Arithmetic on Your Phone: A Large Scale Investigation of Simple Additions and Multiplications

Autores
Zimmerman, Federico Guido; Shalóm, Diego Edgar; Gonzalez, Pablo A.; Garrido, Juan Manuel; Alvarez Heduan, Facundo; Dehaene, Stanislas; Sigman, Mariano; Rieznik, Andrés Anibal
Año de publicación
2016
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We present the results of a gamified mobile device arithmetic application which allowed us to collect vast amount of data in simple arithmetic operations. Our results confirm and replicate, on a large sample, six of the main principles derived in a long tradition of investigation: size effect, tie effect, size-tie interaction effect, five-effect, RTs and error rates correlation effect, and most common error effect. Our dataset allowed us to perform a robust analysis of order effects for each individual problem, for which there is controversy both in experimental findings and in the predictions of theoretical models. For addition problems, the order effect was dominated by a max-then-min structure (i.e 7+4 is easier than 4+7). This result is predicted by models in which additions are performed as a translation starting from the first addend, with a distance given by the second addend. In multiplication, we observed a dominance of two effects: (1) a max-then-min pattern that can be accounted by the fact that it is easier to perform fewer additions of the largest number (i.e. 8�3 is easier to compute as 8+8+8 than as 3+3+⋯+3) and (2) a phonological effect by which problems for which there is a rhyme (i.e. "seis por cuatro es veinticuatro") are performed faster. Above and beyond these results, our study bares an important practical conclusion, as proof of concept, that participants can be motivated to perform substantial arithmetic training simply by presenting it in a gamified format.
Fil: Zimmerman, Federico Guido. Universidad de Buenos Aires; Argentina. Universidad Torcuato Di Tella; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Shalóm, Diego Edgar. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; Argentina
Fil: Gonzalez, Pablo A.. No especifíca;
Fil: Garrido, Juan Manuel. No especifíca;
Fil: Alvarez Heduan, Facundo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Dehaene, Stanislas. Inserm; Francia
Fil: Sigman, Mariano. Universidad Torcuato Di Tella; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Rieznik, Andrés Anibal. Universidad Torcuato Di Tella; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Materia
ARITHMETIC
GAMES
PHONOLOGY
LEARNING
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:11336/117522
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/117522
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Arithmetic on Your Phone: A Large Scale Investigation of Simple Additions and MultiplicationsZimmerman, Federico GuidoShalóm, Diego EdgarGonzalez, Pablo A.Garrido, Juan ManuelAlvarez Heduan, FacundoDehaene, StanislasSigman, MarianoRieznik, Andrés AnibalARITHMETICGAMESPHONOLOGYLEARNINGhttps://purl.org/becyt/ford/1.2https://purl.org/becyt/ford/1We present the results of a gamified mobile device arithmetic application which allowed us to collect vast amount of data in simple arithmetic operations. Our results confirm and replicate, on a large sample, six of the main principles derived in a long tradition of investigation: size effect, tie effect, size-tie interaction effect, five-effect, RTs and error rates correlation effect, and most common error effect. Our dataset allowed us to perform a robust analysis of order effects for each individual problem, for which there is controversy both in experimental findings and in the predictions of theoretical models. For addition problems, the order effect was dominated by a max-then-min structure (i.e 7+4 is easier than 4+7). This result is predicted by models in which additions are performed as a translation starting from the first addend, with a distance given by the second addend. In multiplication, we observed a dominance of two effects: (1) a max-then-min pattern that can be accounted by the fact that it is easier to perform fewer additions of the largest number (i.e. 8�3 is easier to compute as 8+8+8 than as 3+3+⋯+3) and (2) a phonological effect by which problems for which there is a rhyme (i.e. "seis por cuatro es veinticuatro") are performed faster. Above and beyond these results, our study bares an important practical conclusion, as proof of concept, that participants can be motivated to perform substantial arithmetic training simply by presenting it in a gamified format.Fil: Zimmerman, Federico Guido. Universidad de Buenos Aires; Argentina. Universidad Torcuato Di Tella; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Shalóm, Diego Edgar. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; ArgentinaFil: Gonzalez, Pablo A.. No especifíca;Fil: Garrido, Juan Manuel. No especifíca;Fil: Alvarez Heduan, Facundo. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Dehaene, Stanislas. Inserm; FranciaFil: Sigman, Mariano. Universidad Torcuato Di Tella; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Rieznik, Andrés Anibal. Universidad Torcuato Di Tella; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaPublic Library of Science2016-12info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/117522Zimmerman, Federico Guido; Shalóm, Diego Edgar; Gonzalez, Pablo A.; Garrido, Juan Manuel; Alvarez Heduan, Facundo; et al.; Arithmetic on Your Phone: A Large Scale Investigation of Simple Additions and Multiplications; Public Library of Science; Plos One; 11; 12; 12-2016; 1-151932-6203CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0168431info:eu-repo/semantics/altIdentifier/doi/10.1371/journal.pone.0168431info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T11:18:33Zoai:ri.conicet.gov.ar:11336/117522instacron: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:34982025-10-22 11:18:34.238CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Arithmetic on Your Phone: A Large Scale Investigation of Simple Additions and Multiplications
title Arithmetic on Your Phone: A Large Scale Investigation of Simple Additions and Multiplications
spellingShingle Arithmetic on Your Phone: A Large Scale Investigation of Simple Additions and Multiplications
Zimmerman, Federico Guido
ARITHMETIC
GAMES
PHONOLOGY
LEARNING
title_short Arithmetic on Your Phone: A Large Scale Investigation of Simple Additions and Multiplications
title_full Arithmetic on Your Phone: A Large Scale Investigation of Simple Additions and Multiplications
title_fullStr Arithmetic on Your Phone: A Large Scale Investigation of Simple Additions and Multiplications
title_full_unstemmed Arithmetic on Your Phone: A Large Scale Investigation of Simple Additions and Multiplications
title_sort Arithmetic on Your Phone: A Large Scale Investigation of Simple Additions and Multiplications
dc.creator.none.fl_str_mv Zimmerman, Federico Guido
Shalóm, Diego Edgar
Gonzalez, Pablo A.
Garrido, Juan Manuel
Alvarez Heduan, Facundo
Dehaene, Stanislas
Sigman, Mariano
Rieznik, Andrés Anibal
author Zimmerman, Federico Guido
author_facet Zimmerman, Federico Guido
Shalóm, Diego Edgar
Gonzalez, Pablo A.
Garrido, Juan Manuel
Alvarez Heduan, Facundo
Dehaene, Stanislas
Sigman, Mariano
Rieznik, Andrés Anibal
author_role author
author2 Shalóm, Diego Edgar
Gonzalez, Pablo A.
Garrido, Juan Manuel
Alvarez Heduan, Facundo
Dehaene, Stanislas
Sigman, Mariano
Rieznik, Andrés Anibal
author2_role author
author
author
author
author
author
author
dc.subject.none.fl_str_mv ARITHMETIC
GAMES
PHONOLOGY
LEARNING
topic ARITHMETIC
GAMES
PHONOLOGY
LEARNING
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.2
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We present the results of a gamified mobile device arithmetic application which allowed us to collect vast amount of data in simple arithmetic operations. Our results confirm and replicate, on a large sample, six of the main principles derived in a long tradition of investigation: size effect, tie effect, size-tie interaction effect, five-effect, RTs and error rates correlation effect, and most common error effect. Our dataset allowed us to perform a robust analysis of order effects for each individual problem, for which there is controversy both in experimental findings and in the predictions of theoretical models. For addition problems, the order effect was dominated by a max-then-min structure (i.e 7+4 is easier than 4+7). This result is predicted by models in which additions are performed as a translation starting from the first addend, with a distance given by the second addend. In multiplication, we observed a dominance of two effects: (1) a max-then-min pattern that can be accounted by the fact that it is easier to perform fewer additions of the largest number (i.e. 8�3 is easier to compute as 8+8+8 than as 3+3+⋯+3) and (2) a phonological effect by which problems for which there is a rhyme (i.e. "seis por cuatro es veinticuatro") are performed faster. Above and beyond these results, our study bares an important practical conclusion, as proof of concept, that participants can be motivated to perform substantial arithmetic training simply by presenting it in a gamified format.
Fil: Zimmerman, Federico Guido. Universidad de Buenos Aires; Argentina. Universidad Torcuato Di Tella; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Shalóm, Diego Edgar. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; Argentina
Fil: Gonzalez, Pablo A.. No especifíca;
Fil: Garrido, Juan Manuel. No especifíca;
Fil: Alvarez Heduan, Facundo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Dehaene, Stanislas. Inserm; Francia
Fil: Sigman, Mariano. Universidad Torcuato Di Tella; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Rieznik, Andrés Anibal. Universidad Torcuato Di Tella; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
description We present the results of a gamified mobile device arithmetic application which allowed us to collect vast amount of data in simple arithmetic operations. Our results confirm and replicate, on a large sample, six of the main principles derived in a long tradition of investigation: size effect, tie effect, size-tie interaction effect, five-effect, RTs and error rates correlation effect, and most common error effect. Our dataset allowed us to perform a robust analysis of order effects for each individual problem, for which there is controversy both in experimental findings and in the predictions of theoretical models. For addition problems, the order effect was dominated by a max-then-min structure (i.e 7+4 is easier than 4+7). This result is predicted by models in which additions are performed as a translation starting from the first addend, with a distance given by the second addend. In multiplication, we observed a dominance of two effects: (1) a max-then-min pattern that can be accounted by the fact that it is easier to perform fewer additions of the largest number (i.e. 8�3 is easier to compute as 8+8+8 than as 3+3+⋯+3) and (2) a phonological effect by which problems for which there is a rhyme (i.e. "seis por cuatro es veinticuatro") are performed faster. Above and beyond these results, our study bares an important practical conclusion, as proof of concept, that participants can be motivated to perform substantial arithmetic training simply by presenting it in a gamified format.
publishDate 2016
dc.date.none.fl_str_mv 2016-12
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/117522
Zimmerman, Federico Guido; Shalóm, Diego Edgar; Gonzalez, Pablo A.; Garrido, Juan Manuel; Alvarez Heduan, Facundo; et al.; Arithmetic on Your Phone: A Large Scale Investigation of Simple Additions and Multiplications; Public Library of Science; Plos One; 11; 12; 12-2016; 1-15
1932-6203
CONICET Digital
CONICET
url http://hdl.handle.net/11336/117522
identifier_str_mv Zimmerman, Federico Guido; Shalóm, Diego Edgar; Gonzalez, Pablo A.; Garrido, Juan Manuel; Alvarez Heduan, Facundo; et al.; Arithmetic on Your Phone: A Large Scale Investigation of Simple Additions and Multiplications; Public Library of Science; Plos One; 11; 12; 12-2016; 1-15
1932-6203
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://journals.plos.org/plosone/article?id=10.1371/journal.pone.0168431
info:eu-repo/semantics/altIdentifier/doi/10.1371/journal.pone.0168431
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
application/pdf
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dc.publisher.none.fl_str_mv Public Library of Science
publisher.none.fl_str_mv Public Library of 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
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