Attending to relations: Proportional reasoning in 3- to 6-year-old children.

Abstract

When proportional information is pit against whole number numerical information, children often attend to the whole number information at the expense of proportional information (e.g., indicating 4/9 is greater than 3/5 because 4 > 3). In the current study, we presented younger (3- to 4-year-olds) and older (5- to 6-year-olds) children a task in which the proportional information was presented either continuously (units cannot be counted) or discretely (countable units; numerical information available). In the discrete conditions, older children showed numerical interference-responding based on the number of pieces instead of the proportion of pieces. However, older children easily overcame this poor strategy selection on discrete trials if they first had some experience with continuous, proportional strategies, suggesting this prevalent reliance on numerical information may be malleable. Younger children, on the other hand, showed difficulty with the proportion task, but showed evidence of proportional reasoning in a simplified estimation-style task, suggesting that younger children may still be developing their proportional and numerical skills in task-dependent ways. Lastly, across both age groups, performance on the proportional reasoning task in continuous contexts, but not discrete contexts, was related to more general analogical reasoning skills. Findings suggest that children's proportional reasoning abilities are actively developing between the ages of 3 and 6 and may depend on domain general reasoning skills. We discuss the implications for this work for both cognitive development and education. (PsycINFO Database Record

Talking about proportion: Fraction labels impact numerical interference in non‐symbolic proportional reasoning

“…This is consistent with research suggesting that comparing probabilities may be easier and younger children may be more readily able to inhibit number-based responding in these contexts than in equivalence tasks (Hurst & Cordes, 2018a). For example, it may be that the visual information included in the training was enough to prompt children to attend to proportion in probabilistic comparison contexts, resulting in non-significant additional impacts of the verbal labels.…”

“…In neither experiment was there a significant difference in overall performance on the numerically consistent and misleading trials, which does not provide clear evidence that children consistently made use of the numerical information, unlike other studies that have investigated this phenomenon directly (Hurst & Cordes, 2018a;Jeong et al, 2007). In neither experiment was there a significant difference in overall performance on the numerically consistent and misleading trials, which does not provide clear evidence that children consistently made use of the numerical information, unlike other studies that have investigated this phenomenon directly (Hurst & Cordes, 2018a;Jeong et al, 2007).…”

“…Comparison task (adapted from Hurst & Cordes, 2018a;Jeong et al, 2007) The comparison task assessed whether children were able to judge the relative magnitude of two probabilistic displays. Children were first introduced to a cardboard spinner (not on the computer, 8 cm in diameter with a small black arrow, approximately 3 cm long) and…”

“…The interference between absolute number and relative proportion has been at the center of a substantial amount of work with symbolic (e.g., Alibali & Sidney, 2015;Durkin & Rittle-Johnson, 2015;Ni & Zhou, 2005) and non-symbolic representations (e.g., Boyer et al, 2008;Boyer & Levine, 2015;Fabbri, Caviola, Tang, Zorzi, & Butterworth, 2012;Hurst & Cordes, 2018a;Jeong, et al, 2007). The interference between absolute number and relative proportion has been at the center of a substantial amount of work with symbolic (e.g., Alibali & Sidney, 2015;Durkin & Rittle-Johnson, 2015;Ni & Zhou, 2005) and non-symbolic representations (e.g., Boyer et al, 2008;Boyer & Levine, 2015;Fabbri, Caviola, Tang, Zorzi, & Butterworth, 2012;Hurst & Cordes, 2018a;Jeong, et al, 2007).…”

“…The interference between absolute number and relative proportion has been at the center of a substantial amount of work with symbolic (e.g., Alibali & Sidney, 2015;Durkin & Rittle-Johnson, 2015;Ni & Zhou, 2005) and non-symbolic representations (e.g., Boyer et al, 2008;Boyer & Levine, 2015;Fabbri, Caviola, Tang, Zorzi, & Butterworth, 2012;Hurst & Cordes, 2018a;Jeong, et al, 2007). Research has pointed to numerous factors that likely contribute to the prevalence of this numerical interference, such as teaching methods, previous experience, strategies, and individual differences in understanding fractions (e.g., Alibali & Sidney, 2015;Boyer & Levine, 2015;Empson, Junk, Dominguex, & Turner, 2006;Hurst & Cordes, 2018a;Spinillo, 2002). For example, children show success comparing and matching proportions when presented continuously (i.e., in the absence of countable numerical information); but when presented discretely, children respond in a way consistent with attending to the number of relevant pieces (i.e., the number of pieces in the "numerator") rather than the relation between the number of relevant and total pieces (Boyer & Levine, 2015;Boyer et al, 2008;Hurst & Cordes, 2018a;Jeong et al, 2007).…”