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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幼儿园的符号数能力可以预测1年级的非符号数能力和数学成绩。

研究表明，虽然两种不同但相关的表示幅度的方法在数字和数学技能的发展中起着基础性的作用：非言语近似数字系统和精确符号数字系统。尽管有大量研究表明这两个系统是数学成绩的重要预测指标，但有关这些基本数字能力是否以及如何在发展上相互关联的争论一直很激烈。具体而言，他们之间关系的因果关系一直是争论的话题：儿童的近似数能力是预测较晚的符号数能力（映射帐户）还是反过来预测（精化帐户）。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，其中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进行了评估，数学成绩在四个时间点进行了评估。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设定的目标变量之间的相互关系的多种理论预测。结果与细化帐户最一致，表明较早的符号数字能力始终是近似数字能力，混合比较能力和算术技能的最强预测指标。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是足够的或几乎足够的。这凸显了将来需要进行研究以对比竞争帐户的必要性，因为我们的结果表明，单独检查任何一个帐户都可能无法揭示最佳拟合的发展模型。（PsycInfo数据库记录（c）2021 APA，保留所有权利）。