Below are some common student misconceptions about the concept of graphing:

A positive slope for a negative velocity means the object is speeding up. (description) (discover) (references)

Students plot position and velocity graphs as the path of the particle. (description) (discover) (references)

Students don't know which quantity in a graph will answer the question (coordinate, slope, or area). (description) (discover) (references)

Students have difficulty relating real world motions to a graph and vice-versa. (description) (discover) (references)

Velocity must be positive, plotted above the time axis. (description) (discover) (references)