We can't, because "der Norden" is a bare nominative, problematic for two reasons:
North is neither the subject nor the predicate, so it has no business being in the nominative case;
There is nothing indicating direction, and German is a stickler for spatial indications, so phrases indicating directions are always different from phrases only indicating position or location. It is reflected both with prepositional adverbials (where dual preposition take the dative to indicate position and the accusative to indicate direction, for example contrast: "wir sind im Kino" vs. "wir gehen ins Kino") and with adverbs (where generally a suffix is added to indicate direction: "wir sind draußen"—"wir gehen hinaus"; "wo bist du?"—"wohin gehst du?"; "ich bin hier"—"komm hierher").
That said, you can avoid using "Richtung", as long as you indicate direction in some way, by saying for example "wir gehen nach Norden" or (as pointed out in a previous comment) "wir gehen nordwärts".
I typed "We go in a northward direction." This should be right. Also, the listed correct answer shown was "We go in a northerly direction." Northerly is a very confusing word in English, because it can mean both "from the north" (when describing a wind) or "to the north" (maybe originally a mistake that has gained acceptance). It's like the word "inflammable", where different people may think of opposite things.
"We go in a northward direction" is a bit verbose, but not ambiguous. It means we're heading north. The usual and unambiguous description for wind is "north wind" = from the north. It unambiguously means from the north (in all weather reports) because knowing which direction the wind is coming from tells you what effect the wind is going to have on your weather. If it's colder to the north, then a north wind is going to make where you are colder. And heading north will be harder, because you'll have a headwind. Agreed, "inflammable" causes confusion. Since there's probably no need to warn people that something won't burn, "inflammable" usually means it's flammable. In which case, it's better to say "flammable."
April 8, 2016 - In English you can say "we are going to THE north" , which indicates a particular place or area. Context will often indicate the area, but you will also find the area specified, as in "We are going to the north of Scotland"
OR, you can say "we are going north" (no TO), which indicates a particular direction. "We are going north on Interstate 5, or the M1". You can also add a destination, "We are going north to Alaska." Note where the TO has been placed.
Neither ‘a’ nor ‘the’ can be implied—not only in such a construction, but ever: a noun without an article means a different things from both a noun with ‘the’ and a noun with ‘a’.
‘In a/the northern direction’ is per se not a great way of expressing this concept in English. Having said that, both are grammatical and express two different things: in one case (‘the direction’) you are most certainly referring to the exact north, or at least to the only path you could take to go north (only this way the ‘northern direction’ can be only one and definite); in the other case (‘a direction’) you are taking any of a number of paths that generally lead north, it is more generic and I'd say a better translation for the German sentence.
Either way, English has much better ways to indicate that one is going north, so you shouldn't use either formulation. Furthermore, as discussed in other comments, when not referring to places in the north, ‘northerly’ is generally preferred to ‘northern’ (but this isn't as clear cut as one could hope).
Apologies, but I wasn't asking for clarification on the English. Native speaker here. I was just trying different sentences for fun and tried that one.
I was asking why Duolingo changed the English from 'the' to 'a'; i.e., whether or not the German was implying 'a' and not 'the'.
Whoops, my bad.
About the German: I'd say in general ‘in a northern direction’ is more similar to what the German sentence is implying, but I think in some contexts one would use ‘the direction’ to translate it. The original sentence is really closer to ‘we are going north’, which could mean ‘we are going in the northern direction’, but only in certain contexts.
German itself isn't implying anything however: an expression akin to ‘in a northerly direction’ would be ‘in nördlicher Richtung’, without any article whatsoever. German simply doesn't use an article for this idiom (I understand the question was whether the German sentence would be best translated in English with a definite or indefinite article, still, I thought it was important to point out the German syntax here).
Although you weren't asking a question about English, for the benefit of non-native English speakers it should be pointed out that "We are going in the northern direction" isn't normal English. One would say instead "We are going north." However, one could say "a northern direction" to indicate the direction is only approximately north. Duo's changing the "the" to "a" both improves the English and makes it closer to the German.
As explained above by quis_lib_duo, it is indeed wrong, because there is nothing in the sentence indicating north is the direction and German always marks direction (as opposed to location) in place adverbials. For that matter, "Norden" is a noun, so it wouldn't work as a location adverbial anyway, you would have to say "(wir sind) im Norden".