Problem Difficulty in Arithmetic Cognition: Humans and Connectionist Models
Problem Difficulty in Arithmetic Cognition: Humans and Connectionist Models
复制标题
算术认知中的问题难点：人类和联结主义模型
DOI：
10.31234/osf.io/mjtdv
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发表时间：
2019
影响因子：
4.6
通讯作者：
Byoung
中科院分区：
文献类型：
--
作者：
Sungjae Cho;Jaeseo Lim;Chris Hickey;Byoung
在数学认知中，问题难度是一个中心变量。在本研究中，问题难度通过五个算术运算符-加法、减法、乘法、除法和模运算符--和正确解决问题所需的进位次数来操作。本研究收集了解决算术问题的人类参与者以及学习算术问题的多层感知器(MLP)的数据。选择二进制数问题是为了尽量减少其他可能影响问题难度的标准，如问题熟悉度和问题大小效应。在人类和MLP中，乘法问题的难度最高，其次是模运算，然后是减法。这项人类研究发现，所有五个运算符的问题难度都随着进位数量的增加而单调增加。此外，在MLP研究中也观察到添加的严格增加。
In mathematical cognition, problem difficulty is a central variable. In the present study, problem difficulty was operationalized through five arithmetic operators --- addition, subtraction, multiplication, division, and modulo --- and through the number of carries required to correctly solve a problem. The present study collected data from human participants solving arithmetic problems, and from multilayer perceptrons (MLPs) that learn arithmetic problems. Binary numeral problems were chosen in order to minimize other criteria that may affect problem difficulty, such as problem familiarity and the problem size effect. In both humans and MLPs, problem difficulty was highest for multiplication, followed by modulo and then subtraction. The human study found that problem difficulty was monotonically increasing with respect to the number of carries, across all five operators. Furthermore, a strict increase was also observed for addition in the MLP study.