Instrumentalization of the symbolic artifact 1st degree equations with two unknowns in a non-digital environment
Autor(a) principal: | |
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Data de Publicação: | 2022 |
Outros Autores: | , , , , |
Tipo de documento: | Artigo |
Idioma: | por |
Título da fonte: | Research, Society and Development |
Texto Completo: | https://rsdjournal.org/index.php/rsd/article/view/36205 |
Resumo: | This article aims to analyse the process of instrumentalization of the symbolic artifact 1st degree equation with two unknowns in 8th grade elementary school students. The theoretical framework used was the Instrumentation Theory from the perspective of Pierre Rabardel. With a qualitative approach and an action-research design, the data were collected from observation, audio and video recordings and material produced by the students. Recognizing that the graphic representation of a 1st degree linear equation with two unknowns is a straight line in the Cartesian plane is the main objective of an instrumentalization process of this mathematical object and constitutes the starting point of the phenomenon of Instrumental Genesis. From the observations took, it was possible to point the groups realized that, even though each one has constructed rectangles of different dimensions, what evidently resulted in tables with different values, the algebraic expression to represent the regularity observed in the tables was the same, diverging only in the letters chosen by each group to represent the rectangle dimensions. Moreover, the groups realized their graphic representations diverged only in the chosen points but it was the same line, thus demonstrating the instrumentalization process of the present mathematic object. |
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Instrumentalization of the symbolic artifact 1st degree equations with two unknowns in a non-digital environmentInstrumentalización del artefacto simbólico ecuaciones de 1er grado con dos incógnitas en un entorno no digitalInstrumentalização do artefato simbólico equações do 1º grau com duas incógnitas em um ambiente não digitalInstrumentaciónEcuación lineal de primer grado con dos incógnitasRepresentación gráficaArtefacto simbólicoEnseñanza.InstrumentalizaçãoEquação linear de 1º grau com duas incógnitasRepresentação gráficaArtefato simbólicoEnsino.Instrumentation1st degree linear equation with two unknownsGraphic representationTeachingSymbolic artifact.This article aims to analyse the process of instrumentalization of the symbolic artifact 1st degree equation with two unknowns in 8th grade elementary school students. The theoretical framework used was the Instrumentation Theory from the perspective of Pierre Rabardel. With a qualitative approach and an action-research design, the data were collected from observation, audio and video recordings and material produced by the students. Recognizing that the graphic representation of a 1st degree linear equation with two unknowns is a straight line in the Cartesian plane is the main objective of an instrumentalization process of this mathematical object and constitutes the starting point of the phenomenon of Instrumental Genesis. From the observations took, it was possible to point the groups realized that, even though each one has constructed rectangles of different dimensions, what evidently resulted in tables with different values, the algebraic expression to represent the regularity observed in the tables was the same, diverging only in the letters chosen by each group to represent the rectangle dimensions. Moreover, the groups realized their graphic representations diverged only in the chosen points but it was the same line, thus demonstrating the instrumentalization process of the present mathematic object.Este artículo tiene como objetivo analizar el proceso de instrumentalización del artefacto simbólico ecuación de 1° grado con dos incógnitas en estudiantes del 8° año de la enseñanza básica. El marco teórico utilizado fue la Teoría de la Instrumentación desde la perspectiva de Pierre Rabardel. Con un enfoque cualitativo y con un diseño de investigación-acción, los datos fueron recolectados a partir de la observación, grabaciones de audio y video y material producido por los estudiantes. Reconocer que la representación gráfica de una ecuación lineal de primer grado con dos incógnitas es una línea recta en el plano cartesiano es el objetivo principal de un proceso de instrumentalización de este objeto matemático y constituye el punto de partida del fenómeno de la Génesis Instrumental. De las observaciones realizadas en el paso, se pudo evidenciar que los grupos se dieron cuenta de que, si bien cada uno había construido rectángulos de diferentes dimensiones, lo que evidentemente resultó en tablas con diferentes valores, la expresión algebraica para representar la regularidad observada en las tablas era el mismo, solo se diferenciaba en las letras elegidas por cada grupo para representar las dimensiones del rectángulo. Además, los grupos se dieron cuenta de que sus representaciones gráficas diferían sólo en los puntos elegidos, pero que se trataba de la misma línea recta, evidenciando así el proceso de instrumentalización del objeto matemático en cuestión.Este artigo tem como objetivo analisar o processo de instrumentalização do artefato simbólico equação do 1º grau com duas incógnitas em estudantes do 8º ano do ensino fundamental. O referencial teórico utilizado foi a Teoria da Instrumentação sob a ótica de Pierre Rabardel. De abordagem qualitativa e com delineamento de uma pesquisa-ação, os dados foram coletados a partir de observação, registros em áudio e vídeo e material produzido pelos estudantes. Reconhecer que a representação gráfica de uma equação linear de 1º grau com duas incógnitas é uma reta no plano cartesiano é o principal objetivo de um processo de instrumentalização desse objeto matemático e constitui-se como ponto de partida do fenômeno da Gênese Instrumental. A partir das observações feitas da etapa, foi possível evidenciar que os grupos perceberam que, mesmo cada um tendo construído retângulos de dimensões diferentes, o que, evidentemente, resultou em tabelas com valores diferentes, a expressão algébrica para representar a regularidade observada nas tabelas era a mesma, diferindo apenas nas letras escolhidas por cada grupo para representar as dimensões do retângulo. Ademais, os grupos perceberam que suas representações gráficas diferiam apenas nos pontos escolhidos, mas que se tratava da mesma reta, evidenciando, dessa forma, o processo de instrumentalização do objeto matemático em questão.Research, Society and Development2022-10-24info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfhttps://rsdjournal.org/index.php/rsd/article/view/3620510.33448/rsd-v11i14.36205Research, Society and Development; Vol. 11 No. 14; e108111436205Research, Society and Development; Vol. 11 Núm. 14; e108111436205Research, Society and Development; v. 11 n. 14; e1081114362052525-3409reponame:Research, Society and Developmentinstname:Universidade Federal de Itajubá (UNIFEI)instacron:UNIFEIporhttps://rsdjournal.org/index.php/rsd/article/view/36205/30245Copyright (c) 2022 Roberta dos Santos Rodrigues; Ana Beatriz Pinheiro Lira; Ewerly Reis Conceição; Kassio Kevy Alves de Souza; Thamillie Ketelen da Costa; Francisco Eteval da Silva Feitosahttps://creativecommons.org/licenses/by/4.0info:eu-repo/semantics/openAccessRodrigues, Roberta dos SantosLira, Ana Beatriz PinheiroConceição, Ewerly ReisSouza, Kassio Kevy Alves de Costa, Thamillie Ketelen da Feitosa, Francisco Eteval da Silva2022-11-08T13:36:27Zoai:ojs.pkp.sfu.ca:article/36205Revistahttps://rsdjournal.org/index.php/rsd/indexPUBhttps://rsdjournal.org/index.php/rsd/oairsd.articles@gmail.com2525-34092525-3409opendoar:2024-01-17T09:50:50.436759Research, Society and Development - Universidade Federal de Itajubá (UNIFEI)false |
dc.title.none.fl_str_mv |
Instrumentalization of the symbolic artifact 1st degree equations with two unknowns in a non-digital environment Instrumentalización del artefacto simbólico ecuaciones de 1er grado con dos incógnitas en un entorno no digital Instrumentalização do artefato simbólico equações do 1º grau com duas incógnitas em um ambiente não digital |
title |
Instrumentalization of the symbolic artifact 1st degree equations with two unknowns in a non-digital environment |
spellingShingle |
Instrumentalization of the symbolic artifact 1st degree equations with two unknowns in a non-digital environment Rodrigues, Roberta dos Santos Instrumentación Ecuación lineal de primer grado con dos incógnitas Representación gráfica Artefacto simbólico Enseñanza. Instrumentalização Equação linear de 1º grau com duas incógnitas Representação gráfica Artefato simbólico Ensino. Instrumentation 1st degree linear equation with two unknowns Graphic representation Teaching Symbolic artifact. |
title_short |
Instrumentalization of the symbolic artifact 1st degree equations with two unknowns in a non-digital environment |
title_full |
Instrumentalization of the symbolic artifact 1st degree equations with two unknowns in a non-digital environment |
title_fullStr |
Instrumentalization of the symbolic artifact 1st degree equations with two unknowns in a non-digital environment |
title_full_unstemmed |
Instrumentalization of the symbolic artifact 1st degree equations with two unknowns in a non-digital environment |
title_sort |
Instrumentalization of the symbolic artifact 1st degree equations with two unknowns in a non-digital environment |
author |
Rodrigues, Roberta dos Santos |
author_facet |
Rodrigues, Roberta dos Santos Lira, Ana Beatriz Pinheiro Conceição, Ewerly Reis Souza, Kassio Kevy Alves de Costa, Thamillie Ketelen da Feitosa, Francisco Eteval da Silva |
author_role |
author |
author2 |
Lira, Ana Beatriz Pinheiro Conceição, Ewerly Reis Souza, Kassio Kevy Alves de Costa, Thamillie Ketelen da Feitosa, Francisco Eteval da Silva |
author2_role |
author author author author author |
dc.contributor.author.fl_str_mv |
Rodrigues, Roberta dos Santos Lira, Ana Beatriz Pinheiro Conceição, Ewerly Reis Souza, Kassio Kevy Alves de Costa, Thamillie Ketelen da Feitosa, Francisco Eteval da Silva |
dc.subject.por.fl_str_mv |
Instrumentación Ecuación lineal de primer grado con dos incógnitas Representación gráfica Artefacto simbólico Enseñanza. Instrumentalização Equação linear de 1º grau com duas incógnitas Representação gráfica Artefato simbólico Ensino. Instrumentation 1st degree linear equation with two unknowns Graphic representation Teaching Symbolic artifact. |
topic |
Instrumentación Ecuación lineal de primer grado con dos incógnitas Representación gráfica Artefacto simbólico Enseñanza. Instrumentalização Equação linear de 1º grau com duas incógnitas Representação gráfica Artefato simbólico Ensino. Instrumentation 1st degree linear equation with two unknowns Graphic representation Teaching Symbolic artifact. |
description |
This article aims to analyse the process of instrumentalization of the symbolic artifact 1st degree equation with two unknowns in 8th grade elementary school students. The theoretical framework used was the Instrumentation Theory from the perspective of Pierre Rabardel. With a qualitative approach and an action-research design, the data were collected from observation, audio and video recordings and material produced by the students. Recognizing that the graphic representation of a 1st degree linear equation with two unknowns is a straight line in the Cartesian plane is the main objective of an instrumentalization process of this mathematical object and constitutes the starting point of the phenomenon of Instrumental Genesis. From the observations took, it was possible to point the groups realized that, even though each one has constructed rectangles of different dimensions, what evidently resulted in tables with different values, the algebraic expression to represent the regularity observed in the tables was the same, diverging only in the letters chosen by each group to represent the rectangle dimensions. Moreover, the groups realized their graphic representations diverged only in the chosen points but it was the same line, thus demonstrating the instrumentalization process of the present mathematic object. |
publishDate |
2022 |
dc.date.none.fl_str_mv |
2022-10-24 |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
https://rsdjournal.org/index.php/rsd/article/view/36205 10.33448/rsd-v11i14.36205 |
url |
https://rsdjournal.org/index.php/rsd/article/view/36205 |
identifier_str_mv |
10.33448/rsd-v11i14.36205 |
dc.language.iso.fl_str_mv |
por |
language |
por |
dc.relation.none.fl_str_mv |
https://rsdjournal.org/index.php/rsd/article/view/36205/30245 |
dc.rights.driver.fl_str_mv |
https://creativecommons.org/licenses/by/4.0 info:eu-repo/semantics/openAccess |
rights_invalid_str_mv |
https://creativecommons.org/licenses/by/4.0 |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
application/pdf |
dc.publisher.none.fl_str_mv |
Research, Society and Development |
publisher.none.fl_str_mv |
Research, Society and Development |
dc.source.none.fl_str_mv |
Research, Society and Development; Vol. 11 No. 14; e108111436205 Research, Society and Development; Vol. 11 Núm. 14; e108111436205 Research, Society and Development; v. 11 n. 14; e108111436205 2525-3409 reponame:Research, Society and Development instname:Universidade Federal de Itajubá (UNIFEI) instacron:UNIFEI |
instname_str |
Universidade Federal de Itajubá (UNIFEI) |
instacron_str |
UNIFEI |
institution |
UNIFEI |
reponame_str |
Research, Society and Development |
collection |
Research, Society and Development |
repository.name.fl_str_mv |
Research, Society and Development - Universidade Federal de Itajubá (UNIFEI) |
repository.mail.fl_str_mv |
rsd.articles@gmail.com |
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1797052773410275328 |