Re: Graphing by Hand

[John Gastineau <gastineau@mindspring.com>]

After reading this, 

At 05:24 PM 9/29/97 +0100, it was written:
> I feell most students feel graphs to be only some magic shape that makes
> the teacher smile and gives them a good grade.  The advent of graphing
> calculators is making this all the more common.  In my role as a high
> school teacher I try my utmost to fight this and make a graph something
> real.  Not only  must they hand plot any and all graphs from which they
> will derive conclusions from their experiments, but we do extensive work
> with qualitative sketching of graphing particular concepts.  I guess it
> depends on whether you emphasis is answers or concepts.  Some of you are
> in the situation where you must emphasize answers, but I feel this
> emphasis will fade quickly whereas once a concept is fully in place it
> will never leave.

it seems to me that we're having a semantics problem. Does "graphing by
hand" include the exercise of _sketching_ a qualitative prediction of your
results, with nothing more than a couple of axes, labels, and a quick
curve drawn to reflect your ideas of how the data will look? If so, then I
think most of the MBL/CBL users ALWAYS have students "graph by hand"
first, and we have no disagreement.

Most, if not all of the lab activities I've ever written start with
"sketch a prediction of...", taking place well before any real data come
in. In that sense yes, students are graphing by hand. Every lab. That
requires them to think about how the variables are related to one another.

The problem comes in having students take a data set of, say, 15 points
and then start counting squares to graph. In my mind, that is a huge waste
of time to do repeatedly. Why? It inhibits playing with your perspective
on the data. There are often many ways to plot the data, and it's very
illuminating to construct lots of different graphs of the same data. 

Here's an example: let's say we do a Boyle's Law experiment, PV=k. If we
plot the data as P vs V, by hand, it's almost impossible to conclude that
the function is an inverse. Yet, it's critical to first plot the raw data.
To go directly to a plot of P vs 1/V is surely a way to teach students
that "a graph is some magic shape that makes the teacher smile,"
especially if the graph is sweated out by hand. Most students just won't
get it. By bypassing the raw data, you've lost the opportunity to teach
the students what an inverse function really looks like, and to connect
the graph with the kinesthetic feelings of having to push harder to make
the volume smaller. THEN go on to more removed ways of plotting the
data--play with it, squeeze it, see what happens. To encourage that sort
of what if? play that is at the heart of science requires making the
trials effortless. 

So, the plot really needs to be done both ways. And more: with many
incarnations of the Boyle's Law experiment, there is a systematic error in
the volume measurement which can be measured by careful but creative
graphing. There's graph #3 or #4. 

There's no reason to punish students by making them do all these by hand.
If students don't seem to be able to interpret graphs, then spend time on
interpreting graphs. Lots of them. Drawing graphs by hand to increase
graph interpretation skills is misguided and a waste of time. It's like
changing the oil when you run out of gas--it's not that it's a bad thing
to do, it just won't help you. 

So, yes, lots of qualitative sketching, aka graphing by hand, is a Good
Thing (tm). MBL/CBL/computer graphing just leaves more time to do that
kind of thing. 

JEG

 __________________________________

John E. Gastineau      gastineau@mindspring.com               KC8IEW
900 B Ridgeway Ave.    http://gastineau.home.mindspring.com        
Morgantown WV 26505    (304) 296-1966