Arithmetic on your phone: A large scale investigation of simple additions and multiplications
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 e...
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| Acceso en línea: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_19326203_v11_n12_p_Zimmerman http://hdl.handle.net/20.500.12110/paper_19326203_v11_n12_p_Zimmerman |
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paper:paper_19326203_v11_n12_p_Zimmerman2023-06-08T16:30:33Z Arithmetic on your phone: A large scale investigation of simple additions and multiplications Sigman, Mariano arithmetic effect size human human experiment prediction theoretical model demography Ganoderma lucidum learning mathematics mobile application reaction time video game Demography Learning Mathematics Mobile Applications Models, Theoretical Reaction Time Reishi Video Games 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. � 2016 Zimmerman et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Fil:Sigman, M. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2016 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_19326203_v11_n12_p_Zimmerman http://hdl.handle.net/20.500.12110/paper_19326203_v11_n12_p_Zimmerman |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
| collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| topic |
arithmetic effect size human human experiment prediction theoretical model demography Ganoderma lucidum learning mathematics mobile application reaction time video game Demography Learning Mathematics Mobile Applications Models, Theoretical Reaction Time Reishi Video Games |
| spellingShingle |
arithmetic effect size human human experiment prediction theoretical model demography Ganoderma lucidum learning mathematics mobile application reaction time video game Demography Learning Mathematics Mobile Applications Models, Theoretical Reaction Time Reishi Video Games Sigman, Mariano Arithmetic on your phone: A large scale investigation of simple additions and multiplications |
| topic_facet |
arithmetic effect size human human experiment prediction theoretical model demography Ganoderma lucidum learning mathematics mobile application reaction time video game Demography Learning Mathematics Mobile Applications Models, Theoretical Reaction Time Reishi Video Games |
| 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. � 2016 Zimmerman et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. |
| author |
Sigman, Mariano |
| author_facet |
Sigman, Mariano |
| author_sort |
Sigman, Mariano |
| title |
Arithmetic on your phone: A large scale investigation of simple additions and multiplications |
| 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 |
| publishDate |
2016 |
| url |
https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_19326203_v11_n12_p_Zimmerman http://hdl.handle.net/20.500.12110/paper_19326203_v11_n12_p_Zimmerman |
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AT sigmanmariano arithmeticonyourphonealargescaleinvestigationofsimpleadditionsandmultiplications |
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