a aprendizagem do cálculo diferencial e integral na perspectiva de David Tall." Pontifícia Universidade Católica de São Paulo, 2013. https://tede2.pucsp.br/handle/handle/10969.
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Previous issue date: 2013-06-07Coordenação de Aperfeiçoamento de Pessoal de Nível Superior
The focus on this research is the learning and teaching of Differential and Integral Calculus, through the reading of articles written by the researcher David Tall. It is a bibliographical theoretical research, in the modality of panorama, in which the organization is also based on elements of Content Analysis, according to Bardin. We present information about the biography of the English researcher and his relationship with the community of national research. The CAPES Thesis Database was studied, with the objective of identifying the use of theories developed by Tall in national researches. The material for analysis, used for the development of the panorama, was based on 14 articles, taken from the session Limits, Infinity & Infinitesimals of the academic website of the English researcher. The theoretical elements and the approaches in teaching formulated to the concepts real numbers, infinity, limits, continuity, derivatives, integral and differential equations are highlighted in this material. The panorama brings summaries and analysis of theoretical elements, besides highlighting important information on the learning and teaching of Differential and Integral Calculus under Tall s perspectives. With this research, we hope to have contributed to both research and teaching practice
Esta pesquisa tem por foco a aprendizagem e o ensino do Cálculo Diferencial e Integral. Trata-se da realização de um panorama de artigos de autoria de David Tall relacionados a esse tema. É um estudo teórico de caráter bibliográfico, na modalidade panorama, cuja organização se pautou também em elementos da Análise de Conteúdo, segundo Bardin. São apresentados dados sobre a biografia do pesquisador inglês e a relação dele com a comunidade de pesquisa nacional. É realizado um levantamento, no banco de dissertações e teses da CAPES, com a intenção de identificar a utilização dos elementos teóricos desenvolvidos por Tall, em pesquisas nacionais. O material de análise, utilizado para o desenvolvimento do panorama, constituiu-se de 14 artigos, retirados da seção Limits, Infinity & Infinitesimals do sítio acadêmico do pesquisador. São destacados, nesse material, os elementos teóricos e as abordagens para o ensino formuladas para os conceitos: números reais, infinito, limites, continuidade, derivada, integral e equações diferenciais. O panorama traz sínteses e análises de elementos teóricos, além de colocar em evidência dados importantes sobre a aprendizagem e o ensino do Cálculo Diferencial e Integral, na perspectiva de Tall. Com a apresentação deste trabalho espera-se ter contribuído tanto com a pesquisa quanto com a prática docente
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Müller, Thaísa Jacintho. "Objetos de aprendizagem multimodais e ensino de cálculo : uma proposta baseada em análise de erros." reponame:Biblioteca Digital de Teses e Dissertações da UFRGS, 2015. http://hdl.handle.net/10183/128914.
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Esta tese teve como objetivo analisar dificuldades de aprendizagem apresentadas por alunos de Cálculo Diferencial e Integral, bem como testar possibilidades de superar tais dificuldades por meio de recursos tecnológicos. Na primeira fase da pesquisa, foram realizadas análises de erros cometidos por estudantes de Cálculo, inicialmente de uma turma de Sistemas de Informação e, na sequência, de uma turma de Engenharia. Em ambos os testes identificou-se que as maiores dificuldades se referiam a conteúdos de Matemática Básica, pré-requisitos para o Cálculo. O trabalho teve como pressupostos teóricos as ideias de Ausubel, Tall, Vinner e de autores que discutem aprendizagem de Álgebra, visto que os erros mais encontrados nas análises se referiam à aplicação da propriedade distributiva da multiplicação sobre a adição. A metodologia de investigação é quanti-qualitativa e está baseada nos pressupostos da Pesquisa Baseada em Design. Foi aplicado, também, um teste de estilos de aprendizagem, a fim de identificar quais os estilos preferenciais dos estudantes, o que guiou a construção de um Objeto de Aprendizagem voltado para a propriedade distributiva. Na segunda fase da pesquisa, foram realizadas atividades na Plataforma MOODLE, com alunos de Cálculo Diferencial e Integral I. Inicialmente, os estudantes responderam a um questionário que envolvia conteúdos de matemática básica, a fim de que fossem identificadas suas dificuldades. A partir delas, os grupos de alunos foram direcionados a objetos de aprendizagem, dentre os quais se tem o objeto construído na primeira etapa. Após o estudo com os objetos, os estudantes foram desafiados a discutir em fóruns, nos quais lançaram-se novas questões sobre as dificuldades encontradas. Nessa discussão, observou-se que muitas das considerações feitas nos pressupostos teóricos foram confirmadas. Por fim, foi aplicado um segundo questionário, semelhante ao primeiro, com fins de comparação do desempenho dos alunos envolvidos na pesquisa. A partir da análise estatística dos resultados, pode-se afirmar que houve uma melhora substancial no desempenho do grupo, o que indica que o trabalho realizado cumpriu com os objetivos propostos. Ainda, foi realizada uma entrevista com uma das professoras responsáveis pelo Laboratório de Aprendizagem da Instituição onde o trabalho foi desenvolvido, na qual foi salientada a importância de realizar uma pesquisa que possa dar subsídios para uso de recursos tecnológicos no Laboratório, para auxiliar os alunos a localizar e remediar suas dificuldades.This thesis aims to analyze learning difficulties presented by students of Differential and Integral Calculus and test possibilities to overcome these difficulties through technological resources. In the first phase of the research, error analyzes were performed using results from a Calculus test, initially from a group of Information Systems students and, afterward, from a group of Engineering students. In both tests, it was found that the main difficulties refer to Basic Mathematics content, prerequisites for the Calculus discipline. The work is based in conceits of Ausubel, Tall, Vinner and other authors who discuss learning Algebra, since the most common errors referred to the application of the distributive property of multiplication over addition. The research methodology is quantitative-qualitative and is based on assumptions of Research-Based Design. It was also applied a learning style test in order to identify the preferred styles of students, which guided the creation of a Learning Object directed to the distributive property. In the second phase of the research, activities were carried out in the MOODLE platform with students from Differential and Integral Calculus I. Initially, students answered a questionnaire involving basic math content in order to identify their difficulties. From these results, groups of students were directed to Learning Objects, among which is the object constructed in the first stage. After studying with these objects, students were challenged to discuss in forums in which were launched new questions about the difficulties encountered. In this discussion, it was noted that many of the considerations made in the theoretical assumptions were confirmed. Finally, a second questionnaire was applied, similar to the first, in order to compare the performance of the students involved in the research. From the statistical analysis, it can be said that there was a substantial improvement in performance of the group, indicating the work complied with the proposed objectives. An interview was conducted with one of the teachers responsible for the Learning Laboratory where the research was developed, in which was highlighted the importance of conducting a study to sustain the use of technological resources in the Laboratory, in order to help students locate and remedy its difficulties.
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Fonseca, Maycon Odailson dos Santos da. "Proposta de tarefas para um estudo inicial de derivadas." Universidade Tecnológica Federal do Paraná, 2017. http://repositorio.utfpr.edu.br/jspui/handle/1/2499.
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Acompanha: Caderno de tarefas: proposta de tarefas para um estudo inicial de derivadasCNPq
Esta dissertação apresenta uma proposta de tarefas para o estudo inicial de derivadas no ensino de cálculo diferencial e integral (CDI) no Ensino Superior, em turmas regulares de um curso de Engenharia da Universidade Tecnológica Federal do Paraná (UTFPR) do campus Londrina. Elencou-se como objetivo geral da pesquisa a proposição de tarefas que oportunizem aos estudantes a exploração de ideias necessárias à compreensão do conceito de derivadas, em especial tarefas a serem aplicadas em momentos que iniciam o estudo de derivadas, em sua abordagem mais formal. Por se tratar de um mestrado em âmbito profissional, intencionou-se a construção de caderno de tarefas (o produto educacional), na qual após a aplicação de dois ciclos de pesquisa, elencaram-se três tarefas para compor o produto final da pesquisa, a qual por meio das análises notou-se a necessidade entre os ciclos a adaptação/reformulação das tarefas, e em especial na tarefa 3 a intencionalidade de uma nova reformulação e aplicação em um novo ciclo de pesquisa.
This dissertation presents a proposal to the initial study of derivatives in the teaching of differential and integral calculus (CDI) in higher education, in regular classes of an engineering degree from the Federal University of technology-Paraná (UTFPR) campus. Presented as general purpose of research the proposition of tasks that create opportunities for students to exploration of ideas necessary for the understanding of the concept of derived in particular tasks to be applied at times to begin the study of derived, in your more formal approach. As a master's degree in professional, intended the construction of notebook (the educational product), in which after two cycles of research, bleeding cool is-if three tasks to compose the final research product, which by means of analyses the need was noted between cycles the adaptation/recasting of tasks, and in particular in task 3 the intentionality of a new makeover and application in a new cycle of research.
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Zarpelon, Edinéia. "Análise do desempenho de alunos calouros de engenharia na disciplina de cálculo diferencial e integral I: um estudo de caso na UTFPR." Universidade Tecnológica Federal do Paraná, 2016. http://repositorio.utfpr.edu.br/jspui/handle/1/2489.
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Acompanha: Manual didático para aplicação de testes estatísticos na análise do desempenho de alunos em disciplinas da graduaçãoEsta pesquisa teve como objetivo analisar variáveis a fim de entender se elas são significativas para a reprovação dos alunos ingressantes nos cursos de Engenharia na disciplina de Cálculo Diferencial e Integral I. Para tanto, adotou-se como hipótese básica que o comprometimento acadêmico é um dos fatores que interfere de forma expressiva neste contexto. O referencial teórico faz um breve apanhado sobre a origem e evolução dos cursos de Engenharia, sobre a importância do Cálculo, bem como sobre as reprovações e possíveis agravantes. Além disso, aborda as principais variáveis associadas à reprovação em Cálculo I apontadas na literatura existente. Trata-se de uma pesquisa com abordagem mista, sendo que as hipóteses secundárias buscavam confirmar ou descartar a influência de seis variáveis - nota obtida pelos estudantes na prova de Matemática do Exame Nacional do Ensino Médio (ENEM), pesos atribuídos às provas de Matemática do ENEM, período de ingresso no curso, carga horária semanal de aulas, conhecimento matemático prévio e metodologia de avaliação diferenciada - no desempenho obtido pelos calouros na disciplina em questão. Para tanto, estudou-se o desempenho de 3.010 alunos da UTFPR, pertencentes aos campi Pato Branco e Ponta Grossa, que ingressaram na instituição de 2010 a 2014. Os dados referentes às variáveis quantitativas foram coletados por meio de consultas ao sistema acadêmico institucional e aplicações de testes aos calouros. Em seguida, estes dados foram analisados com auxílio de ferramentas estatísticas. A coleta de dados referentes à variável qualitativa (comprometimento acadêmico) ocorreu por meio de entrevistas semiestruturadas realizadas junto a dezessete alunos, sendo que a análise se amparou na metodologia de Análise do Conteúdo, proposta por Bardin (1977). Os resultados sugerem a dependência entre cinco variáveis quantitativas analisadas e o desempenho obtido na disciplina de Cálculo I. Além disso, apontam que as posturas discentes adotadas frente a disciplina de Cálculo Diferencial e Integral I foram determinantes para o bom ou mau desempenho na disciplina. Como produto final foi confeccionado um aplicativo web que permitirá a reaplicação da metodologia de análise dos dados quantitativos nos outros câmpus da UTFPR e em outras instituições de ensino superior.
This research aims to analyse factors in order to understand their significance to the failure of Engineering freshmen students in Differential and Integral Calculus I. To this purpose, the basic hypothesis adopted is that academic commitment is a variable that expressively affects this setting. The theoretical framework summarizes the origin and evolution of Engineering courses, the relevance of the subject and respective failures, as well as potential aggravating circumstances. In addition, it approaches key factors related to failure in Calculus discussed in current literature. This is a mixed approach research and secondary hypotheses intended to either confirm or disregard the impact of certain variables, namely: grade achieved by students in Mathematics exam conducted in Brazilian High School National Exam (Exame Nacional do Ensino Médio, ENEM); weights assigned to ENEM Mathematics test; term of course admission (fall or spring); quantity of courses per week; previous knowledge on Mathematics; and distinct evaluation methodology. The research studies the performance of 3,010 students of UTFPR of both Pato Branco and Ponta Grossa campuses enrolled in the institution from 2010 to 2014. Data related to quantitative variables were collected through searches in the institution’s academic system and conduction of tests to first-year students. Subsequently, this data was analysed using statistics tools. The data accrual related to the qualitative variable (academic commitment) occurred through semi-structured interviews conducted along with some students and analysis was supported by Content Analysis methodology proposed by Bardin (1977). Results suggest the dependency among the five quantitative variables analysed and the performance achieved in the subject Calculus I. Furthermore, they indicate that students’ behaviour regarding the subject Differential and Integral Calculus I was definitive for either good or poor performance in the subject. The final product was the construction of a web applicative which allows the reutilization of quantitative data analysis methodology in other UTFPR campuses and college institutions.
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Barbosa, Sandra Malta [UNESP]. "Tecnologias da informação e comunicação, função composta e regra de cadeia." Universidade Estadual Paulista (UNESP), 2009. http://hdl.handle.net/11449/102124.
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Baseando-me na noção de coletivo pensante seres-humanos-com-mídias, o objetivo desta pesquisa foi responder à pergunta diretriz Como o coletivo, formado por alunos-comtecnologias, produz o conhecimento acerca de função composta e regra da cadeia, a partir de uma abordagem gráfica? O processo de visualização implícito nessa pergunta é potencializado pelas Tecnologias da Informação e Comunicação (TIC), que transformam o modo como o conhecimento é produzido, reorganizando a forma de interagir e pensar. Os dados foram coletados com alguns alunos ingressantes no Curso de Matemática da UNESP - Rio Claro durante os “Experimentos de Ensino”. Foram elaborados cinco episódios que apresentaram subsídios para responder à pergunta diretriz desta pesquisa. Tais episódios indicam que a produção do conhecimento dos alunos envolvidos, acerca de função composta e regra da cadeia, ocorreu por meio de elaborações de conjecturas, formuladas durante o processo de visualização potencializado pelas TIC. Tais conjecturas foram confirmadas ou refutadas levando-se em conta o entrelaçamento das representações múltiplas, que permearam todas as atividades, e um coletivo pensante seres-humanos-com-mídias, no qual o ser humano transforma e é transformado pelas mídias em um processo interativo. A partir desses resultados, outras indagações surgiram sobre o papel do professor-pesquisador e sua prática na sala de aula.
Based on the notion of thinking collectives of humans-with-media, the objective of this research was to respond to the research question How does a collective composed of studentswith- technologies produce knowledge about the Composition of Functions and the Chain Rule using a graphic approach? The visualization process implicit in this question is potentiated by Information and Communication Technologies (ICT), which transform the way knowledge is produced, reorganizing interaction and thinking. Data was collected with some university students enrolled within the undergraduate Mathematics Program at UNESP – Rio Claro during “Teaching Experiments”. Five episodes were selected that were particularly informative with respect to the research question. The episodes indicate that students’ knowledge production regarding composition of functions and the chain rule occurred through the elaborations of conjectures formulated during the process of visualization potentiated by the ICT. These conjectures were confirmed or rejected based on the interweaving of multiple representations that permeated all the activities, and a humans-with-media thinking collective, in which the human transforms and is transformed by the media in an interactive process. Based on these findings, new questions emerged regarding the role of the researcher-professor and teaching practice in the classroom.
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Barbosa, Sandra Malta. "Tecnologias da informação e comunicação, função composta e regra de cadeia /." Rio Claro : [s.n.], 2009. http://hdl.handle.net/11449/102124.
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Orientador: Marcelo de Carvalho BorbaBanca: Márcia Maria Fusaro Pinto
Banca: Maria Helena Sebastiana Sahão Bizelli
Banca: Edna Maura Zuffi
Banca: Henrique Lazari
Resumo: Baseando-me na noção de coletivo pensante seres-humanos-com-mídias, o objetivo desta pesquisa foi responder à pergunta diretriz Como o coletivo, formado por alunos-comtecnologias, produz o conhecimento acerca de função composta e regra da cadeia, a partir de uma abordagem gráfica? O processo de visualização implícito nessa pergunta é potencializado pelas Tecnologias da Informação e Comunicação (TIC), que transformam o modo como o conhecimento é produzido, reorganizando a forma de interagir e pensar. Os dados foram coletados com alguns alunos ingressantes no Curso de Matemática da UNESP - Rio Claro durante os "Experimentos de Ensino". Foram elaborados cinco episódios que apresentaram subsídios para responder à pergunta diretriz desta pesquisa. Tais episódios indicam que a produção do conhecimento dos alunos envolvidos, acerca de função composta e regra da cadeia, ocorreu por meio de elaborações de conjecturas, formuladas durante o processo de visualização potencializado pelas TIC. Tais conjecturas foram confirmadas ou refutadas levando-se em conta o entrelaçamento das representações múltiplas, que permearam todas as atividades, e um coletivo pensante seres-humanos-com-mídias, no qual o ser humano transforma e é transformado pelas mídias em um processo interativo. A partir desses resultados, outras indagações surgiram sobre o papel do professor-pesquisador e sua prática na sala de aula.
Abstract: Based on the notion of thinking collectives of humans-with-media, the objective of this research was to respond to the research question How does a collective composed of studentswith- technologies produce knowledge about the Composition of Functions and the Chain Rule using a graphic approach? The visualization process implicit in this question is potentiated by Information and Communication Technologies (ICT), which transform the way knowledge is produced, reorganizing interaction and thinking. Data was collected with some university students enrolled within the undergraduate Mathematics Program at UNESP - Rio Claro during "Teaching Experiments". Five episodes were selected that were particularly informative with respect to the research question. The episodes indicate that students' knowledge production regarding composition of functions and the chain rule occurred through the elaborations of conjectures formulated during the process of visualization potentiated by the ICT. These conjectures were confirmed or rejected based on the interweaving of multiple representations that permeated all the activities, and a humans-with-media thinking collective, in which the human transforms and is transformed by the media in an interactive process. Based on these findings, new questions emerged regarding the role of the researcher-professor and teaching practice in the classroom.
Doutor
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Paranhos, Marcos de Miranda. "Parametrização e movimentação de curvas e superfícies para uso em Modelação Matemática." Pontifícia Universidade Católica de São Paulo, 2015. https://tede2.pucsp.br/handle/handle/11029.
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Previous issue date: 2015-03-24This research is themed content traditionally taught in mathematical disciplines of Higher Education. The curves and surfaces studied in the Differential and Integral Calculus and Analytic Geometry and transformations of Linear Algebra are some content. The proposed question is what are the development of systematic activities possibilities, articulation and application of mathematical objects studied in the disciplines of CDI, GA and AL, for further study of these subjects? It was the way they are taught to present deepening proposals, articulation and application thereof, in view of Mathematical Modelling in order to enhance the results achieved in their learning and use. Were developed using the methodology of Didactic Engineering Mathematical Modelling activities in computational environment to be worked with students who have studied these disciplines. In the first stage there were four proposed activities to familiarize the student with the parameterization of curves and surfaces, with the changes and using the Winplot software. This step aimed to enable students to describe and move objects of reality in computing environment, using expressions and objects of mathematics. In the second stage, were proposed four activities to reproduce situations of reality, which can be expressed and modified by means of mathematical objects studied and modeled in the first stage. The forms of work presented in the survey do not dispense what is already done, but have favorable prospects especially in two respects: the depth that can be given to the objects studied, bringing difficult issues to deal with in other contexts, and in the form of work shown enjoyable and stimulating
Esta pesquisa tem como tema conteúdos tradicionalmente ministrados nas disciplinas matemáticas do Ensino Superior. As curvas e superfícies estudadas no Cálculo Diferencial e Integral e na Geometria Analítica e as transformações da Álgebra Linear são alguns desses conteúdos. A questão proposta é quais são as possibilidades de elaboração de atividades de sistematização, articulação e aplicação de objetos matemáticos estudados nas disciplinas de CDI, GA e AL, para aprofundar o estudo dessas disciplinas? Verificou-se a forma como eles são ensinados para apresentar propostas de aprofundamento, articulação e aplicação dos mesmos, na perspectiva da Modelação Matemática, a fim de aprimorar os resultados obtidos no seu aprendizado e utilização. Foram desenvolvidas com o uso da metodologia da Engenharia Didática atividades de Modelação Matemática em ambiente computacional para serem trabalhadas com alunos que já cursaram essas disciplinas. Em uma primeira etapa foram propostas quatro atividades para familiarizar o aluno com a parametrização de curvas e superfícies, com as transformações e com o uso do software Winplot. Essa etapa visou a habilitar os alunos a descrever e movimentar objetos da realidade em ambiente computacional, usando expressões e objetos da Matemática. Na segunda etapa, foram propostas quatro atividades para reproduzir situações da realidade, que podem ser expressas e modificadas por meio dos objetos matemáticos estudados e modelados na primeira etapa. As formas de trabalho apresentadas na pesquisa não dispensam aquilo que já é realizado, mas apresentam perspectivas favoráveis especialmente em dois aspectos: na profundidade que se pode dar aos objetos estudados, trazendo questões difíceis de se tratar em outros contextos, e na forma de trabalho que se mostra agradável e estimulante
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Pires, Luiz Fernando Rodrigues. "As influências das tecnologias da informação e comunicação nas estratégias de ensino e aprendizagem de cálculo diferencial e integral." Universidade Federal de Juiz de Fora (UFJF), 2016. https://repositorio.ufjf.br/jspui/handle/ufjf/3663.
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O objetivo desta presente pesquisa é investigar e analisar “Quais as influências das Tecnologias da Informação e Comunicação nas Estratégias de Ensino e Aprendizagem de Cálculo Diferencial e Integral”. Tendo como foco buscar compreender a relação entre homem e máquina durante a prática educacional de professores e estudantes de Cálculo. Para isso, partimos da hipótese de que as ocorrências dessas relações possam estar sendo ocasionadas pela disseminação e apropriação das tecnologias digitais perante a sociedade. Nesse âmbito, evidenciase um aprimoramento da forma de realizar operações matemáticas por meio dos aplicativos instalados nos aparelhos móveis. Para compreensão deste questionamento a pesquisa utilizou-se de dois cenários de investigação como procedimentos metodológicos, sendo um formado por entrevistas semiestruturadas com seis professores de Cálculo, com intuito de investigar o que esses professores sabem, pensam e acham sobre sua prática e a técnica de realizar operações matemáticas por meio das influências das TIC. E outro para análise das influências das TIC nas estratégias de aprendizagem dos estudantes, por meio de um questionário on-line. Mediante aos procedimentos e as análises das entrevistas e do questionário, os resultados mostram que foi possível verificar o reconhecimento desses novos instrumentos em meio às estratégias de aprendizagem dos estudantes, mas fora das estratégias dos professores, confirmando que a influência da técnica exposta poderá ou talvez já possa estar sendo mais uma problemática para o ensino e aprendizagem da matemática. Com esta consequência, podemos dizer que a transferência do esforço material e mental para as máquinas retrata uma situação auspiciosa e tem em princípio o valor de libertação ao homem requisitando, neste momento, estudos e pesquisas para que professores possam conhecer e saberem como trabalhar com essas máquinas de calcular para o processo de ensino e aprendizagem, de modo a gerar aprendizagens significativas além das atividades procedimentais do somente calcular.
The purpose of this research is to investigate and analyze "What are the influences of Information and Communication Technologies in Differential and Integral Calculus Teaching and Learning Strategies". With the aim of understanding the relationship between man and machine during the educational practice of teachers and students of Calculus. For this, we start from the hypothesis that the occurrences of these relations may be caused by the dissemination and appropriation of digital technologies in society. In this context, it is evident an improvement in the way of performing mathematical operations through the applications installed in mobile devices. In order to understand this questioning, the research used two research scenarios as methodological procedures, one consisting of semi-structured interviews with six Calculus teachers, in order to investigate what these teachers know, think and think about their practice and the technique of Mathematical operations through the influences of TIC. And another to analyze the influences of TIC in student learning strategies, through an online questionnaire. Through the procedures and analyzes of the interviews and the questionnaire, the results show that it was possible to verify the recognition of these new instruments in the student learning strategies, but outside of the teachers' strategies, confirming that the influence of the exposed technique may or may not May already be more problematic for the teaching and learning of mathematics. With this consequence, we can say that the transfer of the material and mental effort to the machines portrays an auspicious situation and has in principle the value of liberation to the man requesting, at the moment, studies and researches for teachers to know how to work with these calculating machines for The process of teaching and learning, in order to generate meaningful learning beyond the procedural activities of the only calculate.
Books on the topic "Differential and integral calculus teaching"
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Horacio, Porta, and Uhl J. J, eds. Calculus&Mathematica: Integrals : measuring accumulated growth. Reading, Mass: Addison-Wesley, 1994.
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Davis, Bill. Calculus&Mathematica: Vector calculus : measuring in two and three dimensions. Reading, Mass: Addison-Wesley, 1994.
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Davis, Bill. Calculus&Mathematica.: Measuring nearness. Reading, Mass: Addison-Wesley, 1994.
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Davis, Bill. Calculus&Mathematica.: Measuring growth. Reading, Mass: Addison-Wesley, 1994.
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Davis, Bill. Calculus&Mathematica.: Measuring accumulated growth. Reading, Mass: Addison-Wesley, 1994.
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Horacio, Porta, and Uhl J. J, eds. Calculus&Mathematica: Derivatives : measuring growth. Reading, Mass: Addison-Wesley, 1994.
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Davis, Bill. Calculus&Mathematica: Approximations : measuring nearness. Reading, Mass: Addison-Wesley Pub. Co., 1994.
Find full textBook chapters on the topic "Differential and integral calculus teaching"
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Mahmudov, E. "Differential Calculus." In Single Variable Differential and Integral Calculus, 107–44. Paris: Atlantis Press, 2013. http://dx.doi.org/10.2991/978-94-91216-86-2_4.
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Hairer, E., and G. Wanner. "Differential and Integral Calculus." In Undergraduate Texts in Mathematics, 80–169. New York, NY: Springer New York, 2008. http://dx.doi.org/10.1007/978-0-387-77036-9_2.
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Lopez, Robert J. "Teaching the Definite Integral." In Maple via Calculus, 49–54. Boston, MA: Birkhäuser Boston, 1994. http://dx.doi.org/10.1007/978-1-4612-0267-7_12.
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Pérez López, César. "Differential Equations." In MATLAB Differential and Integral Calculus, 181–213. Berkeley, CA: Apress, 2014. http://dx.doi.org/10.1007/978-1-4842-0304-0_8.
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Pérez López, César. "Symbolic Differential and Integral Calculus." In MATLAB Differential Equations, 125–71. Berkeley, CA: Apress, 2014. http://dx.doi.org/10.1007/978-1-4842-0310-1_8.
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Drábek, Pavel, and Jaroslav Milota. "Abstract Integral and Differential Calculus." In Methods of Nonlinear Analysis, 109–48. Basel: Springer Basel, 2012. http://dx.doi.org/10.1007/978-3-0348-0387-8_3.
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Godement, Roger. "Multivariate Differential and Integral Calculus." In Universitext, 133–273. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-16053-5_2.
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Mahmudov, E. "The Indefinite Integral." In Single Variable Differential and Integral Calculus, 223–58. Paris: Atlantis Press, 2013. http://dx.doi.org/10.2991/978-94-91216-86-2_8.
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Mahmudov, E. "The Definite Integral." In Single Variable Differential and Integral Calculus, 259–334. Paris: Atlantis Press, 2013. http://dx.doi.org/10.2991/978-94-91216-86-2_9.
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Pérez López, César. "Introduction and the MATLAB Environment." In MATLAB Differential and Integral Calculus, 1–15. Berkeley, CA: Apress, 2014. http://dx.doi.org/10.1007/978-1-4842-0304-0_1.
Full textConference papers on the topic "Differential and integral calculus teaching"
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Carmo, Shirlene, Luís Souto, and Carlos Silva. "THE INTERDISCIPLINARITY OF FORENSIC SCIENCES IN THE EDUCATIONAL SPHERE: AN ANALYSIS OF THIS CONTEXT IN SECONDARY SCHOOL." In International Conference on Education and New Developments. inScience Press, 2021. http://dx.doi.org/10.36315/2021end041.
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Many students when entering higher education, mainly in courses of exact or natural sciences and engineering, have difficulties in following the initial contents taught, due in part to the lack of knowledge arising from unique traditional methodology applied during their training. Some graduations even promote leveling courses in order to try reducing the deficits brought from previous education. Subjects such as Differential and Integral Calculus that are on the curricular basis of these courses, show high failure rates, strongly linked to gaps in previously acquired knowledge in mathematics. These factors directly contribute to the increase in retention rates and school dropout. So, there is a relentless search for improvement in the teaching-learning of these sciences, in order to motivate students, still in required education to knowledge building. It is commonly observed that young people are very attracted to the scientific disclosures broadcast by the media, as can be seen in the investigative series, which use forensic expertise for solving cases of a judiciary nature. In this sense, this work aimed to summarize studies that have been developed and implemented about the use of forensic sciences in the promotion of teaching-learning in secondary schools. The methodology was based on exploratory qualitative research. The results are based on experiences that occurred in the school context in USA, Brazil and Portugal, where it appears that students are more involved in the development of educational activities when integrated in a forensic like context, benefiting from collaborative work when trying to arrive to a common goal, similar to the assignment of a true forensic scientist. This allows them to recognize the importance of these contents, facilitates the presentation before the classroom, while improving the interaction with the social environment in which they are inserted. Teacher’s feedback confirms the beneficial implementation of these activities in the educational context and considers it with potential to attract attention and awaken the interest of these students in the sciences, thus improving the comprehension of theoretical concepts of the contents integrated in the school curriculum. The interdisciplinarity implemented on the production and socialization of knowledge is necessary and decisive to promote effective teaching and learning. The Forensic Sciences contemplate this interdisciplinarity and contribute that students feel more involved and motivated in learning, reducing retention rates and school dropout and increasing the search for science and technological careers.
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Edalat, Abbas. "Extensions of Domain Maps in Differential and Integral Calculus." In 2015 30th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS). IEEE, 2015. http://dx.doi.org/10.1109/lics.2015.47.
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Lepellere, Maria Antonietta, Stefano Urbinati, and Nizar Salahi Al Asbahi. "TEACHING MULTIVARIABLE DIFFERENTIAL CALCULUS USING GEOGEBRA AND QUIZZES." In 14th International Technology, Education and Development Conference. IATED, 2020. http://dx.doi.org/10.21125/inted.2020.2474.
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Tang, Howe Eng, Nor Hazizah Julaihi, Li Li Voon, and Kelvin Goh. "Students' perceptions on teaching and learning of integral calculus through e-Integral Map." In 2017 International Conference on Computer and Drone Applications (IConDA). IEEE, 2017. http://dx.doi.org/10.1109/iconda.2017.8270390.
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Sepriyanti, Nana, Remiswal, and Hutomo Atman Maulana. "Developing Interactive Multimedia Learning for Teaching Integral Calculus in College." In The Second International Conference on Social, Economy, Education, and Humanity. SCITEPRESS - Science and Technology Publications, 2019. http://dx.doi.org/10.5220/0009185104260432.
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Gomes, Luciana T., and Laecio C. Barros. "Fuzzy calculus via extension of the derivative and integral operators and fuzzy differential equations." In NAFIPS 2012 - 2012 Annual Meeting of the North American Fuzzy Information Processing Society. IEEE, 2012. http://dx.doi.org/10.1109/nafips.2012.6290965.
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Retumban, Joseph D., Cinderella D. S. Dancel, Romeo Q. Tolentino, Alexa Ray R. Fernando, and Cresencia M. Vahdanipour. "An Empirical Study on the Impact of Pre-recorded Lectures on Students' Performance in Integral Calculus." In 2018 IEEE International Conference on Teaching, Assessment, and Learning for Engineering (TALE). IEEE, 2018. http://dx.doi.org/10.1109/tale.2018.8615360.
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Zetriuslita and Rezi Ariawan. "The Development of Integration Technique Teaching Materials based on Problem Based Learning in Integral Calculus Course." In The Second International Conference on Social, Economy, Education, and Humanity. SCITEPRESS - Science and Technology Publications, 2019. http://dx.doi.org/10.5220/0009094701230129.
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Ławrynowicz, Julian, Tatsuro Ogata, and Osamu Suzuki. "Differential and integral calculus for a Schauder basis on a fractal set (I) (Schauder basis 80 years after)." In Lvov Mathematical School in the Period 1915-45. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2009. http://dx.doi.org/10.4064/bc87-0-11.
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Tangpong, X. W., and Om P. Agrawal. "Fractional Optimal Control of Distributed Systems." In ASME 2007 International Mechanical Engineering Congress and Exposition. ASMEDC, 2007. http://dx.doi.org/10.1115/imece2007-43046.
Full textAbstract:
This paper presents a formulation and a numerical scheme for Fractional Optimal Control (FOC) for a class of distributed systems. The fractional derivative is defined in the Caputo sense. The performance index of a Fractional Optimal Control Problem (FOCP) is considered as a function of both the state and the control variables, and the dynamic constraints are expressed by a Partial Fractional Differential Equation (PFDE). The scheme presented rely on reducing the equations for distributed system into a set of equations that have no space parameter. Several strategies are pointed out for this task, and one of them is discussed in detail. This involves discretizing the space domain into several segments, and writing the spatial derivatives in terms of variables at space node points. The Calculus of Variations, the Lagrange multiplier, and the formula for fractional integration by parts are used to obtain Euler-Lagrange equations for the problem. The numerical technique presented in [1] for scalar case is extended for the vector case. In this technique, the FOC equations are reduced to Volterra type integral equations. The time domain is also descretized into several segments. For the linear case, the numerical technique results into a set of algebraic equations which can be solved using a direct or an iterative scheme. The problem is solved for various order of fractional derivatives and various order of space and time discretizations. Numerical results show that for the problem considered, only a few space grid points are sufficient to obtain good results, and the solutions converge as the size of the time step is reduced. The formulation presented is simple and can be extended to FOC of other distributed systems.