There is robust research about the different factors that influence student achievement. While teacher skill and communication is important, there are a number of influential factors for student success that happen outside of school. In fact, research shows that supportive behavior from parents or guardians correlates with student achievement.
Sometimes the details former students recall from class is nothing short of amazing. A few years ago I had a student named Abby in my history class, who had always been in self-contained special education classrooms. Her teacher wanted her in my class for socialization purposes, and she did well.