Re: Am I teaching what I should in HS physics?

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

> My students don't tend to know that the scale is supposed to be
> even on a graph.  Heck, in my algebra class, they don't know the
> difference between the x and y axis.
>
> The other problem is that they use a scale of 1 block per 1 unit
> for large numbers getting huge graphs.

Or microscopic on one axis and huge on the other!!!!

> Tina

I think that the inability to make a graph is partly the result of lack of
experience, and partly the result of the way in which graphs are presented
in texts.  Go through the average K-12 science or math text and look at the
graphs.  They tend to be overly neat with points nicely lined up on grid
lines, most of them go through zero ...  The result is that students try to
make every graph go through zero, and there is a tendency to force them to
be straight lines.  They are seldom asked to graph data in math where the
points fall at odd locations. Many math courses ignore the topic of graphs.

Again the same problem happens when they are asked to do a scale drawing.
The inability to use proportional reasoning makes it difficult for them to
use the scale.  Also many of them when asked to use a scale drawing, will
give the answers in cm or inches instead of in the scaled quantity.  This is
a basic misconception because they are concrete operational thinkers.  They
have difficulty correctly handling the idea of using a drawing as a
representation.  The formal operational thinkers generally do not have this
problem.  MOP has some nice activities on these topics.

Then of course there is difficulty understanding the difference between a
graph and a scale drawing.  Actually my students have already been told
these things in math and other science courses, so telling was part of the
problem.  I never tell, I ask.

One way to get students to really understand X and Y is to have them program
pictures using X, Y coordinates.  I spend about 3 weeks in computer science
having the students use a standard simple graphics package.  They are given
some examples of how to create graphics then they are required to draw a
house with a peaked (gable) roof, 1 door, and 1 window.  Then they have to
draw a face with a mouth, and 2 round or oval eyes.  Finally they have to
draw a complete picture with a number of elements, colors, fill colors ...
They get 5 points for doing animation.  I spend my whole time asking them
questions such as how wide is the rectangle (specified by 2 X,Y pairs on
diagonal corners).  "What would you change to move the whole thing up.
Really?  Try it."  They quickly discover that their assumptions were wrong,
and the idea of X, Y pairs becomes much more real at a concrete level.

Then the more advanced students figure out how to move things at various
angles in various directions inside loops.  Essentially they discover some
of the elements of parametric equations.  Many of them have actually had
this in math, but by making them use it to animate things they begin to
understand it.

Does this actually work?  Students tell me that they understand math much
better after my 1 semester course in comp. sci., but until recently I have
had little hard evidence.  Two students recently said they thought about the
way we solved comp. sci. problems while taking the math SAT.  One rose 40
points over the previous time, and the other rose 100 points.  This is only
2 data points, but it was a gratifying pair of points.

John M. Clement
Houston, TX