Poster #34 - Proportional Reasoning as a Spatial Foundation of Number Line Estimation

• In Event: 3-206 - Poster Session 13
  In Poster Session: PS 13 Section - Cognitive Processes

Integrative Statement

Spatial skills significantly predict performance in science and mathematics (e.g., Newcombe, 2010; Wai et al., 2009) though the specific mechanisms driving this relationship, especially in children, are relatively unknown. Number line estimation (NLE), which involves linking spatial and numerical magnitudes, may mediate relations between spatial skills and numeracy. Both mental rotation and a composite spatial measure (focused on mental rotation) have been linked to NLE development (Gunderson et al., 2012; LeFevre et al., 2013). However, there is little research linking NLE to a broader set of spatial skills, including proportional reasoning, spatial working memory, and approximate number systems, which have been seen as strong predictors of numeracy (Mohring et al., 2016; Libertus et al., 2011; Witt, 2011). Proportional reasoning, though unstudied as it relates to NLE, is especially interesting given evidence that NLE involves proportional strategies in both children and adults (Barth & Paladino, 2011; Cohen & Blanc-Goldhammer, 2011; Slusser, Santiago, & Barth, 2013).
We explored the relationship between specific spatial skills and NLE. We hypothesized that proportional reasoning (Möhring et al., 2015) would significantly predict NLE performance over other spatial skills (mental rotation, mental transformation, spatial working memory, and non-symbolic numerical comparison) due to proportional strategies on NLE tasks. We also examined estimation models on proportional reasoning and NLE to better understand the relationship between these tasks.
Pre-K to 3rd-graders (N=517, Mage=6.77 years, SDage=1.35; nfemale=290) completed number line tasks dependent on their age: 0-10 (pre-K & kindergartners), 0-100 (pre-k-2nd-graders), and 0-1000 (1st-3rd-graders) and age-appropriate measures of spatial skill (Figure 1). To determine which spatial task best predicted concurrent NLE performance, we ran simultaneous multiple regressions controlling for performance on all spatial tasks, verbal ability (KBIT-2; Kaufman & Kaufman, 2004), grade-level, and gender. Proportional reasoning significantly predicted performance on most number line ranges: 0-10 (Pre-K & K: β=.14, p=.182), 0-100 (Pre-K & K: β=.19, p=.046; 1st -2nd-graders: β=.29, p=.001), and 0-1000 (1st-3rd-graders: β=.16, p=.033).
We next examined whether individual participants’ NLE and proportional reasoning responses were best fit by unbounded power, 1-cycle power, or 2-cycle power models (Table 1). For many children, performance was poor and no model explained more than 25% of the variance in responses. We treated best-fitting model sophistication as an ordinal variable (no model, power, 1-cycle, 2-cycle). The relation of grade-level to model sophistication was significant for proportional reasoning (rs=.32, p<.001), 0-100 NL (rs=.25, p<.001) and 0-1000 NL (rs=.13, p=.003,) and marginal for 0-10 NL (rs =.13, p=.089). Further, proportional reasoning model sophistication was significantly related to model sophistication for all NL ranges (0-10: rs=.34, p<.001, 0-100: rs=.20, p=.002; 0-1000: rs=.27, p<.001). However, when excluding children with no model these relations were not significant, suggesting that the difference between no model and some type of best-fitting model drove these relations.
These results indicate that proportional reasoning uniquely relates to NLE performance. Results from estimation models are consistent with a developmental trajectory from poor performance to increasingly sophisticated power models on proportional reasoning and NLE tasks, and with a relation between these tasks in model sophistication.

Authors

• Lindsey Hildebrand, Boston College
  Presenting Author

• Elizabeth Gunderson, Temple University
  Non-Presenting Author