Numerical cognition
Do preschoolers see numbers on a log scale or a straight line?
Open access · cc by · source: Europe PMC
Even 3- to 5-year-olds who could not yet count placed dot sets on a number line in a more evenly spaced (linear) than compressed (logarithmic) way, which challenges the idea that young children's number sense starts out logarithmic.
Study at a glance
- Design
- Human experiment — Three computerised number-line experiments with non-symbolic (dot-set) stimuli: 1–20 lines in both directions (Exp 1), a 1–9 left-to-right line (Exp 2) and a forced-choice position-to-number version (Exp 3); children grouped by counting-principle knowledge using the Give-a-number task
- N
- Separate samples per experiment: Exp 1 had 35 subset-knowers and 29 CP-knowers (61 analysed after exclusions); Exp 2 had 64 children; Exp 3 had 95 children. The Methods section for Experiment 1 is missing from the available text.
- Population
- Polish preschool children aged roughly 3 to 6 years from preschools in Warsaw
- Outcome
- Fit of linear versus logarithmic (and cyclic power) models to children's placements, percent absolute error, variance of estimates, and effects of line direction and counting knowledge
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Key findings
Across all three experiments the linear model fitted better than the logarithmic model, including in subset-knowers, although individual fits in Experiment 1 were low and estimates imprecise. The direction of the line made no difference, and Bayesian tests gave moderate evidence for no effect. In Experiment 2 the spread of estimates grew with the size of the number, the pattern expected from a linear representation with scalar variability. CP-knowers were more precise than subset-knowers in every experiment, and in Experiments 2 and 3 counting knowledge explained this better than age alone.
Methodology
Preschoolers were first sorted into 'subset-knowers' (who only know the meaning of a few small number words) and 'CP-knowers' (who understand how counting works) using the Give-a-number task. They then played a touch-screen game placing plates of dots on a line anchored by 1 dot and 20 dots, run left-to-right and right-to-left (Experiment 1), or by 1 and 9 dots (Experiment 2). In Experiment 3 the task was reversed: a position on the line was marked and children chose which of three dot sets belonged there. The authors compared how well linear and logarithmic functions fitted children's estimates.
Limitations
The study cannot tell whether the number-line task reveals the child's internal number representation or just a strategy for mapping numbers onto space on the spot; the authors themselves conclude the mapping may be built ad hoc for the task. Experiment 3 was dominated by an anchoring strategy of choosing the set most like the nearer end of the line, and Experiment 1's test of scalar variance came out null. Because the design is cross-sectional, counting knowledge and age are confounded, and the link between counting knowledge and precision could reflect other skills such as executive function. Dot sets could not be fully controlled for area or density cues given the small number of trials young children can tolerate.
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