[Phys-L] Re: student difficulties with velocity as a vector?

[clement at HAL-PC.ORG (John Clement)]

Perhaps a look at the latest McDermott paper in AJP would be enlightening.
She points out that even graduate students have difficulty with vectors and
kinematics.

Another point is that instead of going over each question when asked using a
classroom response system, it is suggested that students discuss it, revote,
and then a student should give the final summary.

This question is actually analogous to one on the FCI, and apparently evoked
a common misconception.  There is also the problem that you are asking for
two variable reasoning.  If you gave the Lawson test of scientific reasoning
you might be able to see if the wrong answers correlate with wrong answers
on the two variable reasoning questions.

Perhaps getting the McDermott tutorials on vectors could help.

John M. Clement
Houston, TX

> The other day, I gave the following problem in class (1st semester of
> algebra-based physics for mostly junior life-science majors; pre-calc
> prerequisite):
>
> A ball rolls off a horizontal table with a speed of 2 m/s.  If we start
> a timer at the exact moment the ball leaves the table, we find it takes
> 0.5 seconds to hit the floor.
>
> I then asked a series of questions:
>
> 1. What is the ball's initial speed (i.e., the speed when the timer was
> started)?
>         A. 2 m/s [78%]
>         B. Greater than 2.5 m/s [9%]
>         C. Less than 1.5 m/s [13%]
>
> 2. What is the ball's initial horizontal velocity?
>         A. 2 m/s [96%]
>         B. Greater than 2.5 m/s [0%]
>         C. Less than 1.5 m/s [4%]
>
> 3. What is the ball's initial vertical velocity?
>         A. 2 m/s [29%]
>         B. Greater than 2.5 m/s [21%]
>         C. Less than 1.5 m/s [50%]
>
> My question to the list is: how do you explain the poor performance on
> question #3?  By the way, each question was asked during class and
> students respond via remotes.  After each question, I go over the answer
> to the question.  Students have been working with vectors for a while
> now, can add/subtract vectors and can break them into components when
> they need to.  They know that during the ball's flight we can assume the
> gravitational force is the only force acting and, in that case, the
> ball's acceleration is 9.8 m/s2 downward.
>
> By the way, I followed this up with these questions:
>
> 4. What is the change in the ball's horizontal velocity during the 0.5
> seconds?
>         A. 2 m/s [0%]
>         B. Greater than 2.5 m/s [22%]
>         C. Less than 1.5 m/s [78%]
>
> 5. What is the change in the ball's vertical velocity during the 0.5
> seconds?
>         A. 2 m/s [4%]
>         B. Greater than 2.5 m/s [78%]
>         C. Less than 1.5 m/s [17%]
>
> 6. What is the ball's final horizontal velocity?
>         A. 2 m/s [39%]
>         B. Greater than 2.5 m/s [4%]
>         C. Less than 1.5 m/s [57%]
>
> 7. What is the ball's final vertical velocity?
>         A. 2 m/s [0%]
>         B. Greater than 2.5 m/s [100%]
>         C. Less than 1.5 m/s [0%]
>
> Again, I discuss each answer before moving on to the next question (and
> answer any questions students may ask about the question).  Notice how
> most students realize the ball's horizontal velocity doesn't change (see
> #4) yet most still think that the ball's final horizontal velocity must
> be small since the ball is going "more down than over".
>
> ____________________________________________________
> Robert Cohen, Chair, Department of Physics
> East Stroudsburg University; E. Stroudsburg, PA 18301
> 570-422-3428; www.esu.edu/~bbq