East Asian students routinely outperform American peers in mathematics. One source of this learning gap may be linguis-tic, such as explicitly naming part-whole relations in fractions (e.g., of four parts, one in Korean vs. one-fourth in English).Our study examined whether adopting such language would improve American children’s number-line estimates. To testthis, 83 10-year-olds were read fractions using either Korean-style or English names over pretest, training, and posttest. Inboth conditions, number-line problems either had no landmarks, landmarks that matched the denominator, or landmarksthat did not match the denominator. As expected, we observed a session by problem type interaction (F=2.71, p¡.05),indicating that feedback improved accuracy most for problems involving matching landmarks. Surprisingly, the effect ofKorean naming was to reduce accuracy across all problems and test phases (ps ¡ .01). Results offer an important warningagainst linguistic reform that may be harmful for American students.

Proficiency in math is critically important given its implications for education and daily life (e.g., finances, health). However, math is a challenging subject, and proficiency requires a complex interplay of content knowledge and general cognitive processes, including Executive Function (EF). In this exploratory study, we used heat maps to examine whether participants' self-reported attention to strategy-specific components of fraction arithmetic equations (i.e., operations, numerators, denominators) was related to their EF and task performance. Our results indicated that participants with stronger EF (indexed by a numerical stroop task) obtained higher fraction arithmetic scores and were also more likely to attend to strategy-specific components in the fraction problems. Additionally, a positive correlation was found between participants’ selection of strategy-specific components and their fraction arithmetic accuracy. Keywords: Fraction arithmetic; Strategy Reports; Executive Function; Inhibitory Control; Attention

Children display an early sensitivity to implicit proportions (e.g., 1 of 5 apples vs 3 of 4 apples) but have considerabledifficulty in learning the explicit, symbolic proportions denoted by fractions (e.g., 1/5 vs 3/4). Theoretically, reducingthe gap between representations of implicit vs explicit proportions would improve understanding of fractions, but littleis known about how the representations develop and interact with one another. To address this, we asked 163 third tofifth graders to estimate the position of proportionally-equivalent integers and fractions on number lines (e.g., 3 on 0-8number line vs 3/8 on 0-1 number line). We found that, with increasing age, children were more accurate and linear inrepresenting both integers and fractions. More importantly, childrens estimates of implicit and explicit proportions becamemore coherent, such that a childs estimates of fractions on a 0-1 number-line was a linear function of the same childsestimates of equivalent integers. This representational coherence independently predicted childrens fraction proficiency inother tasks, suggest- ing that building a coherent understanding of proportions is an educationally-important goal.