Speaking as a mathematican(ok, grad student but close enough for this purpose), this isn't learning almost nothing. Once one has gone through an example and can see where an attempted proof breaks down one can then look at that part in more detail. Of course one won't learn much if one only cares about identifying the problematic line, whether in a school setting or another setting; one always needs to generalize and integrate knowledge. Don't blame the teacher if one isn't going to take steps to do that.