Research has shown that two different, though related, ways of representing magnitude play foundational roles in the development of numerical and mathematical skills: a nonverbal approximate number system and an exact symbolic number system. While there have been numerous studies suggesting that the two systems are important predictors of math achievement, there has been substantial debate regarding whether and how these basic numerical competencies may be developmentally interrelated. Specifically, the causal direction of their relation has been the subject of debate: whether children's approximate number abilities predict later symbolic number abilities (the mapping account) or the other way around (the refinement account). Our sample included 622 kindergarten children (mean age = 62 months, SD = 3.5, 279 females, 75 born outside Canada), whose dot comparison, number comparison, and mixed comparison skills were assessed over three time-points and math achievement assessed over four time-points. We contrasted multiple theoretical predictions of the interrelations between the variables of interest posited by these two developmental accounts using longitudinal random intercept cross-lagged models. Results were most consistent with the refinement account, suggesting that earlier symbolic number ability is consistently the strongest predictor of approximate number ability, mixed-comparison ability, and arithmetic skills. Notably, our results demonstrated that, when individual models are examined in isolation, model fit was adequate or near adequate for all models tested. This highlights the need for future research to contrast competing accounts, as our results suggest the examination of any one account in isolation may not reveal the best fitting developmental model. (PsycInfo Database Record (c) 2021 APA, all rights reserved).

中文翻译：

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幼儿园儿童的符号数能力可预测 1 年级的非符号数能力和数学成绩。

研究表明，两种不同但相关的表示幅度的方式在数值和数学技能的发展中起着基础性作用：非语言近似数系统和精确符号数系统。虽然有大量研究表明这两个系统是数学成绩的重要预测因素，但关于这些基本的数字能力是否以及如何在发展上相互关联，存在大量争论。具体来说，他们关系的因果方向一直是争论的主题：儿童的近似数能力是预测后来的符号数能力（映射说明）还是相反（精化说明）。我们的样本包括 622 名幼儿园儿童（平均年龄 = 62 个月，SD = 3.5，279 名女性，75 名在加拿大境外出生），他们的点比较、数字比较和混合比较技能在三个时间点上进行评估，数学成绩在四个时间点上进行评估。我们使用纵向随机截距交叉滞后模型对比了这两个发展账户所假设的感兴趣变量之间相互关系的多个理论预测。结果与细化描述最一致，表明早期的符号数能力始终是近似数能力、混合比较能力和算术能力的最强预测指标。值得注意的是，我们的结果表明，当单独检查单个模型时，模型拟合对于所有测试的模型都足够或接近足够。这凸显了未来研究对比竞争账户的必要性，正如我们的结果表明，孤立地检查任何一个帐户可能无法揭示最合适的发展模型。（PsycInfo 数据库记录 (c) 2021 APA，保留所有权利）。