AN ANALYSIS OF THE CONCEPT OF SIMILARITY PRESENTED IN TEXTBOOKS IN BRAZIL AND THE UNITED STATES
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Data de Publicação: | 2021 |
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Tipo de documento: | preprint |
Idioma: | eng |
Título da fonte: | SciELO Preprints |
Texto Completo: | https://preprints.scielo.org/index.php/scielo/preprint/view/2225 |
Resumo: | This paper is a product of a research that investigates the presence of Geometry in textbooks, that is part of project of a Theorem – Reflection on Geometry and Mathematics Education research group. The focus here is to present results of the international study: how textbooks present the concept of similarity? For this, a qualitative research were developed and textbooks of three collections from Brazil and three from United States were examined. A synthesis of the literature related to the search for textbooks and the teaching and learning of the concept of similarity is presented, and the theoretical framework explores similarity as positioned at the crossroads of geometry and number to describe the ways in which different textbooks approach it. Sequence of topics and tasks presented in each textbook are described and then comparisons are made. There were theorems and problem types that were presented consistently across all textbooks, but differences in expectations related to proof and the use of coordinates and geometric transformations were identified. Only textbooks in the US included the use of transformations and coordinates and placed more emphasis on formal proof. Implications for the teaching and learning of similarity are provided. |
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AN ANALYSIS OF THE CONCEPT OF SIMILARITY PRESENTED IN TEXTBOOKS IN BRAZIL AND THE UNITED STATESANÁLISIS DEL CONCEPTO DE SEMEJANZA PRESENTADO EN LIBROS DE TEXTO EN BRASIL Y ESTADOS UNIDOSUMA ANÁLISE DO CONCEITO DE SEMELHANÇA APRESENTADO EM LIVROS DIDÁTICOS NO BRASIL E NOS ESTADOS UNIDOSTextbook analysismathematical tasksinternational textbook comparisonAnálisis de libros de textosimilitudtareas matemáticascomparación internacional de libros de textoAnálise de livros didáticossemelhançatarefas matemáticascomparação internacional de livros didáticosThis paper is a product of a research that investigates the presence of Geometry in textbooks, that is part of project of a Theorem – Reflection on Geometry and Mathematics Education research group. The focus here is to present results of the international study: how textbooks present the concept of similarity? For this, a qualitative research were developed and textbooks of three collections from Brazil and three from United States were examined. A synthesis of the literature related to the search for textbooks and the teaching and learning of the concept of similarity is presented, and the theoretical framework explores similarity as positioned at the crossroads of geometry and number to describe the ways in which different textbooks approach it. Sequence of topics and tasks presented in each textbook are described and then comparisons are made. There were theorems and problem types that were presented consistently across all textbooks, but differences in expectations related to proof and the use of coordinates and geometric transformations were identified. Only textbooks in the US included the use of transformations and coordinates and placed more emphasis on formal proof. Implications for the teaching and learning of similarity are provided.Este artículo es producto de una investigación que investiga la presencia de la geometría en los libros de texto. El enfoque aquí es presentar los resultados del estudio: ¿cómo presentan los libros de texto el concepto de similitud? Para ello, se examinaron libros de texto de tres colecciones de Brasil y tres de Estados Unidos. Se presenta una síntesis de la literatura relacionada con la investigación de libros de texto y la enseñanza y aprendizaje del concepto de similitud, y el marco teórico explora la similitud posicionada en la encrucijada de la geometría y el número para describir las formas en que diferentes libros de texto la abordan. Se describe la secuencia de temas y tareas presentados en cada libro de texto y luego se hacen las comparaciones. Hubo teoremas y tipos de problemas que se presentaron de manera consistente en todos los libros de texto, pero se identificaron diferencias en las expectativas relacionadas con la demostración y el uso de coordenadas y transformaciones geométricas. Solo los libros de texto en los Estados Unidos incluyeron el uso de transformaciones y coordenadas y pusieron más énfasis en la prueba formal. Se proporcionan las implicaciones para la enseñanza y el aprendizaje de la similitud.Este artigo é fruto de uma pesquisa que investiga a presença da Geometria nos livros didáticos. O foco aqui é apresentar os resultados do estudo cuja pergunta diretriz é: como os livros didáticos apresentam o conceito de semelhança? Para isso, foram examinados livros didáticos de três coleções do Brasil e três dos Estados Unidos. Uma síntese da literatura relacionada à pesquisa de livros didáticos e ao ensino e aprendizagem do conceito de semelhança é apresentada, e o referencial teórico explora semelhança como posicionada na encruzilhada da geometria e do número para descrever as maneiras pelas quais diferentes livros didáticos a abordam. A sequência de tópicos e tarefas presentes em cada livro são descritas e, em seguida, as comparações são feitas. Havia teoremas e tipos de problemas apresentados de maneira consistente em todos os livros didáticos, mas foram identificadas diferenças nas expectativas relacionadas à prova e ao uso de coordenadas e transformações geométricas. Apenas os livros didáticos nos Estados Unidos incluíam o uso de transformações e coordenadas e colocavam mais ênfase na prova formal. Ainda são apresentadas implicações para o ensino e aprendizagem da semelhançaSciELO PreprintsSciELO PreprintsSciELO Preprints2021-05-26info:eu-repo/semantics/preprintinfo:eu-repo/semantics/publishedVersionapplication/pdfhttps://preprints.scielo.org/index.php/scielo/preprint/view/222510.1590/SciELOPreprints.2225enghttps://preprints.scielo.org/index.php/scielo/article/view/2225/3701Copyright (c) 2021 Rúbia Amaral-Schio, Karen Hollebrandshttps://creativecommons.org/licenses/by/4.0info:eu-repo/semantics/openAccessAmaral-Schio, RúbiaHollebrands, Karenreponame:SciELO Preprintsinstname:SciELOinstacron:SCI2021-05-25T00:19:21Zoai:ops.preprints.scielo.org:preprint/2225Servidor de preprintshttps://preprints.scielo.org/index.php/scieloONGhttps://preprints.scielo.org/index.php/scielo/oaiscielo.submission@scielo.orgopendoar:2021-05-25T00:19:21SciELO Preprints - SciELOfalse |
dc.title.none.fl_str_mv |
AN ANALYSIS OF THE CONCEPT OF SIMILARITY PRESENTED IN TEXTBOOKS IN BRAZIL AND THE UNITED STATES ANÁLISIS DEL CONCEPTO DE SEMEJANZA PRESENTADO EN LIBROS DE TEXTO EN BRASIL Y ESTADOS UNIDOS UMA ANÁLISE DO CONCEITO DE SEMELHANÇA APRESENTADO EM LIVROS DIDÁTICOS NO BRASIL E NOS ESTADOS UNIDOS |
title |
AN ANALYSIS OF THE CONCEPT OF SIMILARITY PRESENTED IN TEXTBOOKS IN BRAZIL AND THE UNITED STATES |
spellingShingle |
AN ANALYSIS OF THE CONCEPT OF SIMILARITY PRESENTED IN TEXTBOOKS IN BRAZIL AND THE UNITED STATES Amaral-Schio, Rúbia Textbook analysis mathematical tasks international textbook comparison Análisis de libros de texto similitud tareas matemáticas comparación internacional de libros de texto Análise de livros didáticos semelhança tarefas matemáticas comparação internacional de livros didáticos |
title_short |
AN ANALYSIS OF THE CONCEPT OF SIMILARITY PRESENTED IN TEXTBOOKS IN BRAZIL AND THE UNITED STATES |
title_full |
AN ANALYSIS OF THE CONCEPT OF SIMILARITY PRESENTED IN TEXTBOOKS IN BRAZIL AND THE UNITED STATES |
title_fullStr |
AN ANALYSIS OF THE CONCEPT OF SIMILARITY PRESENTED IN TEXTBOOKS IN BRAZIL AND THE UNITED STATES |
title_full_unstemmed |
AN ANALYSIS OF THE CONCEPT OF SIMILARITY PRESENTED IN TEXTBOOKS IN BRAZIL AND THE UNITED STATES |
title_sort |
AN ANALYSIS OF THE CONCEPT OF SIMILARITY PRESENTED IN TEXTBOOKS IN BRAZIL AND THE UNITED STATES |
author |
Amaral-Schio, Rúbia |
author_facet |
Amaral-Schio, Rúbia Hollebrands, Karen |
author_role |
author |
author2 |
Hollebrands, Karen |
author2_role |
author |
dc.contributor.author.fl_str_mv |
Amaral-Schio, Rúbia Hollebrands, Karen |
dc.subject.por.fl_str_mv |
Textbook analysis mathematical tasks international textbook comparison Análisis de libros de texto similitud tareas matemáticas comparación internacional de libros de texto Análise de livros didáticos semelhança tarefas matemáticas comparação internacional de livros didáticos |
topic |
Textbook analysis mathematical tasks international textbook comparison Análisis de libros de texto similitud tareas matemáticas comparación internacional de libros de texto Análise de livros didáticos semelhança tarefas matemáticas comparação internacional de livros didáticos |
description |
This paper is a product of a research that investigates the presence of Geometry in textbooks, that is part of project of a Theorem – Reflection on Geometry and Mathematics Education research group. The focus here is to present results of the international study: how textbooks present the concept of similarity? For this, a qualitative research were developed and textbooks of three collections from Brazil and three from United States were examined. A synthesis of the literature related to the search for textbooks and the teaching and learning of the concept of similarity is presented, and the theoretical framework explores similarity as positioned at the crossroads of geometry and number to describe the ways in which different textbooks approach it. Sequence of topics and tasks presented in each textbook are described and then comparisons are made. There were theorems and problem types that were presented consistently across all textbooks, but differences in expectations related to proof and the use of coordinates and geometric transformations were identified. Only textbooks in the US included the use of transformations and coordinates and placed more emphasis on formal proof. Implications for the teaching and learning of similarity are provided. |
publishDate |
2021 |
dc.date.none.fl_str_mv |
2021-05-26 |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/preprint info:eu-repo/semantics/publishedVersion |
format |
preprint |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
https://preprints.scielo.org/index.php/scielo/preprint/view/2225 10.1590/SciELOPreprints.2225 |
url |
https://preprints.scielo.org/index.php/scielo/preprint/view/2225 |
identifier_str_mv |
10.1590/SciELOPreprints.2225 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
https://preprints.scielo.org/index.php/scielo/article/view/2225/3701 |
dc.rights.driver.fl_str_mv |
Copyright (c) 2021 Rúbia Amaral-Schio, Karen Hollebrands https://creativecommons.org/licenses/by/4.0 info:eu-repo/semantics/openAccess |
rights_invalid_str_mv |
Copyright (c) 2021 Rúbia Amaral-Schio, Karen Hollebrands 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 |
SciELO Preprints SciELO Preprints SciELO Preprints |
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SciELO Preprints SciELO Preprints SciELO Preprints |
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