Poster #28 - Developing Data Sense: The Properties of Number Sets Influence Children’s Data Comparisons

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

Integrative Statement

Data sense refers to fluidity with sets of numbers, which includes individual numbers and the unique properties of number sets (e.g., means). Surprisingly, little is known about how data sense develops. Data must be represented in some form, and one hypothesis is that data are represented not as individual values, but as summaries, such that comparisons between sets reflect the properties of the sets themselves (e.g., Obrecht et al., 2007). To investigate this possibility, the relations between the properties of data sets and children’s accuracy, confidence, and eye fixation patterns were measured. We predicted that accuracy and confidence will be higher and the number of fixations lower given (a) larger ratio of means, (b) smaller set variance, (c) smaller set sizes, and (d) when these factors interact to make sets less distinct (e.g., low contrast sets).
Participants were 44 4th grade (M = 9.78, SD= .60, 48% female) and 38 6th grade (M = 12.14, SD= .44, 53% female) students from three public schools in the Midwestern US. We presented children with a data comparison task – determining which of two batters hit a baseball farther based on sets of hits for each player– and measured their accuracy, confidence (4-point scale), and eye fixation patterns for each trial. Participants saw 36 numerical set pairs in two columns on a screen, that varied on: (a) set size: 4, 6, or 8 three-digit numbers per set, (b) mean ratio: between-set ratio of means of either 4:5 or 9:10, and (c) coefficient of variation within set of either .10 or .20 (equivalent between sets).
We conducted a within-subjects factorial ANOVA, resulting in a 3 (set size: 4, 6, & 8) x 2 (mean ratio: Large vs. Small) x 2 (coefficient of variation: High vs. Low) analysis. We found that accuracy and confidence were related to set properties as predicted (see Table 1). Sixth graders were more accurate than third graders, and accuracy and confidence was higher for sets with larger ratios of means. and for smaller set sizes, suggesting that representing properties was easier for smaller sets. Variance did not produce any main effects but consistently interacted with mean ratios and set sizes by magnifying their effects (in congruence with Obrecht et al, 2007). Specifically, children were highly accurate and confident with high contrast sets (i.e., set with large mean differences, low variance) and significantly less so with low contrast sets (i.e., sets with small mean differences, high variance). Eye fixation data provided converging evidence; participants made fewer fixations for high contrast sets compared to low contrast sets, suggesting that more attention was recruited to distinguish low contrast sets. These results suggest that less distinct summary values cued the search for additional information for comparisons. Our results suggest that children quickly and accurately detect differences between sets of numbers (though the skill improves with age), suggesting a data sense that allows children to quickly grasp the properties of number sets.

Authors

• Bradley J Morris, Kent State University
  Presenting Author

• Amy Masnick, Hofstra University
  Non-Presenting Author

• Christopher A Was, Kent State University
  Non-Presenting Author