ROBERT J. BEICHNER
Kinematics Graph Interpretation Project
Department of Physics
North Carolina State University, Raleigh, NC 27695-8202, USA
Kimberly D. C. Benjamin
St. Mary's School
This research was supported, in part, by the National Science Foundation (MDR-9154127).
Opinions expressed are those of the author and not necessarily those of the Foundation.
Additional support came from RasterOps Corporation, SONY of America, and Apple Computer.
The primary goal of the Kinematics Graphing Project is to investigate
the ability of students to interpret kinematics graphs and to generate a set of
suggestions for faculty teaching the subject.
Recent work has uncovered a consistent set of student difficulties with graphs of
position, velocity, and acceleration versus time. These include misinterpreting graphs as
pictures, slope/height confusion, problems finding the slopes of lines not passing through
the origin, and the inability to interpret the meaning of the area under various graph
curves. For this particular study, data from 895 students at the high school and college
level was collected and analyzed. The test used to collect the data is included at the end
of the article and should prove useful for other researchers studying kinematics learning
as well as instructors teaching the material. The process of developing and analyzing the
test is fully documented and is suggested as a model for similar assessment projects.
Our research group has been involved in
the rigorous development and evaluation of instruments for uncovering student
misconceptions in kinematics graph interpretation (TUG-K), direct current circuits
(DIRECT), and ray optics. As part of our development methodology, we interview students
who have taken open-ended and multiple choice versions of our instruments. During the
writing process we make assumptions about what students are thinking as they answer items.
Interviewing gives us insight into the validity of those assumptions and often suggests
entirely new approaches. 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
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
- Students believe the value of the dependent variable at t = 0 is always part of the
Rather than finding the slope just around the point of interest, a student calculates Dy/Dx using the initial value, even though there is not a line between the two
points used in the calculation.
- 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
- 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
- Students see graphs as representing the physical path of motion.
Given the situation of a ball rolling down a hill, a student would draw a graph that
looks like a hill.
- Students do not look for consistency of slopes and heights between graphs.
A student does not make the segment of greatest slope in a position-time graph match
the segment of greatest height in a velocity-time graph.
Provide examples that require students to make qualitative comparisons between graphs.
- Students are unable to qualitatively discriminate between slopes.
A student cannot tell which of two slopes is steeper.
- Students do not recognize situations that require them to calculate area if there is no
A student who was taught to calculate area under the curve by counting the squares does
not know how to approach a graph because there were no "little bars."
Require students to verbalize their thoughts about problems.
- Students use kinematics terms interchangeably and inappropriately.
In a situation where the position is changing uniformly, a student uses the term
"acceleration" when she should say "velocity."
- Students misunderstand basic definitions.
A student believes a velocity-time graph should look like the corresponding
position-time graph because "position over time is velocity."
Emphasize graphing calculations that are unique and different from
- Students use simple formulae or unit analysis when they should be calculating slope or
area under the curve.
Knowing the units of velocity are m/s, a student divides the position value by the time
value instead of finding the slope.
- Students read off the ordinate value when they should be finding slope.
On a position-time graph, a student gives the value of the position as the value of the
velocity at that point in time.
- Students do not understand the meaning of area under the curve.
A student does not realize that change in velocity is found by calculating the area
under the curve of an acceleration-time graph.
Load an article describing
the project, in Acrobat pdf format.
The test itself is available by mail or electronically. Please contact Bob Beichner.