I realize this discussion was held quite some time ago, but I am just seeing it for the first time now. Initially, I was steadfastly in support of paolobrien and several others on this issue, but I have since softened my stance. The topic piqued my curiosity, so I did a search of "speak slower" and "speak more slowly" with Google's Ngram and these were the results:
I did a similar search of Google pages and found that "speak more slowly" was more frequent than "speak slower" by a ratio of 3:1. What Lbark is saying may be true, but if what he is saying is true, it appears to only be true for his circle of friends, acquaintances, et alia.
Having said all of that, I decided to look up "slow" in a dictionary and learned that it can be used as both an adjective and an adverb, even without an -ly ending. So, that vindicates Lbark to some degree. Excerpt from the source I found is below. I added some formatting for emphasis.
As an adverb, slow has two forms, slow and slowly. Slowly appeared first in the 15th century; slow came into use shortly thereafter. Both are standard today in certain uses. Originally, slow was used both preceding and following the verb it modified. Today, it is used chiefly in imperative constructions with short verbs of motion ( drive, run, turn, walk, etc.), and it follows the verb: Drive slow. Don't walk so slow.This use is more common in speech than in writing, although it occurs widely on traffic and road signs. Slow also combines with present participles in forming adjectives: slow-burning; slow-moving.In this use it is standard in all varieties of speech and writing. Slowly is by far the more common form of the adverb in writing. In both speech and writing it is the usual form in preverb position ( He slowly drove down the street. The couple slowly strolled into the park) and following verbs that are not imperatives ( He drove slowly down the street. The couple strolled slowly through the park).
So "you speak slower" means "you speak more slowly". So when some one says "who speaks more slowly?" then the response could be "you speak slower?" Is that right? Sorry if I am being dense (I am not being sarcastic). To me this expression is either wrong (in need of correction) or meaningless in my version of English.
As a basic statement, "You speak slower" isn't correct English...not even in the USA. In order to distinguish further, you need additional context. When simply describing the speed of my own speech pattern, though, I would either say that "I speak quickly" or "I speak slowly". Yes, you'll find people stating they "speak fast" and, yes, it perfectly understandable, but that doesn't make it grammatically correct.
In 90% of the scenarios provided in this particular exchange, however, the statement "I speak slower" is being used as a comparative with a silently inferred comparison. In the instance of it being an answer to the question "Who speaks slower?" (which is, again, understandable but not actually correct) the silent and inferred comparison would be the other person(s) in the group originally asked. Yes, both "You speak more slowly" and "You speak slower" are currently accepted by Duolingo. I balk at the notion of the latter statement being considered /correct/ when, in actuality, it is simply understood, though.
That's akin to stating the /correct/ word for the flashing light on your vehicle which indicates the direction you intend to turn is "blinker" instead of "turn signal"; everyone will definitely understand you but that doesn't mean you shouldn't try to get it right.
We'd be far more likely to actually say "Who speaks slower?" than "Who speaks more slowly?" even though they're identical in meaning and are both possible utterances. I don't know why, that's just how it is. (In the actually case you mentioned, I'd probably simply say "You do.")
There's a whole bunch of comparative adjectives that are mostly used unaltered as comparative adverbs - "fast" is one for which there is no alternate adverb form ("more fastly" being impossible), but there are a lot for which there is, technically, a choice. E.g. you could say "He sings louder than she does" or "He sings more loudly than she does." Identical in meaning, but I don't know any speakers who would be likely to use the second option (even though it is technically admissible, which is why I suggested accepting it as a translation).
Frankly I'm surprised to hear that this is a U.S.-centric thing, if indeed it is. It's so widespread that I'd never even considered that there would be speakers who don't have "He sings louder than her" or whatever as an option.
I'll answer you in British English, slowly is an adverb qualifying the verb speak, so we should say " you speak slowly". more slowly is (for me) an incorrect way of saying "slower" which is a comparison so we should say " you speak slower (here you need the comparison) than I (he, she, George). You will find people that don't agree with me but that is what I learnt at school and I passed all my exams with flying colours.
It is easy to get confused so don't forget - adjective endings change when they come immediately before the noun depending on gender and case. So... "ein langsamer Baer" = "a slow bear". It is an adjective (langsam) which has "er" added to show it is a masculine subject. "Ein langsamerer Baer" = "A slower bear". But... "The bear is slow" = "Der Baer ist langsam" and "The bear is slower" = "Der Baer ist langsamer". I hope this helps.