Counting to Infinity: Does Learning the Syntax of the Count List Predict Knowledge That Numbers Are Infinite?
Counting to Infinity: Does Learning the Syntax of the Count List Predict Knowledge That Numbers Are Infinite?
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数到无穷大：学习计数列表的语法是否可以预测数字是无穷大的知识？
DOI：
10.1111/cogs.12875
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发表时间：
2020
影响因子：
2.5
通讯作者：
Barner, David
中科院分区：
文献类型：
--
作者：
Chu, Junyi;Cheung, Pierina;Schneider, Rose M.;Sullivan, Jessica;Barner, David
到了5岁半左右，美国的许多孩子就认为数字永远不会结束，而且总是可以在一组数字中添加1。当被要求在添加一个对象后标记集合的数量时，这些相同的孩子通常也表现良好（例如，判断标记为“五”的集合现在应该是“六”）。这些发现表明，儿童对“后继函数”具有内隐知识：每个自然数n都有一个后继数n+ 1。在这里，我们探讨了儿童如何发现这种递归功能，以及它是否可能与发现管理语言特定计数例程的生产性形态规则有关（例如，表示base10结构的英语规则）。我们用三个任务测试了4岁和5岁儿童的计数知识，然后我们将其与（a）儿童相信1总是可以加到任何数字（后继函数）和（B）他们相信数字永远不会结束（无穷大）相关联。表现出生产性计数规则知识的儿童更有可能相信数字是无限的（即，不存在最大数目），尽管这种计数知识本身并不直接与后继函数的知识相关联。此外，我们的研究结果表明，年仅4岁的儿童能够实施规则定义的口头计数列表，以产生超出其自发计数范围的数字单词，这可能会支持他们获得的口头计数序列的推理，推断数字永远不会结束。
By around the age of 5½, many children in the United States judge that numbers never end, and that it is always possible to add 1 to a set. These same children also generally perform well when asked to label the quantity of a set after one object is added (e.g., judging that a set labeled “five” should now be “six”). These findings suggest that children have implicit knowledge of the “successor function”: Every natural number,n, has a successor,n+ 1. Here, we explored how children discover this recursive function, and whether it might be related to discovering productive morphological rules that govern language‐specific counting routines (e.g., the rules in English that represent base‐10 structure). We tested 4‐ and 5‐year‐old children’s knowledge of counting with three tasks, which we then related to (a) children’s belief that 1 can always be added to any number (the successor function) and (b) their belief that numbers never end (infinity). Children who exhibited knowledge of a productive counting rule were significantly more likely to believe that numbers are infinite (i.e., there is no largest number), though such counting knowledge was not directly linked to knowledge of the successor function, per se. Also, our findings suggest that children as young as 4 years of age are able to implement rules defined over their verbal count list to generate number words beyond their spontaneous counting range, an insight which may support reasoning over their acquired verbal count sequence to infer that numbers never end.
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影响因子：
2.6
作者：
Le Corre M;Li P;Huang BH;Jia G;Carey S
通讯作者：
Carey S
论数的逻辑
影响因子：
4.5
作者：
C. Peirce
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C. Peirce
年轻人的无限想法
影响因子：
3.2
作者：
J. Monaghan
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J. Monaghan
土著农耕采集群体中的儿童学习数字词。
影响因子：
3.7
作者：
S. Piantadosi;J. Jara;E. Gibson
通讯作者：
E. Gibson
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影响因子：
1.8
作者：
K. Miller;J. Stigler
通讯作者：
J. Stigler