A problematic student is the student who creates many problems and resolves few or nothing. I think it is a street form of talking more that an academic term.
Life is problem - We have to face it - We have to accept it & to consider the challenge of the life. Where we talked about the problem, we remember our mother that in which line they have faced it when mother see the child ,crying non stop in which way her mind was relating as the problem with the inner feelings for their children with the sentiments within it .
The problems in the life are many & variable & in this case our duty with our experience,training ,study ,should take out the problem which are not for immediate reaction so that our mind becomes little bit more comfortable stage.
With this by viewing the problems which come to us we should give the same in an impartial manner & if we missed the train in this respect , we have to face further problem which may keeps us in tension,& disturbing modes .
Norchene - I believe you have something more specific in mind in your question than simply the word problematic. What is the context of 'problematic' that you are trying to teach? The following quote from slate.com might help define the search better" :
Problematic—“constituting or presenting a problem or difficulty; difficult to resolve; doubtful, uncertain, questionable”—doesn't actually capture the speaker's complaint, which is about harm, not difficulty or uncertainty. The speaker is trying to suggest that something in the text constitutes a moral wrong.