Translation:The girl is already walking towards the school.
I submitted a "my answer should have been accepted" report for "The girl is already going to school".
In it, I mentioned that I acknowledge the given translation is better, as it doesn't leave room for ambiguity, but that my offering should be accepted also, as it's the more commonly used form to mean exactly the same thing, and the context makes it clear which meaning is meant.
Upon getting this a second time, it occurs to me that (while both the given translation and mine should be accepted too), the best translation is actually "the girl is walking to school".
The reason for "walking" rather than "going" is that it shows it doesn't merely mean "the girl is of school age and attends school".
The reason for "to" rather than "towards" is that - assuming this is the intention of the Russian, though the Russian also is a touch ambiguous here technically, and only "common sense" assumptions show us which is most likely - if one says "towards", it rather implies she might not get there.
If she is walking "to school", I fully expect that at 09:00 or whenever the appropriate time is, she'll be responding to register in the classroom.
If she is mere walking "towards school", it somewhat implies the high probability that there was a reason that I didn't say "to school", that I, as speaker/writer, know she's not going to get there; maybe she gets murdered on the way, or maybe she decides to veer off and go somewhere else instead.
The only other reason one might say "towards" in this context is if meeting someone on the way, and wanting to convey that contextually, the route is more important than the destination (not in the Zen sense, but rather, if you're walking the other way along the road, you'll meet her on the way- ok, that still sounds like a Buddhist proverb, but you hopefully get the idea).
Short version: My understanding of the Russian is the implication that the girl is walking to school at this very moment, is expected to arrive there successfully, and that this is the most important thing to be conveyed by this sentence.
If this is so, then the best translation is "The girl is already walking to school", with other translations being quite acceptable, such as "The girl is already walking towards school", "The girl is already going towards school", and "the girl is already going to school".
Your understanding of the Russian isn't quite right. This sentence says that she's walking in the direction of the school. It doesn't say that she's going to the school, that would be expressed with в школу (and в школу is what would be used in the case cherub mentioned of a little girl walking to school in the morning). The meaning is in fact what you described as the meaning of the sentence with "towards". "Is going/walking to (the) school" strongly implies that the school is her destination, which the Russian doesn't, so it won't be accepted.
"The girl is already going toward the school" was marked wrong because DL evidently wanted "towards." Sorry, but the word "toward" is correct:
This is just per dictionary.com, but Merriam Webster agrees:
to·ward tôrd,t(ə)ˈwôrd/Submit preposition 1. in the direction of. "I walked toward the front door" synonyms: in the direction of, to; on the way to, on the road to, en route to "they were driving toward her apartment"
"toward" sounds like an accurate translation of "к" in this instance.
Exactly the point. We are learning how Russian works, here. Seems to me this sentence is included so we can learn the difference between using в школу and к школе, which seems like a pretty useful thing to know. We already know how we say it in English. The volunteers who gave who knows how many hours of their time to creating this course can't seem to win. If the translation had been worded in a way that English speakers would find more natural (at least in the US), like, "The girl was headed toward(s) the school," this argument would be about how it's not an exact translation from the Russian and whether it's 'toward' or 'towards'... Sorry - I'm not picking on you specifically or trying to start a fight. I come to the forums to pick up tips and hints and help from the excellent Russian speakers who contribute so much to these forums, and I feel like I have to wade through pages and pages of nitpicking over the best English translation. It gets old. I wonder what the very polite and patient Russians who come to these forums to answer questions must think of us...