Arithmetic thinking as the basis of children's generative number concepts

IF 5.7 1区 心理学 Q1 PSYCHOLOGY, DEVELOPMENTAL Developmental Review Pub Date : 2023-03-01 DOI:10.1016/j.dr.2022.101062
Diego Guerrero , Joonkoo Park
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引用次数: 3

Abstract

Predominant psychological theories of number acquisition posit that children acquire natural number concepts as they acquire the successor principle, or the knowledge that every natural number is succeeded by another natural number that is exactly-one more than it. However, exactly how children acquire the successor principle remains largely unexplained. Recently developed ideas within this family of theories posit that an abstract recursive successor function is acquired from the recursive structure of number words; however, the types of recursion underlying the successor function and number words are distinctively different (one is a self-referential function and the other is a self-embedded structure), making it difficult to theorize how one type triggers the acquisition of another. Moreover, our analysis of the literature questions if the knowledge about the successor principle is even empirically measurable. Here, we argue that number acquisition is a process of understanding a generative rule that governs the system of natural numbers and point out that the successor principle is not the only generative rule that governs the natural number system. We propose an alternative hypothesis that generative number concepts emerge from children's realization about how the combinatorial rules of numerals allow arithmetic (specifically additive and multiplicative) representations of quantity. Importantly, under addition and multiplication—which are historically rooted in concatenation and grouping of physical objects—natural numbers are mathematically closed. As a corollary, the system of infinitely generative natural numbers is conceptualized. This new theoretical framework allows the construction of novel empirical questions and testable hypotheses based on the formalized rules of numerical syntax and numeration systems, and therefore opens a new avenue for studying later stages of children's acquisition of number concepts.

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算术思维是儿童生成数概念的基础
关于数字习得的主流心理学理论认为,儿童在获得继承原则的过程中获得了自然数概念,或者知道每个自然数都是由另一个比它多一个的自然数继承的。然而,儿童究竟是如何获得继承原则仍在很大程度上无法解释。这一理论家族中最近发展起来的思想认为,抽象的递归后继函数是从数字词的递归结构中获得的;然而,后继函数和数字词背后的递归类型有着明显的不同(一种是自指函数,另一种是嵌入结构),这使得很难理论化一种类型是如何触发另一种类型的获取的。此外,我们对文献的分析质疑,关于后继原理的知识是否是经验可测量的。在这里,我们认为数的获取是一个理解支配自然数系统的生成规则的过程,并指出后继原理并不是支配自然数系统的唯一生成规则。我们提出了另一种假设,即生成数字概念是从儿童对数字组合规则如何允许数量的算术(特别是加法和乘法)表示的认识中产生的。重要的是,在加法和乘法(历史上植根于物理对象的串联和分组)下,自然数在数学上是封闭的。作为推论,无限生成自然数的系统被概念化了。这一新的理论框架允许基于数字语法和计数系统的形式化规则构建新颖的经验问题和可检验的假设,从而为研究儿童数字概念习得的后期阶段开辟了一条新的途径。
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来源期刊
Developmental Review
Developmental Review PSYCHOLOGY, DEVELOPMENTAL-
CiteScore
11.00
自引率
3.00%
发文量
27
审稿时长
51 days
期刊介绍: Presenting research that bears on important conceptual issues in developmental psychology, Developmental Review: Perspectives in Behavior and Cognition provides child and developmental, child clinical, and educational psychologists with authoritative articles that reflect current thinking and cover significant scientific developments. The journal emphasizes human developmental processes and gives particular attention to issues relevant to child developmental psychology. The research concerns issues with important implications for the fields of pediatrics, psychiatry, and education, and increases the understanding of socialization processes.
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