Icon arrays help younger children's proportional reasoning

Abstract

We investigated the effects of two context variables, presentation format (icon arrays or numerical frequencies) and time limitation (limited or unlimited time), on the proportional reasoning abilities of children aged 7 and 10 years, as well as adults. Participants had to select, between two sets of tokens, the one that offered the highest likelihood of drawing a gold token, that is, the set of elements with the greater proportion of gold tokens. Results show that participants performed better in the unlimited time condition. Moreover, besides a general developmental improvement in accuracy, our results show that younger children performed better when proportions were presented as icon arrays, whereas older children and adults were similarly accurate in the two presentation format conditions. Statement of contribution What is already known on this subject? There is a developmental improvement in proportional reasoning accuracy. Icon arrays facilitate reasoning in adults with low numeracy. What does this study add? Participants were more accurate when they were given more time to make the proportional judgement. Younger children's proportional reasoning was more accurate when they were presented with icon arrays. Proportional reasoning abilities correlate with working memory, approximate number system, and subitizing skills.

First and Second Graders Successfully Reason About Ratios With Both Dot Arrays and Arabic Numerals

“…We further provide the first evidence that young children intuitively reason about ratios with symbolic numerals. While one previous study found that slightly older 7‐ to 10‐year‐old children could compare ratios presented as a frequency distribution (e.g., 4 tokens out of 10 are gold), the stimuli in that study were constructed such that children could have attended only to the numerator rather than truly evaluating the ratio of the numerator to the denominator (Ruggeri, Vagharchakian, & Xu, 2018). This study is thus the first to demonstrate that 6‐ to 8‐year‐old children can perform approximate ratio comparisons with a symbolic format without relying on unidimensional comparison heuristics.…”

Can we count on early numerical abilities for early probabilistic reasoning abilities?

“…Ruggeri et al (2018) found positive correlations between the numerical and probabilistic reasoning abilities across age groups and within the youngest age group. Notably, Ruggeri et al (2018) only assessed children's ability to compare probabilities. In their literature review, Bryant and Nunes (2012) described probability as a complex concept for which we have to fall back on our understanding of different sub-concepts: randomness, sample space, quantification and comparison of probabilities, and correlation.…”

“…In binary choice tasks, participants have to choose the best of two sets, each containing desired and undesired elements, to blindly draw from (Falk et al, 2012). Ruggeri et al (2018) found positive correlations between the numerical and probabilistic reasoning abilities across age groups and within the youngest age group. Notably, Ruggeri et al (2018) only assessed children's ability to compare probabilities.…”

“…However, this hypothesis has not been explicitly investigated so far. In one study, Ruggeri et al (2018) investigated the impact of number sense and the Approximate Number System (assessed by the Panamath test) on the performance of 7-and 10-year olds and adults on a probabilistic binary choice task. In binary choice tasks, participants have to choose the best of two sets, each containing desired and undesired elements, to blindly draw from (Falk et al, 2012).…”

“…Assessing the full understanding of probability in one study might be a utopian ideal. Nonetheless, findings of Ruggeri et al (2018) raised the question whether early numerical abilities relate to all aspects of probability in the same way. For example, quantification and comparison of probabilities is directly related to children's proportional reasoning abilities, while this relation is less prominent for other aspects of probability (Bryant & Nunes, 2012).…”