Investigating Approximate Number System Computation in Children

研究儿童近似数系计算

基本信息

批准号：
1844155
负责人：
Melissa Kibbe
金额：
$ 57.86万
依托单位：
Trustees of Boston University
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2019
资助国家：
美国
起止时间：
2019-07-01 至 2023-06-30
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1844155&HistoricalAwards=false
关键词：
Investigating Approximate Number System Computation

项目摘要

This project investigates children's capacity for arithmetic computation without symbols or formal notation, before they encounter formal mathematics training in school. The Approximate Number System (ANS), a cognitive system which is operational from early infancy onward, allows humans to approximately quantify sets of items without language or symbols. Research suggests that the ANS could potentially support arithmetic operations, such as addition and subtraction, and that the ANS could therefore serve as a bridge to learning formal mathematics. However, the arithmetic capacity of the ANS, and how this capacity develops, is not well understood. This project fills that knowledge gap by systematically examining the computational capacity of the ANS using a series of experiments designed to assess young children before they learn the formal rules of arithmetic in school. The project addresses theoretical debates about the early cognitive architecture of the ANS and its role in arithmetic computation. The project will identify potential ways that educators could leverage children's pre-symbolic mathematical intuitions in order to help them learn formal mathematics. This has implications for STEM (Science, Technology, Engineering, and Mathematics) education. This project will examine the degree to which computations performed over ANS representations parallel true arithmetic computations. The development of the computational capacity of the ANS will be examined. Symbolic arithmetic computation obeys a set of functional rules. For example, the result of an arithmetic computation like 5+6 is a new, independent quantity that is just as precise as the quantities it was derived from, and which can be manipulated and used in further computations. These functional rules make symbolic arithmetic computation both powerful and flexible. This project aims to identify the functional rules of non-symbolic arithmetic with the ANS. In a series of experiments, four to six year-old children will be asked to solve non-symbolic problems with unknown addends (e.g., 5+__=11). This task requires children to perform arithmetic-like computation, holding two separate ANS representations in mind (e.g. approximately five and approximately 11) and performing a computation over them (e.g. subtracting approximately five from approximately 11) to derive a solution. Each experiment is aimed at examining different components of the functional rules of non-symbolic arithmetic, including the representational structure and precision of the solutions to ANS computations and the extent to which these solutions can be used in further computations. Additional measures of working memory capacity, symbolic math performance, and ANS representational precision are used to elucidate contributions of these cognitive systems to the computational capacity and development of the ANS. Data will be analyzed using a combination of traditional null hypothesis significance testing, Bayes factor analysis, and logistic regression. The project will therefore compliment what is known about the representational structure of the ANS by shedding light on its computational architecture and the development of this architecture in early childhood.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

该项目调查儿童在学校接受正式数学训练之前在没有符号或正式符号的情况下进行算术计算的能力。近似数字系统（ANS）是一种从婴儿早期开始运行的认知系统，它允许人类在没有语言或符号的情况下近似量化一组物品。研究表明，ANS 可能支持算术运算，例如加法和减法，因此 ANS 可以充当学习形式数学的桥梁。然而，ANS 的算术能力以及这种能力如何发展尚不清楚。该项目通过一系列旨在评估幼儿在学校学习正式算术规则之前评估 ANS 的计算能力的实验，系统地检查了 ANS 的计算能力，从而填补了这一知识空白。该项目解决了有关 ANS 早期认知架构及其在算术计算中的作用的理论争论。该项目将确定教育工作者利用儿童的前符号数学直觉来帮助他们学习正规数学的潜在方法。这对 STEM（科学、技术、工程和数学）教育具有影响。该项目将检查 ANS 表示上执行的计算与真实算术计算并行的程度。将检查 ANS 计算能力的发展。符号算术计算遵循一组函数规则。例如，像 5+6 这样的算术计算的结果是一个新的、独立的量，它与派生它的量一样精确，并且可以在进一步的计算中进行操作和使用。这些函数规则使符号算术计算既强大又灵活。该项目旨在通过 ANS 识别非符号算术的功能规则。在一系列实验中，四到六岁的孩子将被要求解决具有未知加数的非符号问题（例如，5+__=11）。此任务要求孩子们执行类似算术的计算，记住两个单独的 ANS 表示（例如，大约 5 和大约 11）并对它们进行计算（例如，从大约 11 中减去大约 5）以得出解决方案。每个实验的目的都是检查非符号算术函数规则的不同组成部分，包括 ANS 计算解的表示结构和精度，以及这些解在进一步计算中的使用程度。工作记忆容量、符号数学性能和 ANS 表征精度的其他测量用于阐明这些认知系统对 ANS 计算能力和发展的贡献。将结合传统的零假设显着性检验、贝叶斯因子分析和逻辑回归来分析数据。因此，该项目将通过揭示其计算架构和该架构在幼儿期的发展来补充对 ANS 表征结构的了解。该奖项反映了 NSF 的法定使命，并通过使用基金会的评估进行评估，被认为值得支持。智力价值和更广泛的影响审查标准。