# Jumping off a cliff

On a quiz in late February. The blanked out parts were my writing and the student’s writing (in pen, while viewing my solutions to the quiz immediately after taking it).

In the comments—

- What was the student thinking? How did he or she decide to make these particular marks on the paper?
- What question or problem would you pose next to help the student make the next step toward understanding?

P.S. I’m looking for more authors for this blog. If you would like to share student work here, please email me at physicsmistakes at gmail dot com so that I can get you set up as one of the blog authors.

Keep calm and mistake on!

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I think that the student is having trouble separating horizontal motion from vertical motion. This explains why he has the velocity going from 3.6 m/s to 0 m/s in the initial diagram. The students model is that gravity is responsible for an acceleration opposite the direction of the runner’s current velocity.

But that only explains how the student thought that the horizontal velocity would be constantly decreasing. It doesn’t explain why the student would think that this is a condition of hitting the ground. What’s counterintuitive there is that at the instant when the runner hits the ground he still has a great deal of velocity — this isn’t like a cart whose motion ends as it constantly accelerates to a smooth stop. (Is it clear yet that I don’t teach physics?)

Anyway, I think I would ask this student to solve a 1D motion problem. What happens when the runner falls off the cliff without any horizontal velocity? Then I would ask the student to compare this problem to that one. What’s different? How does that impact the problem?

Michael’s comment above points to a really interesting aspect of this blog that I think is worthy of our attention. Let me first try to explain what I see Michael doing above, and why I think it’s worth talking about.

First, I see Michael identifying the “trouble the student is having”. In other words, Michael describes the student thinking in terms of the absence of a something an expert would understand or be able to do (i.e., separating motions). Then he comes up with a way of making sense of the student work as a model: He proposes that the student work is consistent with a model in which the “acceleration is opposing the runner’s initial velocity”. Third, Michael identifies another “piece” of the students’ thinking: student might think that hitting the ground has the condition that velocity is zero. Fourth, Michael explains why a student might think that (i.e., there’s something counter intuitive about velocity at instant just before hitting the ground).

Proposing some Trouble or Difficulty that the Student is Having (i.e., difficulty separating)

Proposing a Model in which Student Work Makes Logical Sense (i.e., gravity opposes the velocity)

Proposing a piece of student knowledge or thinking (i.e., hitting the ground means no velocity)

Explaining why a particular idea, difficulty, or piece of knowledge exists.

To me, each of these moves is somewhat different, although 2 and 3 are similar (one being more about an organizing model that explains the work in its entirety, the other being about an element of thinking that influenced it). I think it’s important for us to think about what we are trying to accomplish in interpreting student work, because part of our work here is not only to practice interpreting student work, but to learn different ways of interpreting student work. The four categories above, by no means, span the possibilities and distinctions we might need to carve out in thinking about the different ways we interpret student work. I’m very interested in not only the specific interpretations we give to student work, but the general way in which we interpret the task of interpreting student work. I’m super interested in what norms we develop for interpreting student work and communicating our interpretations to student work.

Sorry this got so long.

I’m looking at this from another level. This student is simply confused. (S)he is taking a bunch of physics that (s)he has learned and has tossed it onto a page in the hope that something sticks. We can see 2-d motion blended with 1-d kinematics graphs, and a little Newton’s second law thrown in for good measure. (S)he needs to change the game (s)he is playing.

Great idea for a blog…even if it was stolen 😉 I will see if I have any good examples to contribute.

The student begins by drawing the v vs t graph with the intention of finding the distance (height) from the area. This method could have lead to the correct solution. Things go off the rails when they confuse the horizontal speed for the vertical and make the common mistake of assuming the final speed to be zero. If instead they had drawn their v/t graph showing the speed increasing from zero over a 2.5 s time interval with a slope of 9.8 m/s/s their method would have lead to success. They clearly understand that the slope of the v/t graph is acceleration but seem to not understand that the acceleration in this case is g. This might be where I start my questioning to help them understand: Why does he fall into the water? Followed up with: What is the acceleration?

I think there is one potential student confusion here that we have missed thus far. The shape of the first graph might not be due to ONLY confusing horizontal and vertical velocity. What I think might be going on is the student has a motion map in the back of his mind and that motion map is influencing how he thinks the velocity graph should look. That is, Throcky runs along the cliff horizontally for a bit, then continues to move forward at a constant speed while he falls down, down, down. Thus the velocity graph should have a nice horizontal part until he gets to the edge of the cliff, then “it” should go down, down, down, right to the bottom.

The second graph in part (b) implies the same thing. The 2.5 s horizontal extent of the graph is, I believe, being presented as “how far Throckster travelled in the horizontal direction.” There’s even a nice 90 degree symbol showing just how steep that cliff is!

Thus confounding what “the motion looks like” and what a graph of “it” looks like might be the starting point of this student’s confusion.

Thanks Mark. That’s very insightful. It may not even be particular to a class that uses motion maps, because it reminds me of “graph as picture” confusions, which seem prevalent in many classrooms.