Re: In-class Examples

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

> > > Unfortunately most end of the chapter problems tend to
> reinforce formulaic
> problem solving.<<
>
> Unfortunately, most of my students can't solve problems involving
> more than one step.  Anything that requires assumptions or
> manipulating equations they have trouble with.
>
> My students can't seem to follow step by step problem solving methods.
>
> This semester might be a little better since these students have
> had Calculus 1 over the summer.

The Heller's material would be a bit stiff for such students.  However the
Minds on Physics problems would be ideal.  Many of the problems are only
slightly rich in context.  The authors make the students look in various
places for the information, without explicitly telling them where to look.
As the problems increase in complexity, they explicitly teach some of the
thinking patterns, and also get the students to distinguish between correct
and incorrect solutions.  The latter strategy is seldom used by most
authors.  Essentially the students are presented with a problem and 2
solutions.  They then have to figure out which is the correct solution, and
explain why the other one is incorrect.  They actually reduce the emphasis
on equations in favor of other methods of solving problems such as analyzing
graphs or using strobe diagrams.  This does not mean they use no equations.
Rather they treat equations as one alternative method among several.
Basically you can pick the level of complexity you wish to use by omitting
the harder problems and questions as necessary.

I have found that even low level students can often use these techniques for
problems they have never seen before.  I have even witnessed precal students
inventing some of the techniques taught in calculus.

John M. Clement
Houston, TX