A unified model of arithmetic with whole numbers, fractions, and decimals.
A unified model of arithmetic with whole numbers, fractions, and decimals.
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包含整数、分数和小数的统一算术模型。
DOI：
10.1037/rev0000440
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发表时间：
2023
影响因子：
5.4
通讯作者：
Siegler, Robert S.
中科院分区：
文献类型：
--
作者：
Braithwaite, David W.;Siegler, Robert S.
本文介绍了UMA（统一模型的算术），一个理论的儿童算术实现为一个计算模型。UMA建立在FARRA（Fraction Arithmetic Reflects Rules and Associations; Braithwaite et al.，2017），一个儿童分数算术模型。而FARRA-像所有以前的算术模型一样-只关注一种类型的数字的算术，UMA模拟整数，分数和小数的算术。该模型在数学教科书系列的一至六年级卷的算术问题上进行了训练;将其在每个年级结束时进行的测试中的表现与先前实证研究中儿童的表现进行了比较。在整数算术（研究1），分数算术（研究2），和十进制算术（研究3），UMA显示的错误类型，错误率的问题特征的影响，和策略使用的个体差异，类似于那些记录在以前的儿童研究。此外，UMA产生的基本和高级算术技能的个体差异之间的相关性类似于算术发展的纵向研究（研究4）中观察到的。结果支持UMA的主要理论假设算术发展：（一）大多数错误反映小偏差标准程序通过两种机制，过度概括和遗漏;（B）问题之间的变化，错误率反映了内在的困难和差异量的做法的影响;和（c）策略使用的个体差异反映了潜在的变化参数的学习和决策。
This article describes UMA (Unified Model of Arithmetic), a theory of children’s arithmetic implemented as a computational model. UMA builds on FARRA (Fraction Arithmetic Reflects Rules and Associations; Braithwaite et al., 2017), a model of children’s fraction arithmetic. Whereas FARRA—like all previous models of arithmetic—focused on arithmetic with only one type of number, UMA simulates arithmetic with whole numbers, fractions, and decimals. The model was trained on arithmetic problems from the first to sixth grade volumes of a math textbook series; its performance on tests administered at the end of each grade was compared to the performance of children in prior empirical research. In whole number arithmetic (Study 1), fraction arithmetic (Study 2), and decimal arithmetic (Study 3), UMA displayed types of errors, effects of problem features on error rates, and individual differences in strategy use that resembled those documented in the previous studies of children. Further, UMA generated correlations between individual differences in basic and advanced arithmetic skills similar to those observed in longitudinal studies of arithmetic development (Study 4). The results support UMA’s main theoretical assumptions regarding arithmetic development:(a) most errors reflect small deviations from standard procedures via two mechanisms, overgeneralization and omission;(b) between-problem variations in error rates reflect effects of intrinsic difficulty and differential amounts of practice; and (c) individual differences in strategy use reflect underlying variation in parameters governing learning and decision making.