83rd Annual Meeting of the Midwestern Psychological Association
Comparing sets of numbers is a critical skill in mathematics, science, and everyday life. It is possible that children possess intuitive strategies for number set comparison in which sets are represented as summary values with approximations of means and variance. We investigated how 8-12 year old children assessed number sets by examining how the properties of the data sets (e.g., mean differences) influence accuracy and confidence in differences. We also looked at the number and location of eye fixations during comparisons to evaluate children's data comparison strategies.
Method. Participants were 12 8-12 year-old children ( M = 10.2). Participants saw 36 data set pairs with the following properties: (a) set size 4 or 8, (b) ratio of means of either 2:3, 4:5 or 9:10, and (c) variance of either 10% or 20% of the mean.
Procedure. Participants were asked to determine which of two golfers (LEFT or RIGHT side) hit the ball farther (accuracy) and rate their confidence in this evaluation on a 4-point scale (1 = NOT AT ALL SURE, 4 = TOTALLY SURE). Data sets were presented on a Tobii T-60 eye tracker. Areas of Interest (AOIs) were defined around the hundreds, tens, and ones columns and around each three-digit number. The number of fixations within each AOI was automatically recorded. We proposed a series of possible evaluation strategies before data collection (see Table 1).
Results and Discussion. As mean ratios decreased and variance increased, accuracy and confidence decreased and the number of fixations increased, suggesting that the statistical properties of the sets influenced comparisons (see Table 2). Most fixations occurred in the hundreds column (77%) with fewer fixations on the tens and ones columns. The modal strategy was gist (68% of trials), followed by first/last (12%), win/loss (10%), and calculation (8%). A child was coded as using a strategy if s/he used the same fixation strategy on at least 75% of trials (10/12 children). Accuracy was related to strategy selection: the gist strategy was the most accurate (94%), followed by calculation (86%), and first/last strategies (61%). The results suggest that children's intuitive strategies for data are quite accurate; when children simply scanned the data, their intuitions about differences are excellent until sets become highly similar (in this case 9:10 ratio). Interestingly, explicit calculation was less accurate than the gist strategy. Children's approximate number system may use both relative means and variances to represent summary values of number sets.