Made available in DSpace on 2014-06-11T19:24:58Z (GMT). No. of bitstreams: 0 Previous issue date: 2003Bitstream added on 2014-06-13T19:11:52Z : No. of bitstreams: 1 rubio_jas_me_mar.pdf: 926247 bytes, checksum: d9b4f1ef42ed8d89cff9ac69ccf885a0 (MD5) / O ensino de Matemática no Brasil vem, ao longo das décadas, sofrendo mudanças, críticas e adaptações. Essas transformações visam uma reformulação nas práticas educativas empregadas na escola e, para se ter um ensino de Matemática calcado em significados para o aluno, tais práticas educativas devem estar em sintonia com as mudanças sociais e os avanços tecnológicos. Os instrumentos tecnológicos podem servir como recursos didáticos nas atividades matemáticas da sala de aula, otimizando o tempo e deixando o aluno livre de procedimentos que não contribuem para seu real desenvolvimento. Um desses instrumentos, que está disponível para todas as crianças em idade escolar e que apresenta muitas possibilidades de aplicação nas aulas de matemática, é a calculadora. Neste trabalho foi feito um estudo, apoiado na realização de atividades com calculadora em alunos de 4ª série, em que se procurou identificar e discutir possibilidades e desafios desse equipamento, enquanto recurso didático nas aulas de matemática. A calculadora pode ser usada objetivando a motivação na realização de tarefas exploratórias e de investigação, verificação de resultados, correção de erros, auto-avaliação entre outros. Cabe ao professor, portanto, propor situações desafiadoras que permitam ao aluno o uso da calculadora como recurso na resolução dessas atividades. / The teaching of Mathematics in Brazil, has been changing with criticals and adaptations. These transformation have as objective a new formulation for educatives practices teached on schools and, get a teaching of Mathematics based on meanings to the pupil, these educative pratices must be allied with the social changings and technological development. The technological instruments may be used as didatic resources for math activities on room classes, optimizing the time and allow a free pupil of procedures that don't increase your real development. One of these instruments, that is disponible to all children with school age, is the calculator. In this work, it was made on study, based on development of activities with calculators to the 4th serial pupil, wich looked for identify and discuss possibilities and chalenges of this equipment, while didatic resource on mathematics classes. It may be used objectiving the motivation to make exploratory and investigation exercises, cheking results, correction of mistakes, self evaluation, among others. It's the teacher, however, that propose challenge situations allowing the pupil use calculator as a resource to solve this activities.

abstract: Type 1 diabetes (T1D) is a chronic disease that affects 1.25 million people in the United States. There is no known cure and patients must self-manage the disease to avoid complications resulting from blood glucose (BG) excursions. Patients are more likely to adhere to treatments when they incorporate lifestyle preferences. Current technologies that assist patients fail to consider two factors that are known to affect BG: exercise and alcohol. The hypothesis is postprandial blood glucose levels of adult patients with T1D can be improved by providing insulin bolus or carbohydrate recommendations that account for meal and alcohol carbohydrates, glycemic excursion, and planned exercise. I propose an evidence-based decision support tool, iDECIDE, to make recommendations to improve glucose control by taking into account meal and alcohol carbohydrates, glycemic excursion and planned exercise. iDECIDE is deployed as a low-cost and easy to disseminate smartphone application. A literature review was conducted on T1D and the state-of-the-art in diabetes technology. To better understand self-management behaviors and guide the development of iDECIDE, several data sources were collected and analyzed: surveys, insulin pump paired with glucose monitoring, and self-tracking of exercise and alcohol. The analysis showed variability in compensation techniques for exercise and alcohol and that patients made unaided decisions, suggesting a need for better decision support. The iDECIDE algorithm can make insulin and carbohydrate recommendations. Since there were no existing in-silico methods for assessing bolus calculators, like iDECIDE, I proposed a novel methodology to retrospectively compare insulin pump bolus calculators. Application of the methodology shows that iDECIDE outperformed the Medtronic insulin pump bolus calculator and could have improved glucose control. This work makes contributions to diabetes technology researchers, clinicians and patients. The iDECIDE app provides patients easy access to a decision support tool that can improve glucose control. The study of behaviors from diabetes technology and self-report patient data can inform clinicians and the design of future technologies and bedside tools that integrate patient’s behaviors and perceptions. The comparison methodology provides a means for clinical informatics researchers to identify and retrospectively test promising insulin blousing algorithms using real-life data. / Dissertation/Thesis / Doctoral Dissertation Biomedical Informatics 2017

Submitted by Viviane Lima da Cunha (viviane@biblioteca.ufpb.br) on 2015-06-02T12:16:09Z No. of bitstreams: 1 arquivototal.pdf: 1083776 bytes, checksum: 399c5b22353566747d56756453686cc3 (MD5) / Approved for entry into archive by Viviane Lima da Cunha (viviane@biblioteca.ufpb.br) on 2015-06-02T12:55:19Z (GMT) No. of bitstreams: 1 arquivototal.pdf: 1083776 bytes, checksum: 399c5b22353566747d56756453686cc3 (MD5) / Made available in DSpace on 2015-06-02T12:55:19Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 1083776 bytes, checksum: 399c5b22353566747d56756453686cc3 (MD5) Previous issue date: 2014-08-26 / This research has as object of study the teaching of Financial Mathematics, with the aid of a tool: the Financial Calculator HP 12C, preparing citizens able to manage their own budgets and the labor market. Preliminary concepts concerning the theme are presented, followed by examples in context, pointing out the main factors that facilitate the understanding of each content. Being approached through practical applications, which makes learning easier, and increases motivation and students' interest. / Este trabalho de pesquisa tem como escopo o ensino da Matemática Financeira, com o auxílio de uma ferramenta: a calculadora financeira HP 12C, preparando cidadãos capazes de administrar suas próprias finanças e para o mercado de trabalho. Apresenta conceitos preliminares ao tema, seguido de exemplos contextualizados, apontando os principais fatores, que facilitam a compreensão em cada conteúdo. Sendo tratado através de aplicações práticas, que facilita a aprendizagem, motivação e interesse do aluno.

Submitted by Liliane Ferreira (ljuvencia30@gmail.com) on 2018-10-09T11:20:31Z No. of bitstreams: 2 Dissertação - Euder Pires da Cunha - 2018.pdf: 1924909 bytes, checksum: 089c0f2b82b719ba10f0f2e940dbf7af (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Rejected by Luciana Ferreira (lucgeral@gmail.com), reason: Na citação o nome entre parênteses não precisa colocar Sociedade.... O certo é: (Mestrado em Matemática em Rede Nacional) CUNHA, E. P. A matemática como ciência e o uso da calculadora no seu ensino. 2018. 129 f. Dissertação (Mestrado em Matemática em Rede Nacional - Sociedade Brasileira de Matemática) - Universidade Federal de Goiás, Catalão, 2018. on 2018-10-09T11:43:05Z (GMT) / Submitted by Liliane Ferreira (ljuvencia30@gmail.com) on 2018-10-09T14:07:20Z No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Dissertação - Euder Pires da Cunha - 2018.pdf: 1924909 bytes, checksum: 089c0f2b82b719ba10f0f2e940dbf7af (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2018-10-10T10:40:35Z (GMT) No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Dissertação - Euder Pires da Cunha - 2018.pdf: 1924909 bytes, checksum: 089c0f2b82b719ba10f0f2e940dbf7af (MD5) / Made available in DSpace on 2018-10-10T10:40:35Z (GMT). No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Dissertação - Euder Pires da Cunha - 2018.pdf: 1924909 bytes, checksum: 089c0f2b82b719ba10f0f2e940dbf7af (MD5) Previous issue date: 2018-10-04 / Mathematics is a science present in the lives of all people, everywhere in situations of their daily lives, whether at home, at leisure or at work. This science has evolved since man appeared on the planet until the present day, being used by the human being so that he can develop different types of activity. In the history of the development of this discipline, several technologies were created to aid in mathematical calculations, as in the case of calculators. This technology, however, is aimed at several debates, as there are those who defend its use in the classroom and there are those who are totally against this feature. Faced with this question, this research intends to analyze the use of the calculator in the teaching of mathematics. The methodological resource used for the elaboration of the research was the bibliographical review, based on works by authors who have already discussed the problematic in question. Subsequently, an analysis of two lesson plans was carried out, one for secondary education and another for the second phase of elementary school, in order to consider how the calculator could be used for the development of different types of activities within this discipline. As final considerations of the research, it is necessary to mention that the calculator can help in the development of students' calculations ability, especially because it is the student who will direct how the calculations are done and, therefore, also have to reflect on them. / A matemática é uma ciência presente na vida de todas as pessoas, em todos os lugares em situações do seu cotidiano, seja em casa, no lazer, no trabalho. Essa ciência evoluiu desde que o homem surgiu no planeta até os dias atuais, sendo utilizada pelo ser humano para que ele possa desenvolver diferentes tipos de atividade. Na história do desenvolvimento dessa disciplina, diversas tecnologias foram criadas para auxiliar nos cálculos matemáticos, como é o caso das calculadoras. Essa tecnologia, porém, é alvo de diversos debates, pois há os que defendem sua utilização em sala de aula e há os que são totalmente contra esse recurso. Diante de tal questão, esta pesquisa pretende analisar o uso da calculadora no ensino de matemática. O recurso metodológico utilizado para a elaboração da pesquisa foi a revisão bibliográfica, baseada em obras de autores que já discutiram a problemática em questão. Posteriormente foi realizada uma proposta e descrição de duas sequências didáticas, uma destinada ao ensino médio e outra à segunda fase do ensino fundamental de forma a traçar considerações sobre como a calculadora poderia ser utilizada para o desenvolvimento de diferentes tipos de atividades dentro dessa disciplina. Como considerações finais da pesquisa é preciso citar que a calculadora pode auxiliar no desenvolvimento da habilidade de cálculos dos alunos, especialmente porque é o aluno quem irá direcionar como os cálculos são feitos e, por isto, também precisa refletir sobre os mesmos.

This thesis attempts to answer how a “braille-only” calculator can be constructed and what needs consideration. An attempt to create such a device has been made. The underlying purpose is the poor selection of braille devices readily available in the market. Braille literacy is very low and the development of easy to use devices that utilize braille actively might encourage the learning of the language. A new design for a braille display, which is the display of the calculator, is proposed and a prototype has been built to test it. The first prototype is promising, albeit impractical and quite large. It functions as a calculator but it requires manual calibration upon startup to set the braille wheels to their starting positions. / Rapporten försöker svara på hur en miniräknare som enbart använder blindskrift can byggas och vad som bör tänkas på. Ett försök till att konstruera en sådan apparat har gjorts. Den bakomliggande anledningen till detta är det tunna utbudet av blindskrifts-apparater på marknaden. Läskunnigheten av blindskrift är väldigt låg och utvecklandet av apparater som aktivt använder blindskrift kan uppmuntra lärandet av språket. En ny design till en braille skärm, som blir skärmen till miniräknaren, föreslås och en prototyp har konstruerats för att testas. Den första prototypen är lovande, även om den är ganska opraktisk och stor. Den fungerar som en miniräknare men kräver manuell kalibrering vid uppstart för att nollställa läget hos braille-hjulen.

[pt] Este trabalho apresenta o resultado de algumas reflexões voltadas para o ensino de matemática, em especial nas áreas de aritmética e álgebra, abordando conteúdos relativos aos conjuntos numéricos presentes no currículo de matemática do ensino fundamental II. Os objetivos dessas reflexões foram verificar o quão importantes podem ser os registros semióticos (ver capítulo 4, seção 4.2.1), a teoria da zona de desenvolvimento proximal (ZPD) proveniente da teoria sócio-construtivista (ver capítulo 4, seções 4.2.2 e 4.2.2.1), e o uso da calculadora na investigação acerca de números decimais e no estudo dos conjuntos numéricos. Com base num espaço democrático e que valoriza o diálogo, a vida cotidiana do aluno com o mundo da matemática e utilizando a troca de experiências entre eles, temos como objetivo a compreensão de conceitos e aprendizagem significativa acerca dos conteúdos abordados. A aritmética, em especial, exige um olhar cuidadoso no que diz respeito às representações e propriedades operatórias que um número pode apresentar. O desenvolvimento de métodos que estimulam esse olhar faz com que o entendimento dos educandos em relação aos números decimais ganhe significados importantes e consideráveis. Por fim, este trabalho também defende a questão da utilização da tecnologia na escola através do uso orientado de calculadoras, nas aulas de matemática, como um recurso pedagógico que pode se mostrar bastante eficiente, visto que a tecnologia está cada vez mais presente no cotidiano da sociedade. Os resultados dessas reflexões foram traduzidos no desenvolvimento de uma atividade aplicada junto aos alunos, e foram expostos ao longo desse trabalho. Atividade essa que foi aplicada predominantemente em turmas do sétimo ano do ensino fundamental, uma vez que eles possuem os pré-requisitos necessários para os questionamentos propostos nela, porém não tiveram ainda grande contato com o conteúdo proposto por essa atividade. E também foi aplicada em uma turma de oitavo ano, como atividade de recuperação paralela. Criamos também uma atividade interessante para a abordagem dos números irracionais na qual exploramos triângulos retângulos. Espera-se que essas reflexões possam colaborar de alguma maneira na educação básica, para o desenvolvimento de uma educação matemática mais autônoma e significativa. / [en] This work presents the result of some reflections on the teaching of mathematics, especially in the areas of arithmetic and algebra, addressing contents related to the numerical sets present in the mathematics curriculum of elementary school II. The objectives of these reflections were to verify how important the semiotic records can be (see chapter 4, section 4.2.1), the zone of proximal development theory (ZPD) derived from the socio-constructivist theory (see chapter 4, sections 4.2.2 and 4.2.2.1), and the use of the calculator in the investigation of decimal numbers and in the study of numerical sets. Based on a democratic space that values dialogue, the student s daily life with the world of mathematics and using the exchange of experiences between them, we aim to understand concepts and meaningful learning about the contents covered. Arithmetic, in particular, requires a careful look at the representations and operative properties that a number can present. The development of methods that stimulate this view makes the student s understanding of decimal numbers gain important and considerable meanings. Finally, this work also defends the question of the use of technology in school through the oriented use of calculators, in mathematics classes, as a pedagogical resource that can prove to be quite efficient, since technology is increasingly present in the daily life of society. The results of these reflections were translated into the development of an applied activity with the students, and were exposed throughout this work. This activity was applied predominantly in classes of the seventh year of elementary school, since they have the necessary prerequisites for the questions proposed in it, but they have not yet had great contact with the content proposed by this activity. It was also applied to an eighth grade class, as a parallel recovery activity. We have also created an interesting activity for addressing irrational numbers in which we explore right triangles. We hope that these reflections can collaborate in some way in basic education, for the development of a more autonomous and meaningful mathematics education.

Heavy precipitation events are expected to increase in intensity and frequency, due to global warming. Sewer systems might overload during heavy rainfall, resulting in floods which potentially affect all municipalities in Sweden. Traditionally, stormwater is seen as pipe-related problem, but a transition towards Sustainable Drainage Systems (SuDS) has started. SuDS aim to reduce the quantity of the runoff from the site, slow down the runoff to allow (in)filtration, and provide treatment of the surface water before discharge. In Sweden, municipalities are responsible for the sewer system and realization and implementation of climate change adaptation measures, like SuDS. Tools and models support the highly complex selection, location, and design of SuDS, by systematically providing the most relevant information that represents the actual drainage system in the best way possible. Furthermore, models are used to predict the behaviour of SuDS, which may form Decision Support Systems (DSS). The highest interest in SuDS modelling and DSS lies in water quantity, however existing models are complex and lack flexibility, transferability, and stakeholder inclusion. The aim of this project is to provide a tool for the Municipality of Östersund that aids in the decision-making and design process for the implementation of SuDS, concerning their capacity to store stormwater. The ‘SuDS water storage capacity calculator’ can be used to test what (combinations of) SuDS are able to store the stormwater of a heavy rainfall event.The following SuDS components were included in the calculator: extensive green roofs, underground infiltration systems, infiltration basins, swales, porous pavements, detention basins, ponds, and wetlands. Secondly, the technical criteria forming the basis of the calculator were identified through a literature review. These criteria were used to calculate precipitation and the water storage capacity of each SuDS. The calculator was then built in Microsoft Powerpoint using Visual Basic for Applications (VBA). Two case studies were selected in Östersund and explored using the calculator. The water storage capacity of each SuDS component was calculated using scenarios in which 25%, 50%, 75%, and 100% of the total available area in each case study was used as input. Finally, four combinations of SuDS were tested concerning their water storage capacity. All calculated water storage capacity was compared to the amount of water falling on the case study areas during a heavy precipitation event that only occurs once every 100 years.The developed calculator can be used to calculate water storage capacity of SuDS and precipitation in a simple way. The tool contains user input and default values, which can still be changed. Furthermore, the calculator allows comparison between the amount of precipitation and water storage capacity. The results of the scenarios show that underground infiltration systems and detention basins have the highest potential to store stormwater, followed by infiltration basins, porous pavements, and ponds or wetlands. The calculator has limited design options, due to its simplification of reality. However, its limits are mostly applicable further in the designing process. The4calculator gives a rough estimate of the potential water storage capacity of a variety of SuDS components. The calculator is a useful tool before the design process has started, by providing an indication of the options that are worthwhile to consider in terms of water storage capacity. Furthermore, opportunities for optimization of the tool were recognized. The water storage capacity resulting from the different scenarios was compared to the precipitation falling on each case study area. Realistically, the amount of precipitation that exceeds the capacity of the sewer system might not fall directly where the SuDS are located. Finally, the calculator allows applications of a wider range of combinations of SuDS components. / <p>2022-06.16</p>

No description available.

Made available in DSpace on 2016-04-27T16:57:21Z (GMT). No. of bitstreams: 1 Sonia de Cassia Santos Prado.pdf: 7281171 bytes, checksum: 0ac5c4214cfe8ef6b2dfeced6c495c16 (MD5) Previous issue date: 2012-11-25 / The aim of this documentary qualitative research is to investigate the insertion of the use of the calculator in Learning Situations proposed to students from Ensino Fundamental II (from 5th to 9 th grade), from the São Paulo State public school in Teacher s Notebooks , using the Advanced Mathematical Thinking. In order to do so, we used the three main chronological points from Content Analysis, pre-analysis, exploring the material and treating the results, inference and interpretation, to investigate the given orientations about the approach from the Learning Situations from the Mathematics Teacher s Notebooks (2009), distributed to all the state s teaching public network. The motivation to choose this theme has come from the fact that the usage of calculators as a resource to learning Maths is still not enough, even though it is known that they help to investigate problem-situations. The usage of calculators is motivated in the official documents that guide the technologies in Ensino Fundamental II. Thus, we have searched elements in ideas of Advanced Mathematical Thinking on how a Mathematical concept can be understood by the student, according to the interaction of the mental processes of the components: representation, visualization, generalization, synthesis and abstraction from the use of the calculator. To reinforce the grounds for this research, we have followed the orientations from official documents: Parâmetros Curriculares Nacionais do Ensino Fundamental II (1998), Proposta Curricular de Matemática (2008), Currículo de Matemática (2010), and Mathematics Teacher s Notebooks (2009) and in researches made about the utilization of this pedagogical tool. Subjectively, we present the analysis of Learning Situations , by using previously established categories that, in some point of its sequential development, proposed the utilization of this pedagogical resource, seeing which of the components of Advanced Mathematical Thinking could be developed. We have found, among 64 Learning Situations proposed to the grades from Ensino Fundamental II, 8 activities that, along by its development, asked to use this resource in some section, and the representation is in 8 activities, the visualization is in 6 activities, the generalization is in 5 activities, the synthesis is in 8 activities and the abstraction is in 7 activities / O trabalho a seguir apresenta uma pesquisa qualitativa do tipo documental que tem como objetivo investigar a inserção do uso da calculadora nas Situações de Aprendizagens propostas ao Ensino Fundamental II, da rede pública do Estado de São Paulo nos Cadernos do Professor, à luz do Pensamento Matemático Avançado. Para tanto nos orientamos pelos três polos cronológicos da Análise de Conteúdo, pré-analise, exploração do material e tratamento dos resultados, inferência e interpretação, de forma a investigar as orientações dadas sobre a abordagem realizada a partir das Situações de Aprendizagem propostas no Caderno do Professor de Matemática (2009), distribuído a toda rede pública estadual. A motivação sobre a escolha deste tema se fez porque a utilização da calculadora como recurso para a aprendizagem em matemática, mesmo apresentando a característica facilitadora na investigação de situações-problema e sua utilização prevista nos documentos oficiais que orientam as práticas e o uso de tecnologias no Ensino Fundamental, ainda não é suficiente. Desta forma, buscamos elementos nas ideias do Pensamento Matemático Avançado sobre como um conceito matemático pode ser compreendido pelo aluno, segundo a interação entre os processos mentais das componentes: representação, visualização, generalização, síntese e abstração a partir da utilização da calculadora. Para embasar ainda esta pesquisa, pautamo-nos nas orientações contidas nos documentos oficiais: Parâmetros Curriculares Nacionais do Ensino Fundamental II (1998), Proposta Curricular de Matemática (2008), Currículo de Matemática (2010), nos Cadernos do Professor de Matemática (2009) e nas pesquisas realizadas acerca da utilização deste recurso pedagógico. Subjetivamente, apresentamos a análise das Situações de Aprendizagens que, em algum momento de seu desenvolvimento sequencial, propuseram a utilização deste recurso pedagógico, observando quais das componentes do Pensamento Matemático Avançado poderiam ser desenvolvidas, nas quais encontramos dentre 64 Situações de Aprendizagem propostas as séries do Ensino Fundamental II, 8 atividades que, ao longo de seu desenvolvimento, solicitaram a utilização deste recurso em alguma seção, e se as referidas atividades promoviam o desenvolvimento das componentes do Pensamento Matemático Avançado: representação, visualização, generalização, síntese e abstração

Made available in DSpace on 2016-04-27T16:57:36Z (GMT). No. of bitstreams: 1 Antonio Sergio dos Santos Oliveira.pdf: 3420485 bytes, checksum: a83bd8f0798c199d29cbfdc9affea731 (MD5) Previous issue date: 2015-03-18 / This paper had the objective of making a group of students from the fifth grade to build meaning to the fundamental operatorial rules with fractional numbers by using scientific calculators with fractional representation. With this in mind, we developed a sequence of teaching with four students of a public school located in the suburb of Belém-PA. We based our theories on the Theory of Didactic Situations (TDS) (Teoria das Situações Didáticas-TSD) and the Theory of Record of Semiotic Representation and the Didactic Engineering as methodology. The TDS helped us to elaborate, experiment and analyze the results of the sequence, while the Theory of Record of Semiotic Representation helped us to articulate among the figure and numeric records. In the analysis of the activities, we verified that the students after using the scientific calculator, they managed to verbalize and write rules to the addition and subtraction of fractional numbers with the same denominator to a multiplication of any fractional numbers and to the division of fractional numbers that presented not only the numerators but also the multiple denominators. However, the students managed not only by using the calculator to perceive the rules for the addition and division of any fractional numbers. We understand that the calculator allowed the students to search for relations and dot not treat the fractional numbers only as two natural numbers. We also should probably have related to other didactic resources so that they could have perceived the relations between numerators and denominators for the addition and subtraction operations / O presente trabalho teve por objetivo levar um grupo de estudantes do quinto ano do ensino fundamental a construir significado para as regras operatórias fundamentais com números fracionários a partir da utilização de calculadoras científicas com representação fracionária. Com esse intuito, desenvolvemos uma sequência de ensino com quatro alunos de uma escola pública situada na periferia de Belém/PA e como aporte teórico utilizamos a Teoria das Situações Didáticas (TSD) e a Teoria de Registros de Representação Semiótica, e a Engenharia Didática como metodologia. A TSD nos auxiliou na elaboração, experimentação e análise dos resultados da sequência, enquanto a Teoria de Registros de Representação Semiótica na articulação entre registros numéricos e figurais. Na análise das atividades verificamos que os alunos conseguiram, após a utilização da calculadora, verbalizar e escrever regras para a adição e subtração de números fracionários com mesmo denominador, para a multiplicação de quaisquer números fracionários e para a divisão de números fracionários que apresentavam tanto os numeradores, quanto os denominadores múltiplos. No entanto, não conseguiram, apenas utilizando a calculadora perceber as regras para a adição e divisão de números fracionários quaisquer. Entendemos que a calculadora permitiu que os alunos buscassem relações e não tratassem os números fracionários apenas como dois números naturais, mas faltou, provavelmente, relacioná-la a outros recursos didáticos para que percebessem as relações entre numeradores e denominadores para as operações de adição e subtração