Word Problems or Problems with Words (was Re: the words used in problems)

[Aaron Titus <titus@MAILAPS.ORG>]

On Wednesday, December 17, 2003, at 04:33 PM, David T. Marx wrote:

> I have wondering recently as to whether studies have been done in
> which problems are written in different ways to determine students'
> success or failure to answer them simply based on the way in which
> the problems are worded.  Also, I had heard recently that using the
> word "you" in a problem is better than using "a physics student" or
> "Jimmy" makes a difference in a student's ability to answer
> questions.  Does anyone have information on these issues?
>
> Thanks in advance,
>
> David Marx
> Illinois State University

I gave a talk at a NCSAAPT meeting a few years ago titled "Word
Problems or Problems with Words?". In that talk, I focused on two
things:

(1) The words we use in intro physics are often confusing and
inconsistent. Because of our experience, we are able to differentiate
"what is meant" from "what is said" but intro students cannot do that.
This certainly causes frustration and likely leads to some so-called
"misconceptions" that we often try so hard to counter.

As a couple of examples of confusing language, consider the following:

(a) We may say that two forces are "equal and opposite". If two vectors
are equal, how can they be opposite? Obviously, we leave out "equal in
magnitude and opposite in direction" because it's a mouthful.

(b) We may draw graphs of "velocity vs. time." A vector cannot be
graphed! You can only graph the velocity components--separately I might
add. In both 1-D and 2-D situations, it is valuable I think for
students to graph 2 or 3 components of the vector, just to practice
sketching graphs and to recognize that there are other components of
the vector even though they may be uninteresting.

(c) We say "time" but sometimes mean "time interval" and sometimes mean
"instant of time".

(d) We say "the centripetal force" and students think it's an applied
force rather than the sum of all applied forces (i.e. the net force).

Of course, Arnold Arons points out many confusing phrases we use and
suggests things like "time interval" rather than "time" and "position"
rather than "distance", etc.

(e) "heat" -- need I say more about the confusion caused by this term
and the fact that we are generally not consistent with our language
when we use the term. Though it's longer, I always say "thermal energy
transferred to (or from) the system" and often add the phrase "as a
result of a temperature difference between the system and the
environment." Note that students still confuse this with the "change in
the thermal energy of the system" but I try to give them lots of
examples where the system is thermally insulated (Q=0) though the
system's thermal energy changes.

(2) The order in which we teach certain topics can lead to confusion.

(a) As just one example of how we should perhaps reorder the topics we
teach, consider the transition from 1-D kinematics to 2-D kinematics.
In the 1-D chapter, students grow accustomed to displacement, velocity,
and acceleration being "positive" or "negative". If velocity is in the
direction of acceleration, the object speeds up. If it is opposite, the
object slows down. These ideas do not transition well to 2-D even
though we jump up and down and wave our arms about the fact that
components are independent that the 1-D ideas can be used for each
component separately. This stood out to me one day when I drew a 2-D
vector, and a student asked me, "Is that vector positive or negative?"
This was after a week of instruction!

(On a side note, I believe that kinematics is the black hole of intro
physics; it gobbles up time and is not as important (i.e. fundamental)
as Newton's second law, conservation of energy (first law of
thermodynamics), and the second law of thermodynamics which deserve
more time than they get.)

After coming to these conclusions somewhat independently, I discovered
that Matter & Interactions addresses the issues I raised in points (1)
and (2) better than any textbook I've seen. I used the textbook for the
first time this semester and enjoyed teaching more than in any semester
in my career (5.5 years). I wholeheartedly recommend it, especially if
you've discovered the same things I have. You will perhaps find the joy
of teaching again.

AT