Re: kinematics language

[Hugh Haskell <hhaskell@MINDSPRING.COM>]

At 11:05 -0500 8/28/02, Joseph Bellina wrote:
> I'm not even sure I would say the y-velocity decreases...it gets less
> positive, only the magnitude of the y-velocity decreases, and then of
> course increases on the way down.  The y-velocity gets less positive
> (assuming up is positive) the whole time, which is consistent with the
> downward acceleration the whole time.
>
> Much of this hinges on the distinction between something, as in the
> value of the y-velocity, and how that quantity is changing.  This is not
> an easy distinction for students, so any language that can add clarity
> about this as well as the vector nature is valuable.
I agree that this can be a confusing issue, especially with us old
fogies who grew up long before anyone worried about these details, at
least before you got to grad school :-). But it may not be as
confusing to the students as we think. I get the impression that in
their math classes, the word "decrease" means "to change in the
negative direction" and is applied irrespective of how the magnitude
of a signed number is changing. Thus if I say this number is
decreasing, and it happens to be negative, the students will
understand that I mean, "getting more negative," in other words, it's
magnitude is increasing, but its sign is negative, so decreasing just
means  the final number is more negative than the beginning number.
On a number line including negative numbers, that would translate to
"increasing" means moving tot he right, and "decreasing" means moving
to the left, regardless of where you are on the line to start with.

The problem with all of these conventions is that all have advantages
and disadvantages, so people tend to pick one, pretty much
arbitrarily (usually because some teacher taught it to them at some
point, and they got used to it). So we end up with different people
using different conventions when they talk to each other, and they
may not bother to inform each other of the convention they may be
using. Until we have all agreed on one convention, it is important
that we make the convention we will use very clear to the students
(and even be willing to change, if most of the students use another),
and do our best to be consistent in its use (not easy, as Aaron has
clearly pointed out).

Hugh
--

Hugh Haskell
<mailto:haskell@ncssm.edu>
<mailto:hhaskell@mindspring.com>

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