Ohisashiburidesu.
I do not have children of my own or those of relatives around me, so this is based on my own experience. Of course it was loooong time ago but as far as I looked up the info on the net, the basics remain unchanged.
Kindergarten is basically a place to learn social skills, i.e. to get on well with others. What we are taught at Japanese kindergartens are:
- simple games to play with friends without using too many things (onigokko, ken-ken-pa, nawatobi, kagome-kagome, hankachi-otoshi, etc.)
- childrens plays (making something with clay, origami, drawings with crayons, etc.)
- seasonal traditions (oshogatsu, setsubun, hinamatsuri, tango no sekku, tanabata, and even Christmas.)
- hiragana
- dancing (oyuugi - nothing too fancy)
- singing (children's songs)
- listening to stories (read by teachers)
Basics for individuals such as using chopsticks, sitting on the floor properly, how to eat one's lunch etc. are expected to be taught at home, not at kindergartens.
Through games and plays children learn basic rules in society, like being kind and considerate to each other, to wait for one's turn, queuing (standing in line), to greet when meeting or parting.
Most of the things except some traditional Japanese stuffs, I believe that they are taught at international pre-schools too.
Here is a simple description of kindergartens in Japan (by MEXT)
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(consists of 3 pages)
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(pictures showing various activities at kindergartens)
I'm sure that other members who have children and/or in the educational field will provide more detailed and practical information.