Praise be to Allah.
What is required is for the people to recite the takbeer and magnify Allah, may He be glorified and exalted, during the days of Eid, and to do so openly.
Raising the volume of recordings of the takbeeraat of Eid is something that will alert the negligent and remind those who forget, so it is prescribed in that sense, so long as it does not cause annoyance to people or disturb them with its loud volume, and so long as it is not done excessively.
We do not say that it comes under the heading of bid‘ah (innovation), because innovation only refers to something for which there was a reason during the era of the righteous early generations (as-salaf as-saalih), but they did not do it; that is what an innovation is. As for devices that play audio recordings, this is something new that did not exist during earlier times, as is well known.
With regard to such things that are set up at the doorways of shops and the like, to remind people of the dhikr for entering and exiting a place, and other regular adhkaar, it does not seem that there is anything wrong with any of that.
As reciting the takbeer during these days is prescribed and is part of the Sunnah, then urging people to do it is also prescribed, in general terms, and at all times, whether that is before or after lessons in schools, when it is appropriate to do so and it will not cause students to miss out on any obligatory duties or to fall short in doing other work.
It should not be limited to the beginning or end of classes; rather it should be done whenever it is possible for them to do it.
If the teacher enters his classroom reciting takbeer so that his students will follow his example, or he instructs them to do it and encourages them to do it, that is Islamically acceptable and is guiding others to righteousness and piety.
Al-Bukhaari narrated in his Saheeh (2/20) that Ibn ‘Umar and Abu Hurayrah used to go out to the marketplace during the first ten days [of Dhu’l-Hijjah] reciting takbeer, and the people would recite takbeer, following their example.
But that is on condition that he does not tell the students to recite it in unison.
See also the answer to question no. 127851.
And Allah knows best.