Is thirty-two three tens and two ones? The embedded structure of cardinal numbers
Is thirty-two three tens and two ones? The embedded structure of cardinal numbers
复制标题
三十二是三十加二吗？
DOI：
10.31234/osf.io/vtk5w
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发表时间：
2019
期刊：
影响因子：
3.4
通讯作者：
Joonkoo Park
中科院分区：
文献类型：
--
作者：
D. Guerrero;Jihyun Hwang;Brynn Boutin;T. Roeper;Joonkoo Park
自然数的获取和表示一直是认知科学的中心课题。然而，这个话题中的一个关键问题--人类如何获得理解数字“无限使用有限的手段”(或数字具有生成性)的能力--一直没有得到回答。虽然以前的理论依赖于后继原则，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的理解--或数字句法--是获得数字概念的重要基础。在两项独立的研究中，我们通过使用一种名为Gave-a-Number-10(Give-N10)的新任务来探索儿童关于基数嵌入结构的知识，以评估他们对数字语法的理解。在Give-N10中，孩子们被要求从一个池中给出大量的物品(例如，32件)，该池以10件为一组。儿童关于数字嵌入结构的知识(例如，知道32个项目由3个10和2个1组成)是从他们使用这些集合的能力来评估的。研究一对说英语的4至10岁儿童进行了测试，发现儿童对数字嵌入结构的理解出现在相对较晚的发展阶段(几个月后进入幼儿园)，超过了他们能够对当地数字序列进行语义归纳的时候。此外，通过评估儿童对支配数字的句法规则(如计数流利性)的知识的其他任务测量来预测在GET-N10中的表现，从而证明了该测量的有效性。在研究2中，我们在单语的韩国幼儿园(5-6岁)中再次测试了这种联系，因为我们的目标是在一种高度规则的数字系统的语言中测试同样的效果。该研究重现了Give-N10成绩与计算流利性之间的联系，同时也表明说韩语的儿童在习得过程中比说英语的同龄人更早理解基数的嵌入结构，这表明数字句法的规律性促进了数字的生成特性的习得。基于这些观察和我们对文献的理论分析，我们提出构建复数词的句法，而不是后继原则，代表了幼儿数字思维的结构平台。
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.