I accidentally missed "to" in front of "school", so I answered "Are you going home or school?". The above, while grammatically incorrect, it is still understandable in English. It is very frustrating when answers are marked wrong based on typos or small inaccuracies like this. This is a Russian basic course, not an English Literature essay quest... You should foresee these circumstances and allow them, perhaps indicating that a typo occurred, but not marking the entire answer as wrong!!!
You can use all the three of them:
- в + Acc. is used when the destination is inside an object (в шко́лу 'to/into the school', в магази́н 'to the shop'),
- на + Acc. is used when the destination is on the surface of an object (на пля́ж 'to the beach', на у́лицу 'to the street'),
- к + Dat. is used when the destination is near the object (к шко́ле 'to the school [but not entering it], к пля́жу 'to the beach [but not entering it]').
This gets more complicated with intangible things (в интерне́т 'into the internet', but на сайт 'to the site'). Also, some set expressions aren't completely logical (на мо́ре 'to the seaside').
You should probably report it when you see this sentence next time. This course is still in the Beta stage, so it has some problems like this.