Your obvious mistake was going into this sector, unless you are targeting either pre-k or graduate students. Otherwise get out now, unless you're just doing lead gen or something.
So let's say you have some software that legitimately creates $30-100 dollars of value per student. In order to sell that software to the school, it's going to take 8 months and $20,000 dollars. That means you're going to have to sell it for at least $125,000 dollars to make it worthwhile. That you're A) reading HN B) asking this question suggests that you probably won't be able to make this sale. And even if you can, you'll essentially just be conning the schools out of money because your software is worth vastly less than what you're selling it for, so you're essentially just depriving kids of things that would actually help them learn.