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Creating a Theory of Decimal Arithmetic Learning

创建十进制算术学习理论

基本信息

批准号：
1844140
负责人：
David Braithwaite
金额：
$ 55万
依托单位：
Florida State 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：
2019-09-01 至 2024-08-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1844140&HistoricalAwards=false
关键词：
Creating Theory Decimal Arithmetic Learning

项目摘要

Proficiency with rational numbers-fractions, decimals, and percentages-is essential for success in more advanced mathematics such as algebra. It is also important for occupational success; majorities of both white- and blue-collar workers report using rational numbers in their jobs. Yet, many children struggle with rational numbers even after years of instruction. The goal of this project is to create a theory of children's learning in one area of rational numbers: decimal arithmetic. The project will identify types of knowledge that help children to learn decimal arithmetic more easily, clarify the mechanisms by which this facilitation occurs, and develop a computational model that simulates the process of learning decimal arithmetic. Based on the results, recommendations will be generated for improving children's learning of decimal arithmetic including recommendations (1) to focus classroom and practice time on conceptual approaches that are used by successful learners, (2) to place special emphasis on types of problem that pose difficulty for children, (3) to devote classroom time to illustrating common errors and explaining why they are incorrect, and (4) to use discussion of common errors as an opportunity to illustrate general concepts. These recommendations are anticipated to have implications for improving mathematics instruction in general. Learning mathematics involves learning both concepts and procedures. Concepts include principles and relations; procedures are step-by-step action sequences for solving problems. Understanding of concepts is believed to help children learn procedures, but how this occurs is not known. This project aims to create a theory of how conceptual understanding - when present - facilitates learning of procedures within a particularly difficult and important area of math: decimal arithmetic. To accomplish this goal, the project will adopt a three-pronged approach including longitudinal, microgenetic, and computational modeling methods. Longitudinal methods will identify specific types of conceptual knowledge that predict success in learning decimal arithmetic procedures; microgenetic methods will provide evidence for specific mechanisms by which these types of conceptual knowledge facilitate learning; computational modeling will be used to describe these mechanisms precisely and to simulate the empirical phenomena observed using the previous two methods. The computational model will build on and extend a modeling architecture previously employed in a model of fraction arithmetic learning, FARRA; its success will be assessed based on its ability to generate levels of accuracy, patterns of errors, and correlations between conceptual and procedural knowledge similar to those observed among children. The proposed research will advance scientific knowledge in three ways: by connecting individual differences in learning outcomes with a theory of learning processes, by advancing understanding of the relations between conceptual and procedural knowledge, and by extending theories of numerical development into a new domain, decimal arithmetic.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.

熟练掌握有理数--分数、小数和算术--对于在更高级的数学如代数中取得成功是必不可少的。它对职业成功也很重要;大多数白色和蓝领工人都报告在工作中使用有理数。然而，许多孩子即使在接受多年的教育后，也难以掌握有理数。这个项目的目标是建立一个理论的儿童学习的一个领域的有理数：十进制算术。该项目将确定有助于儿童更容易学习十进制算术的知识类型，阐明这种促进发生的机制，并开发一个模拟学习十进制算术过程的计算模型。根据研究结果，将提出改善儿童学习十进制算术的建议，包括建议（1）将课堂和练习时间集中在成功学习者使用的概念方法上，（2）特别强调对儿童造成困难的问题类型，（3）将课堂时间用于说明常见错误并解释为什么它们是不正确的，（4）利用讨论常见错误的机会来说明一般概念。预计这些建议将对改善数学教学产生影响。学习数学包括学习概念和过程。概念包括原则和关系;过程是解决问题的一步一步的行动序列。理解概念被认为有助于儿童学习程序，但这是如何发生的尚不清楚。该项目旨在创建一个理论，说明概念理解如何在存在时促进数学中一个特别困难和重要的领域：十进制算术中的程序学习。为了实现这一目标，该项目将采用三管齐下的方法，包括纵向，微观遗传和计算建模方法。纵向的方法将确定特定类型的概念知识，预测在学习十进制算术程序的成功;微观方法将提供证据的具体机制，这些类型的概念知识促进学习;计算建模将被用来精确地描述这些机制，并模拟使用前两种方法观察到的经验现象。该计算模型将建立在之前在分数算术学习模型FARRA中使用的建模架构的基础上并进行扩展;其成功将根据其生成准确性水平、错误模式以及概念和程序知识之间的相关性的能力来评估，类似于在儿童中观察到的知识。拟议的研究将以三种方式推进科学知识：通过将学习结果的个体差异与学习过程理论联系起来，通过推进对概念和程序知识之间关系的理解，以及通过将数字发展理论扩展到一个新的领域，该奖项反映了NSF的法定使命，并通过使用基金会的智力价值进行评估，被认为值得支持和更广泛的影响审查标准。

项目成果

期刊论文数量（10）

专著数量（0）

科研奖励数量（0）

会议论文数量（0）

专利数量（0）

The Sleep of Reason Produces Monsters: How and When Biased Input Shapes Mathematics Learning

理性的沉睡产生了怪物：有偏见的输入如何以及何时塑造数学学习

DOI：
10.1146/annurev-devpsych-041620-031544
发表时间：
2020
期刊：
Annual Review of Developmental Psychology
影响因子：
0
作者：
Siegler, Robert S.;Im, Soo-hyun;Schiller, Lauren K.;Tian, Jing;Braithwaite, David W.
通讯作者：
Braithwaite, David W.

Distributions of textbook problems predict student learning: Data from decimal arithmetic.

教科书问题的分布预测学生的学习：来自十进制算术的数据。