🚀 go-pugleaf

Hi, Judy!  Remember me?  We've attended workshops together, and didn't you take
over my teaching slot at West Springfield when I left?

With regard to math in physics, the NCTM math reform emphasizes open-ended
problem solving and exploring alternate ways to approach a problem.   I'm
concerned when a math teacher insists a problem must be done by one method and
not another, when either would give you the right answer.  Show the kids both
ways of combining vectors--x and y components and law of cosines and sines--and
let them decide which they prefer.  I would much rather use the x and y
components, for you can add a large number of vectors at once.  With the law of
cosines and sines, you can only add two vectors at a time.

The math reformers are also calling for teachers in science to challenge
students to use "higher math." Not use it in an algorithmic sense where the
students mechanically plug into complicated formulas that they don't
understand, but in an exploratory, intuitive way.  Even non-AP students are
typically taking functions or pre-calc concurrently with physics.  In these
courses they usually learn about such things as simple derivatives, slopes, and
the area under a curve.  So I think it's important for physics teachers to USE
some of this stuff to reinforce the math.

Even though we might not go through a rigorous derivation, students can see the
need for calculus when they're trying to determine gravitational, electrical,
or spring potential energy, where force varies constantly with distance.   Or
the problem of the astronaut who got separated from her space ship--how long
would it it take for the mutual gravitational force between astronaut and space
ship to bring them together again?  That problem requires a differential
equation, as I recall--but at least the kids can conceptually understand what
the problem is and realize the need for "higher math."

Lois Nicholson
Coordinating Council for Education
National Research Council, Washington, D.C.