Consistency of individual differences across number line tasks

• In Event: Poster Session 12
  In Poster Session: PS 12 Topic - Cognitive Processes

Abstract

Numerical estimation is a skill with which children eventually become proficient during their years of formal schooling; according to a recent meta-analysis, it is associated with mathematical competence (e.g., counting, mental and written arithmetic), school grades, and performance on standardized tests (Schneider et al., 2018). Numerical estimation is assessed through number line tasks, where participants indicate the position of a given number (or sometimes give the number, given a position). In traditional (bounded) number line tasks, participants are asked to indicate the position of a number in a number line with two endpoints, bookended by 0 and a decade number (e.g., 10, 100, 1000); however other variants have captured the attention of many researchers. In anchored number line tasks, two random numbers are used as endpoints; in unbounded number line tasks, a starting point of 0 is indicated, as well as a unit marker (e.g., 1, 5, 10). Many continue to debate whether performance on these tasks, reflect knowledge of numerical magnitudes or strategies, like proportional estimation (Cohen & Sarnecka, 2014; Kim & Opfer, 2017; Barth & Paladino, 2011).

In this study, we address whether individual differences are consistent across the tasks and whether there are individual differences in cognitive skills or representations that are needed in order to complete the tasks. Our sample included 86 adults from Amazon Mechanical Turk (median age = 35 years, range of 20 and 70 years). Participants completed three number line tasks in random order: bound, unbound and anchored. Each task consisted of 40 trials, which were randomized for each participant. On each trial, participants used the mouse to indicate where on the line a given number (1 to 1000) should go. For each task, we measured participants' percent absolute error (PAE) and estimation pattern. Three hypotheses were tested: 1) Participants’ will show significant positive correlations of PAEs between the bound, unbound, and anchored number line tasks; 2) Participants’ errors will differ significantly between the unbound, bound, and anchored number line tasks; and 3) Participants’ estimation pattern (log, linear, power) on the bound number line will be positively correlated with their estimation patterns on the unbound number line.

Results were as follows 1) We found significant correlations between PAEs, but not estimation errors, across each task; 2) Pairwise comparisons showed that participants' errors were significantly different between each person; 3) Participants' estimates between tasks were more highly correlated with linear and power best-fit lines (R2s=.44 and .47 and ps<.001) than with logarithmic best-fit lines (R2=.12, p=.27). In addition, we learned that in the anchored number line, the position of the target value affected PAEs and participants overestimated the targets on the left side of the number line; in the unbounded number line, the unit size affects participants' estimations. Overall, these results suggest that adult participants participants use both proportional estimation and cognitive representations of number in numerical estimation task.

Authors

• Josh Medrano, University of Maryland - College Park
  Presenting Author

• Richard Prather, University of Maryland - College Park
  Non-Presenting Author