title: Arithmetic on Your Phone: A Large Scale Investigation of Simple Additions and Multiplications.
abstract: 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. 8x3 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.
authors.affiliation: Laboratorio de Neurociencia, Universidad Torcuato Di Tella, Buenos Aires, Argentina.|Departamento de Ingeniería Biomédica, Facultad de Ingeniería, Universidad de Buenos Aires, Buenos Aires, Argentina.
authors.forename: Federico
authors.initials: F
authors.lastname: Zimmerman
authors.affiliation: Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Buenos Aires, Argentina.|Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Buenos Aires, Argentina.
authors.forename: Diego
authors.initials: D
authors.lastname: Shalom
authors.affiliation: El Gato y La Caja, Buenos Aires, Argentina.
authors.forename: Pablo A
authors.initials: PA
authors.lastname: Gonzalez
authors.affiliation: El Gato y La Caja, Buenos Aires, Argentina.
authors.forename: Juan Manuel
authors.initials: JM
authors.lastname: Garrido
authors.affiliation: El Gato y La Caja, Buenos Aires, Argentina.
authors.forename: Facundo
authors.initials: F
authors.lastname: Alvarez Heduan
authors.affiliation: Cognitive Neuroimaging Unit, INSERM, Université Paris-Sud, Université Paris-Saclay, NeuroSpin center, Gif/Yvette, France.|Collège de France, Paris, France.
authors.forename: Stanislas
authors.initials: S
authors.lastname: Dehaene
authors.affiliation: Laboratorio de Neurociencia, Universidad Torcuato Di Tella, Buenos Aires, Argentina.|Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Buenos Aires, Argentina.
authors.forename: Mariano
authors.initials: M
authors.lastname: Sigman
authors.affiliation: Laboratorio de Neurociencia, Universidad Torcuato Di Tella, Buenos Aires, Argentina.|Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Buenos Aires, Argentina.|El Gato y La Caja, Buenos Aires, Argentina.
authors.forename: Andres
authors.initials: A
authors.lastname: Rieznik
mesh_terms: D003710:Demography; D007858:Learning; D008433:Mathematics; D063731:Mobile Applications; D008962:Models, Theoretical; D011930:Reaction Time; D020940:Reishi; D018910:Video Games