Another .02 worth wrt the issue of problem solving.
IMHO problem solving needs to be one of the cornerstones of any physics
course. In my view this sits along with conceptual development,
experimental work and appreciation of the beauty and elegance of physics
as some of the key pillars on which i base my physics curriculum.
The rest of this monologue will focus on problem solving. This will make
my approach appear to be skewed towards problems as the essence of
physics. This is not the case.
Problem construction:
The ensemble of problems which we assign to students should include the
following. In my opinion, most/all textbooks are deficient in this area.
1. There should be some plug and chug problems. Just as a musician
needs to continually play scales and NBA players start each warm up with
layups some direct substitution problems need to be part of the problem
mix. These serve a couple of purposes, including making the student
aware of the equation, providing some experience with the symbols and in
some cases it is a confidence booster. Depending on your students these
could be made optional, allowing students who do not need this type of
practice to choose not to do them.
2. Problems which explore the limits to the equation. As part of
learning the conceptual relationships between two variables it is
essential that students learn where/how the equation is valid and
where/when it breaks down. (i.e. when exploring refraction a simple
example of where the equation reaches its limit is in the case of total
internal reflection)
3. Problems which explore the relationships between variables. These
would include problems in which one variable is doubled.... what happens
to the other variables. (i.e. in the shm equations for a mass on a
spring what happens to the period when the spring is replaced with one
whose linear density is 1/2 the density of the original spring. During
the course of the year examination of linear, quadratic, inverse,
logrithmic, exponential etc. functional relationships should be examined
in this way. In a calc based course, additional development of
functional relationships involving calc relationships.
4. Problems which involve graphs. Students should learn how to do
tangents and areas using approximation techniques.
5. Approximation problems. What more needs be said.
6. Mini dramas. Problems are much more readable and in my experience
students remember/work better if the problems are couched in a mini
story. The dry recitation of mass, initial velocity, final velocity etc
etc can be spiced up with a story.
7. Problems should have more information than is needed to solve the
problem. Using a strategy of example matching, or variable substitution
is quickly (well maybe not quickly) discarded if it doesn't work for the
problems you assign. In my experience, one of the skills of problem
solving in real world situations requires the ability to separate the
wheat from the chaff.
8. Some problems should not have enough information to solve them. This
is particularly devious. (ergo i like it). The correct response is then
for the student to identify what additional information is needed to
solve the problem.
With properly constructed problems, students who have been exposed to the
conceptual development of a relationship and performed experiments or
activities designed to allow them to construct a mental model of the
phenomena can use the problems to explore the limits, relationships,
predictive capabilities and power of the mathematical relationships
between physical quantities.
Bruce Esser
Physics Teacher Something witty
Marian High School Should go here
Omaha NE http://marian.creighton.edu