You do something encouragingly when the way you do it gives another person hope and a bit of courage — a nod, a smile, a quiet go on. Reports also use it for facts that look hopeful: numbers rose encouragingly; the first tests went encouragingly well. It is the adverb of encouraging, so it tells you how something is done, or how a situation looks, not what kind of person someone is. The tone is warm and ordinary; teachers and parents use it a lot. It does not promise a happy ending — only that there is a reason not to give up.