Translation:The children are learning English.
I don't think håller på has been fully explained on this course (or I missed it!). Why does this take och and other sentences take att? Does it differentiate between I am about to... and I am busy doing.... Am I right in thinking:
Barnen håller på att lära sig engelska = The children are about to learn English
Barnen håller på och lär sig engelska = The children are busy learning English
Check out the "tips notes" for section "Continuous Forms" https://www.duolingo.com/skill/sv/Continuous-Forms
no, there is no difference, both means ''...in the process of doing...'' which can in both E and S mean right now or this school year and only interrupted by sleep and som other stuff ;-) I learned in school abont 100 years ago that 'och' here was wrong and only used in spoken S. Maybe it has changed while I was abroan for the last 20+ years, but 'att' here is always right. Did that help ?
oops -- I have no edit button -- 'och' and 'att' are only interchangeable in the sense of the meaning, but 'och' just sort of continues and takes the same verb form as the verb prior to 'och', but 'att' of course always takes the infinitive ! But (some of) you already noticed that.
"...keep learning English" sounds very strange to my (native American English) ear. The expression "keep learning" isn't unknown, but it's generally restricted to the idea that people should continue to learn new things over a lifetime. Here's an example: https://blog.adioma.com/how-to-keep-learning-infographic/ .
Sig is actually the reflexive pronoun used with de (and also with han/hon).
→ Barnen lär sig svenska.
You can see here the reflexive pronouns: https://www.duolingo.com/skill/sv/Verbs%3A-Present-3/tips-and-notes.
Dem is not a reflexive pronoun, but an object pronoun (https://www.duolingo.com/skill/sv/Pronouns-objective/tips-and-notes). It's a bit tricky because some reflexive and some object pronouns are identical (mig, dig, oss, er), but reflexive and object pronouns are different sets of pronouns. So you could say for example: Jag ser dem (= object pronoun), but not Jag ser sig (= reflexive pronoun).
I could add, to add to the confusion, that the verb att lära is a bit tricky because it has two meanings. It has a reflexive form, att lära sig, meaning "to learn", and also a non-reflexive form, att lära, meaning "to teach". So if you get the pronoun wrong and use a object pronoun rather than a reflexive one, you can actually change the meaning of your verb.
It's interesting that this construction is used here, since, according to the tips (describing håller på att): "You will likely also come across it with och plus the present tense, but this is colloquial and not accepted in the course."
I can only assume that this means it won't be accepted as an answer, but still appears here as something that may be encountered in Swedish?