We just finished kinematics, concluding as we usually do
with free-fall, which I treat as a very specific case of constant acceleration.
This year, I flipped my classroom, and had the students watch a video about
free-fall and take notes. The
students reported liking this practice. They can stop the video, and start it
again when they have finished taking notes on a particular problem. Students
who write slowly have time to listen, understand and then write down what they
need to remember. Students who grasp everything the first time you say it can
watch the video once and be done.

The individual who created this particular free-fall video
solved several sample problems, including one dropped object and one object
thrown vertically upward. In one case, the positive direction was chosen as
downward, since the ball was dropped, and all motion was downward. In the other example, the ball was
thrown upward, so up was chosen as positive, and down was thus negative. I
really liked the way the presenter emphasized that if down is chosen as the
positive direction, then a = g = 9.8 m/s

^{2}; if up is chosen as positive, then the acceleration a = -g = -9.8 m/s^{2}. I liked it because when I use the letter “g”, I intend it to mean the gravitational field strength or 9.8 m/s^{2}or 9.8 N/kg. Always positive.
But no matter how slowly the students play the video, they
always seem to misunderstand. “But Ms. Lietz! The guy on the video said that
when the ball is moving down, it’s positive and when it’s moving up it’s
negative.” [Their tendency to overuse the word “it” could fill an entire blog
entry.] No, sorry. That’s not what he said. But I understand how you came to
your interpretation.

I want my students to be flexible, I want them to be able to
choose either direction as positive and be able to solve a free-fall problem. Some
of them can. Most of them can’t
initially. So we had to have a long conversation about positive and negative
and what they mean. I know we will
have many more to come.

One of my favorite demonstrations to address this particular
challenge involves a Vernier motion sensor, Logger Pro and an oversized tennis
ball I found at Wal-Mart (roughly the size of a child’s basketball). I hang the motion detector from the ceiling and drop the ball
below it, letting it bounce a few times. All their other experiments have used
“away from the motion detector” as positive, and toward as negative. I explain
to them that I have set the program to “reverse direction” for the motion detector.
That means that away from the detector, which is downward, is now negative. Then
we “zero” the motion detector when it is pointed at the floor. This has the
effect of making the graph look like it would if the motion detector were on
the floor, without having to bounce the ball on the motion detector. Up is
positive and down is negative. Now
it’s time for them to predict what the motion graphs will look like for this
motion

In my first class, I asked them to predict all three motion
graphs at the same time, before dropping the ball. This led to lots of confusion and all kinds of crazy
graphs. So, having the luxury of three more tries, in my next classes I had
them predict the position graph first. They had success with this relatively
easy task before we moved on to the velocity and acceleration predictions. The
velocity predictions were much more accurate once they saw the accurate
position graph. And the acceleration graphs are much more accurate as well. I
use these graphs to reinforce many concepts. First, the velocity at the top is zero (we are still talking
about one-dimensional motion). We look at the graph of velocity vs. time and
see that on the way up, the velocity is positive and decreasing, while on the
way down, the velocity of the ball is negative and increasing. I point out that
in both of those cases, the acceleration, as evidenced by the slope of the
velocity graph, is negative, and thus downward, for the entire trip. As the ball moves upward, the acceleration is negative,
and as it moves downward, the acceleration is negative. At this point we broke into groups and started working on
solving free-fall word problems using the equations of constant
acceleration.

I post annotated images of these graphs on my website for
them to refer to later. Each
time a student needs help solving a free-fall problem, we can look at these
graphs and remember that the acceleration is down, for the whole trip. If up is positive, then
down is negative.

This strategy requires that the students are first
comfortable with the relationships between the position, velocity and
acceleration graphs. When this is true, that understanding can be used to make
sense of new concepts.
Nevertheless, the direction of acceleration remains a challenging
concept for students, and I am always trying new approaches, new
demonstrations. The ball drop
demo, however, is a must. Many
students are helped simply by restricting their coordinate system to “up is
positive” and always using that rule. The weaker students initially need rules to cling to
and things that are “always true.”
Others can be flexible. Even in a tracked curriculum, at a school with
three levels of first-year physics, the spectrum of abilities is broad. So my repertoire of
demonstrations and other pedagogy must be extensive, and responsive to their
needs. Of course, my
patience needs to be great as well, because as soon as I finished my fourth
time through this demonstration in one day, some student got a practice problem
wrong, and exclaimed, “But I
thought the acceleration was positive on the way down! That’s what the guy said in the video.”