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A Study on Congruency Effects and Numerical Distance in Fraction Comparison by Expert Undergraduate Students
Indexado
WoS WOS:000548372600001
Scopus SCOPUS_ID:85087443671
DOI 10.3389/FPSYG.2020.01190
Año 2020
Tipo artículo de investigación

Citas Totales

Autores Afiliación Chile

Instituciones Chile

% Participación
Internacional

Autores
Afiliación Extranjera

Instituciones
Extranjeras


Abstract



School mathematics comprises a diversity of concepts whose cognitive complexity is still poorly understood, a chief example being fractions. These are typically taught in middle school, but many students fail to master them, and misconceptions frequently persist into adulthood. In this study, we investigate fraction comparison, a task that taps into both conceptual and procedural knowledge of fractions, by looking at performance of highly mathematically skilled young adults. Fifty-seven Chilean engineering undergraduate students answered a computerized fraction comparison task, while their answers and response times were recorded. Task items were selected according to a number of mathematically and/or cognitively relevant characteristics: (a) whether the fractions to be compared shared a common component, (b) the numerical distance between fractions, and (c) the applicability of two strategies to answer successfully: a congruency strategy (a fraction is larger if it has larger natural number components than another) and gap thinking (a fraction is larger if it is missing fewer pieces than another to complete the whole). In line with previous research, our data indicated that the congruency strategy is inadequate to describe participants' performance, as congruent items turned out to be more difficult than incongruent ones when fractions had no common component. Although we hypothesized that this lower performance for congruent items would be explained by the use of gap thinking, this turned out not to be the case: evidence was insufficient to show that the applicability of the gap thinking strategy modulated either participants' accuracy rates or response times (although individual-level data suggest that there is an effect for response times). When fractions shared a common component, instead, our data display a more complex pattern that expected: an advantage for congruent items is present in the first experimental block but fades as the experiment progresses. Numerical distance had an effect in fraction comparison that was statistically significant for items without common components only. Altogether, our results from experts' reasoning reveal nuances in the fraction comparison task with respect to previous studies and contribute to future models of reasoning in this task.

Revista



Revista ISSN
Frontiers In Psychology 1664-1078

Métricas Externas



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Disciplinas de Investigación



WOS
Psychology, Multidisciplinary
Scopus
Psychology (All)
SciELO
Sin Disciplinas

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Publicaciones WoS (Ediciones: ISSHP, ISTP, AHCI, SSCI, SCI), Scopus, SciELO Chile.

Colaboración Institucional



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Autores - Afiliación



Ord. Autor Género Institución - País
1 Morales, Nicolas Hombre Universidad de Chile - Chile
2 DARTNELL-ROY, PABLO RICARDO Hombre Universidad de Chile - Chile
3 GOMEZ-ROJAS, DAVID MAXIMILIANO Hombre Universidad de O`Higgins - Chile
Universidad de O’Higgins - Chile

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Financiamiento



Fuente
Fondo Nacional de Desarrollo Científico y Tecnológico
Basal Funds for Centers of Excellence
ANID/PIA/Basal Funds for Centers of Excellence
Agencia Nacional de Investigación y Desarrollo
ANID/FONDECYT
Prix Inspiration Arctique

Muestra la fuente de financiamiento declarada en la publicación.

Agradecimientos



Agradecimiento
The research leading to these results has been supported by the programs ANID/Fondecyt (grant 1160188, awarded to DG) and ANID/PIA/Basal Funds for Centers of Excellence (grants FB0003-CIAE and AFB170001-CMM).
The authors thank Eduardo Díaz and Héctor Díaz, for their work in data collection and project administration, as well as anonymous reviewers. Funding. The research leading to these results has been supported by the programs ANID/Fondecyt (grant 1160188, awarded to DG) and ANID/PIA/Basal Funds for Centers of Excellence (grants FB0003-CIAE and AFB170001-CMM).

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