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

Abstract

Across two experiments, we investigated how verbal labels impact the way young children attend to proportional information, well before the introduction of formal fraction education. Five-to seven-year-old children were introduced to equivalent non-symbolic proportions labeled in one of three ways: (a) a single, categorical label for multiple fractions (both 3/4 and 6/8 referred to as "blick"), (b) labels that focused on the numerator [e.g., 3/4 labeled as "three blicks" (Experiment 1) or "three-fourths" (Experiment 2)], or (c) labels that had a complete part-whole structure ("three-out-offour"). Children then completed measures of non-symbolic proportional reasoning that pitted whole-number information against proportional information for novel proportions. Across both experiments, children who heard the categorical labels were more likely to match non-symbolic displays based on proportion than children in any of the other conditions, who demonstrated higher levels of numerical interference. These findings suggest that fraction labels have the potential to shape children's attention to proportional information even in the context of non-symbolic part-whole displays and for children who are not familiar with formal fraction symbols. We discuss these findings in terms of children's developing understanding of proportional reasoning and its implications for fraction education. K E Y W O R D Sfractions, labels, proportion, whole number interference

Spontaneous and directed attention to number and proportion.

“…For example, despite the availability of both numerical and proportional information, proportional information may be more salient (or at least, as salient as number) in the case of continuous displays that have been made discrete (e.g., dividing a rectangle into pieces) or discrete displays that have been clustered together (e.g., partitioned dot displays with all the red dots grouped together and all the blue dots grouped together). Some work suggests that, at least in the case of continuous representations that are made discrete, it is possible to encourage young children to attend to proportion and ignore number, preventing numerical interference (Boyer & Levine, 2015; Hurst & Cordes, 2018a, 2019). Thus, future work should further investigate how variability across contexts may impact the relative saliency of both number and proportion.…”

“…For example, with only a short period of experience comparing continuous proportional amounts (i.e., judging proportion in a context in which contrasting whole-number information is not available), children are less likely to rely on a numerical strategy in subsequent trials where discrete quantities are available (Boyer & Levine, 2015; Hurst & Cordes, 2018a). In addition, introducing children to equivalent proportions using categorical, as opposed to numerical, language may help them attend to the relations over absolute number (Hurst & Cordes, 2019). Thus, although numerical interference is evident early in development and remains in adulthood, the malleability of this numerical interference suggests that it may not be an inherent or necessary aspect of thinking about proportion.…”

Fraction Symbols and their Relation to Conceptual Knowledge

“…Educators recommend describing the fractional parts with precise words such as numerator and denominator and describing the fractional unit with one label (i.e., "threefourths") because imprecise language such as describing the fraction ¾ as "3 over 4" or describing 3 as the "top number" can reinforce the misconception that the fraction is two distinct numbers (Hughes et al, 2016;Powell et al, 2019). Moreover, research has suggested that congruent fraction labels support improved fraction mapping (Hurst & Cordes, 2019;Mix & Paik, 2008). Specifically, when the fraction quantity ¾ was labelled with one word ("blick") compared to a numerator-focused label ("3 blicks") or a structural label ("three-out-of-four blicks"), students aged 6 to 7 years were better able to recognize images showing equivalent proportions.…”

“…Misunderstanding or misapplying academic language however, can hinder students' understanding of fractions (Riccomini, 2016;Riccomini et al, 2015). Further, limited or imprecise mathematical vocabulary can be a source of mathematical errors (Hughes et al, 2016;Hurst & Cordes, 2019;Powell et al, 2019;Rubenstein & Thompson, 2002;Thompson & Rubenstein, 2014). As an example, when I was working with a student, I described a fraction as "1 over 5", to my chagrin, the student misunderstood my meaning and instead of writing the fraction , the student wrote exactly what I had said (see Figure 7.4).…”

Who's the winner? Children's math learning in competitive and collaborative scenarios

“…In contrast, it was predicted that girls would underperform in the Competition condition relative to Baseline. In light of studies suggesting that performance on Conflict trials is particularly vulnerable to contextual influences (e.g., Hurst & Cordes, 2019), it was predicted that performance differences across conditions would be apparent on these trials. Specifically, because competition and self-comparison is thought to promote anxiety and thus likely increase cognitive load in girls (e.g., Hwang et al, 2013), girls were predicted to be more inclined to resort to whole number biases (i.e., perform below chance levels on the Conflict trials) in the Competition condition relative to Baseline.…”