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Poster #44 - Vertical Space-Number Associations in Children

Thu, March 21, 4:00 to 5:15pm, Baltimore Convention Center, Floor: Level 1, Exhibit Hall B

Integrative Statement

The nature of children’s estimation skills is of central importance since proficiency at estimation is highly correlated with several aspects of numerical understanding (Siegler & Booth, 2004). Estimation involves translating between alternative quantitative representations such as space and number (Siegler & Booth, 2004). Adults and older children typically represent numbers along a horizontal number line, locating smaller numbers at the left and larger numbers at the right (Booth & Siegler, 2006). Although estimated magnitude should increase linearly with actual magnitude, children devote more space to small numbers, exhibiting a logarithmic mapping of numbers (Siegler & Booth, 2004).

The horizontal number line might be the natural way of representing number (Dehaene, Bossini, and Giraux, 1993), but adults can also flexibly represent numbers along the vertical axis (Holmes & Lourenco, 2012). But no research investigates children’s vertical space-number associations. Here we ask whether children can organize number in vertical space: Do they produce linear estimates of magnitude in a vertical number line task? Is there evidence for logarithmic compression of numbers on the vertical axis?

In Study 1, twenty-two 6–8-year-olds saw a vertical number line flanked by 0 at the bottom and 100 at the top. Children marked the locations of 22 numbers along the number line on paper. A linear regression analysis revealed an effect of magnitude on participants’ estimates (β = 0.64 , SE = 0.29 , p < 0.001). The mean estimates for the group were used to calculate linear and logarithmic regression models (Figure 1), and the residuals were entered into a paired-samples t-test. No significant differences were found (p=0.077).

Study 2 presented dot arrays between 0-10 on a touch screen, owing to limited experience with symbolic numbers and variable motor skills in this age-range. Twenty-eight 3–5-year-olds saw a vertical number line flanked by an empty circle at the bottom and a circle with 10 dots at the top. Children indicated the location of each dot array by touching a position on the number line. A linear regression analysis revealed an effect of magnitude (β = 0.16, SE = 0.49, p < 0.001). A group graph of mean estimates was used to calculate both a linear and logarithmic regression model (Figure 2), and the residuals were entered into a paired-samples t-test. No significant differences were found (p=0.982).

Our study shows that children exhibit vertical space-number associations. Children in both groups produce linear estimates of magnitudes on the vertical axis. The absence of a difference between logarithmic and linear models of estimates in both age groups suggests a mixture of linear and logarithmic representations that may indicate ongoing development (Siegler & Booth, 2004). Children’s numerical-spatial associations along the vertical axis could emerge from exposure to physical correlations and language: increases in quantity co-occur with greater vertical extension and metaphorical expressions link quantity and vertical orientation, e.g., “high number” (Holmes & Lourenco, 2012). Our research reveals that the organization of magnitudes in space is flexible and not limited to a single, horizontal, dimension even in young children.

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