Fractal geometry in secondary education: characterization of mathematical and didactic-pedagogical knowledge through continuing teacher training

Autores
Artigue, Victoria; Fanaro, Maria de Los Angeles; Gak Szollosy, Joel
Año de publicación
2025
Idioma
inglés
Tipo de recurso
parte de libro
Estado
versión publicada
Descripción
This study examines the teaching of fractal geometry in secondary education and its integration into the professional development of mathematics teachers in Uruguay. A sequence of activities was designed to develop the mathematical and pedagogical knowledge required to teach fractals, including applications such as multiband fractal antennas based on self-similarity. The sequence was implemented in two online professional development courses in 2023 with 83 teachers, with revisions in the second edition emphasizing the formalization of intuitively taught concepts. The activities received positive evaluations and were effective even for teachers with no prior knowledge of fractal geometry. Teacher responses were analyzed using the Mathematical Knowledge for Teaching (MKT) framework and its extension MTSK, focusing on levels of formalization and mathematical richness. Teachers showed significant improvement in addressing key concepts such as self-similarity and fractal dimension. A Goodman–Kruskal bivariate analysis revealed a strong association between common and curricular knowledge, indicating that teachers successfully connected prior knowledge with official curricula. These findings support the inclusion of fractal geometry in secondary education.
Fil: Artigue, Victoria. Universidad Católica del Uruguay; Uruguay
Fil: Fanaro, Maria de Los Angeles. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Tandil; Argentina. Universidad Nacional del Centro de la Provincia de Buenos Aires. Facultad de Ciencias Humanas. Núcleo de Estudios Educacionales y Sociales; Argentina
Fil: Gak Szollosy, Joel. Universidad Católica del Uruguay; Uruguay
Materia
FRACTAL GEOMETRY
SECONDARY EDUCATION
MATHEMATICAL AND DIDACTIC-PEDAGOGICAL KNOWLEDGE
TEACHER TRAINING
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/279640
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/279640
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Fractal geometry in secondary education: characterization of mathematical and didactic-pedagogical knowledge through continuing teacher trainingArtigue, VictoriaFanaro, Maria de Los AngelesGak Szollosy, JoelFRACTAL GEOMETRYSECONDARY EDUCATIONMATHEMATICAL AND DIDACTIC-PEDAGOGICAL KNOWLEDGETEACHER TRAININGhttps://purl.org/becyt/ford/5.3https://purl.org/becyt/ford/5This study examines the teaching of fractal geometry in secondary education and its integration into the professional development of mathematics teachers in Uruguay. A sequence of activities was designed to develop the mathematical and pedagogical knowledge required to teach fractals, including applications such as multiband fractal antennas based on self-similarity. The sequence was implemented in two online professional development courses in 2023 with 83 teachers, with revisions in the second edition emphasizing the formalization of intuitively taught concepts. The activities received positive evaluations and were effective even for teachers with no prior knowledge of fractal geometry. Teacher responses were analyzed using the Mathematical Knowledge for Teaching (MKT) framework and its extension MTSK, focusing on levels of formalization and mathematical richness. Teachers showed significant improvement in addressing key concepts such as self-similarity and fractal dimension. A Goodman–Kruskal bivariate analysis revealed a strong association between common and curricular knowledge, indicating that teachers successfully connected prior knowledge with official curricula. These findings support the inclusion of fractal geometry in secondary education.Fil: Artigue, Victoria. Universidad Católica del Uruguay; UruguayFil: Fanaro, Maria de Los Angeles. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Tandil; Argentina. Universidad Nacional del Centro de la Provincia de Buenos Aires. Facultad de Ciencias Humanas. Núcleo de Estudios Educacionales y Sociales; ArgentinaFil: Gak Szollosy, Joel. Universidad Católica del Uruguay; UruguayInternational Society for Technology, Education and ScienceKhan, Abid AliOzturk, Mahmut SamiUnal, Mevlut2025info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/bookParthttp://purl.org/coar/resource_type/c_3248info:ar-repo/semantics/parteDeLibroapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/279640Artigue, Victoria; Fanaro, Maria de Los Angeles; Gak Szollosy, Joel; Fractal geometry in secondary education: characterization of mathematical and didactic-pedagogical knowledge through continuing teacher training; International Society for Technology, Education and Science; 2025; 47-101978-1-952092-76-3CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.istes.org/booksinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2026-02-26T10:04:25Zoai:ri.conicet.gov.ar:11336/279640instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982026-02-26 10:04:25.753CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Fractal geometry in secondary education: characterization of mathematical and didactic-pedagogical knowledge through continuing teacher training
title Fractal geometry in secondary education: characterization of mathematical and didactic-pedagogical knowledge through continuing teacher training
spellingShingle Fractal geometry in secondary education: characterization of mathematical and didactic-pedagogical knowledge through continuing teacher training
Artigue, Victoria
FRACTAL GEOMETRY
SECONDARY EDUCATION
MATHEMATICAL AND DIDACTIC-PEDAGOGICAL KNOWLEDGE
TEACHER TRAINING
title_short Fractal geometry in secondary education: characterization of mathematical and didactic-pedagogical knowledge through continuing teacher training
title_full Fractal geometry in secondary education: characterization of mathematical and didactic-pedagogical knowledge through continuing teacher training
title_fullStr Fractal geometry in secondary education: characterization of mathematical and didactic-pedagogical knowledge through continuing teacher training
title_full_unstemmed Fractal geometry in secondary education: characterization of mathematical and didactic-pedagogical knowledge through continuing teacher training
title_sort Fractal geometry in secondary education: characterization of mathematical and didactic-pedagogical knowledge through continuing teacher training
dc.creator.none.fl_str_mv Artigue, Victoria
Fanaro, Maria de Los Angeles
Gak Szollosy, Joel
author Artigue, Victoria
author_facet Artigue, Victoria
Fanaro, Maria de Los Angeles
Gak Szollosy, Joel
author_role author
author2 Fanaro, Maria de Los Angeles
Gak Szollosy, Joel
author2_role author
author
dc.contributor.none.fl_str_mv Khan, Abid Ali
Ozturk, Mahmut Sami
Unal, Mevlut
dc.subject.none.fl_str_mv FRACTAL GEOMETRY
SECONDARY EDUCATION
MATHEMATICAL AND DIDACTIC-PEDAGOGICAL KNOWLEDGE
TEACHER TRAINING
topic FRACTAL GEOMETRY
SECONDARY EDUCATION
MATHEMATICAL AND DIDACTIC-PEDAGOGICAL KNOWLEDGE
TEACHER TRAINING
purl_subject.fl_str_mv https://purl.org/becyt/ford/5.3
https://purl.org/becyt/ford/5
dc.description.none.fl_txt_mv This study examines the teaching of fractal geometry in secondary education and its integration into the professional development of mathematics teachers in Uruguay. A sequence of activities was designed to develop the mathematical and pedagogical knowledge required to teach fractals, including applications such as multiband fractal antennas based on self-similarity. The sequence was implemented in two online professional development courses in 2023 with 83 teachers, with revisions in the second edition emphasizing the formalization of intuitively taught concepts. The activities received positive evaluations and were effective even for teachers with no prior knowledge of fractal geometry. Teacher responses were analyzed using the Mathematical Knowledge for Teaching (MKT) framework and its extension MTSK, focusing on levels of formalization and mathematical richness. Teachers showed significant improvement in addressing key concepts such as self-similarity and fractal dimension. A Goodman–Kruskal bivariate analysis revealed a strong association between common and curricular knowledge, indicating that teachers successfully connected prior knowledge with official curricula. These findings support the inclusion of fractal geometry in secondary education.
Fil: Artigue, Victoria. Universidad Católica del Uruguay; Uruguay
Fil: Fanaro, Maria de Los Angeles. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Tandil; Argentina. Universidad Nacional del Centro de la Provincia de Buenos Aires. Facultad de Ciencias Humanas. Núcleo de Estudios Educacionales y Sociales; Argentina
Fil: Gak Szollosy, Joel. Universidad Católica del Uruguay; Uruguay
description This study examines the teaching of fractal geometry in secondary education and its integration into the professional development of mathematics teachers in Uruguay. A sequence of activities was designed to develop the mathematical and pedagogical knowledge required to teach fractals, including applications such as multiband fractal antennas based on self-similarity. The sequence was implemented in two online professional development courses in 2023 with 83 teachers, with revisions in the second edition emphasizing the formalization of intuitively taught concepts. The activities received positive evaluations and were effective even for teachers with no prior knowledge of fractal geometry. Teacher responses were analyzed using the Mathematical Knowledge for Teaching (MKT) framework and its extension MTSK, focusing on levels of formalization and mathematical richness. Teachers showed significant improvement in addressing key concepts such as self-similarity and fractal dimension. A Goodman–Kruskal bivariate analysis revealed a strong association between common and curricular knowledge, indicating that teachers successfully connected prior knowledge with official curricula. These findings support the inclusion of fractal geometry in secondary education.
publishDate 2025
dc.date.none.fl_str_mv 2025
dc.type.none.fl_str_mv info:eu-repo/semantics/publishedVersion
info:eu-repo/semantics/bookPart
http://purl.org/coar/resource_type/c_3248
info:ar-repo/semantics/parteDeLibro
status_str publishedVersion
format bookPart
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/279640
Artigue, Victoria; Fanaro, Maria de Los Angeles; Gak Szollosy, Joel; Fractal geometry in secondary education: characterization of mathematical and didactic-pedagogical knowledge through continuing teacher training; International Society for Technology, Education and Science; 2025; 47-101
978-1-952092-76-3
CONICET Digital
CONICET
url http://hdl.handle.net/11336/279640
identifier_str_mv Artigue, Victoria; Fanaro, Maria de Los Angeles; Gak Szollosy, Joel; Fractal geometry in secondary education: characterization of mathematical and didactic-pedagogical knowledge through continuing teacher training; International Society for Technology, Education and Science; 2025; 47-101
978-1-952092-76-3
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://www.istes.org/books
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv International Society for Technology, Education and Science
publisher.none.fl_str_mv International Society for Technology, Education and Science
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
_version_ 1858305106358829056
score 13.176822

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