Explaining Variability: Numerical Representations in 4- to 8-Year-Old Children

Abstract

The present study aims to examine relations between number representations and various sources of individual differences within early stages of development of number representations. The mental number line has been found to develop from a logarithmic to a more linear representation. Sources under investigation are counting skills and executive functions and are set out against mental number lines from 0 to 10 and 0 to 100 in a sample of 4- to 8-year-old children (N = 80). Findings indicate that counting skills, inhibition, and updating are the most important predictors of the shape of the mental number line over and above age-related developmental differences, with number lines from 0 to 10 being linear to a large extent and number lines from 0 to 100 developing from a random pattern toward logarithmic representations. The shape of the mental number line was found to predict scores on the number comparison task only on the smaller-scale comparison task.

Notes

*Mean age and standard deviations given in months.

Note. Count = score on verbal counting task; WRB = score on Word Recall Backwards; OOO = score on Odd One Out task; Flanker = percentage correct on the Flanker task; DCCS = percentage correct on the Dimensional Change Card-Sorting Test; Comparison = percentage correct on number comparison task.

Note. Correlations below the diagonal display correlations of number lines with a range from 0 to 10 (N = 78); correlations above the diagonal display correlations of number lines with a range from 0 to 100 (N = 76).

Count = verbal counting task; WRB = Word Recall Backwards; OOO = Odd One Out task; Flanker = Flanker task; DCCS = Dimensional Change Card-Sorting Test; Comparison = score on the number comparison task.

*p < .05. **p < .01.

*p < .05. **p < .01.

Count = counting skills; WRB = score on Word Recall Backwards; OOO = score on Odd One Out task; Flanker = score on Flanker task; DCCS = score on the Dimensional Change Card-Sorting Test.

Note. Linear fit number lines 0–10: R ²  = .197.**

Logarithmic fit number lines 0–10: R ²  = .129.**

Linear fit number lines 0–100: R ²  = .316.**

Logarithmic fit number lines 0–100: R ²  = .291.**

Count = score on the verbal counting task; Flanker = score on the Flanker task; OOO = score on the Odd One Out task.

†p < .10. *p < .05. **p < .01. ***p < .001.

Note. Comparison scores 0–10: R ²  = .0221*** for Step 1; ΔR ² s = .101** for Step 2.

Comparison scores 0–100: R ²  = .077* for Step 1; ΔR ² s < .030 for Step 2.

†p < .10. *p < .05. **p < .01. ***p < .001.