A student's construction of transformations of functions in a multiple representational environment
Autor(a) principal: | |
---|---|
Data de Publicação: | 1996 |
Outros Autores: | |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UNESP |
Texto Completo: | http://dx.doi.org/10.1007/BF00376325 http://hdl.handle.net/11449/223805 |
Resumo: | This paper reports on a case study of a 16-year-old student working on transformations of functions in a computer-based, multi-representational environment. The didactic approach to reflections, translations and stretches began with visualization exercises, and then was extended to investigate the implications of visual changes in data points, and subsequently, in algebraic symbolism. A detailed analysis of the student's work during the transition from the use of visualization and analysis of discrete points to the use of algebraic symbolism is presented. Two new semiotic forms are introduced as an alternative kind of algebraic symbolism and as a means to facilitate the transition to f(x) notation: covariational equations and the horseshoe display for transformations. The implications of this case for the redesign and modification of the software are discussed. © 1996 Kluwer Academic Publishers. |
id |
UNSP_b7e0279c1fca690d2681530b1bd1c68c |
---|---|
oai_identifier_str |
oai:repositorio.unesp.br:11449/223805 |
network_acronym_str |
UNSP |
network_name_str |
Repositório Institucional da UNESP |
repository_id_str |
2946 |
spelling |
A student's construction of transformations of functions in a multiple representational environmentThis paper reports on a case study of a 16-year-old student working on transformations of functions in a computer-based, multi-representational environment. The didactic approach to reflections, translations and stretches began with visualization exercises, and then was extended to investigate the implications of visual changes in data points, and subsequently, in algebraic symbolism. A detailed analysis of the student's work during the transition from the use of visualization and analysis of discrete points to the use of algebraic symbolism is presented. Two new semiotic forms are introduced as an alternative kind of algebraic symbolism and as a means to facilitate the transition to f(x) notation: covariational equations and the horseshoe display for transformations. The implications of this case for the redesign and modification of the software are discussed. © 1996 Kluwer Academic Publishers.Mathematics Department Graduate Program of Mathematics Education State University of Sao Paulo (UNESP) Rio Claro Sao Paulo, P.O. Box 178, 13500-230 Rio Claro, SPDepartment of Education Cornell University, Ithaca, NY 14853-4203Mathematics Department Graduate Program of Mathematics Education State University of Sao Paulo (UNESP) Rio Claro Sao Paulo, P.O. Box 178, 13500-230 Rio Claro, SPUniversidade Estadual Paulista (UNESP)Cornell UniversityBorba, Marcelo C. [UNESP]Confrey, Jere2022-04-28T19:53:14Z2022-04-28T19:53:14Z1996-01-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article319-337http://dx.doi.org/10.1007/BF00376325Educational Studies in Mathematics, v. 31, n. 3, p. 319-337, 1996.1573-08160013-1954http://hdl.handle.net/11449/22380510.1007/BF003763252-s2.0-0000064913Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengEducational Studies in Mathematicsinfo:eu-repo/semantics/openAccess2022-04-28T19:53:14Zoai:repositorio.unesp.br:11449/223805Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T22:52:23.740806Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false |
dc.title.none.fl_str_mv |
A student's construction of transformations of functions in a multiple representational environment |
title |
A student's construction of transformations of functions in a multiple representational environment |
spellingShingle |
A student's construction of transformations of functions in a multiple representational environment Borba, Marcelo C. [UNESP] |
title_short |
A student's construction of transformations of functions in a multiple representational environment |
title_full |
A student's construction of transformations of functions in a multiple representational environment |
title_fullStr |
A student's construction of transformations of functions in a multiple representational environment |
title_full_unstemmed |
A student's construction of transformations of functions in a multiple representational environment |
title_sort |
A student's construction of transformations of functions in a multiple representational environment |
author |
Borba, Marcelo C. [UNESP] |
author_facet |
Borba, Marcelo C. [UNESP] Confrey, Jere |
author_role |
author |
author2 |
Confrey, Jere |
author2_role |
author |
dc.contributor.none.fl_str_mv |
Universidade Estadual Paulista (UNESP) Cornell University |
dc.contributor.author.fl_str_mv |
Borba, Marcelo C. [UNESP] Confrey, Jere |
description |
This paper reports on a case study of a 16-year-old student working on transformations of functions in a computer-based, multi-representational environment. The didactic approach to reflections, translations and stretches began with visualization exercises, and then was extended to investigate the implications of visual changes in data points, and subsequently, in algebraic symbolism. A detailed analysis of the student's work during the transition from the use of visualization and analysis of discrete points to the use of algebraic symbolism is presented. Two new semiotic forms are introduced as an alternative kind of algebraic symbolism and as a means to facilitate the transition to f(x) notation: covariational equations and the horseshoe display for transformations. The implications of this case for the redesign and modification of the software are discussed. © 1996 Kluwer Academic Publishers. |
publishDate |
1996 |
dc.date.none.fl_str_mv |
1996-01-01 2022-04-28T19:53:14Z 2022-04-28T19:53:14Z |
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/BF00376325 Educational Studies in Mathematics, v. 31, n. 3, p. 319-337, 1996. 1573-0816 0013-1954 http://hdl.handle.net/11449/223805 10.1007/BF00376325 2-s2.0-0000064913 |
url |
http://dx.doi.org/10.1007/BF00376325 http://hdl.handle.net/11449/223805 |
identifier_str_mv |
Educational Studies in Mathematics, v. 31, n. 3, p. 319-337, 1996. 1573-0816 0013-1954 10.1007/BF00376325 2-s2.0-0000064913 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Educational Studies in Mathematics |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
319-337 |
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 |
|
_version_ |
1808129468725723136 |