Poster #28 - Concreteness Fading as an Intervention for Fraction Learning

• In Event: 2-055 - Poster Session 06
  In Poster Session: PS 06 Section - Cognitive Processes

Integrative Statement

The formation of a strong foundation in early math education can enable a child to develop a deeper understanding of math in their future academic endeavors. Complex math concepts (e.g., fractions) are particularly challenging for elementary-age children to grasp (Bailey et al., 2012; Department of Education, 1997). In the current study, we explored children’s ability to learn and generalize novel fraction concepts through an abstraction task in the face of varying perceptual information (as encountered in the real world).

Four to six year old children (N=95, M=5.03 years, SD=0.90 years) participated in a pre-post test design, separated by a passive viewing of a series of exemplars of novel visual fractions that progressed from perceptually impoverished to perceptually rich (simple-to-complex abstraction, or concreteness fading; per Fyfe et al., 2014). In Experiment 1, children were randomly assigned to one of three conditions: (1) Control (no training), (2) Single Exemplar (children were trained on 3/4 and tested on 3/4), or (3) Multiple Exemplar (children were trained on 3/4 but tested on multiple fractions). In Experiment 2, we manipulated the label presented to children during training (otherwise identical to Single Exemplar) in order to examine whether their performance in Experiment 1 was due to a visual strategy (Dax Exemplar; e.g., this fraction “looks like” the exemplar) or a whole number strategy (Three Exemplar; e.g., there are three pieces colored in, regardless of the total number of pieces). Our dependent variables were (a) accuracy on the abstraction task (Figure 1) and (b) pre- to post-test gains on our more traditional fraction task (Figure 2).

Results from Experiment 1 indicate that accuracy on the Single and Multiple Exemplar conditions did not differ (p>.3, Cohen’s d=.30). No training (Control) differed statistically from the Single Exemplar condition (p=.001, Cohen’s d=1.1). Children demonstrated significant pre- to post-test gains on a more traditional fraction task following training in the Multiple Exemplar (p=.033, Cohen’s d=1.3), but not Single Exemplar (p>.7, Cohen’s d=.16) or Control (p>.4, Cohen’s d=.35), conditions. In Experiment 2, we compared performance on the Single Exemplar condition to that of the Dax Exemplar (p>.3, Cohen’s d=.15) and Three Exemplar conditions (p>.2, Cohen’s d=.37). Children demonstrated significant pre-post test gains in Three Exemplar Conditions (p=.027, Cohen’s d=1.1), but not in the Dax Exemplar Conditions (p>.4, Cohen’s d=.32).

Data from Experiment 1 show that children could learn a novel fraction concept through this concreteness training in an abstraction task, both for trained and untrained fractions. Gains in the Multiple Exemplar condition suggest that the additional examples may have facilitated an understanding of the broader concept. Experiment 2 explored the mechanism behind children’s success in the original abstraction task and suggests that children used of a visual strategy when identifying a trained exemplar (similar gains in Single/Dax conditions), but appeared to use a whole number strategy when presented with untrained fractions (similar gains in Multiple/Three conditions), such that they succeeded in identifying a new fraction if they could successfully identify its numerator. These findings have implications for curriculum development and teacher training.

Authors

• Madison Ramirez, George Washington University
  Presenting Author

• Tasha Posid, The Ohio State University
  Non-Presenting Author