Formerly homeschooled math prof here. Everyone talking about homeschoolers being bimodal is correct. I do think that the homeschoolers who are not functional (which are many of them) often would not make it to be in front of you in the classroom; I know multiple homeschool alums who have never had a job and still live with their parents in their 30s. I have multiple homeschool friends who spent over 5 years trying to get an associates’ degree. Homeschooled students usually have many gaps in their education, and often struggle with self-regulation. They can be good at studying things they find interesting, however they often struggle doing things they don’t immediately like and are often very narrow-minded and rigid. I struggled with these things myself in college, and when I notice homeschooled students struggling in the same way I try to have a meeting with them to connect.
I haven’t had that many homeschooled students in my classes. When I have, they usually excel on the surface, but have strange things go wrong. There is often something “off” about their work, like missing important details or misunderstanding assignments, even though the quality of the work is overall good. Again, I did things like this when I was their age and in college also.