邓克辐射难题

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邓克辐射难题（英语：Duncker’s Radiation Problem），是由格式塔学派心理学家[[:{{#if:邓克|邓克|Karl Duncker}}|{{#if:邓克|邓克|Karl Duncker}}]]（英语：Karl Duncker）在1920年构想出来的心理学问题，用以测试人类的问题解决能力<ref>Hopping, David. Thinking Further Outside the Box. Changing Welfare. Boston, MA: Springer US. 2003: 179–199 [2019-04-07]. ISBN 9781461348702. （原始内容存档于2019-06-13）. </ref>{{#if: |{{ safesubst:#ifeq:| 

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}}。这个问题启发了不同认知心理学的研究，例如教导小朋友应用学校的知识在日后的生活上、创造力背后的心理机制、如何训练出具有人工智能的机器<ref name=":2">Gick, Mary L.; Holyoak, Keith J. -{R|Analogical problem solving (PDF). Cognitive Psychology. 1980-07, 12 (3): 306–355. ISSN 0010-0285. doi:10.1016/0010-0285(80)90013-4. （原始内容存档于2006-09-12）. </ref>。日常有不少东西都会用到类推（英语：Analogy）来加速人类的思考，如英国医生威廉·哈维将血液循环的过程类比成水泵抽水，简单化成一个科学却有效的生理模型。在1983年，两位美国心理学家合作应用了这个邓克辐射难题，研究并测试类比式思考（英语：Analogical Thinking）如何帮助人们学习新事物<ref>Analogical thinking - Cognitive Psychology. cognitivepsychology.wikidot.com. [2019-04-02]. （原始内容存档于2019-04-02）. </ref>，以及理清人们何时才留意训练情景与现实环境相关性。

实验概览[编辑 | 编辑源代码]

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假如你是一个医生，遇到一个有恶性肿瘤的病患需要接受放射线治疗。如果用很强的放射线，虽然可以杀死肿瘤，但体内的健康细胞也会受到破坏；如果改为使用比较弱的放射线，虽然不会影响健康细胞，但又不能杀死肿瘤。在这个情况下，请问可以怎么做？

实验还给受试者提供了不同的小故事<ref name=":0">Gick, Mary L.; Holyoak, Keith J. -{R|Schema induction and analogical transfer. Cognitive Psychology. 1983-01, 15 (1): 1–38 [2019-04-07]. ISSN 0010-0285. doi:10.1016/0010-0285(83)90002-6. （原始内容存档于2019-06-13）. </ref>，用以测试这些故事如何影响他们想出答案。其中一个故事是将军攻城<ref>Gick, Mary L.; Holyoak, Keith J. Schema Induction and Analogical Transfer (PDF). Cognitive Psychology. 1980-07, 12 (3): 306–355. ISSN 0010-0285. doi:10.1016/0010-0285(80)90013-4. （原始内容存档于2019-04-03）. </ref>{{#if: |{{ safesubst:#ifeq:| 

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}}<ref>-{R|Analogical Problem Solving. www.cog.brown.edu. [2019-04-02]. （原始内容存档于2019-04-03）. </ref>：将军把军队分成几个小队，从不同的地方出发。以下是将军攻城故事的基本版本<ref>Orita, Ryo; Hattori, Masasi. Positive and Negative Affects Facilitate Insight Problem‐Solving in Different Ways: A Study with Implicit Hints. Japanese Psychological Research. 2018-11-28, 61 (2): 94–106 [2019-04-07]. ISSN 0021-5368. doi:10.1111/jpr.12237. （原始内容存档于2019-06-13）. </ref>{{#if: |{{ safesubst:#ifeq:| 

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}}<ref>Catrambone, Richard; Holyoak, Keith J. -{R|Overcoming contextual limitations on problem-solving transfer.. Journal of Experimental Psychology: Learning, Memory, and Cognition. 1989, 15 (6): 1147–1156 [2019-04-07]. ISSN 0278-7393. doi:10.1037//0278-7393.15.6.1147. （原始内容存档于2019-06-13）. </ref>。

一个小国家有一个独裁者，住在一个固不透风的城堡中。城堡是在国家心脏地带，附近有一些田地及村落，有很多路可以通往该城堡，一个反叛将军想去城堡那里去讨伐该独裁者。他召集他的大军去到其中一条路前，准备大杀一场。他知道他的大军如果一次过去参与讨伐就一定能成功归来。但是，他收到消息指独裁者一早在所有路上埋下了不少地雷。因为要方便自己的军队及工人，这些地雷设计成几个人走过没有问题，而多人走过就会引爆它们。最重要问题是，如果真的引爆了，映及的不只路，还会破坏附近的村落。所以，反叛将军暂时停下来再思索一下。幸好，他修改一下计划。他改为将大军分组，各自一小组去包围城堡。当所有士兵包围好城堡，反叛将军一声令下，成功将城堡拿下并除去了独裁者的宝座。

第二个故事是消防员使用多支水管扑灭大火。实验员也写下了解答难题的原理：“分散力量，再聚合到同一个目标”。随后给每个学生分一叠工作纸，纸的最后一页写着辐射难题，但不同分组的前面几页纸的内容不一样：一半的人工作纸里会概括地提示，故事与医生的问题“有关”，另外一半则没有提示。然后比较这些不同如何影响学生解题。下表是成功想出辐射难题解答的学生比例<ref name="#1">Pedone, Roberto; Hummel, John E.; Holyoak, Keith J. The use of diagrams in analogical problem solving. Memory & Cognition. 2001-03, 29 (2): 214–221 [2019-04-07]. ISSN 0090-502X. doi:10.3758/bf03194915. （原始内容存档 (PDF)于2019-04-03）. </ref>{{#if:

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{{{col2_data7}}}{{#if:{{#if:|{{{col2_comment7}}}|}}|({{#if:|{{{col2_comment7}}}|}})|}}
}} {{#if:|
{{{col3_data7}}}{{#if:{{#if:|{{{col3_comment7}}}|}}|({{#if:|{{{col3_comment7}}}|}})|}}
}} {{#if:|
{{{col4_data7}}}{{#if:{{#if:|{{{col4_comment7}}}|}}|({{#if:|{{{col4_comment7}}}|}})|}}
}} {{#if:|
{{{col5_data7}}}{{#if:{{#if:|{{{col5_comment7}}}|}}|({{#if:|{{{col5_comment7}}}|}})|}}
}} {{#if:|
{{{col6_data7}}}{{#if:{{#if:|{{{col6_comment7}}}|}}|({{#if:|{{{col6_comment7}}}|}})|}}
}} {{#if:|
{{{col7_data7}}}{{#if:{{#if:|{{{col7_comment7}}}|}}|({{#if:|{{{col7_comment7}}}|}})|}}
}} {{#if:|
{{{col8_data7}}}{{#if:{{#if:|{{{col8_comment7}}}|}}|({{#if:|{{{col8_comment7}}}|}})|}}
}} {{#if:|
{{{col9_data7}}}{{#if:{{#if:|{{{col9_comment7}}}|}}|({{#if:|{{{col9_comment7}}}|}})|}}
}}
{{{label8}}} {{{comment8}}}|}}|({{#if:|{{{comment8}}}|}})|}}

}} {{#if:|

{{{col2_data8}}}{{#if:{{#if:|{{{col2_comment8}}}|}}|({{#if:|{{{col2_comment8}}}|}})|}}
}} {{#if:|
{{{col3_data8}}}{{#if:{{#if:|{{{col3_comment8}}}|}}|({{#if:|{{{col3_comment8}}}|}})|}}
}} {{#if:|
{{{col4_data8}}}{{#if:{{#if:|{{{col4_comment8}}}|}}|({{#if:|{{{col4_comment8}}}|}})|}}
}} {{#if:|
{{{col5_data8}}}{{#if:{{#if:|{{{col5_comment8}}}|}}|({{#if:|{{{col5_comment8}}}|}})|}}
}} {{#if:|
{{{col6_data8}}}{{#if:{{#if:|{{{col6_comment8}}}|}}|({{#if:|{{{col6_comment8}}}|}})|}}
}} {{#if:|
{{{col7_data8}}}{{#if:{{#if:|{{{col7_comment8}}}|}}|({{#if:|{{{col7_comment8}}}|}})|}}
}} {{#if:|
{{{col8_data8}}}{{#if:{{#if:|{{{col8_comment8}}}|}}|({{#if:|{{{col8_comment8}}}|}})|}}
}} {{#if:|
{{{col9_data8}}}{{#if:{{#if:|{{{col9_comment8}}}|}}|({{#if:|{{{col9_comment8}}}|}})|}}
}}
{{{label9}}} {{{comment9}}}|}}|({{#if:|{{{comment9}}}|}})|}}

}} {{#if:|

{{{col2_data9}}}{{#if:{{#if:|{{{col2_comment9}}}|}}|({{#if:|{{{col2_comment9}}}|}})|}}
}} {{#if:|
{{{col3_data9}}}{{#if:{{#if:|{{{col3_comment9}}}|}}|({{#if:|{{{col3_comment9}}}|}})|}}
}} {{#if:|
{{{col4_data9}}}{{#if:{{#if:|{{{col4_comment9}}}|}}|({{#if:|{{{col4_comment9}}}|}})|}}
}} {{#if:|
{{{col5_data9}}}{{#if:{{#if:|{{{col5_comment9}}}|}}|({{#if:|{{{col5_comment9}}}|}})|}}
}} {{#if:|
{{{col6_data9}}}{{#if:{{#if:|{{{col6_comment9}}}|}}|({{#if:|{{{col6_comment9}}}|}})|}}
}} {{#if:|
{{{col7_data9}}}{{#if:{{#if:|{{{col7_comment9}}}|}}|({{#if:|{{{col7_comment9}}}|}})|}}
}} {{#if:|
{{{col8_data9}}}{{#if:{{#if:|{{{col8_comment9}}}|}}|({{#if:|{{{col8_comment9}}}|}})|}}
}} {{#if:|
{{{col9_data9}}}{{#if:{{#if:|{{{col9_comment9}}}|}}|({{#if:|{{{col9_comment9}}}|}})|}}
}}
{{{label10}}} {{{comment10}}}|}}|({{#if:|{{{comment10}}}|}})|}}

}} {{#if:|

{{{col2_data10}}}{{#if:{{#if:|{{{col2_comment10}}}|}}|({{#if:|{{{col2_comment10}}}|}})|}}
}} {{#if:|
{{{col3_data10}}}{{#if:{{#if:|{{{col3_comment10}}}|}}|({{#if:|{{{col3_comment10}}}|}})|}}
}} {{#if:|
{{{col4_data10}}}{{#if:{{#if:|{{{col4_comment10}}}|}}|({{#if:|{{{col4_comment10}}}|}})|}}
}} {{#if:|
{{{col5_data10}}}{{#if:{{#if:|{{{col5_comment10}}}|}}|({{#if:|{{{col5_comment10}}}|}})|}}
}} {{#if:|
{{{col6_data10}}}{{#if:{{#if:|{{{col6_comment10}}}|}}|({{#if:|{{{col6_comment10}}}|}})|}}
}} {{#if:|
{{{col7_data10}}}{{#if:{{#if:|{{{col7_comment10}}}|}}|({{#if:|{{{col7_comment10}}}|}})|}}
}} {{#if:|
{{{col8_data10}}}{{#if:{{#if:|{{{col8_comment10}}}|}}|({{#if:|{{{col8_comment10}}}|}})|}}
}} {{#if:|
{{{col9_data10}}}{{#if:{{#if:|{{{col9_comment10}}}|}}|({{#if:|{{{col9_comment10}}}|}})|}}
}}
{{{label11}}} {{{comment11}}}|}}|({{#if:|{{{comment11}}}|}})|}}

}} {{#if:|

{{{col2_data11}}}{{#if:{{#if:|{{{col2_comment11}}}|}}|({{#if:|{{{col2_comment11}}}|}})|}}
}} {{#if:|
{{{col3_data11}}}{{#if:{{#if:|{{{col3_comment11}}}|}}|({{#if:|{{{col3_comment11}}}|}})|}}
}} {{#if:|
{{{col4_data11}}}{{#if:{{#if:|{{{col4_comment11}}}|}}|({{#if:|{{{col4_comment11}}}|}})|}}
}} {{#if:|
{{{col5_data11}}}{{#if:{{#if:|{{{col5_comment11}}}|}}|({{#if:|{{{col5_comment11}}}|}})|}}
}} {{#if:|
{{{col6_data11}}}{{#if:{{#if:|{{{col6_comment11}}}|}}|({{#if:|{{{col6_comment11}}}|}})|}}
}} {{#if:|
{{{col7_data11}}}{{#if:{{#if:|{{{col7_comment11}}}|}}|({{#if:|{{{col7_comment11}}}|}})|}}
}} {{#if:|
{{{col8_data11}}}{{#if:{{#if:|{{{col8_comment11}}}|}}|({{#if:|{{{col8_comment11}}}|}})|}}
}} {{#if:|
{{{col9_data11}}}{{#if:{{#if:|{{{col9_comment11}}}|}}|({{#if:|{{{col9_comment11}}}|}})|}}
}}
{{{label12}}} {{{comment12}}}|}}|({{#if:|{{{comment12}}}|}})|}}

}} {{#if:|

{{{col2_data12}}}{{#if:{{#if:|{{{col2_comment12}}}|}}|({{#if:|{{{col2_comment12}}}|}})|}}
}} {{#if:|
{{{col3_data12}}}{{#if:{{#if:|{{{col3_comment12}}}|}}|({{#if:|{{{col3_comment12}}}|}})|}}
}} {{#if:|
{{{col4_data12}}}{{#if:{{#if:|{{{col4_comment12}}}|}}|({{#if:|{{{col4_comment12}}}|}})|}}
}} {{#if:|
{{{col5_data12}}}{{#if:{{#if:|{{{col5_comment12}}}|}}|({{#if:|{{{col5_comment12}}}|}})|}}
}} {{#if:|
{{{col6_data12}}}{{#if:{{#if:|{{{col6_comment12}}}|}}|({{#if:|{{{col6_comment12}}}|}})|}}
}} {{#if:|
{{{col7_data12}}}{{#if:{{#if:|{{{col7_comment12}}}|}}|({{#if:|{{{col7_comment12}}}|}})|}}
}} {{#if:|
{{{col8_data12}}}{{#if:{{#if:|{{{col8_comment12}}}|}}|({{#if:|{{{col8_comment12}}}|}})|}}
}} {{#if:|
{{{col9_data12}}}{{#if:{{#if:|{{{col9_comment12}}}|}}|({{#if:|{{{col9_comment12}}}|}})|}}
}}
{{{label13}}} {{{comment13}}}|}}|({{#if:|{{{comment13}}}|}})|}}

}} {{#if:|

{{{col2_data13}}}{{#if:{{#if:|{{{col2_comment13}}}|}}|({{#if:|{{{col2_comment13}}}|}})|}}
}} {{#if:|
{{{col3_data13}}}{{#if:{{#if:|{{{col3_comment13}}}|}}|({{#if:|{{{col3_comment13}}}|}})|}}
}} {{#if:|
{{{col4_data13}}}{{#if:{{#if:|{{{col4_comment13}}}|}}|({{#if:|{{{col4_comment13}}}|}})|}}
}} {{#if:|
{{{col5_data13}}}{{#if:{{#if:|{{{col5_comment13}}}|}}|({{#if:|{{{col5_comment13}}}|}})|}}
}} {{#if:|
{{{col6_data13}}}{{#if:{{#if:|{{{col6_comment13}}}|}}|({{#if:|{{{col6_comment13}}}|}})|}}
}} {{#if:|
{{{col7_data13}}}{{#if:{{#if:|{{{col7_comment13}}}|}}|({{#if:|{{{col7_comment13}}}|}})|}}
}} {{#if:|
{{{col8_data13}}}{{#if:{{#if:|{{{col8_comment13}}}|}}|({{#if:|{{{col8_comment13}}}|}})|}}
}} {{#if:|
{{{col9_data13}}}{{#if:{{#if:|{{{col9_comment13}}}|}}|({{#if:|{{{col9_comment13}}}|}})|}}
}}
{{{label14}}} {{{comment14}}}|}}|({{#if:|{{{comment14}}}|}})|}}

}} {{#if:|

{{{col2_data14}}}{{#if:{{#if:|{{{col2_comment14}}}|}}|({{#if:|{{{col2_comment14}}}|}})|}}
}} {{#if:|
{{{col3_data14}}}{{#if:{{#if:|{{{col3_comment14}}}|}}|({{#if:|{{{col3_comment14}}}|}})|}}
}} {{#if:|
{{{col4_data14}}}{{#if:{{#if:|{{{col4_comment14}}}|}}|({{#if:|{{{col4_comment14}}}|}})|}}
}} {{#if:|
{{{col5_data14}}}{{#if:{{#if:|{{{col5_comment14}}}|}}|({{#if:|{{{col5_comment14}}}|}})|}}
}} {{#if:|
{{{col6_data14}}}{{#if:{{#if:|{{{col6_comment14}}}|}}|({{#if:|{{{col6_comment14}}}|}})|}}
}} {{#if:|
{{{col7_data14}}}{{#if:{{#if:|{{{col7_comment14}}}|}}|({{#if:|{{{col7_comment14}}}|}})|}}
}} {{#if:|
{{{col8_data14}}}{{#if:{{#if:|{{{col8_comment14}}}|}}|({{#if:|{{{col8_comment14}}}|}})|}}
}} {{#if:|
{{{col9_data14}}}{{#if:{{#if:|{{{col9_comment14}}}|}}|({{#if:|{{{col9_comment14}}}|}})|}}
}}
{{{label15}}} {{{comment15}}}|}}|({{#if:|{{{comment15}}}|}})|}}

}} {{#if:|

{{{col2_data15}}}{{#if:{{#if:|{{{col2_comment15}}}|}}|({{#if:|{{{col2_comment15}}}|}})|}}
}} {{#if:|
{{{col3_data15}}}{{#if:{{#if:|{{{col3_comment15}}}|}}|({{#if:|{{{col3_comment15}}}|}})|}}
}} {{#if:|
{{{col4_data15}}}{{#if:{{#if:|{{{col4_comment15}}}|}}|({{#if:|{{{col4_comment15}}}|}})|}}
}} {{#if:|
{{{col5_data15}}}{{#if:{{#if:|{{{col5_comment15}}}|}}|({{#if:|{{{col5_comment15}}}|}})|}}
}} {{#if:|
{{{col6_data15}}}{{#if:{{#if:|{{{col6_comment15}}}|}}|({{#if:|{{{col6_comment15}}}|}})|}}
}} {{#if:|
{{{col7_data15}}}{{#if:{{#if:|{{{col7_comment15}}}|}}|({{#if:|{{{col7_comment15}}}|}})|}}
}} {{#if:|
{{{col8_data15}}}{{#if:{{#if:|{{{col8_comment15}}}|}}|({{#if:|{{{col8_comment15}}}|}})|}}
}} {{#if:|
{{{col9_data15}}}{{#if:{{#if:|{{{col9_comment15}}}|}}|({{#if:|{{{col9_comment15}}}|}})|}}
}}
{{{label16}}} {{{comment16}}}|}}|({{#if:|{{{comment16}}}|}})|}}

}} {{#if:|

{{{col2_data16}}}{{#if:{{#if:|{{{col2_comment16}}}|}}|({{#if:|{{{col2_comment16}}}|}})|}}
}} {{#if:|
{{{col3_data16}}}{{#if:{{#if:|{{{col3_comment16}}}|}}|({{#if:|{{{col3_comment16}}}|}})|}}
}} {{#if:|
{{{col4_data16}}}{{#if:{{#if:|{{{col4_comment16}}}|}}|({{#if:|{{{col4_comment16}}}|}})|}}
}} {{#if:|
{{{col5_data16}}}{{#if:{{#if:|{{{col5_comment16}}}|}}|({{#if:|{{{col5_comment16}}}|}})|}}
}} {{#if:|
{{{col6_data16}}}{{#if:{{#if:|{{{col6_comment16}}}|}}|({{#if:|{{{col6_comment16}}}|}})|}}
}} {{#if:|
{{{col7_data16}}}{{#if:{{#if:|{{{col7_comment16}}}|}}|({{#if:|{{{col7_comment16}}}|}})|}}
}} {{#if:|
{{{col8_data16}}}{{#if:{{#if:|{{{col8_comment16}}}|}}|({{#if:|{{{col8_comment16}}}|}})|}}
}} {{#if:|
{{{col9_data16}}}{{#if:{{#if:|{{{col9_comment16}}}|}}|({{#if:|{{{col9_comment16}}}|}})|}}
}}
{{{label17}}} {{{comment17}}}|}}|({{#if:|{{{comment17}}}|}})|}}

}} {{#if:|

{{{col2_data17}}}{{#if:{{#if:|{{{col2_comment17}}}|}}|({{#if:|{{{col2_comment17}}}|}})|}}
}} {{#if:|
{{{col3_data17}}}{{#if:{{#if:|{{{col3_comment17}}}|}}|({{#if:|{{{col3_comment17}}}|}})|}}
}} {{#if:|
{{{col4_data17}}}{{#if:{{#if:|{{{col4_comment17}}}|}}|({{#if:|{{{col4_comment17}}}|}})|}}
}} {{#if:|
{{{col5_data17}}}{{#if:{{#if:|{{{col5_comment17}}}|}}|({{#if:|{{{col5_comment17}}}|}})|}}
}} {{#if:|
{{{col6_data17}}}{{#if:{{#if:|{{{col6_comment17}}}|}}|({{#if:|{{{col6_comment17}}}|}})|}}
}} {{#if:|
{{{col7_data17}}}{{#if:{{#if:|{{{col7_comment17}}}|}}|({{#if:|{{{col7_comment17}}}|}})|}}
}} {{#if:|
{{{col8_data17}}}{{#if:{{#if:|{{{col8_comment17}}}|}}|({{#if:|{{{col8_comment17}}}|}})|}}
}} {{#if:|
{{{col9_data17}}}{{#if:{{#if:|{{{col9_comment17}}}|}}|({{#if:|{{{col9_comment17}}}|}})|}}
}}
{{{label18}}} {{{comment18}}}|}}|({{#if:|{{{comment18}}}|}})|}}

}} {{#if:|

{{{col2_data18}}}{{#if:{{#if:|{{{col2_comment18}}}|}}|({{#if:|{{{col2_comment18}}}|}})|}}
}} {{#if:|
{{{col3_data18}}}{{#if:{{#if:|{{{col3_comment18}}}|}}|({{#if:|{{{col3_comment18}}}|}})|}}
}} {{#if:|
{{{col4_data18}}}{{#if:{{#if:|{{{col4_comment18}}}|}}|({{#if:|{{{col4_comment18}}}|}})|}}
}} {{#if:|
{{{col5_data18}}}{{#if:{{#if:|{{{col5_comment18}}}|}}|({{#if:|{{{col5_comment18}}}|}})|}}
}} {{#if:|
{{{col6_data18}}}{{#if:{{#if:|{{{col6_comment18}}}|}}|({{#if:|{{{col6_comment18}}}|}})|}}
}} {{#if:|
{{{col7_data18}}}{{#if:{{#if:|{{{col7_comment18}}}|}}|({{#if:|{{{col7_comment18}}}|}})|}}
}} {{#if:|
{{{col8_data18}}}{{#if:{{#if:|{{{col8_comment18}}}|}}|({{#if:|{{{col8_comment18}}}|}})|}}
}} {{#if:|
{{{col9_data18}}}{{#if:{{#if:|{{{col9_comment18}}}|}}|({{#if:|{{{col9_comment18}}}|}})|}}
}}
{{{label19}}} {{{comment19}}}|}}|({{#if:|{{{comment19}}}|}})|}}

}} {{#if:|

{{{col2_data19}}}{{#if:{{#if:|{{{col2_comment19}}}|}}|({{#if:|{{{col2_comment19}}}|}})|}}
}} {{#if:|
{{{col3_data19}}}{{#if:{{#if:|{{{col3_comment19}}}|}}|({{#if:|{{{col3_comment19}}}|}})|}}
}} {{#if:|
{{{col4_data19}}}{{#if:{{#if:|{{{col4_comment19}}}|}}|({{#if:|{{{col4_comment19}}}|}})|}}
}} {{#if:|
{{{col5_data19}}}{{#if:{{#if:|{{{col5_comment19}}}|}}|({{#if:|{{{col5_comment19}}}|}})|}}
}} {{#if:|
{{{col6_data19}}}{{#if:{{#if:|{{{col6_comment19}}}|}}|({{#if:|{{{col6_comment19}}}|}})|}}
}} {{#if:|
{{{col7_data19}}}{{#if:{{#if:|{{{col7_comment19}}}|}}|({{#if:|{{{col7_comment19}}}|}})|}}
}} {{#if:|
{{{col8_data19}}}{{#if:{{#if:|{{{col8_comment19}}}|}}|({{#if:|{{{col8_comment19}}}|}})|}}
}} {{#if:|
{{{col9_data19}}}{{#if:{{#if:|{{{col9_comment19}}}|}}|({{#if:|{{{col9_comment19}}}|}})|}}
}}
{{{label20}}} {{{comment20}}}|}}|({{#if:|{{{comment20}}}|}})|}}

}} {{#if:|

{{{col2_data20}}}{{#if:{{#if:|{{{col2_comment20}}}|}}|({{#if:|{{{col2_comment20}}}|}})|}}
}} {{#if:|
{{{col3_data20}}}{{#if:{{#if:|{{{col3_comment20}}}|}}|({{#if:|{{{col3_comment20}}}|}})|}}
}} {{#if:|
{{{col4_data20}}}{{#if:{{#if:|{{{col4_comment20}}}|}}|({{#if:|{{{col4_comment20}}}|}})|}}
}} {{#if:|
{{{col5_data20}}}{{#if:{{#if:|{{{col5_comment20}}}|}}|({{#if:|{{{col5_comment20}}}|}})|}}
}} {{#if:|
{{{col6_data20}}}{{#if:{{#if:|{{{col6_comment20}}}|}}|({{#if:|{{{col6_comment20}}}|}})|}}
}} {{#if:|
{{{col7_data20}}}{{#if:{{#if:|{{{col7_comment20}}}|}}|({{#if:|{{{col7_comment20}}}|}})|}}
}} {{#if:|
{{{col8_data20}}}{{#if:{{#if:|{{{col8_comment20}}}|}}|({{#if:|{{{col8_comment20}}}|}})|}}
}} {{#if:|
{{{col9_data20}}}{{#if:{{#if:|{{{col9_comment20}}}|}}|({{#if:|{{{col9_comment20}}}|}})|}}
}}
{{{label21}}} {{{comment21}}}|}}|({{#if:|{{{comment21}}}|}})|}}

}} {{#if:|

{{{col2_data21}}}{{#if:{{#if:|{{{col2_comment21}}}|}}|({{#if:|{{{col2_comment21}}}|}})|}}
}} {{#if:|
{{{col3_data21}}}{{#if:{{#if:|{{{col3_comment21}}}|}}|({{#if:|{{{col3_comment21}}}|}})|}}
}} {{#if:|
{{{col4_data21}}}{{#if:{{#if:|{{{col4_comment21}}}|}}|({{#if:|{{{col4_comment21}}}|}})|}}
}} {{#if:|
{{{col5_data21}}}{{#if:{{#if:|{{{col5_comment21}}}|}}|({{#if:|{{{col5_comment21}}}|}})|}}
}} {{#if:|
{{{col6_data21}}}{{#if:{{#if:|{{{col6_comment21}}}|}}|({{#if:|{{{col6_comment21}}}|}})|}}
}} {{#if:|
{{{col7_data21}}}{{#if:{{#if:|{{{col7_comment21}}}|}}|({{#if:|{{{col7_comment21}}}|}})|}}
}} {{#if:|
{{{col8_data21}}}{{#if:{{#if:|{{{col8_comment21}}}|}}|({{#if:|{{{col8_comment21}}}|}})|}}
}} {{#if:|
{{{col9_data21}}}{{#if:{{#if:|{{{col9_comment21}}}|}}|({{#if:|{{{col9_comment21}}}|}})|}}
}}
{{{label22}}} {{{comment22}}}|}}|({{#if:|{{{comment22}}}|}})|}}

}} {{#if:|

{{{col2_data22}}}{{#if:{{#if:|{{{col2_comment22}}}|}}|({{#if:|{{{col2_comment22}}}|}})|}}
}} {{#if:|
{{{col3_data22}}}{{#if:{{#if:|{{{col3_comment22}}}|}}|({{#if:|{{{col3_comment22}}}|}})|}}
}} {{#if:|
{{{col4_data22}}}{{#if:{{#if:|{{{col4_comment22}}}|}}|({{#if:|{{{col4_comment22}}}|}})|}}
}} {{#if:|
{{{col5_data22}}}{{#if:{{#if:|{{{col5_comment22}}}|}}|({{#if:|{{{col5_comment22}}}|}})|}}
}} {{#if:|
{{{col6_data22}}}{{#if:{{#if:|{{{col6_comment22}}}|}}|({{#if:|{{{col6_comment22}}}|}})|}}
}} {{#if:|
{{{col7_data22}}}{{#if:{{#if:|{{{col7_comment22}}}|}}|({{#if:|{{{col7_comment22}}}|}})|}}
}} {{#if:|
{{{col8_data22}}}{{#if:{{#if:|{{{col8_comment22}}}|}}|({{#if:|{{{col8_comment22}}}|}})|}}
}} {{#if:|
{{{col9_data22}}}{{#if:{{#if:|{{{col9_comment22}}}|}}|({{#if:|{{{col9_comment22}}}|}})|}}
}}
{{{label23}}} {{{comment23}}}|}}|({{#if:|{{{comment23}}}|}})|}}

}} {{#if:|

{{{col2_data23}}}{{#if:{{#if:|{{{col2_comment23}}}|}}|({{#if:|{{{col2_comment23}}}|}})|}}
}} {{#if:|
{{{col3_data23}}}{{#if:{{#if:|{{{col3_comment23}}}|}}|({{#if:|{{{col3_comment23}}}|}})|}}
}} {{#if:|
{{{col4_data23}}}{{#if:{{#if:|{{{col4_comment23}}}|}}|({{#if:|{{{col4_comment23}}}|}})|}}
}} {{#if:|
{{{col5_data23}}}{{#if:{{#if:|{{{col5_comment23}}}|}}|({{#if:|{{{col5_comment23}}}|}})|}}
}} {{#if:|
{{{col6_data23}}}{{#if:{{#if:|{{{col6_comment23}}}|}}|({{#if:|{{{col6_comment23}}}|}})|}}
}} {{#if:|
{{{col7_data23}}}{{#if:{{#if:|{{{col7_comment23}}}|}}|({{#if:|{{{col7_comment23}}}|}})|}}
}} {{#if:|
{{{col8_data23}}}{{#if:{{#if:|{{{col8_comment23}}}|}}|({{#if:|{{{col8_comment23}}}|}})|}}
}} {{#if:|
{{{col9_data23}}}{{#if:{{#if:|{{{col9_comment23}}}|}}|({{#if:|{{{col9_comment23}}}|}})|}}
}}
{{{label24}}} {{{comment24}}}|}}|({{#if:|{{{comment24}}}|}})|}}

}} {{#if:|

{{{col2_data24}}}{{#if:{{#if:|{{{col2_comment24}}}|}}|({{#if:|{{{col2_comment24}}}|}})|}}
}} {{#if:|
{{{col3_data24}}}{{#if:{{#if:|{{{col3_comment24}}}|}}|({{#if:|{{{col3_comment24}}}|}})|}}
}} {{#if:|
{{{col4_data24}}}{{#if:{{#if:|{{{col4_comment24}}}|}}|({{#if:|{{{col4_comment24}}}|}})|}}
}} {{#if:|
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File:Windsor Castle at Sunset - Nov 2006.jpg
分散兵力包围城堡来捉拿独裁者

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}}）。但问题是，理解观念不代表知道怎么运用。说明原理加上1个例子之所以不够好，是因为学生不知道原理还能应用在哪些情况中。问题的答案是——从多个角度同时使用较弱的放射线，就可以杀死肿瘤而不影响健康细胞。那些读到原理、学会从许多条小路聚集攻城的学生，不知道原来这个原理还能运用在其他情境，而看到2个例子的学生则知道原理可以用在多种情况。虽然实验员没有指明如何应用故事到医生问题，但当问题相关性强调出来，引导注意力在适当的地方上，学生就很自然想出到治病的方法<ref>Vosniadou, Stella; Ortony, Andrew. -{R|Similarity and Analogical Reasoning. Cambridge University Press. 1989 [2019-04-07]. ISBN 9780521389358. （原始内容存档于2019-06-13） （English）. </ref>{{#if: |{{ safesubst:#ifeq:| 

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之后的跟进实验要求另一组受试者“背”下独裁者的故事，但没有提示故事的用途，结果还是不能提升成功作答率<ref name=":2" />Template:Rp，说明无法应用故事不是因为“忘记了故事”。另外，实验组的受试者虽然在答题前得到提示，但因为告知这个提示只是“故事”，这种提示误导受试者，限制了思考，阻碍了之后的应用<ref name=":0" />Template:Rp。总之，类比的作用在解决问题上很显著。

在认知心理学中，表面特征（Surface features）是指不同故事间的相似物；而结构特征（Structural features）指的是问题背后的机制。这两个问题可以总结成<ref>Template:Cite bookTemplate:Dead link</ref>Template:Rp：

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  2. 对应：将来源问题对应（mapping）到想解答的问题目标（target）
  3. 应用：想出一个等同的方案去用去想解答的问题中
问题 领域 表面特征 结构特征 最终目标
来源问题 军事 资源：士兵

针对：独裁者

大批军队前往城堡会令附近村落受害 倒戈一个独裁者
目标问题 医学 资源：放射线

针对：肿瘤

大量射线照入体内会令周边组织受损 去除去一个肿瘤

从上表中可以看到，即使2个问题的领域完全不同，但是大部分的元素都可一对一对应。问题的方法大约都是用大量力量去解决核心目标。在原本的实验中，其实军事的类比也限制了人如何思考更多的新的方法，例如邓克提供开放式答案<ref name=":2" />Template:Rp有，减少射线与健康组织接触、先令恶性肿瘤更易受射线影响等解决方法。学习需要排除内容上的障碍，才能正向转移至其他范畴身上。

专家通常会考虑更多结构特征，例如元素与问题间的因果关系。但普通人大多只留意与解决方法无关的事物，如元素如何表达出来。例如其他学者研究为何有些学生虽然明白一些物理知识的逻辑，但当问题换一换问法时不能应用出来。这是因为学生们没有真的明白到书上的例子与考试问题之间结构特征<ref name=":1">Template:Cite journal</ref>。解决方法就是老师提供更多类比的问题（analogical transfer），让学习者领悟问题背后的结构特征<ref name=":5" />Template:Rp。

教育应用[编辑 | 编辑源代码]

如何表达一个问题Template:Anchor[编辑 | 编辑源代码]

Template:Image frame问题的定义是指目前情况与欲达目标之间有一些阻碍，而且没有即时方法去排除这些障碍<ref name="#2">Template:Cite book</ref>Template:Rp。通常很难的。用一个已解决的问题来应用于其他相似的问题上，作为一种捷思法<ref>Template:Cite book</ref>Template:Rp，这种归纳技巧可以帮助解决问题。在文学上，这种方法称为比喻。

如棋盘问题称作肢解国际象棋盘问题（Template:Lang-en）<ref>Template:Cite book</ref>。所罗门·格伦布，以及杂志《科学人》的专栏作者马丁·加德纳都曾提到此问题：一个标准的8x8格国际象棋横盘，对角的2个方块被移除，余下62个方块。可不可以用31个完整的2x1格骨牌，来拼凑成余下的62个方块的形状呢？<ref name=":3">三轮和久, & 寺井仁. (2003). 洞察问题解决の性质: 认知心理学から见たチャンス発见 (< 特集> チャンス発见). 人工知能学会志, 18(3), 275-282.</ref>Template:Rp。

心理学家将问题改成棋盘上格子改成不同样子。不同的测试组分别是所提供的讯息有多少。类似眼动追踪，透过使用出声思维法（Template:Lang-en），心理学家让受试者边思考边读出自己当刻的想法（如正看着那个部分），用来理解人如何，最重要何时留意问题中不同元素。

  1. 标准国际象棋盘
  2. 只有格子，没有颜色或文字
  3. 只有格子，但格子印上“黑色”或“粉红色”（像右图棕色与浅黄色）
  4. 只有格子，但格子写上“面包”或“牛油”
File:Gestalt Problem of Circle.gif
换个角度就能求出<math display="inline">x</math>的数值<ref>Goldstein, E. B. (2014). Cognitive psychology: Connecting mind, research and everyday experience (4th ed.). Belmont, CA: Wadsworth Cengage Learning.</ref><ref>Kohler, W. (1929). Gestaltpyschology. New York: Liveright.</ref>

面包与牛油组最能突出2个元素的分别。2个元素虽然不同，却互相联系。而净格子组提供很少资料去启发受试者去想出答案。当实验将同一个问题改成另一个表达方式时，受试者想到答案的机会大幅增加。善用类比，受试者改阅读以下的婚姻问题（注：以当时的社会背景只考虑异性婚姻）。答案就很变得很明显，就是村的媒人不能撮合31对婚事。

在一个俄罗斯的小村落，有32个未婚的适龄女住民。村的媒人很努力终于成就了32对幸福的婚姻。但在婚礼举行之前的一晚，2个单身汉赌那个人有更好的酒量，最后他们两个都饮酒过量致死。媒人因而很苦恼，究竟余下62个人还可不可以撮合31对婚事呢？

棋盘与婚姻问题在抽象层面上（结构特征）大致都是一样，如果问题改成抽走2种颜色而不是原本对角的同色方块，那就会大大增加解答的难度。或者在上述辐射难题与军队的例子，辐射问题改为要取出而非消除肿瘤，就会令问题间较难去对应得到<ref name="#2"/>Template:Rp。

File:Duncker’s Radiation Problem.svg
图表化邓克辐射难题，用多个较少功率的射线来代替一个集中高强度射线

理解问题结构的策略[编辑 | 编辑源代码]

不同的说明方法都可以增加洞察力。老师或教练的引导，可以帮助到学习者理解问题<ref>Template:Cite journal</ref>。例如在教导统计学的假设检定，教授会一步一步去教学生，好像先计出分别观察值、假设值，到最后到比较拒绝域来达出答案。学生理解每一个部分的义意后，就之后更容易掌握不同统计方法。另外，老师也可以向学生展示更多例题，问他们不同解法的相似性<ref name=":0" />Template:Rp<ref name=":5">Template:Cite journal</ref>Template:Rp。还有，在原本实验中（第2个）中，及其他用了相同的辐射难题的𧗠生实验<ref>Template:Cite web</ref><ref>Template:Cite journal</ref>，也发现如果单靠加上一些静态图表，像是一个小提示，就能直率地视觉化整个问题而令成功解答率提升<ref>Template:Cite journal</ref><ref>Template:Cite journal</ref>，而动画的效果就最大<ref name="#1"/>。换言之，把问题变成“看得到”也可以帮助解题<ref name=":3" />Template:Rp，因为视觉化的类比例子能提供学习者一个实在的东西去思考一些抽象的问题<ref name=":4">The Role of Analogies in Chemistry Teaching. Chapter 8 In Chemists’ Guide to Effective Teaching, N. Pienta, M. Cooper, and T. Greenbowe, Ed. Prentice-Hall: Upper Saddle River, NY, 2005, pp. 90-105.</ref>。不过如果学习者对所提供的类比不太熟识，可能会导致误解目标问题，如用细胞类比成工厂，学生可能会理解细胞只有很少出入口工厂而非多个工作部分合成的地方<ref name=":4" />。学习者或不能明白某类比自身的局限性。另外，实验也讨论学习者读出学习的过程（self-explanations）<ref name=":1" />Template:Rp，能帮助留意到一些关键部分。

参看[编辑 | 编辑源代码]

参考书目[编辑 | 编辑源代码]

  • Mary L. Gick (1986) Problem-Solving Strategies , Educational Psychologist, 21:1-2, 99-120, DOI: 10.1080/00461520.1986.9653026
  • Robertson, S. I. (2016). Problem solving: Perspectives from cognition and neuroscience. Psychology Press.

引用来源[编辑 | 编辑源代码]

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