"Perhaps real high school teachers will share some ideas on the
subject of "less is more". "
While I teach in an independent school with a highly motivated and
socio-economically privileged student base, I will take a crack at Ludwik's
request.
First, let me define "more" in two ways. The first is "more" as the table of
contents of a typical text book. The content is a general survey of kinematics,
dynamics, statics, momentum, energy, thermodynamics, fluids, electricity,
magnetism (including induction), atomic, nuclear, and 'modern' physics. An
alternate definition might be the content tested on the SAT II Physics or the AP-B
(non-calculus) Physics test.
The second definition of "more" is the mathematics driven first course in
physics. The mathematical representation of the implications of what the class
has experienced is important! But I think it works best as an extension at the
end of a unit, not as the introduction (as found in many texts.)
The corresponding definitions of "less" are as follows. First, the simple version
of "less" is working with just a carefully selected sub-set of the possible topics
of physics. This necessarily gives the instructor some flexibility in choosing
and varying topics year-to-year. It also means the kids will NOT be prepared for
a national, standardized exam. This requires some strength and willingness to
take heat from parents. It requires the administration stand squarely behind the
teacher!
Second, "less" is concentrating on how we communicate and distill our
understanding of our experience in the real world. This includes testing the
implications of our understanding. In a phrase: My experience is the guide to my
understanding.
In my course, I work for the first two months to shift the student thinking from
"I can't do the math" to the need to work with and coordinate many representations
of phenomena. Some of the representations that we explicitly work with are
verbal/written, graphical, algebraic, and analogic. The kids already 'know' that
physics (and math) do NOT represent the real world but are a convenient
idealization that corresponds nicely with the answers to the odd problems at the
back of the book. Many students arrive prepared to memorize methods, claimed
results, and recipes for achieving desired answers and call this physics. This
preparatory attitude includes the total suspension of critical thinking. In an
atmosphere where demands to memorize are supplanted by insistence on developing
personally persuasive reasons for positing and using such-and-such a definition or
way of organizing experience, I find it possible to overcome the suspension of
critical thinking.
I start with the issues of "what does it mean to know" and "how do I know what
someone other than me knows." The kids want to resort to 'everything out there
might be a figment of my imagination so I can't know and thus the need to think
(about this) is obviated." I explicitly disallow this. We learn that agreed on
definitions are the starting point of communication.
I build all of mechanics and kinematics on the idea of 'state of motion'
(descriptive term is velocity, no explicit cause is posited or needed, we find),
what changes the motion (descriptive term is acceleration but causal term is
force) and inertia (a property of matter). We explore the ability to use math to
communicate in a highly precise manner. We explore such things as multiplication
as a transformation and revealing of information (rotation of coordinate space, if
you will). The analogy I use is to show a spherical solid and transform it to a
point by rotating its shadow (The shadow of a sphere is a disk, rotate the disk
and you can get a shadow that goes from circular disk to a line. Rotate the line
and it shortens to a point.)
The first real investigation into predictive power comes with projectile motion.
We have defined our description of motion and the change of motion (velocity).
We have worked out the implications (the usual kinematics equations but I
emphasize the ability to say the equations in real words) and arrive at a stunning
and counter-intuitive prediction: the description of horizontal motion is
independent of the description of vertical motion. I ask the kids to design an
experiment to test this, to carry it out, and to make an argument, based on the
reliability of the procedure, as to whether the prediction is supported and thus
the work we have done (over the course of 2 months) is 'good'.
My course continues with forces (motivated by mousetrap cars built from discarded
items) and the kinds of predictions that can be made by multiplying the force by
the time or distance (sonic rangers and force sensors) through which it acts. We
can then use rotational motion as an assessment of the kids ability to 'do'
physics. This would take me through the year if I wished. Another path (the one
I am choosing this year) is to build on harmonic motion to investigate systems of
particles, develop 'waves' and do sound. I hope to do enough Electricity to say I
have done something with electricity. Any magnetism may show up on the final
exam as an demonstration of the ability to do physics.
The real question is "How can an outsider tell if a kid has taken my physics
course". I would like to think certain habits of mind (reflective consideration,
willingness to share and modify understanding, ability to identify testable
predictions, use of multiple representations to truly study and communicate about
a phenomenon) are explicitly evident in everything the kid does and says. At a
minimum, the kid won't say "I had no idea what he was talking about but I still
got the right answers."