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. 2008 Sep;44(5):1466-77.
doi: 10.1037/a0013046.

Nonsymbolic, approximate arithmetic in children: abstract addition prior to instruction

Hilary Barth  1 , Lacey Beckmann, Elizabeth S Spelke
Affiliations

Nonsymbolic, approximate arithmetic in children: abstract addition prior to instruction

Hilary Barth et al. Dev Psychol. 2008 Sep.

Abstract

Do children draw upon abstract representations of number when they perform approximate arithmetic operations? In this study, kindergarten children viewed animations suggesting addition of a sequence of sounds to an array of dots, and they compared the sum to a second dot array that differed from the sum by 1 of 3 ratios. Children performed this task successfully with all the signatures of adults' nonsymbolic number representations: accuracy modulated by the ratio of the sum and the comparison quantity, equal performance for within- and cross-modality tasks and for addition and comparison tasks, and performance superior to that of a matched subtraction task. The findings provide clear evidence for nonsymbolic numerical operations on abstract numerical quantities in children who have not yet been taught formal arithmetic.

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Figures

Figure 1
Figure 1
Schematic depictions of test displays and narration for (A) the addition test trials of Experiment 1 (B) the comparison test trials of Experiment 2, and (C) the subtraction test trials of Experiment 3.
Figure 2
Figure 2
Accuracy data for the cross-modal addition task (Experiment 1) and matched comparison task (Experiment 2). Chance is 50% for all plots. A. Accuracy scores (mean and SEM) are plotted against the ratio of the numerosities to be compared. B. Accuracy at each comparison ratio for addition trials whose first array represented extreme numerical values (near the low end or the high end of the range of numerosities used) and for addition trials whose first array included only mid-range values. C. Accuracy at each comparison ratio for addition trials whose second array represented extreme numerical values (near the low end or the high end of the range of numerosities used) and for addition trials whose second array included only mid-range values.
Figure 3
Figure 3
Accuracy data for the cross-modal comparison and subtraction tasks of Experiment 3 (chance is 50%). A. Accuracy scores (mean and SEM) are plotted against the ratios of the numerosities to be compared. B. Accuracy at each comparison ratio for subtraction trials whose first array represented extreme numerical values (near the low end or the high end of the range of numerosities used) and for subtraction trials whose first array included only mid-range values. C. Accuracy at each comparison ratio for subtraction trials whose second array represented extreme numerical values (near the low end or the high end of the range of numerosities used) and for subtraction trials whose second array included only mid-range values.
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References

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