Álgebra e aspectos do pensamento algébrico : um estudo com resolução de problemas na licenciatura em Ciências Naturais e Matemática - UFMT/Sinop

Detalhes bibliográficos
Autor(a) principal: Laier, Simone Simionato dos Santos
Data de Publicação: 2014
Tipo de documento: Dissertação
Idioma: por
Título da fonte: Repositório Institucional da UFMT
Texto Completo: http://ri.ufmt.br/handle/1/318
Resumo: This master's research is aimed at studying the aspects of algebraic thinking shown by the students of the Licentiate’s Degree program in Natural Sciences and Mathematics, with specialization in Mathematics, of UFMT (The Federal University of Mato Grosso) – Sinop Campus, MT. This is a qualitative, exploratory and investigative research, in which we seek to study the manifestations of students in relation to algebra, using the procedure of mathematical problem solving. Data for this research were collected through questionnaires aimed at the profiling of subjects, eight mathematical problems and audiovisual records. From what was produced by the subjects, the data were organized and the analysis proceeded in two distinct approaches: the first one intended to identify aspects of algebraic thinking revealed by solving mathematical problems and the elements of the problem solving that could reveal a sequence of steps or procedures used to reach the answer, as well as check whether there would be a production of meaning for the activity in question; the second approach aimed to consider the concepts of algebra presented and the stance in relation to mathematical problem solving. For the first approach, we identified in the records presented, that the subjects proceeded with some regularity in operations and developed some kind of generalization process for the problems, in addition to using algebraic language to express themselves mathematically. Regarding the steps taken to solve the problems, we noted that each subject maintained a regularity of the solutions presented, i.e., they applied the same resources used to solve a problem to the other ones, as if it were a personal characteristic to organize their own ideas. For the second approach, what the subjects presented about their algebraic knowledge provided some support for our reflecting on how these prospective teachers perceive algebra and the activities involving mathematical problem solving. These results suggest that the subjects had had no experiences that provided the opportunity to work with problem solving encouraging a new way of working and exploring mathematical content. In what learning mathematics through problem solving is concerned, the possibility of learning from this methodology was not, in fact, identified, even though they consider it important for the development process of reasoning and algebraic thinking. Regarding the aspects of algebraic thinking that were revealed, we can conclude that, in relation to the extent of algebra, it predominantly stands out as generalized arithmetic, using letters to express a mathematical model in its functional aspect. The subjects operated with variables, using letters to express relations and functions, in order to establish equations that use letters as unknowns.
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spelling Álgebra e aspectos do pensamento algébrico : um estudo com resolução de problemas na licenciatura em Ciências Naturais e Matemática - UFMT/SinopÁlgebraPensamento algébricoResolução de problemasProdução de significadosFormação inicial de professoresCNPQ::CIENCIAS HUMANAS::EDUCACAOAlgebraAlgebraic thinkingProblem solvingProduction of meaningInitial teacher educationThis master's research is aimed at studying the aspects of algebraic thinking shown by the students of the Licentiate’s Degree program in Natural Sciences and Mathematics, with specialization in Mathematics, of UFMT (The Federal University of Mato Grosso) – Sinop Campus, MT. This is a qualitative, exploratory and investigative research, in which we seek to study the manifestations of students in relation to algebra, using the procedure of mathematical problem solving. Data for this research were collected through questionnaires aimed at the profiling of subjects, eight mathematical problems and audiovisual records. From what was produced by the subjects, the data were organized and the analysis proceeded in two distinct approaches: the first one intended to identify aspects of algebraic thinking revealed by solving mathematical problems and the elements of the problem solving that could reveal a sequence of steps or procedures used to reach the answer, as well as check whether there would be a production of meaning for the activity in question; the second approach aimed to consider the concepts of algebra presented and the stance in relation to mathematical problem solving. For the first approach, we identified in the records presented, that the subjects proceeded with some regularity in operations and developed some kind of generalization process for the problems, in addition to using algebraic language to express themselves mathematically. Regarding the steps taken to solve the problems, we noted that each subject maintained a regularity of the solutions presented, i.e., they applied the same resources used to solve a problem to the other ones, as if it were a personal characteristic to organize their own ideas. For the second approach, what the subjects presented about their algebraic knowledge provided some support for our reflecting on how these prospective teachers perceive algebra and the activities involving mathematical problem solving. These results suggest that the subjects had had no experiences that provided the opportunity to work with problem solving encouraging a new way of working and exploring mathematical content. In what learning mathematics through problem solving is concerned, the possibility of learning from this methodology was not, in fact, identified, even though they consider it important for the development process of reasoning and algebraic thinking. Regarding the aspects of algebraic thinking that were revealed, we can conclude that, in relation to the extent of algebra, it predominantly stands out as generalized arithmetic, using letters to express a mathematical model in its functional aspect. The subjects operated with variables, using letters to express relations and functions, in order to establish equations that use letters as unknowns.A presente pesquisa de mestrado tem por objetivo estudar Aspectos do Pensamento Algébrico revelados por acadêmicos da Licenciatura em Ciências Naturais e Matemática, com Habilitação em Matemática, da UFMT - Campus de Sinop/MT. Trata-se de uma pesquisa de natureza qualitativa, exploratória e investigativa, em que buscamos estudar as manifestações dos acadêmicos em relação à Álgebra, usando como procedimento a Resolução de Problemas matemáticos. Os instrumentos utilizados para a produção de dados incluíram a aplicação de questionários para a caracterização do perfil dos sujeitos; oito problemas matemáticos e registros audiovisuais. A partir do que foi produzido pelos sujeitos, organizamos os dados e procedemos à análise em dois enfoques: o primeiro para identificar aspectos do pensamento algébrico revelados na resolução dos problemas matemáticos, elementos na resolução que evidenciassem uma sequência de etapas ou procedimentos para chegarem à resposta, além de verificarmos se haveria a produção de algum significado para a atividade em questão; o segundo enfoque visou considerar as concepções de Álgebra apresentadas e o posicionamento em relação à Resolução de Problemas matemáticos. Diante disso, para o primeiro enfoque, identificamos nos registros apresentados, que os sujeitos procederam com certa regularidade nas operações, desenvolveram algum tipo de processo de generalização nos problemas, além de usar linguagem algébrica ao expressarem-se matematicamente. No que tange às etapas para a resolução dos problemas, percebemos que cada sujeito manteve uma regularidade nas soluções apresentadas, ou seja, lançaram mão dos mesmos recursos que utilizaram para resolver um problema, nos demais, como se fosse uma característica pessoal para organizarem suas ideias. Para o segundo enfoque, o que apresentaram, acerca de seus conhecimentos algébricos, nos ofereceu a possibilidade de refletir sobre como esses futuros professores lidam com a Álgebra e atividades envolvendo a Resolução de Problemas matemáticos. Disto, conseguimos identificar que os sujeitos não tiveram experiências que proporcionassem o trabalho com a Resolução de Problemas a favor de uma nova forma de trabalhar e explorar os conteúdos matemáticos. Em relação à aprendizagem da matemática por meio da Resolução de Problemas, não identificaram, de fato, a possibilidade de aprender com essa metodologia, mesmo considerando-a importante para o processo de desenvolvimento do raciocínio e pensamento algébrico. Sobre os Aspectos do Pensamento Algébrico que foram revelados, podemos concluir que, em relação às dimensões da Álgebra, predominantemente ela se destaca como aritmética generalizada com uso das letras para expressar um modelo aritmético em seu aspecto funcional. Operaram com a variação de grandezas, com o uso de letras expressando relações e funções e para o estabelecimento de equações que utilizam letras como incógnitas.Universidade Federal de Mato GrossoBrasilInstituto de Educação (IE)UFMT CUC - CuiabáPrograma de Pós-Graduação em EducaçãoWielewski, Gladys Denisehttp://lattes.cnpq.br/4154014326253864Wielewski, Gladys Denise502.478.161-91http://lattes.cnpq.br/4154014326253864Wielewski, Sergio Antonio388.861.709-04http://lattes.cnpq.br/1203599061747785502.478.161-91Cyrino, Márcia Cristina de Costa Trindade120.959.788-89http://lattes.cnpq.br/0809818122632169Laier, Simone Simionato dos Santos2017-05-29T12:09:40Z2014-04-232017-05-29T12:09:40Z2014-04-15info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesisLAIER, Simone Simionato dos Santos. Álgebra e aspectos do pensamento algébrico: um estudo com resolução de problemas na licenciatura em Ciências Naturais e Matemática - UFMT/Sinop. 2014. 163 f. Dissertação (Mestrado em Educação) - Universidade Federal de Mato Grosso, Instituto de Educação, Cuiabá, 2014.http://ri.ufmt.br/handle/1/318porinfo:eu-repo/semantics/openAccessreponame:Repositório Institucional da UFMTinstname:Universidade Federal de Mato Grosso (UFMT)instacron:UFMT2017-05-31T07:01:06Zoai:localhost:1/318Repositório InstitucionalPUBhttp://ri.ufmt.br/oai/requestjordanbiblio@gmail.comopendoar:2017-05-31T07:01:06Repositório Institucional da UFMT - Universidade Federal de Mato Grosso (UFMT)false
dc.title.none.fl_str_mv Álgebra e aspectos do pensamento algébrico : um estudo com resolução de problemas na licenciatura em Ciências Naturais e Matemática - UFMT/Sinop
title Álgebra e aspectos do pensamento algébrico : um estudo com resolução de problemas na licenciatura em Ciências Naturais e Matemática - UFMT/Sinop
spellingShingle Álgebra e aspectos do pensamento algébrico : um estudo com resolução de problemas na licenciatura em Ciências Naturais e Matemática - UFMT/Sinop
Laier, Simone Simionato dos Santos
Álgebra
Pensamento algébrico
Resolução de problemas
Produção de significados
Formação inicial de professores
CNPQ::CIENCIAS HUMANAS::EDUCACAO
Algebra
Algebraic thinking
Problem solving
Production of meaning
Initial teacher education
title_short Álgebra e aspectos do pensamento algébrico : um estudo com resolução de problemas na licenciatura em Ciências Naturais e Matemática - UFMT/Sinop
title_full Álgebra e aspectos do pensamento algébrico : um estudo com resolução de problemas na licenciatura em Ciências Naturais e Matemática - UFMT/Sinop
title_fullStr Álgebra e aspectos do pensamento algébrico : um estudo com resolução de problemas na licenciatura em Ciências Naturais e Matemática - UFMT/Sinop
title_full_unstemmed Álgebra e aspectos do pensamento algébrico : um estudo com resolução de problemas na licenciatura em Ciências Naturais e Matemática - UFMT/Sinop
title_sort Álgebra e aspectos do pensamento algébrico : um estudo com resolução de problemas na licenciatura em Ciências Naturais e Matemática - UFMT/Sinop
author Laier, Simone Simionato dos Santos
author_facet Laier, Simone Simionato dos Santos
author_role author
dc.contributor.none.fl_str_mv Wielewski, Gladys Denise
http://lattes.cnpq.br/4154014326253864
Wielewski, Gladys Denise
502.478.161-91
http://lattes.cnpq.br/4154014326253864
Wielewski, Sergio Antonio
388.861.709-04
http://lattes.cnpq.br/1203599061747785
502.478.161-91
Cyrino, Márcia Cristina de Costa Trindade
120.959.788-89
http://lattes.cnpq.br/0809818122632169
dc.contributor.author.fl_str_mv Laier, Simone Simionato dos Santos
dc.subject.por.fl_str_mv Álgebra
Pensamento algébrico
Resolução de problemas
Produção de significados
Formação inicial de professores
CNPQ::CIENCIAS HUMANAS::EDUCACAO
Algebra
Algebraic thinking
Problem solving
Production of meaning
Initial teacher education
topic Álgebra
Pensamento algébrico
Resolução de problemas
Produção de significados
Formação inicial de professores
CNPQ::CIENCIAS HUMANAS::EDUCACAO
Algebra
Algebraic thinking
Problem solving
Production of meaning
Initial teacher education
description This master's research is aimed at studying the aspects of algebraic thinking shown by the students of the Licentiate’s Degree program in Natural Sciences and Mathematics, with specialization in Mathematics, of UFMT (The Federal University of Mato Grosso) – Sinop Campus, MT. This is a qualitative, exploratory and investigative research, in which we seek to study the manifestations of students in relation to algebra, using the procedure of mathematical problem solving. Data for this research were collected through questionnaires aimed at the profiling of subjects, eight mathematical problems and audiovisual records. From what was produced by the subjects, the data were organized and the analysis proceeded in two distinct approaches: the first one intended to identify aspects of algebraic thinking revealed by solving mathematical problems and the elements of the problem solving that could reveal a sequence of steps or procedures used to reach the answer, as well as check whether there would be a production of meaning for the activity in question; the second approach aimed to consider the concepts of algebra presented and the stance in relation to mathematical problem solving. For the first approach, we identified in the records presented, that the subjects proceeded with some regularity in operations and developed some kind of generalization process for the problems, in addition to using algebraic language to express themselves mathematically. Regarding the steps taken to solve the problems, we noted that each subject maintained a regularity of the solutions presented, i.e., they applied the same resources used to solve a problem to the other ones, as if it were a personal characteristic to organize their own ideas. For the second approach, what the subjects presented about their algebraic knowledge provided some support for our reflecting on how these prospective teachers perceive algebra and the activities involving mathematical problem solving. These results suggest that the subjects had had no experiences that provided the opportunity to work with problem solving encouraging a new way of working and exploring mathematical content. In what learning mathematics through problem solving is concerned, the possibility of learning from this methodology was not, in fact, identified, even though they consider it important for the development process of reasoning and algebraic thinking. Regarding the aspects of algebraic thinking that were revealed, we can conclude that, in relation to the extent of algebra, it predominantly stands out as generalized arithmetic, using letters to express a mathematical model in its functional aspect. The subjects operated with variables, using letters to express relations and functions, in order to establish equations that use letters as unknowns.
publishDate 2014
dc.date.none.fl_str_mv 2014-04-23
2014-04-15
2017-05-29T12:09:40Z
2017-05-29T12:09:40Z
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.uri.fl_str_mv LAIER, Simone Simionato dos Santos. Álgebra e aspectos do pensamento algébrico: um estudo com resolução de problemas na licenciatura em Ciências Naturais e Matemática - UFMT/Sinop. 2014. 163 f. Dissertação (Mestrado em Educação) - Universidade Federal de Mato Grosso, Instituto de Educação, Cuiabá, 2014.
http://ri.ufmt.br/handle/1/318
identifier_str_mv LAIER, Simone Simionato dos Santos. Álgebra e aspectos do pensamento algébrico: um estudo com resolução de problemas na licenciatura em Ciências Naturais e Matemática - UFMT/Sinop. 2014. 163 f. Dissertação (Mestrado em Educação) - Universidade Federal de Mato Grosso, Instituto de Educação, Cuiabá, 2014.
url http://ri.ufmt.br/handle/1/318
dc.language.iso.fl_str_mv por
language por
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 Mato Grosso
Brasil
Instituto de Educação (IE)
UFMT CUC - Cuiabá
Programa de Pós-Graduação em Educação
publisher.none.fl_str_mv Universidade Federal de Mato Grosso
Brasil
Instituto de Educação (IE)
UFMT CUC - Cuiabá
Programa de Pós-Graduação em Educação
dc.source.none.fl_str_mv reponame:Repositório Institucional da UFMT
instname:Universidade Federal de Mato Grosso (UFMT)
instacron:UFMT
instname_str Universidade Federal de Mato Grosso (UFMT)
instacron_str UFMT
institution UFMT
reponame_str Repositório Institucional da UFMT
collection Repositório Institucional da UFMT
repository.name.fl_str_mv Repositório Institucional da UFMT - Universidade Federal de Mato Grosso (UFMT)
repository.mail.fl_str_mv jordanbiblio@gmail.com
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