Re: Graphing d vs t

[John Clement <clement@HAL-PC.ORG>]

When one does an MBL experiment, both time and distance (or velocity, or
acceleration) are both measured quantities.  The question of which goes on
the horizontal axis is very difficult for students to figure out.  Indeed a
conventional bowling ball experiment is often done by laying out the
distances and them measuring the time at various positions.  One really
wants the students to graph position vs time so that they can then use the
slope to find velocity.  If the teacher does not state that other quantities
are generally graphed vs time, and that time is practically never put on the
vertical axes, students will make the graph with time on the vertical, take
the slope, and declare it to be the velocity.

A science instructor should never be too dogmatic, but on this point it is
wise to be firm.  The formal thinkers will understand the necessity of
graphing the quantities correctly, and the concrete thinkers will be spared
some problems.  It sounds like the speaker was being dogmatic rather than
firm, bit it is difficult to judge from a single paragraph.

As far as dependent vs independent goes, students have an extremely
difficult time sorting them out.  Students also mistake graphs for maps.
They will put different scales on the X and Y axes of a 2 dimensional strobe
(motion) diagram, and will act like they are drawing a graph.  The subject
of graphing preconceptions goes much deeper.

John M. Clement
Houston, TX

> At 12:45 PM 11/12/01 -0500, Hugh Haskell wrote:
> > > ...when
> > > graphing distance vs time, time was ALWAYS on the
> > > horizontal axis.  I thought it depended upon what was
> > > being controlled. If I control time and measure distance,
> > > then time is on the horizontal axis but if I control
> > > distance and measure time than distance should be on
> > > the horizontal axis. Any thoughts?
>
>
>
> > . Since the usual thing you want from a d vs. t
> > graph is a slope that gives velocity, it makes sense to put time on
> > the horizontal axis. But in relativity and Feynman diagrams we
> > routinely put time on the vertical axis, because we are looking for
> > something other than the slope.
> >
> > Students learn in middle school, and sometimes in their math classes
> > that there is something magic about always putting the "dependent
> > variable" on the vertical axis and the "independent variable" on the
> > horizontal. But often which variable is dependent and which is
> > independent is a function of which is easier to measure and which is
> > easier to choose, not any sort of causal reason. So I would say that
> > how you orient the graph depends on what use you intend to make of
> > it, rather than which variable is dependent and which is independent.
> >
> > Hugh
>
>
> I get a reassuring sense that Hugh speaks with a voice of quiet reason.
> So it is a surprise to find I am with the middle school kids and agin him.
>
> There is only one occasion I know of, when time is a function of
> something,
> and that something is c In that case, I advocate time on the ordinate.
>
> Elsewhere, most anything can only be a function of time, and I see
> no great error (excepting the absolutism ) in offering that time occupies
> the abscissa.
>
>
>
>
>
> Brian Whatcott
>    Altus OK                      Eureka!