Yes, yes it is a profound lack of knowledge. But he's still a fifth grader, and once you diagnose the problem (pattern matching gone wrong), you can fix it. In

Yes, yes it is a profound lack of knowledge. But he's still a fifth grader, and once you diagnose the problem (pattern matching gone wrong), you can fix it. In this case, the teacher identified that there was a sloppiness error (note it and allow them to work on being less sloppy using grades as motivation), as well as the misunderstanding of "remainder" vs "decimal part". The goal isn't just to grade the student, but to actually fix the things that are blocking their learning.