[Physltest] [Phys-L] Re: sign of velocity (was: California standards test in physics)

[John Denker <jsd@AV8N.COM>]

Richard Tarara wrote:

> Question 8 has a problem that we all have to be careful about.  Since the
> velocity is a vector quantity, and mathematically we consider negative
> quantities to be less than positive quantities, none of the answers are
> mathematically correct.

We agree that in general vector quantities cannot be considered positive
or negative, and that students are often confused by this.  However, there
is a big fat exception for one-dimensional vectors.  And since the item we
are discussing is explicitly one-dimensional, it beats this rap.

One-dimensional vectors are isomorphic to plain old numbers, and can be
considered positive, zero, or negative.

> However, if one argues that a negative velocity IS
> NOT 'less' than a positive velocity, just in a different direction,

There's no chance of that.  Take a look at the number line.  Negative
numbers *are* less than positive numbers.  No choice.

> .... The question SHOULD have asked about the speed of the ball
> to eliminate this confusion.

Yup.  BTW it's not a "confusion".  It's a gross error.  All four
choices are so grossly wrong that it is impossible to choose a "best"
answer ... except by assuming that the person who composed the question
doesn't know anything about physics.  The question has very limited
value in assessing students' knowledge, and strongly negative value
in terms of teaching-via-the-exam.

===========

Impossible questions are encountered quite frequently in the real world,
and students should learn how to deal with them.  But in the real world,
questions are not encountered in "exam" format.  There is generally a
process for refining the question, e.g. by asking "excuse me, sir,
didn't you mean minimum _speed_?"  Exams promote a sort of adversarial
atmosphere (student versus test, or worse, student versus teacher)
whereas in the real world there is more of a collaborative relationship
between the question-asker and the question-answerer.
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