Poster #40 - The Relation Between Children’s Numerical Predictions, Numerical Representations, and Working Memory Capacity?

• In Event: 3-003 - Poster Session 09
  In Poster Session: PS 09 Section - Cognitive Processes

Integrative Statement

Surprisingly little is known about how children generate numerical predictions. Is prediction, like estimation, related to children’s number concepts? Young children’s numerical magnitude estimations for 0-1000 often show logarithmic compression for larger numbers whereas older children show linear representations (Siegler, Thompson, Opfer, 2009). We predict that numerical predictions should reflect the underlying number representations in that predictions by older children should fit a linear function more closely than younger children. Are predictions generated explicitly? Working memory capacity (e.g., information updating) could play a role in prediction accuracy, however, children appear to estimate and compare number sets without explicit processing (Morris & Masnick, 2015). This experiment investigates the relations between numerical prediction accuracy, magnitude representations, and working memory capacity.

Forty-seven third-graders (Mage = 9.32, SD = .38, 22 females) and seventeen sixth-graders (Mage = 12.27, SD = .34, 10 females) were given a working memory task (Alphabet Span; Kail, Lervag, Hulme, 2016) in which the experimenter read lists of letters aloud (2-6 letters) and had children recall the letters in alphabetical order. Working memory score was the largest set correctly recalled. The numerical prediction task was placed in a home run derby framework such that children were told, “Let’s play the home run derby game! Each slide will show distances of how far a player hit baseballs. Your job is to tell me how far you think the next ball will go.”. On a computer, children viewed thirty slides containing sets of 3-digit numbers: five slides each with sets of 4, 5, 8, or 9 numbers and ten slides with a set of 13 numbers (and two initial practice slides with three numbers). After viewing each slide, children were prompted to make a prediction (Figure 1). Numerical prediction accuracy was determined by subtracting the prediction from each number set mean.

A multiple regression analysis was conducted to examine whether the set mean, grade, and working memory accounted for unique variance in numerical predictions. Results indicated the predictors explained 2% of the variance (R2 = .02, F(3, 1825) = 10.19, p < .001). Working memory did not account for unique variance (β = 8.89, p = .22) suggesting that numerical predictions did not require explicit processing. Grade accounted for unique variance (β = 45.83, p < .001), as sixth-graders’ predictions were closer to the set mean than third graders and predictions of third-graders tended to be larger than sixth graders. Additionally, set mean accounted for unique variance (β = -.17, p < .001) indicating that both third- and sixth-grade children tended to under-predict for larger sets (>600). A series of curve fit regressions indicated that a linear function, rather than a logarithmic function, was the best fit, though the fit was significantly better for sixth graders (r2 = .62) than third- graders (r2 = .25, see Figure 2). This is consistent with research on individual number estimates (Siegler & Opfer, 2003) and suggests that accuracy of numerical predictions is in part a function of the accuracy of the underlying numerical magnitude representations.

Authors

• Rachael D Todaro, Kent State University
  Presenting Author

• Tracy Arner, Kent State University
  Non-Presenting Author

• Bradley J Morris, Kent State University
  Non-Presenting Author