Understanding fractions is critical to mathematical development, yet many children struggle with fractions even after years of instruction. Fraction arithmetic is particularly challenging. The present study employed a computational model of fraction arithmetic learning, FARRA (Fraction Arithmetic Reflects Rules and Associations; Braithwaite, Pyke, and Siegler, 2017), to investigate individual differences in children's fraction arithmetic. FARRA predicted four qualitatively distinct patterns of performance, as well as differences in math achievement among the four patterns. These predictions were confirmed in analyses of two datasets using two methods to classify children's performance-a theory-based method and a data-driven method, Latent Profile Analysis. The findings highlight three dimensions of individual differences that may affect learning in fraction arithmetic, and perhaps other domains as well: effective learning after committing errors, behavioral consistency versus variability, and presence or absence of initial bias. Methodological and educational implications of the findings are discussed.

中文翻译：

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分数算术学习的个体差异

理解分数对于数学发展至关重要，但即使经过多年的教学，许多孩子仍为分数而苦恼。分数运算尤其具有挑战性。本研究采用分数算术学习的计算模型 FARRA（分数算术反映规则和关联；Braithwaite、Pyke 和 Siegler，2017 年）来调查儿童分数算术的个体差异。FARRA 预测了四种质量上截然不同的表现模式，以及四种模式之间数学成绩的差异。这些预测在使用两种方法对儿童的表现进行分类的两个数据集的分析中得到证实 - 基于理论的方法和数据驱动的方法，潜在轮廓分析。研究结果突出了可能影响分数算术学习的个体差异的三个维度，也许还有其他领域：犯错误后的有效学习，行为一致性与可变性，以及初始偏差的存在与否。讨论了研究结果的方法论和教育意义。