The processing of symbolic and nonsymbolic ratios in school-age children

PLoS One. 2013 Nov 29;8(11):e82002. doi: 10.1371/journal.pone.0082002. eCollection 2013.

Abstract

This study tested the processing of ratios of natural numbers in school-age children. Nine- and eleven-year-olds were presented collections made up of orange and grey dots (i.e., nonsymbolic format) and fractions (i.e., symbolic format). They were asked to estimate ratios between the number of orange dots and the total number of dots and fractions by producing an equivalent ratio of surface areas (filling up a virtual glass). First, we tested whether symbolic notation of ratios affects their processing by directly comparing performance on fractions with that on dot sets. Second, we investigated whether children's estimates of nonsymbolic ratios of natural numbers relied at least in part on ratios of surface areas by contrasting a condition in which the ratio of surface areas occupied by dots covaried with the ratio of natural numbers and a condition in which this ratio of surface areas was kept constant across ratios of natural numbers. The results showed that symbolic notation did not really have a negative impact on performance among 9-year-olds, while it led to more accurate estimates in 11-year-olds. Furthermore, in dot conditions, children's estimates increased consistently with ratios between the number of orange dots and the total number of dots even when the ratio of surface areas was kept constant but were less accurate in that condition than when the ratio of surface areas covaried with the ratio of natural numbers. In summary, these results indicate that mental magnitude representation is more accurate when it is activated from symbolic ratios in children as young as 11 years old and that school-age children rely at least in part on ratios of surface areas to process nonsymbolic ratios of natural numbers when given the opportunity to do so.

Publication types

  • Research Support, Non-U.S. Gov't

MeSH terms

  • Child
  • Female
  • Humans
  • Male
  • Mathematics*

Grants and funding

This research was supported by a doctoral and post-doctoral fellowship granted to Gaëlle Meert by the Fund for Scientific Research of the French-Speaking Community of Belgium (FRS–FNRS), and by the research fund ARC05/10–327 granted to Marie-Pascale Noël and Jacques Grégoire by the Université catholique de Louvain. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.