Starting small: exploring the origins of successor function knowledge,Developmental Science

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Starting small: exploring the origins of successor function knowledge
Developmental Science ( IF 3.1 ) Pub Date : 2021-02-02 , DOI: 10.1111/desc.13091
Rose M Schneider ₁ , Ashlie Pankonin _{1,

2} , Adena Schachner ₁ , David Barner _{1,

3}

Affiliation

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.

中文翻译：

从小处着手：探寻后继函数知识的起源

尽管大多数美国儿童可以在 4 岁之前准确地数数，但许多人无法理解数数和数字之间的结构类比——在集合中加 1 对应于计数列表中的 1 个单词。虽然孩子们在理论上建立这种结构映射与学习如何使用计数来生成集合一致，但他们最初对这种关系有基于项目的理解，并且可以推断，例如，“五”加 1 是“六”，而未能推断出，例如，在“二十五”上加 1 是“二十六”，尽管能够在大声数数时背诵这些数字。儿童成功推理基数变化与计数列表之间关系的项目特定性质增加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取决于学习计数。我们在两个实验中检验了这个假设，并发现证据表明儿童可以在成为有能力的计数器之前执行基于项目的加法运算。即使在孩子们学会了数数之后，我们发现他们执行加法运算的能力仍然基于项目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。我们讨论了数字单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。即使在孩子们学会了数数之后，我们发现他们执行加法运算的能力仍然基于项目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。我们讨论了数字单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。即使在孩子们学会了数数之后，我们发现他们执行加法运算的能力仍然基于项目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。我们讨论了数字单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。

更新日期：2021-02-02

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