Descriptions of Common Student Difficulties with Graphing
Students often display difficulty in graphing the motions of particles. They appear to lack the skill of dissociating the motion of the particle from the path that it is taking. Thus they redraw the path of the particle when asked to graph the particle's position or velocity versus time.
Many students lack the knowledge of exactly what information the coordinate value, slope, or area under a graph provides. This causes them to look for obvious features on the graph to answer questions, regardless of the pertinence of those features.
Many students lack the ability to properly graph the position, velocity, and/or acceleration of an object whose motion is exhibited for them. Likewise, they lack the ability to demonstrate the motion represented by a position, velocity, and/or acceleration graph given to them.
Many students have difficulty in associating a reverse in direction with a change in sign. Some students will insist that, like speed, velocity must be positive.
Many student's interpret a positive slope as speeding up (and a negative slope as slowing down) irrespective of the direction (sign) of the velocity.