Someone explained it somewhere else but I can't find it right now. Basically, names of languages work a little bit unusually. The -ce, -ca, -çe, -ça suffix is originally an adverb suffix, so türkçe kind of literally means "in the manner of the Turks". Türkçe konuşuyorum essentially means "I'm speaking like Turks do" and it's come to be used as the name of the language and is used as a noun, but it still keeps this little bit of ambiguity of word class. So essentially, names of languages don't tend to take case endings as often as you'd expect them to.
I'm sure someone can explain it better, but since no one has answered until now, I thought I'd jump in ...
"Annem Türkçe bilmiyor." Translation: My mother does not know Turkish.
Duo has evolved as this question & answer is accurate.
"My mother does not speak Turkish." - Annem Türkçe konuşmuyor.
Four months ago there was much debate over the accuracy of Duo's question & this has now been remedied.