Starting small: exploring the origins of successor function knowledge
Starting small: exploring the origins of successor function knowledge
复制标题
从小事做起：探索后继函数知识的起源
DOI：
10.1111/desc.13091
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发表时间：
2021
影响因子：
3.7
通讯作者：
Barner, David
中科院分区：
文献类型：
--
作者：
Schneider, Rose M.;Pankonin, Ashlie;Schachner, Adena;Barner, David
虽然大多数美国儿童在4岁时就能准确地数出一组单词，但许多人无法理解计数和数字之间的结构类比——在一组单词中加1相当于在计数列表中数出一个单词。虽然从理论上讲，孩子们建立这种结构映射与学习如何使用计数来生成集合是一致的，但他们最初对这种关系有一个基于项目的理解，并且可以推断，例如，将1加到“5”是“6”，而无法推断，例如，将1加到“25”是“26”，尽管他们能够在大声计数时背诵这些数字。儿童在推理基数变化和计数表之间的关系方面取得成功的特定项目性质，提高了这种结构映射在发展后期出现的可能性，并且这种能力最初并不依赖于学习计数。我们在两个实验中验证了这一假设，并发现儿童在成为称职的计数器之前可以执行基于项目的加法操作的证据。即使在孩子们学会数数之后，我们发现他们执行加法运算的能力仍然是基于项目的，并且仅限于非常小的数字，而不是利用计数列表如何表示数字的一般知识。我们讨论了数字词和集合之间的这些早期基于项目的关联如何在构建计数和数量之间的广义结构映射中发挥作用。
Although most U. S. children can accurately count sets by 4 years of age, many fail to understand the structural analogy between counting and number — that adding 1 to a set corresponds to counting up 1 word in the count list. While children are theorized to establish this Structure Mapping coincident with learning how counting is used to generate sets, they initially have an item‐based understanding of this relationship, and can infer that, e.g, adding 1 to “five” is “six”, while failing to infer that, e.g., adding 1 to “twenty‐five” is “twenty‐six” despite being able to recite these numbers when counting aloud. The item‐specific nature of children's successes in reasoning about the relationship between changes in cardinality and the count list raises the possibility that such a Structure Mapping emerges later in development, and that this ability does not initially depend on learning to count. We test this hypothesis in two experiments and find evidence that children can perform item‐based addition operations before they become competent counters. Even after children learn to count, we find that their ability to perform addition operations remains item‐based and restricted to very small numbers, rather than drawing on generalized knowledge of how the count list represents number. We discuss how these early item‐based associations between number words and sets might play a role in constructing a generalized Structure Mapping between counting and quantity.