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Re: [Phys-l] "Looking up" results on a graph



Suppose you go to a local stream and measure the temperature and the speed of flow of the water. A plot of temperature vs time has an obvious dependent and independent variable - because you are in control of the time. Likewise for flow speed vs time. But suppose you decide to plot the two variables temperature and speed of flow against each other - which is dependent - which is independent?

Unless you have deliberate control over the choice of one of the variables, I don't really see where dependency and independency enter the choice of axes. I simply state to my students that the expression "plot A vs B" has a standard interpretation of A on the vertical axes and B on the horizontal.

Bob at PC



-----Original Message-----
From: phys-l-bounces@carnot.physics.buffalo.edu [mailto:phys-l-
bounces@carnot.physics.buffalo.edu] On Behalf Of John Clement
Sent: Friday, January 13, 2012 11:21 AM
To: 'Forum for Physics Educators'
Subject: Re: [Phys-l] "Looking up" results on a graph

Absolutely. This is essentially one of my points. The P-V diagram is a case in
point. When you put V on the horizontal axis it is an analogy with an F-x
graph. Essentially you are talking about working. And the P-V implies that P
is the dependent variable, or the variable you wish to look at. It is the same
grammar as "Plot P vs. V". If you put V on the vertical axis it should be called
a V-P graph. Yes, grammar is merely a set of guidelines and it is often
violated. Math uses strict grammatical rules, unlike science and common
speech. So in math the horizontal axis always is the independent variable.
Are students ever told that math rules are often really grammar? And they
do change with the fashion. As I have pointed out AB/CD used to be
(AB)/(CD) and now it is (AB/C)D, and there is a math journal that insists on
this.

We do have normal grammatical rules in math and science. The left hand side
of the equation is often treated as the dependent variable, and it can be
helpful for students to think that way. Trying to introduce pure abstraction
early on in variables is the kiss of death. At first students have to understand
that most variables are things you can measure and that equations establish
relationships. Of course this is taught in math, but only in the context of X
and Y. Graphs of Y vs. X are really maps, and not graphs. As a result when
many seniors in HS are asked to find the area under a scaled graph they
resort to counting the blocks as if it is a map.

Then the use of calculus to figure things like the area under a graph, or slopes
has only been presented to students where the horizontal variable is the
independent variable. Doing it with the vertical variable as the independent
variable poses huge problems to students. There are also other issues such
as multiple representations. Students have to learn to create and interpret
motion maps, graphs, descriptions, and equations. So making t-X graphs
would make this harder. You do X-t graphs and maps of motion on the X axis,
and X=... equations. When they can translate between the various
representations, they understand the physics. There are a number of
articles in JRST about this going back probably 40 years.

So from a purely abstract point of view it really makes no difference which is
on which axis, but from a practical, and human conceptual point of view it can
make a huge difference. And the usual math terminology obfuscates things.
Students do not think of the axes as being abscissa and ordinate, they think
of them as X and Y which is very unfortunate. They don't have the
connection between variables and physical quantities. It is just a math game.
Indeed even the term horizontal is not in their active vocabulary.
If it were they would not use straight as a synonym for horizontal.

So I think the rule of independent variable on the horizontal axis should be
presented as the conventional rule to use when you don't have a reason for
doing it the other way. The important thing students have to learn is how
variables work, and which ones are independent. They also have to learn
how to handle multiple representations.

John M. Clement
Houston, TX


There are many cases where the choice of which variable to put on
which axis has to do with ease of interpretation of the data. In
meteorology, when plotting the state of the atmosphere at a particular
time, it makes most sense to plot altitude (or pressure) on the
vertical axis and temperature and dew point on the horizontal. This
gives one a mental "snapshot" of the air above. Sticking with the
dependent-independent rule would give the same information but would
be less intuitive and harder to interpret.


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