Duolingo usually insists on literal translations, unless those are unnatural. So:
- I do not want to sleep = Я не хочу спать
- I do not want sleep = *Я не хочу сна (although this sounds unnatural in Russian, not sure about English)
What's the difference between "я не хочу спать" and "я не хочу поспать"?
"Я не хочу поспать" means I don't want to take a nap. Adding the prefix по- changes the aspect (in this instance) to mean "for a short time," in other words, to take a nap. However, you will probably not hear this often, since the progressive aspect is usually more appropriate.
See JohnNatter1's comment below for more nuance.
…and how does one say "I'm not sleepy" ? Can you say "я не сонный" ? Or would a child, say, be more likely to say "я не хочу спать" ?
http://chehov.niv.ru/chehov/text/spat-hochetsya.htm [СПАТЬ ХОЧЕТСЯ] This story of Chekhov is always titled "sleepy" in translations. "I am not sleepy" should count as a correct translation.
Both хочу and сплю are personal verb form.
In Russian, only the main verb in the sentence has the personal verb form, and other verbs are put into a special verb form, infinitive. Here, хочу is the main verb, and спать is subordinated to it, so спать is put into the infinitive: Я хочу спать.
(Not all Slavic languages are like this. For example, Bulgarian doesn’t have infinitive and uses personal verb forms in its place.)
спать (spatʹ) [spatʲ] impf (perfective поспа́ть) "to sleep" From Proto-Slavic sъpati, from Proto-Indo-European swep- (“to sleep”). Cognates include Russian сон (son, "dream; sleep"), obsolete English asweve (“to put to sleep, to stupefy”) and sweven ("a dream; a vision"), Norwegian sove ("to sleep"), Lithuanian sãpnas ("dream"), Ancient Greek ὕπνος (húpnos, "sleep", whence English hypnosis), Latin somnus ("sleep", whence English somnolent) and sopor, Spanish sueño "sleepiness; sleep", Irish suan, Persian خواب (xvāb, “dream”), Sanskrit स्वप्न (svapna, "sleep; dream") and स्वपिति (svápiti, “to sleep”).
In "I don't want to sleep", "sleep" is being used as a verb. If you say "I don't want sleep" then you'd need to use the noun "сон" appropriately declined: https://en.wiktionary.org/wiki/%D1%81%D0%BE%D0%BD#Russian .
Your sentence, which I think should be "Я не хочу сплю́" BTW, means, "I don't want I sleep".
Generally speaking, all contractions ("don't" for "do not") are accepted. If you made some other error, the top item in Duo's list of answers, the one which will be shown to you, will likely be the one with "do not", but that doesn't mean that your "don't" was wrong.
Next time, a screen shot would be good.