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mc1-001 · MATHEMATICS EXTENSION

一只苏格兰乌鸦A Scotch Crow

数学学习拓展 约 9 分钟阅读 中文English

内容概述

  • 数学故事
  • 动物数感 / 计数能力
  • 叙事

苏格兰一位乡绅因乌鸦在庄园瞭望塔筑巢而恼火,多次试图射杀未果——每当有人靠近,乌鸦便飞到远处树上观望,等人离开再返回。乡绅设计实验测试乌鸦的计数能力:先派两人入塔、一人离开(乌鸦不上当);次日三人入塔、两人离开(仍不上当);四人也失败;直到五人入塔、四人离开时,乌鸦终于分不清四和五,飞回了巢中。故事以乡绅对这只聪明乌鸦产生敬意作结。

中文正文

1° 一只苏格兰乌鸦

这是一个动人而真实的故事:一只鸟能识数。一个苏格兰乡绅非常恼火,乌鸦竟在他庄园的了望塔上筑巢。于是,他决定用枪把它打下来。不知他多少次跑进塔楼,每当他走近时,那乌鸦都飞出巢去,远远地躲在一棵树上看着他。等疲惫的主人离开塔楼时,鸟儿又飞回来。乡绅不甘心被鸟儿耍弄,终于想出一个妙计。一天,他找来一个邻居帮忙。两人一起走进塔楼,然后一个人走出来,离开了,另一个人留在里面。可乌鸦没有上当,它还呆在那树上,一直等着留在塔里的那个人也走出来。似乎成心要和鸟儿竞赛,第二天,三个人走进了塔楼,然后两个人走出来,一个人留下等那只可恶的乌鸦。可惜鸟儿又没上当,它还呆在那树上,一直等着留在塔里的那个人也走出来。第三天,四个人来了,可还是没有成功。最后,五个人走进塔楼,四个人走出来,一个人留在里面。

这回乌鸦似乎数不过来了,分不清四和五,它飞回了塔里的窝。

故事的结局没有流传下来,不过,经过最后那个实验,乡绅大概对那只乌鸦满怀爱怜和敬意,让它继续在塔楼里筑巢。

英文正文

1° A Scotch Crow. There is a touching and authentic story about a bird that seemed to possess a number sense. A squire in Scotland became annoyed by a raucous crow that had made its nest in the watchtower of his estate, and he determined to shoot the bird. Repeatedly he tried to enter the tower to blast the bird, but each time at the man's approach the crow would leave its nest and take up a watchful position in a distant tree. When the wearied squire would finally leave the tower, the bird would return to its nest. Not wishing to be outsmarted by a bird-brain, the squire resorted to a ruse. He secured the assistance of a neighbor one day. The two men entered the tower, one man came out and went away, and the other remained within. But the crow was not deceived; it stayed in the distant tree until the man within the tower came out. The experiment now became a contest, and the next day three men entered the tower, two came out and went away, and the third waited within to blast the pesky bird. But the crow was not fooled; it remained in the distant tree until the man within the tower came out. The next day the experiment was repeated with four men, but still without success. Finally five men entered the tower, four came out and went away, and the fifth remained inside. At this point the crow seemed to have lost count and, unable to distinguish between four and five, it returned to its nest in the tower.

The conclusion of the story has not been recorded, but it is hoped that by the time of the final experiment a sufficient affection and respect had been built up for the crow so that the bird was allowed to remain nesting in the tower.

相关题目

  • 题目:无(原书本节为叙事性内容,未设习题)
  • 提示:无
  • 解答或证明:无

我们可以从故事中思考什么

  • 动物是否真的"理解"数字,还是仅对视觉刺激的数量变化做出反应?如何设计更严格的实验来区分这两者?
  • 如果你是那位乡绅,在确认乌鸟能数到 4 之后,你会选择继续实验还是放它一马?
  • 人类的"数感"与动物的"数感"有何异同?这种能力是天生的还是后天习得的?

核心知识点讲解:数感(Number Sense)与计数上限

选择理由

整个故事的悬念完全建立在"乌鸦能数到几"这一问题上,是理解动物认知能力的经典入门案例。

概念介绍

数感指生物体对数量变化的直观感知与判断能力,无需依赖符号或语言即可运作。人类婴儿和许多动物都表现出对不超过 4–5 个物体的数量敏感。

具体内容

  • Subitizing(瞬时辨认):人可在约 200 ms 内辨认 1–4 个物体而不逐一计数。
  • 故事中的乌鸦展现了至少到 4 的准确计数能力,但在 5 处失效。
  • 现代动物行为学研究表明,多种鸟类、灵长类、甚至鱼类具备类似能力。

应用场景

  • 儿童早期数学教育:利用实物培养数感。
  • 动物认知研究:通过"延迟匹配样本"等范式测试动物计数能力。
  • UI/UX 设计:图标数量不宜超过 5 个,否则用户需逐个数。

与生活的联系

我们在生活中经常"一眼看出"盘子里的苹果有几个(不超过 5 时),这就是 subitizing 在起作用——和那只苏格兰乌鸦用的可能是同一种能力。

主要思想方法与延伸讨论

主要思想方法

  • 递进式实验法:逐步增加人数(2→3→4→5),系统探测被试的能力边界。
  • 控制变量法:每次只改变"进出人数"这一变量,保持其他条件不变。

延伸讨论

  • 动物计数能力的现代研究:灰鹦鹉 Alex 能数到 6 并理解"零"的概念;黑猩猩经训练可完成简单加法。
  • "四定律"(the law of four):许多文化中"4"都是数词与模糊量词("许多")的分界点,这是否反映了某种普遍的认知限制?