Uma abordagem diferente para o ensino da função exponencial no Ensino Médio
Autor(a) principal: | |
---|---|
Data de Publicação: | 2014 |
Tipo de documento: | Dissertação |
Idioma: | por |
Título da fonte: | Repositório Institucional da UFSCAR |
Texto Completo: | https://repositorio.ufscar.br/handle/ufscar/7266 |
Resumo: | The objective of this essay is to propose a different approach to teaching the exponential function in high school. This new approach aims to provide a meaningful learning related to the subject exponential function, since students and teachers sometimes have difficulty understanding this concept, especially when it comes to real exponents. The work was based on preparation of some activities based on the Theory of Didactical Situations and applied following the methodology of the Didactic Engineering. There were basically five activity sheets, three of them were printed and two of them were spreadsheets. The problems and exercises aimed to examine and extend the validity of the fundamental property of exponential functions, that is, f(m + n) = f(m):f (n) for the dominance of natural numbers, integer, rational, real, and for the last one, we only worked with spreadsheets, specifically in the activity sheet number 5, to afford students an understanding about how the calculator obtains the approximate result of 2 √2 for example. The spreadsheet was also used in the activity sheet number 4, which deals with rational exponents. On this one we present an algorithm for the approximate calculation of nth roots of any real number. The activity sheets have been developed in order to provide students with maximum autonomy so that they could resolve them, being interspersed with adjunct sheets in order to introduce the new concept and theory discussed in the following activity sheet. The activities were implemented at a state school in It´apolis, and the results in a final analysis showed that this approach supplied a significant learning compared to traditional teaching. |
id |
SCAR_2b990f6d6570f1298f0b1ad5e16103e0 |
---|---|
oai_identifier_str |
oai:repositorio.ufscar.br:ufscar/7266 |
network_acronym_str |
SCAR |
network_name_str |
Repositório Institucional da UFSCAR |
repository_id_str |
4322 |
spelling |
Angelucci, MichelCosta, Ivo Machado dahttp://lattes.cnpq.br/1111331485581633http://lattes.cnpq.br/02309259127634639b5a625a-ea67-4fb1-9cab-3f6d7e9047762016-09-20T14:02:53Z2016-09-20T14:02:53Z2014-01-24ANGELUCCI, Michel. Uma abordagem diferente para o ensino da função exponencial no Ensino Médio. 2014. Dissertação (Mestrado em Ensino de Ciências Exatas) – Universidade Federal de São Carlos, São Carlos, 2014. Disponível em: https://repositorio.ufscar.br/handle/ufscar/7266.https://repositorio.ufscar.br/handle/ufscar/7266The objective of this essay is to propose a different approach to teaching the exponential function in high school. This new approach aims to provide a meaningful learning related to the subject exponential function, since students and teachers sometimes have difficulty understanding this concept, especially when it comes to real exponents. The work was based on preparation of some activities based on the Theory of Didactical Situations and applied following the methodology of the Didactic Engineering. There were basically five activity sheets, three of them were printed and two of them were spreadsheets. The problems and exercises aimed to examine and extend the validity of the fundamental property of exponential functions, that is, f(m + n) = f(m):f (n) for the dominance of natural numbers, integer, rational, real, and for the last one, we only worked with spreadsheets, specifically in the activity sheet number 5, to afford students an understanding about how the calculator obtains the approximate result of 2 √2 for example. The spreadsheet was also used in the activity sheet number 4, which deals with rational exponents. On this one we present an algorithm for the approximate calculation of nth roots of any real number. The activity sheets have been developed in order to provide students with maximum autonomy so that they could resolve them, being interspersed with adjunct sheets in order to introduce the new concept and theory discussed in the following activity sheet. The activities were implemented at a state school in It´apolis, and the results in a final analysis showed that this approach supplied a significant learning compared to traditional teaching.O objetivo desta dissertação é propor uma abordagem diferente para o ensino da função exponencial no Ensino Médio. Essa nova abordagem visa proporcionar uma Aprendizagem significativa no que diz respeito ao assunto função exponencial, visto que alunos e professores, por vezes, apresentam dificuldades no entendimento desse conceito, principalmente quando se trata de expoentes reais. O trabalho foi baseado na elaboração de folhas de atividades pautadas na teoria das Situações Didáticas e aplicadas seguindo a metodologia da Engenharia Didática. Foram basicamente cinco folhas de atividades, sendo que três delas foram impressas e duas na forma de planilhas eletrônicas. Os problemas e exercícios contidos nas folhas de atividades tinham como objetivo analisar, bem como estender, a validade da propriedade fundamental das funções exponenciais, isto é, f(m + n) = f(m):f (n), para o domínio dos naturais, inteiros, racionais e reais, sendo que neste último, trabalhamos apenas com as planilhas, mais especificamente na folha de atividade 5, para proporcionar aos alunos uma noção de como a calculadora obtém o resultado aproximado de 2 √2, por exemplo. A planilha eletrônica também foi utilizada na folha de atividade 4, que trata de expoentes racionais. Nesta fornecemos um algoritmo para o cálculo aproximado de raízes n-ésimas de um número real qualquer. As folhas de atividades foram desenvolvidas tendo em vista proporcionar aos alunos o máximo de autonomia para que os mesmos pudessem resolve-las, sendo intercaladas por folhas de complemento que buscam dar introdução e fundamentação téorica ao novo conceito abordado na folha de atividade seguinte. As atividades foram aplicadas em uma escola estadual da cidade de Itápolis, e os resultados obtidos nas análises a posteriori mostraram que essa abordagem proporcionou um aprendizado significativo, quando comparado com o ensino tradicional.Não recebi financiamentoporUniversidade Federal de São CarlosCâmpus São CarlosPrograma de Pós-Graduação em Ensino de Ciências Exatas - PPGECEUFSCarEnsino de MatemáticaFunção exponencialEngenharia DidáticaSituações didáticasTeaching of MathematicsExponential functionDidactic (or Teaching) EngineeringDidactic (or Teaching) situationsCIENCIAS EXATAS E DA TERRA::MATEMATICA::ANALISEUma abordagem diferente para o ensino da função exponencial no Ensino Médioinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesisOnline600600b3bcc5d4-e52a-4d89-9546-afbac7f4e935info:eu-repo/semantics/openAccessreponame:Repositório Institucional da UFSCARinstname:Universidade Federal de São Carlos (UFSCAR)instacron:UFSCARORIGINALDissMA.pdfDissMA.pdfapplication/pdf27125711https://repositorio.ufscar.br/bitstream/ufscar/7266/1/DissMA.pdf4ad39606591072bc308496b81c242b4dMD51LICENSElicense.txtlicense.txttext/plain; charset=utf-81957https://repositorio.ufscar.br/bitstream/ufscar/7266/2/license.txtae0398b6f8b235e40ad82cba6c50031dMD52TEXTDissMA.pdf.txtDissMA.pdf.txtExtracted texttext/plain242205https://repositorio.ufscar.br/bitstream/ufscar/7266/3/DissMA.pdf.txt1cfdf5e8a0a1a14dcbb4b57d603c9750MD53THUMBNAILDissMA.pdf.jpgDissMA.pdf.jpgIM Thumbnailimage/jpeg6408https://repositorio.ufscar.br/bitstream/ufscar/7266/4/DissMA.pdf.jpg6ba68f343575b0624d611cafd20080feMD54ufscar/72662023-09-18 18:30:49.033oai:repositorio.ufscar.br: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Repositório InstitucionalPUBhttps://repositorio.ufscar.br/oai/requestopendoar:43222023-09-18T18:30:49Repositório Institucional da UFSCAR - Universidade Federal de São Carlos (UFSCAR)false |
dc.title.por.fl_str_mv |
Uma abordagem diferente para o ensino da função exponencial no Ensino Médio |
title |
Uma abordagem diferente para o ensino da função exponencial no Ensino Médio |
spellingShingle |
Uma abordagem diferente para o ensino da função exponencial no Ensino Médio Angelucci, Michel Ensino de Matemática Função exponencial Engenharia Didática Situações didáticas Teaching of Mathematics Exponential function Didactic (or Teaching) Engineering Didactic (or Teaching) situations CIENCIAS EXATAS E DA TERRA::MATEMATICA::ANALISE |
title_short |
Uma abordagem diferente para o ensino da função exponencial no Ensino Médio |
title_full |
Uma abordagem diferente para o ensino da função exponencial no Ensino Médio |
title_fullStr |
Uma abordagem diferente para o ensino da função exponencial no Ensino Médio |
title_full_unstemmed |
Uma abordagem diferente para o ensino da função exponencial no Ensino Médio |
title_sort |
Uma abordagem diferente para o ensino da função exponencial no Ensino Médio |
author |
Angelucci, Michel |
author_facet |
Angelucci, Michel |
author_role |
author |
dc.contributor.authorlattes.por.fl_str_mv |
http://lattes.cnpq.br/0230925912763463 |
dc.contributor.author.fl_str_mv |
Angelucci, Michel |
dc.contributor.advisor1.fl_str_mv |
Costa, Ivo Machado da |
dc.contributor.advisor1Lattes.fl_str_mv |
http://lattes.cnpq.br/1111331485581633 |
dc.contributor.authorID.fl_str_mv |
9b5a625a-ea67-4fb1-9cab-3f6d7e904776 |
contributor_str_mv |
Costa, Ivo Machado da |
dc.subject.por.fl_str_mv |
Ensino de Matemática Função exponencial Engenharia Didática Situações didáticas |
topic |
Ensino de Matemática Função exponencial Engenharia Didática Situações didáticas Teaching of Mathematics Exponential function Didactic (or Teaching) Engineering Didactic (or Teaching) situations CIENCIAS EXATAS E DA TERRA::MATEMATICA::ANALISE |
dc.subject.eng.fl_str_mv |
Teaching of Mathematics Exponential function Didactic (or Teaching) Engineering Didactic (or Teaching) situations |
dc.subject.cnpq.fl_str_mv |
CIENCIAS EXATAS E DA TERRA::MATEMATICA::ANALISE |
description |
The objective of this essay is to propose a different approach to teaching the exponential function in high school. This new approach aims to provide a meaningful learning related to the subject exponential function, since students and teachers sometimes have difficulty understanding this concept, especially when it comes to real exponents. The work was based on preparation of some activities based on the Theory of Didactical Situations and applied following the methodology of the Didactic Engineering. There were basically five activity sheets, three of them were printed and two of them were spreadsheets. The problems and exercises aimed to examine and extend the validity of the fundamental property of exponential functions, that is, f(m + n) = f(m):f (n) for the dominance of natural numbers, integer, rational, real, and for the last one, we only worked with spreadsheets, specifically in the activity sheet number 5, to afford students an understanding about how the calculator obtains the approximate result of 2 √2 for example. The spreadsheet was also used in the activity sheet number 4, which deals with rational exponents. On this one we present an algorithm for the approximate calculation of nth roots of any real number. The activity sheets have been developed in order to provide students with maximum autonomy so that they could resolve them, being interspersed with adjunct sheets in order to introduce the new concept and theory discussed in the following activity sheet. The activities were implemented at a state school in It´apolis, and the results in a final analysis showed that this approach supplied a significant learning compared to traditional teaching. |
publishDate |
2014 |
dc.date.issued.fl_str_mv |
2014-01-24 |
dc.date.accessioned.fl_str_mv |
2016-09-20T14:02:53Z |
dc.date.available.fl_str_mv |
2016-09-20T14:02:53Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/masterThesis |
format |
masterThesis |
status_str |
publishedVersion |
dc.identifier.citation.fl_str_mv |
ANGELUCCI, Michel. Uma abordagem diferente para o ensino da função exponencial no Ensino Médio. 2014. Dissertação (Mestrado em Ensino de Ciências Exatas) – Universidade Federal de São Carlos, São Carlos, 2014. Disponível em: https://repositorio.ufscar.br/handle/ufscar/7266. |
dc.identifier.uri.fl_str_mv |
https://repositorio.ufscar.br/handle/ufscar/7266 |
identifier_str_mv |
ANGELUCCI, Michel. Uma abordagem diferente para o ensino da função exponencial no Ensino Médio. 2014. Dissertação (Mestrado em Ensino de Ciências Exatas) – Universidade Federal de São Carlos, São Carlos, 2014. Disponível em: https://repositorio.ufscar.br/handle/ufscar/7266. |
url |
https://repositorio.ufscar.br/handle/ufscar/7266 |
dc.language.iso.fl_str_mv |
por |
language |
por |
dc.relation.confidence.fl_str_mv |
600 600 |
dc.relation.authority.fl_str_mv |
b3bcc5d4-e52a-4d89-9546-afbac7f4e935 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.publisher.none.fl_str_mv |
Universidade Federal de São Carlos Câmpus São Carlos |
dc.publisher.program.fl_str_mv |
Programa de Pós-Graduação em Ensino de Ciências Exatas - PPGECE |
dc.publisher.initials.fl_str_mv |
UFSCar |
publisher.none.fl_str_mv |
Universidade Federal de São Carlos Câmpus São Carlos |
dc.source.none.fl_str_mv |
reponame:Repositório Institucional da UFSCAR instname:Universidade Federal de São Carlos (UFSCAR) instacron:UFSCAR |
instname_str |
Universidade Federal de São Carlos (UFSCAR) |
instacron_str |
UFSCAR |
institution |
UFSCAR |
reponame_str |
Repositório Institucional da UFSCAR |
collection |
Repositório Institucional da UFSCAR |
bitstream.url.fl_str_mv |
https://repositorio.ufscar.br/bitstream/ufscar/7266/1/DissMA.pdf https://repositorio.ufscar.br/bitstream/ufscar/7266/2/license.txt https://repositorio.ufscar.br/bitstream/ufscar/7266/3/DissMA.pdf.txt https://repositorio.ufscar.br/bitstream/ufscar/7266/4/DissMA.pdf.jpg |
bitstream.checksum.fl_str_mv |
4ad39606591072bc308496b81c242b4d ae0398b6f8b235e40ad82cba6c50031d 1cfdf5e8a0a1a14dcbb4b57d603c9750 6ba68f343575b0624d611cafd20080fe |
bitstream.checksumAlgorithm.fl_str_mv |
MD5 MD5 MD5 MD5 |
repository.name.fl_str_mv |
Repositório Institucional da UFSCAR - Universidade Federal de São Carlos (UFSCAR) |
repository.mail.fl_str_mv |
|
_version_ |
1802136303841574912 |