Compare and contrast the different types of educational systems (public-live, private/religious-live, homeschooling, online, blended).
As there are so many different types of schooling, it is impossible to compare and contrast each possible pair. Let us look, instead, at some general positive things that can be said of each type.
Live schooling is similar in many ways whether it be religious or secular, public or private. Live schooling provides children with many opportunities to socialize with their peers. It provides them with in-person interaction with a teacher who is not related to them. It is generally decently-funded and can afford to provide things like lab classes as well as extracurriculars. In these ways, it can be seen as an ideal type of education.
Homeschooling has its merits as well. First, it allows the family to closely monitor what the children are being taught. This is the best way to ensure that only the values that you believe in are being imparted to your children. It also, even more than a religious school, prevents children from being exposed to negative influences. It can also be very good for children who are at a very different level from their peers or who learn in non-traditional ways.
Online schooling, in my view, does not have as much going for it. The main benefit of online schooling is that it is asynchronous and flexible. There are students whose situations make it hard for them to attend regular school and who do not have parents capable of homeschooling them. For these students, online education may be the best alternative. It is also something that can be good for students in rural areas and for school districts that cannot afford to provide a wide variety of live classes.
Thus, each of these forms of schooling has positive aspects.