A staple in kid lit, this relationship is one that most people have experienced firsthand. So even for an adult with the school years firmly in their rearview mirror, it can play a part in backstory. Some factors that could influence relationship dynamics include the age of the student, individual personalities, student challenges (learning disabilities, problems at home, lack of parental involvement, etc.), and extraneous pressures on the teacher at the time (facing a chronic illness, the death of a parent, financial difficulties, etc.).

For other relationships in the school environment, see PRINCIPAL AND TEACHER and HEADMASTER AND STUDENT.

Below are a wide range of dynamics that may accompany this relationship. Use the ideas that suit your story and work best for your characters to bring about and/or resolve the necessary conflict. 

The two parties showing mutual respect for each other
A teacher helping a reluctant or struggling student bloom
A teacher knowing the student well enough that they're able to recognize and meet missing needs outside of the classroom
A willing teacher paired with an apathetic or hostile student
A teacher not knowing how to properly service a student with learning or behavioral disabilities
A student being taught by a tenured teacher who is just going through the motions
A willing learner being paired with a teacher whose personal issues make them apathetic or distant
A student being taught by a teacher with unrealistic expectations
A teacher belittling or disparaging their students
A student constantly challenging the teacher's authority 

A personal situation for the teacher impacting their ability to effectively teach
The student having to take a job to help provide for the family, which limits their academic productivity
The teacher's relationship with the student being questioned and scrutinized
The student having to move to a different school district
The student making new friends who negatively influence his or her attitude toward school
The teacher being offered an administrative promotion that would take him or her out of the classroom
A willing learner being hampered by unmet needs (being hungry, not getting enough sleep, suffering abuse at home, etc.)
An apathetic, enabling, or over-involved parent entering the picture