Maybe. And I am a Dane, so take my comment only as someone trying to understand. And what I seem to understand is that the point in general seems to be that where English uses a verb with "ing" to stress the process ("I am chopping wood" vs. "I chop wood") Danish tends to use rather a double verb ("I am standing and chopping wood.")
Is this because just using the verb is somewhat ambiguous, where as in English the ending would express the idea?
I realize I left out a very important word. I am NOT a Dane. I AM working on understanding. That part at least is correct! In Danish that would be "Jeg sidder og prøver lære dansk"....
"Jeg sidder og prøver at lære dansk" means you're sitting down, trying to learn danish -- right now. I gather from your conversation that you wanted to express that you are learning danish as a continuous action -- in that case use "Jeg er ved at lære dansk".
How I love the Danish language. I might as well read colloquial Afrikaans: "Hy staan en praat met haar" (Literally: He stands and talks with her), with the only difference having the (AF: nou / DK: nu / EN: now) completely erased, for it is redundant - it automatically shows the present tense. Unless you want to emphasise time. The same with "Jeg sidder og spiser" ("Ek sit en eet") - also meaning "I'm eating now."