Poster #41 - Self-Reported Proportional Reasoning Strategies as Predictors of Performance

• In Event: 2-163 - Poster Session 08
  In Poster Session: PS 08 Section - Cognitive Processes

Integrative Statement

Proportional reasoning is widely used in everyday life, such as calculating speed, density, and gas mileage (Karplus, 1983), and is a strong foundational component for fraction knowledge (Möhring et al., 2016) and algebra readiness (NMAP, 2008; Booth & Newton, 2012). In fact, proportional reasoning as a predictor of algebra readiness has been shown to supersede other tested predictors, such as central executive span, intelligence, whole number arithmetic, number fluency, and number line tasks (Bailey, Hoard, Nugent, & Geary, 2012). Children’s proportional reasoning performance substantially improves from kindergarten to 4th grade (Boyer, Levine, & Huttenlocher, 2008). However, little is known about the strategies used when completing proportional reasoning tasks, or how these strategies relate to performance. An understanding of this relationship is important as it will provide a more fine-grained understanding of performance, insight into conceptual change not captured by accuracy, and the extent to which children can explicitly report strategies otherwise possibly implicit or unconscious.
Kindergarten through 4th-graders (N=342; 199 female) completed a 15-item proportional reasoning task (Figure 1; Möhring et al., 2015). Performance was measured via average percent absolute error (PAE) (|child’s estimate - correct response|). Then, children were shown three additional items and were asked to describe their strategy while the researcher transcribed their response. We coded responses for comparative language (“more”, “less”, “bigger”, etc., e.g., “more water than cherry”) and/or magnitude language (“big”, “small”, “little”, etc., e.g., “big water”).
We categorized children as using comparative language (at least once, with or without magnitude language; 55.6% of children), using magnitude language only (without comparative; 26.9%), or neither (did not mention comparative or magnitude language; 17.5%; not analyzed further because this group confounds low conceptual knowledge and refusal to cooperate). Because proportional reasoning requires focusing on comparative relations rather than absolute magnitudes, we hypothesized that children who used comparative language would be older and have better task performance than those who used magnitude language only.
The average grade level was higher among children who used comparative language (M=2.27, SD=1.29), than those who only used magnitude language (M=1.67, SD=1.42, t(280)=3.52, p<.001). Children who used comparative language also had better proportional reasoning task performance (lower PAE, M=.13, SD=.07) than those who used magnitude language (M=.17, SD=.10, t(275)=3.95, p<.001). In a simultaneous linear regression, comparative language was a significant predictor of proportional reasoning PAE (β=-.16, p=.004), controlling for grade level, which was also significant (β=-.38, p<.001) (Figure 2).
Older children were more likely to use comparative language instead of only magnitude language during proportional reasoning tasks, and children’s self-reported strategy was a good indicator of students’ performance. This shows that children’s use of comparison strategies, versus focusing on absolute magnitude, was explicit and verbalizable. Determining types of strategies used and their developmental sequence is an important initial step toward a broader investigation of factors affecting proportional reasoning strategy use. Furthermore, examining strategy use can act as a lens onto what children are actually doing in the classroom and advance teaching applications.

Authors

• Alysa Cannon, Temple University
  Presenting Author

• Lindsey Hildebrand, Boston College
  Non-Presenting Author

• Elizabeth Gunderson, Temple University
  Non-Presenting Author