Bringing small children to Shul:
[It is a Mitzvah and obligation upon a parent to educate his child to go to Shul and participate in a Minyan, once they have reached the age of Chinuch.] One is to teach his young children and educate them to answer Amen. From the moment that a child answers Amen he has a portion in the world to come. One is to educate his children to stand [i.e. behave in Shul] with awe and fear. However, children who run around in Shul for fun, [and make noise and] disturb their parents [and others] in their Davening are not to be brought to Shul at all. [Bringing such children to Shul, asides for it disturbing the prayers and it being a desecration of the holy place, also educates them to treat a Shul improperly, and makes them continue their ways even when they become older. Accordingly, children who are below the age of Chinuch and are unable to sit still in Shul without disrupting, are not to be brought to Shul at all. However, those children who are above the age of Chinuch are to be brought and educated to participate properly in the Minyan and act with the appropriate respect.]
The words of the Shlah:
In today’s times, there are children who come to Shul who cause those who bring them to get punished, as they come to desecrate the holiness of the Shul, and play in it like they play in the streets. One kid laughs with another, another kid hits another, another sings, another cries, another shouts, another runs around and chases a friend. Some children even do their needs in Shul and are required to be cleaned and removed. At times, the father gives his child a Sefer and the child throws it on the floor, or tears it. To summarize, in conclusion these children disturb the worshipers and desecrate the name of Hashem. One who brings such children to Shul should not aspire to receive reward and is rather to worry of the punishment that is befitting him. This is similar to a master who brings his retarded slave with him to speak with the king, and the salve mocks and disturbs the entire conversation. Surely the king will release his wrath not on the imbecile slave, but on the master who brought him along. Furthermore, at times the parent begins playing with the child during his own prayer. The greatest evil of all this is that the child will grow up accustomed to his ill treatment of Davening and a Shul and continue to do so when older. Accordingly, one is not to bring very small children to Shul as he only loses out by doing so.
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 M”B 98/3; See Admur 98/1 124/10; Admur 343/2 “It is a Rabbinical command for a father to educate his son and daughter in both negative and positive commands”
 Seemingly this includes even children who are below the age of Chinuch. [See Piskeiy Teshuvos 215 footnote 9]
 Admur 124/10; Rama 124/7 in name of Kol Bo
 Admur 124/10; M”A 124/11; Shlah p. 256
 Admur 98/1 “Children who disturb their parents, are not to be brought to Shul at all” and 124/10 “Children who run around in shul for fun it is better not to bring them to Shul at all”; M”A 98/1; Elya Raba 98/2; Shlah p. 256 in name of Derech Chaim; M”B 98/3; Kaf Hachaim 98/13
 Shlah ibid; M”B 98/3
 Machatzis Hashekel 98/1; M”B 98/3; Kaf Hachaim 98/13; See also Shlah ibid “Bottom line, one is not to bring very small children to Shul”
 Shlah p. 256