In our work on the TUG-K, students exhibited thinking that was consistent with the findings of previous research but also revealed problem areas not seen before. The following presentation organizes previous and new findings under headings designed to help teachers work on improving their students ability to work with kinematics graphs. Provide a greater number of examples with varying levels of complexity. Students can use incorrect methods to get correct answers for certain problems. Multiplying axis values can give the same answer as calculating area under the curve if the area happens to be a rectangle.
Students tend to generalize hints to inappropriate situations.
A student remembers his teacher showing him how to calculate the area under the curve when the graph forms a triangle. He encounters another graph that forms a triangle shape and calculates its area, even though this problem actually requires him to find the slope. Compare graphs of position, velocity, and acceleration versus time for a given situation. Students believe kinematics variables behave identically or very similarly and should therefore be graphed identically or very similarly. A student reasons that if the acceleration is decreasing then the velocity must be decreasing.