The Use of Digital Technology to Estimate a Value of Pi: Teachers’ Solutions on Squaring the Circle in a Graduate Course in Brazil
Autor(a) principal: | |
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Data de Publicação: | 2021 |
Outros Autores: | , , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UNESP |
Texto Completo: | http://dx.doi.org/10.1007/s11858-021-01246-1 http://hdl.handle.net/11449/206030 |
Resumo: | In this research we investigate how mathematics teachers, as graduate students, estimate the value of π by exploring the problem of squaring the circle using digital technology. Initially, we mention some aspects of teaching and learning of calculus in the literature, emphasizing studies that use the notion of humans-with-media to highlight the role of technology in mathematical thinking and knowledge production. Insights on the history of mathematics in calculus are also discussed. We developed a qualitative study based on three different solutions created by groups of teachers using the software GeoGebra and Microsoft Excel. All the teachers’ solutions improved the approximation (8/9)2≈ π/4, by determining p and q for (p/q)2≈ π/4. The first two solutions with GeoGebra emphasized experimentation and visualization, improving the approximation from one to three decimal places. The third solution with Excel pointed out the elaboration of a formula and improved it up to six decimal places. We emphasize how media shaped the strategies and solutions of the groups. Based on these solutions, we explore an approach for cubing the sphere, discussing approximations for π, highlighting the role of media in enhancing conceptual complexity in the solution of mathematical problems. The nature of the strategies for solving a problem is discussed, especially regarding different ways of thinking-with-technology developed by collectives of teachers-with-media. Although we acknowledge an alternative design for the proposed task, the exploration of problems using aspects of the history of mathematics contributes to the state of the art concerning the studies in calculus developed by the Research Group on Technology, other Media, and Mathematics Education in Brazil. |
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The Use of Digital Technology to Estimate a Value of Pi: Teachers’ Solutions on Squaring the Circle in a Graduate Course in BrazilCalculusGPIMEMHistory of MathematicsHumans-with-mediaIn this research we investigate how mathematics teachers, as graduate students, estimate the value of π by exploring the problem of squaring the circle using digital technology. Initially, we mention some aspects of teaching and learning of calculus in the literature, emphasizing studies that use the notion of humans-with-media to highlight the role of technology in mathematical thinking and knowledge production. Insights on the history of mathematics in calculus are also discussed. We developed a qualitative study based on three different solutions created by groups of teachers using the software GeoGebra and Microsoft Excel. All the teachers’ solutions improved the approximation (8/9)2≈ π/4, by determining p and q for (p/q)2≈ π/4. The first two solutions with GeoGebra emphasized experimentation and visualization, improving the approximation from one to three decimal places. The third solution with Excel pointed out the elaboration of a formula and improved it up to six decimal places. We emphasize how media shaped the strategies and solutions of the groups. Based on these solutions, we explore an approach for cubing the sphere, discussing approximations for π, highlighting the role of media in enhancing conceptual complexity in the solution of mathematical problems. The nature of the strategies for solving a problem is discussed, especially regarding different ways of thinking-with-technology developed by collectives of teachers-with-media. Although we acknowledge an alternative design for the proposed task, the exploration of problems using aspects of the history of mathematics contributes to the state of the art concerning the studies in calculus developed by the Research Group on Technology, other Media, and Mathematics Education in Brazil.São Paulo State University UNESPFederal University of Pelotas UFPELSão Paulo State University UNESPUniversidade Estadual Paulista (Unesp)Universidade Federal de Pernambuco (UFPE)da Silva, Ricardo Scucuglia Rodrigues [UNESP]Barbosa, Lara Martins [UNESP]Borba, Marcelo C. [UNESP]Ferreira, André Luis Andrejew2021-06-25T10:25:23Z2021-06-25T10:25:23Z2021-01-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://dx.doi.org/10.1007/s11858-021-01246-1ZDM - Mathematics Education.1863-97041863-9690http://hdl.handle.net/11449/20603010.1007/s11858-021-01246-12-s2.0-85102308118Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengZDM - Mathematics Educationinfo:eu-repo/semantics/openAccess2021-10-22T20:42:38Zoai:repositorio.unesp.br:11449/206030Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T22:26:25.895474Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false |
dc.title.none.fl_str_mv |
The Use of Digital Technology to Estimate a Value of Pi: Teachers’ Solutions on Squaring the Circle in a Graduate Course in Brazil |
title |
The Use of Digital Technology to Estimate a Value of Pi: Teachers’ Solutions on Squaring the Circle in a Graduate Course in Brazil |
spellingShingle |
The Use of Digital Technology to Estimate a Value of Pi: Teachers’ Solutions on Squaring the Circle in a Graduate Course in Brazil da Silva, Ricardo Scucuglia Rodrigues [UNESP] Calculus GPIMEM History of Mathematics Humans-with-media |
title_short |
The Use of Digital Technology to Estimate a Value of Pi: Teachers’ Solutions on Squaring the Circle in a Graduate Course in Brazil |
title_full |
The Use of Digital Technology to Estimate a Value of Pi: Teachers’ Solutions on Squaring the Circle in a Graduate Course in Brazil |
title_fullStr |
The Use of Digital Technology to Estimate a Value of Pi: Teachers’ Solutions on Squaring the Circle in a Graduate Course in Brazil |
title_full_unstemmed |
The Use of Digital Technology to Estimate a Value of Pi: Teachers’ Solutions on Squaring the Circle in a Graduate Course in Brazil |
title_sort |
The Use of Digital Technology to Estimate a Value of Pi: Teachers’ Solutions on Squaring the Circle in a Graduate Course in Brazil |
author |
da Silva, Ricardo Scucuglia Rodrigues [UNESP] |
author_facet |
da Silva, Ricardo Scucuglia Rodrigues [UNESP] Barbosa, Lara Martins [UNESP] Borba, Marcelo C. [UNESP] Ferreira, André Luis Andrejew |
author_role |
author |
author2 |
Barbosa, Lara Martins [UNESP] Borba, Marcelo C. [UNESP] Ferreira, André Luis Andrejew |
author2_role |
author author author |
dc.contributor.none.fl_str_mv |
Universidade Estadual Paulista (Unesp) Universidade Federal de Pernambuco (UFPE) |
dc.contributor.author.fl_str_mv |
da Silva, Ricardo Scucuglia Rodrigues [UNESP] Barbosa, Lara Martins [UNESP] Borba, Marcelo C. [UNESP] Ferreira, André Luis Andrejew |
dc.subject.por.fl_str_mv |
Calculus GPIMEM History of Mathematics Humans-with-media |
topic |
Calculus GPIMEM History of Mathematics Humans-with-media |
description |
In this research we investigate how mathematics teachers, as graduate students, estimate the value of π by exploring the problem of squaring the circle using digital technology. Initially, we mention some aspects of teaching and learning of calculus in the literature, emphasizing studies that use the notion of humans-with-media to highlight the role of technology in mathematical thinking and knowledge production. Insights on the history of mathematics in calculus are also discussed. We developed a qualitative study based on three different solutions created by groups of teachers using the software GeoGebra and Microsoft Excel. All the teachers’ solutions improved the approximation (8/9)2≈ π/4, by determining p and q for (p/q)2≈ π/4. The first two solutions with GeoGebra emphasized experimentation and visualization, improving the approximation from one to three decimal places. The third solution with Excel pointed out the elaboration of a formula and improved it up to six decimal places. We emphasize how media shaped the strategies and solutions of the groups. Based on these solutions, we explore an approach for cubing the sphere, discussing approximations for π, highlighting the role of media in enhancing conceptual complexity in the solution of mathematical problems. The nature of the strategies for solving a problem is discussed, especially regarding different ways of thinking-with-technology developed by collectives of teachers-with-media. Although we acknowledge an alternative design for the proposed task, the exploration of problems using aspects of the history of mathematics contributes to the state of the art concerning the studies in calculus developed by the Research Group on Technology, other Media, and Mathematics Education in Brazil. |
publishDate |
2021 |
dc.date.none.fl_str_mv |
2021-06-25T10:25:23Z 2021-06-25T10:25:23Z 2021-01-01 |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://dx.doi.org/10.1007/s11858-021-01246-1 ZDM - Mathematics Education. 1863-9704 1863-9690 http://hdl.handle.net/11449/206030 10.1007/s11858-021-01246-1 2-s2.0-85102308118 |
url |
http://dx.doi.org/10.1007/s11858-021-01246-1 http://hdl.handle.net/11449/206030 |
identifier_str_mv |
ZDM - Mathematics Education. 1863-9704 1863-9690 10.1007/s11858-021-01246-1 2-s2.0-85102308118 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
ZDM - Mathematics Education |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.source.none.fl_str_mv |
Scopus reponame:Repositório Institucional da UNESP instname:Universidade Estadual Paulista (UNESP) instacron:UNESP |
instname_str |
Universidade Estadual Paulista (UNESP) |
instacron_str |
UNESP |
institution |
UNESP |
reponame_str |
Repositório Institucional da UNESP |
collection |
Repositório Institucional da UNESP |
repository.name.fl_str_mv |
Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP) |
repository.mail.fl_str_mv |
|
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1808129427169607680 |