Poster #36 - Number Line Estimation is More than Numerical: Evidence from Nonstandard Number Lines

• In Event: 3-053 - Poster Session 10
  In Poster Session: PS 10 Section - Cognitive Processes

Integrative Statement

Children’s number line estimation ability predicts their future math achievement (e.g., Bailey et al., 2014). Some have interpreted number line estimation as a transparent measure of children’s mental representations of number, with developmental improvements indicating a shift from logarithmic to linear numerical mental representations (e.g., Siegler & Booth, 2004). However, alternative accounts suggest that estimation tasks are not purely numerical, but rather are a complex measure of children’s proportional reasoning skills (e.g., Slusser et al., 2013). Indeed, psychophysical models of proportion judgment often fit children’s number line performance better than logarithmic or linear functions (Slusser & Barth, 2017) and directly account for the use of reference points (Slusser et al., 2013).

The current study tested these competing accounts by asking children to complete estimations on different number line ranges. If children’s number line estimation is truly driven by their mental representations of number, which are more linear for more familiar numbers, children who can accurately produce linear estimates on larger ranges (e.g., 0-100) should also produce accurate estimates on smaller ranges (0-7, 0-18, etc.). However, if children’s estimation is dependent on proportion judgments, children should not necessarily be more accurate with smaller number line ranges, because proportional reference points may be more accessible for powers of 10 than for other numbers. For example, children may easily recognize that 50 is half or 25 is one quarter of 100 but struggle to identify half of 7 or one quarter of 18.

Thirty-eight children in grades 2-5 completed three number line estimation tasks (Figure 1): two traditional (range: 0-10, 0-100) and one nonstandard task in which the range varied from 2 to 24 across trials. Children indicated where each stimulus belonged on the number line using a mouse. Percent Absolute Error (PAE; |answer – correct answer|/numerical range; Siegler & Booth, 2004) was calculated to measure performance on the tasks. A lower PAE indicated higher estimation accuracy.

Contrary to the logarithmic-to-linear-shift account, we found that 2nd-5th graders performed worse on number lines with ranges from 2 to 24 than on 0-100 number lines (Figure 2). Using ANOVA, we found significant effects of range and grade on PAE (ps < .001). Children’s average PAE was lowest for 0-10 (M = .05, SD = .05) and 0-100 number lines (M = .07, SD = .08). Estimates were less accurate for the nonstandard number line ranges (M = .10, SD = .11). Unsurprisingly, older children performed better than younger children on all tasks.

These results add evidence that number line estimation is not a simple reflection of mental representation of number. It is unlikely that children’s mental representation of “9” changed between trials, leading them to be more accurate on 0-100 than on 0-13 lines. Rather, the nonstandard ranges required children to flexibly adjust their estimates relative to the number line range. Future analyses will investigate the fit of linear, logarithmic, and cyclic power functions. If the patterns hold, these findings will contribute to our interpretation of number line estimation tasks and may motivate proportional reasoning interventions.

Authors

• Alexandria A. Viegut, University of Wisconsin - Madison
  Presenting Author

• Yunji Park, University of Wisconsin-Madison
  Non-Presenting Author

• Percival Matthews, University of Wisconsin-Madison
  Non-Presenting Author