Does skill with number lines drive children's math growth?
Spatial ability predicted children's improvement on a number line task, but number line skill did not play a special causal role in their later arithmetic growth.
Source
Charting the role of the number line in mathematical development
Study at a glance
- Design
- Cohort — Two annual waves of testing (Time 3 and Time 4) from a larger longitudinal study, analysed with cross-lagged path models controlling grade, sex and vocabulary.
- N
- N=101 · 101 children who completed the 0-1000 number line task at both waves; grade breakdown reported as 52, 27 and 21, which sums to 100.
- Population
- Mostly middle-class Canadian children in grades 2-4 at the first analysed wave, recruited from schools in two cities.
- Outcome
- Number line estimation (slope of linear fit), calculation and numeration (number system knowledge) scores one year later.
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What they did
The researchers analysed 101 Canadian primary school children who had been tested twice, a year apart, as part of a larger longitudinal study. At each wave children placed numbers on a line running from 0 to 1000 and completed standardised calculation and numeration tests; spatial ability was measured with a spatial reasoning test and a spatial memory span task. Cross-lagged path models tested which earlier skills predicted growth in which later skills, controlling for grade, sex and vocabulary.
What they found
Spatial ability predicted growth in number line performance across the year, replicating earlier work with slightly older children. However, the indirect path from spatial ability to later calculation running through earlier calculation (0.188) was clearly larger than the path running through number line performance (0.052), and the links between number line and calculation ran in both directions with similar size. Knowledge of the number system (numeration) predicted later number line growth, but number line performance did not predict later numeration.
The limits
What it doesn't show
This is correlational panel data, so the cross-lagged paths cannot rule out unmeasured skills driving growth in both number line and calculation. The sample was small for the analyses, predominantly middle class, and could not be analysed grade by grade, so developmental differences are blurred. Spatial ability was measured with only two tasks, which may not capture distinct spatial skills such as mental rotation. The study did not test a number line training intervention, so it cannot say whether practising number lines would help arithmetic.
Key terms
- Number line estimation task
- A task where a child marks where a given number belongs on a line with labelled endpoints, such as 0 and 1000.
- Cross-lagged panel analysis
- A method using two or more waves of data to test whether skill A at time 1 predicts skill B at time 2 more than B at time 1 predicts A at time 2.
- Spatial ability
- The capacity to reason about and remember shapes, locations and spatial relations.
- Numeration
- Knowledge of how the number system works, including ordering numbers and place value.
- Indirect effect
- The part of one variable's influence on an outcome that passes through an intermediate variable.
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Quiz yourself
What range did the number line task in this study cover?
Common questions
If number line skill and calculation are correlated, why don't the authors think one causes the other?
The predictive links ran both ways with similar strength, and earlier calculation carried much more of spatial ability's influence than number line skill did, which fits shared underlying skills better than a one-way causal chain.
Should teachers stop using number lines?
No. The study suggests number line performance reflects number system knowledge plus spatial strategy, so it is a useful indicator, but practising number line placement alone should not be expected to transfer automatically to calculation.
Why did the researchers use the slope rather than R squared to score number line performance?
R squared values were heavily skewed in this age group, while the slope better captured how accurately children placed numbers across the whole line.
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