During various discussions, the idea of a spiral approach to education has
espoused several times by various members. Typically, this is within the
context of revisiting the same topic at greater depth over several years,
e.g. elementary, high school, general physics, upper division. But the
thought occurred to me, why not do the same thing within 1st year general
physics? One common complaint is that students see little connection
between various topics. After the exam on N's laws, the next chapters on
energy & momentum require a completely different set of tools.
Furthermore, the problems at the end of each chapter are typically designed
to work (easily) with only one approach. Other than quick "derivations" of
N2 -> work-energy and N3 -> conservation (which is probably lost on most
students), I'm sure these topics come across as mostly disconnected to
students.
I know the semester is busy already, but what about spending, say, the
first 2-3 weeks outlining the topics and presenting some basic concepts
without much mathematical detail? I might even be tempted to work
"backwards", presenting the fundamental ideas of energy & momentum first,
but then backtracking to say that it is easier to build up toward these
abstract ideas from more concrete ideas like x, v, a, t, & F.
Many conceptual questions of the type in the FCI or Mazur's "ConcepTests"
could be tackled in the intro period. Perhaps you could throw in some math
practice for those who are weak. Once outline of the course and the basic
topics are established, then you explore the mathematical details --
showing how to calculate specific quantities, how to relate the
mathematical, graphical, and verbal descriptions of a concept, how to use
several approaches to the same problem.
I haven't thought this through completely, but I am liking it more and more
as I think about it.
Has anyone tried something like this?
Are there major pitfalls I am overlooking?
Would it be an improvement over the "standard" approach?
It seems like it would be compatible with most of the various PER
approaches to teaching/learning. The performance on the earlier concepts
could be used as a spring board to later discussions ("Many of you had
trouble understanding what it meant to have velocity and acceleration in
opposite directions, so let's look at just how we define velocity and
acceleration.") You can also foreshadow more effectively ("We will see
that N3 is equivalent to conservation of momentum). Thus the students have
a better vision not only of where they were, but where they are going.