Department of Psychological and Brain Sciences, University of Massachusetts Amherst, USA.
Department of Linguistics, University of Massachusetts Amherst, USA.
Cognition. 2020 Oct;203:104331. doi: 10.1016/j.cognition.2020.104331. Epub 2020 Jun 23.
The acquisition and representation of natural numbers have been a central topic in cognitive science. However, a key question in this topic about how humans acquire the capacity to understand that numbers make 'infinite use of finite means' (or that numbers are generative) has been left unanswered. While previous theories rely on the idea of the successor principle, we propose an alternative hypothesis that children's understanding of the syntactic rules for building complex numerals-or numerical syntax-is a crucial foundation for the acquisition of number concepts. In two independent studies, we assessed children's understanding of numerical syntax by probing their knowledge about the embedded structure of cardinal numbers using a novel task called Give-a-number Base-10 (Give-N10). In Give-N10, children were asked to give a large number of items (e.g., 32 items) from a pool that is organized in sets of ten items. Children's knowledge about the embedded structure of numbers (e.g., knowing that thirty-two items are composed of three tens and two ones) was assessed from their ability to use those sets. Study 1 tested English-speaking 4- to 10-year-olds and revealed that children's understanding of the embedded structure of numbers emerges relatively late in development (several months into kindergarten), beyond when they are capable of making a semantic induction over a local sequence of numbers. Moreover, performance in Give-N10 was predicted by other task measures that assessed children's knowledge about the syntactic rules that govern numerals (such as counting fluency), demonstrating the validity of the measure. In Study 2, this association was tested again in monolingual Korean kindergarteners (5-6 years), as we aimed to test the same effect in a language with a highly regular numeral system. It replicated the association between Give-N10 performance and counting fluency, and it also demonstrated that Korean-speaking children understand the embedded structure of cardinal numbers earlier in the acquisition path than English-speaking peers, suggesting that regularity in numerical syntax facilitates the acquisition of generative properties of numbers. Based on these observations and our theoretical analysis of the literature, we propose that the syntax for building complex numerals, not the successor principle, represents a structural platform for numerical thinking in young children.
自然数的获取和表示一直是认知科学的核心议题。然而，这个主题中一个关键问题尚未得到解答，即人类如何获得理解数字“无限使用有限手段”（即数字是生成性的）的能力。虽然之前的理论依赖于后继原则的概念，但我们提出了一个替代假设，即儿童对构建复杂数字的句法规则——即数字句法——的理解是获得数字概念的关键基础。在两项独立的研究中，我们通过一项名为“Give-a-number Base-10”（Give-N10）的新任务来评估儿童对数字句法的理解，该任务旨在探查他们对基数的嵌套结构的知识。在 Give-N10 中，孩子们被要求从一组以十个为一组的物品中取出大量物品（例如，32 个物品）。通过他们使用这些集合的能力来评估他们对数字嵌套结构的知识（例如，知道 32 个物品由三个十和两个一组成）。研究 1 测试了以英语为母语的 4 至 10 岁儿童，结果表明，儿童对数字嵌套结构的理解在发展过程中出现得相对较晚（进入幼儿园几个月后），超过了他们能够对局部数字序列进行语义归纳的能力。此外，Give-N10 的表现可以通过其他任务指标来预测，这些指标评估了儿童对支配数字的句法规则的知识（例如计数流利度），证明了该测量方法的有效性。在研究 2 中，我们在单语韩语幼儿园儿童（5-6 岁）中再次测试了这种关联，因为我们旨在测试在一种具有高度规则数字系统的语言中是否存在相同的效应。该研究复制了 Give-N10 表现与计数流利度之间的关联，并表明韩语儿童在数字句法习得路径上比英语儿童更早地理解基数的嵌套结构，这表明数字句法的规律性有助于儿童获得数字的生成属性。基于这些观察结果和我们对文献的理论分析，我们提出，构建复杂数字的句法而不是后继原则，代表了幼儿数字思维的结构平台。
