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心算中的竞争偏差:除法为何更多而乘法为何更少。

Competing Biases in Mental Arithmetic: When Division Is More and Multiplication Is Less.

作者信息

Shaki Samuel, Fischer Martin H

机构信息

Department of Behavioral Sciences, Ariel University Ariel, Israel.

Division of Cognitive Science, University of Potsdam Potsdam, Germany.

出版信息

Front Hum Neurosci. 2017 Feb 1;11:37. doi: 10.3389/fnhum.2017.00037. eCollection 2017.

DOI:10.3389/fnhum.2017.00037
PMID:28203152
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC5285382/
Abstract

Mental arithmetic exhibits various biases. Among those is a tendency to overestimate addition and to underestimate subtraction outcomes. Does such "operational momentum" (OM) also affect multiplication and division? Twenty-six adults produced lines whose lengths corresponded to the correct outcomes of multiplication and division problems shown in symbolic format. We found a reliable tendency to over-estimate division outcomes, i.e., reverse OM. We suggest that anchoring on the first operand (a tendency to use this number as a reference for further quantitative reasoning) contributes to cognitive biases in mental arithmetic.

摘要

心算存在各种偏差。其中之一是高估加法结果和低估减法结果的倾向。这种“运算动量”(OM)是否也会影响乘法和除法呢?26名成年人画出的线段长度与以符号形式呈现的乘除法问题的正确结果相对应。我们发现了一种可靠的高估除法结果的倾向,即反向运算动量。我们认为,以第一个操作数为锚定(一种将这个数字用作进一步定量推理参考的倾向)会导致心算中的认知偏差。

https://cdn.ncbi.nlm.nih.gov/pmc/blobs/78d1/5285382/2207523f865e/fnhum-11-00037-g0001.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/78d1/5285382/2207523f865e/fnhum-11-00037-g0001.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/78d1/5285382/2207523f865e/fnhum-11-00037-g0001.jpg

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Measuring spatial-numerical associations: evidence for a purely conceptual link.测量空间数字关联:纯概念性联系的证据。
Psychol Res. 2016 Jan;80(1):109-12. doi: 10.1007/s00426-015-0646-0. Epub 2015 Jan 24.
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Addition goes where the big numbers are: evidence for a reversed operational momentum effect.加法运算在大数所在的位置进行:反向操作动量效应的证据。
Psychol Res. 2019 Feb;83(1):64-83. doi: 10.1007/s00426-018-1053-0. Epub 2018 Jul 18.
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Addition and Subtraction but Not Multiplication and Division Cause Shifts of Spatial Attention.加法和减法而非乘法和除法会引起空间注意力的转移。
Front Hum Neurosci. 2018 May 3;12:183. doi: 10.3389/fnhum.2018.00183. eCollection 2018.
Psychon Bull Rev. 2015 Aug;22(4):993-1000. doi: 10.3758/s13423-014-0786-z.
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PLoS One. 2014 Aug 14;9(8):e104777. doi: 10.1371/journal.pone.0104777. eCollection 2014.
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Spatial associations in numerical cognition--from single digits to arithmetic.数字认知中的空间关联——从个位数到算术运算
Q J Exp Psychol (Hove). 2014;67(8):1461-83. doi: 10.1080/17470218.2014.927515.
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Operational momentum affects eye fixation behaviour.操作动量会影响眼睛注视行为。
Q J Exp Psychol (Hove). 2014;67(8):1614-25. doi: 10.1080/17470218.2014.902976. Epub 2014 Apr 9.
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Can approximate mental calculation account for operational momentum in addition and subtraction?近似心算能否解释加减法中的运算动量?
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