The phrase "half understanding" is correct and can be used in written English.
You can use it when describing a situation where someone only partially comprehends a concept or idea. Example: Sarah had a half understanding of the instructions, which led her to make several mistakes while completing the project.
The public is likewise split on the cause of global warming, with just over half understanding that humans are primarily responsible.
It tells the story of Joe Alston, a retired literary agent who feels that "he has gone downstream like a stick, getting hung up in eddies and getting flushed out again, only half understanding what he floated past, and understanding less with every year.
"All of us would like someone to sweep up after us," Ms. Cunanan said, half understanding, half resentful, as her brother listened, his eyelids drooping from exhaustion.
A skilled producer of what The New Yorker has asked from her ("what we want is a postcard, a snapshot, with lots of wonderful details"), Batuman's trade book about her academic writing jumps from wacky re-caps of Russian novels to her own equally madcap experiences in cross-cultural doctoral mis-understanding, or "half understanding," built "...out of associations and half-grasped words".
When they fail, allusions leave us exposed: either enmeshed in inelegant, patronizing explanations or cast adrift with insufficient provisions on the murky seas of a childlike half-understanding.
Over 170 prisoners with learning disabilities and learning difficulties give harrowing accounts of what it is like to go from police stations to courts to prison in a fog of anxiety and well-founded fear of bullying, not understanding or half-understanding what is happening to you.
Before, it had been Richard's wife who played intermediary; now it was Richard who phoned in the excuses for the boys; Richard who attended the parent-teacher conferences, too, Bonita sitting beside him nodding, listening but only half-understanding what was being carefully noted about her son.
We are firmly in the land of children here, with flicks of whimsy and half-understandings of the religious event at hand.
That half-understanding sometimes protects Lucian from the pain of his injury's permanence.
I would remember trying out for musicals half-knowing that I would be writing my own ticket to being an outcast and half-understanding that my parents would never let me go through with the role.
It's part of what makes New York New York -- not understanding half of what goes on, or why.
