.י"ז Children in Shul?

אֲמַר לֵיהּ רַב לְרַבִּי חִיָּיא: נָשִׁים בְּמַאי זָכְיָין? בְּאַקְרוֹיֵי בְּנַיְיהוּ לְבֵי כְנִישְׁתָּא, וּבְאַתְנוֹיֵי גַּבְרַיְיהוּ בֵּי רַבָּנַן, וְנָטְרִין לְגַבְרַיְיהוּ עַד דְּאָתוּ מִבֵּי רַבָּנַן

:רש"י ד"ה לבי כנישתא – תינוקות של בית רבן היו רגילין להיות למדים לפני רבן בבית הכנסת

There is something very significant to be gleaned from this innocent line - from the "What's bothering Rashi" department. We are talking about younger children as older children are (or should be) already responsible for themselves. So Rashi is perturbed - what are these kids doing in shul? Surely, they are not there for davening! So it must be that they are there because that was traditionally the location of their cheder.