Children can successfully compare continuous proportions as early as age 4, yet struggle to compare discrete proportions least to age 10, especially when the discrete information is misleading. This study examined whether inhibitory control contributes to individual differences in discrete proportional reasoning and whether reasoning could be enhanced by priming continuous information. Forty-nine second-graders completed two tasks. In the Hearts and Flowers (H&F) task, a measure of inhibition, children pressed either on the corresponding or opposite side depending on the identity of the displayed figure. In the Spinners task, a measure of proportional reasoning, children chose the spinner with the proportionally larger red area, across continuous and two discrete formats. In the discrete adjacent format, the continuous stimuli were segmented into sections, which could be compatible with the proportional information or misleading; the discrete mixed format interspersed the colored sections from the discrete adjacent conditions. Finally, two priming groups were formed. Children who saw the continuous immediately before the discrete adjacent format formed the Continuous-priming group (n =26). Children who saw discrete mixed immediately before the discrete adjacent format formed the Discrete-priming group (n =23). Our results showed that children who performed better in the H&F task also had better performance on the discrete counting misleading trials. Furthermore, children in the Continuous-priming group outperformed children in the Discrete-priming group, specifically in contexts where discrete information was misleading. These results suggest that children's proportional reasoning may be improved by fostering continuous representations of discrete stimuli and by enhancing inhibitory control skills.

Children can successfully compare continuous proportions as early as age 4, yet struggle to compare discrete proportions least to age 10, especially when the discrete information is misleading. This study examined whether inhibitory control contributes to individual differences in discrete proportional reasoning and whether reasoning could be enhanced by priming continuous information. Forty-nine second-graders completed two tasks. In the Hearts and Flowers (H&F) task, a measure of inhibition, children pressed either on the corresponding or opposite side depending on the identity of the displayed figure. In the Spinners task, a measure of proportional reasoning, children chose the spinner with the proportionally larger red area, across continuous and two discrete formats. In the discrete adjacent format, the continuous stimuli were segmented into sections, which could be compatible with the proportional information or misleading; the discrete mixed format interspersed the colored sections from the discrete adjacent conditions. Finally, two priming groups were formed. Children who saw the continuous immediately before the discrete adjacent format formed the Continuous-priming group (n =26). Children who saw discrete mixed immediately before the discrete adjacent format formed the Discrete-priming group (n =23). Our results showed that children who performed better in the H&F task also had better performance on the discrete counting misleading trials. Furthermore, children in the Continuous-priming group outperformed children in the Discrete-priming group, specifically in contexts where discrete information was misleading. These results suggest that children’s proportional reasoning may be improved by fostering continuous representations of discrete stimuli and by enhancing inhibitory control skills.

The persistent educational challenges that fractions pose call for developing novel instructional methods to better prepare students for fraction learning. Here, we examined the effects of a 24-session, Cuisenaire rod intervention on a building block for symbolic fraction knowledge, continuous and discrete non-symbolic proportional reasoning, in children who have yet to receive fraction instruction. Participants were 34 second-graders who attended the intervention (intervention group) and 15 children who did not participate in any sessions (control group). As attendance at the intervention sessions was irregular (median = 15.6 sessions, range = 1–24), we specifically examined the effect of the number of sessions completed on their non-symbolic proportional reasoning. Our results showed that children who attended a larger number of sessions increased their ability to compare non-symbolic continuous proportions. However, contrary to our expectations, they also decreased their ability to compare misleading discretized proportions. In contrast, children in the Control group did not show any change in their performance. These results provide further evidence on the malleability of non-symbolic continuous proportional reasoning and highlight the rigidity of counting knowledge interference on discrete proportional reasoning.

The persistent educational challenges that fractions pose call for the development of novel instructional methods to better prepare students for fraction learning. Here, we examined the effects of a 24-session, Cuisenaire rod intervention on a building block for symbolic fraction knowledge, continuous and discrete non-symbolic proportional reasoning, in children who have yet to receive fraction instruction. Participants were 40 second graders divided into three groups: the Full intervention group who attended nearly all the sessions (n = 14), the Partial intervention group who participated in a small number of sessions (n = 11), and Control group (n = 15). Children in the Full intervention group increased their ability to compare non-symbolic continuous proportions in representations in which they did not receive any practice (annulus-shaped figures). However, contrary to our expectations, children in this group also decreased their ability to compare misleading discrete proportions. In contrast, children in the Control group did not show any change in their performance, and children in the Partial intervention group showed a similar, but not significant pattern of effects as the Full intervention group. These results provide further evidence on non-symbolic continuous proportional reasoning’s malleability and highlights the rigidity of counting knowledge interference on discrete proportional reasoning.