Mencius's mother moved several times
To create a good environment for one's children to learn and study
Positive
古时候有“孟母三迁，择邻而居”，现在的父母对孩子的关爱比起孟母有过之而无不及。 | Gǔ shíhòu yǒu “mèng mǔ sān qiān, zé lín ér jū”, xiànzài de fùmǔ duì háizi de guān'ài bǐ qǐ mèng mǔ yǒuguò zhī ér wúbù jí.
In ancient times, people would work hard to find the best home and learning environment for one's children. Modern parents go even further than that for their kids.
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The 三 (sān) in this story actually means "several," not "three"
There are several versions of this story, and I've only translated one of them here
《孟子题词》(Mèng Zǐ Tí Cí), a work by later Hàn (东汉, Dōng Hàn, 25 - 220) author 赵歧（Zhào Qí).
When the great Confucian scholar 孟子 (Mèng Zǐ, or Mencius) was little, his father passed away. At the time, the family was living near a graveyard, and 孟子 and the neighbors' children started mimicking the behaviors of graveyard visitors when playing. They would pretend to weep loudly and pay respects to the dead, and they would even put on fake funeral processions. When 孟子's mother saw this, she thought to herself: "This is not okay. I can't let my child live here!" And so, they moved.
Their new home was close to the city marketplace, and was especially close to the marketplace's butcher in particular. 孟子 and the neighbors' children soon learned how to barter like a businessman and how to slaughter various kinds of animals. When his mother learned of this, she said, "I can't let my child live here either!" And so, she moved them again.
This time, their new home was by a school. Local officials often came to a Confucian temple to offer respects, and from this, 孟子 learned proper behavior and etiquette. This satisfied his mother, and they didn't move again after that.