One of the standard elements of most academic hiring and promotion applications, at least at a small liberal arts college, is some sort of statement from the candidate about teaching. This is called different things at different places– “statement of teaching philosophy” is a common term for it, and the tenure process here calls for a “statement of teaching goals.”
I spent hours and hours on this, because I get a little obsessive about written work. It did get read closely by the ad hoc committee, at least– at my first meeting with them, they asked a couple of questions about details of the statement– but I put enough time into it that I’m going to get some more use out of it, by recycling it as a blog post.
This has been lightly edited from the original text– I converted the LaTeX formatting codes to HTML, and concealed some of the student names (I’m not quite sure why, as they’d be trivial to figure out, but it seemed like the right thing to do). I was advised after my reappointment review (in my third year) that I needed to make the statement more philosophical, so, well, here’s what I sound like when I expound on my philosophy of teaching physics:
Statement of Teaching Goals
My main goal in teaching physics, whether in the classroom or in
the laboratory, is for my students to learn something about what
it means to think like a physicist. Physics, like any other
discipline, has a characteristic approach to dealing with the
world, and an important part of the process of education is for
students to see what this approach is and how it differs from that
of other disciplines. The aim is not necessarily for all my
students to become physicists (though it’s always flattering
when some do), but rather for them to gain some appreciation of
physics as more than a collection of trivia.
Classroom Teaching
When I teach our introductory classes, I state this goal
explicitly on the first day of class. Most students who take
Physics 120 and 121 do so to fulfill a requirement for some other
major, and they often view physics as little more than a nuisance,
a collection of arbitrary formulae to be memorized for later use.
I point out to them that if the goal were only for them to
memorize a handful of facts, there would be no reason for the
class to be taught by a physicist. The real purpose of the class,
particularly at a liberal arts college, is to learn something
about the process of doing physics.
I give them a four-step outline of this process: 1) first,
identify some phenomenon in the real world that we want to
describe physically, 2) break that phenomenon down into simpler
processes, 3) find universal rules governing those simpler
processes, and 4) using those rules, recombine the simple cases to
describe the original phenomenon of interest. Following this
procedure not only allows physicists to describe the particular
phenomenon we started with, but also allows us to make predictions
about new and different phenomena based on the universal rules we
obtained.
To choose an example from Physics 120, if we want to explain the
behavior of an extended object flying through the air, tumbling
end over end, we can break that down into two separate behaviors:
the motion through the air, which is treated as if all the mass
was concentrated at the center of mass of the object; and the
tumbling motion, which is treated as if the object was fixed in
place and rotating about the center of mass. By considering only
the center-of-mass motion, we arrive at universal principles like
Newton’s Laws and the conservation of energy and momentum. By
considering only the rotational motion, we arrive at the idea of
conservation of angular momentum. Putting those principles together
allows us to explain not just the original example, but any
combination of linear and rotational motions.
I try to organize my teaching around this process, especially in
the introductory classes. One way I do this is to introduce new
techniques by illustrating the need for them with some phenomenon
that can not be easily described with previous methods. For
example, when we move from discussing Newton’s Laws to
conservation of energy, I show the class a toy roller coaster that
makes a loop. Using only Newton’s Laws, it is extremely difficult
to predict the starting height required for a car to make it
around the loop; this demonstrates the need for a new technique
and leads the way into the development of conservation of energy.
At the end of the energy unit, I return to the roller coaster
example and show the students that what was a nearly insoluble
problem becomes almost trivial using energy methods.
I also make an effort to introduce new formulae by placing them in
a physical context. In Physics 121, rather than simply presenting
Ohm’s Law as a new formula to be memorized, I explain how it can
be understood as the result of the microscopic motion of electrons
in a solid. Starting with the well-understood behavior of a single
electron in free flight, we can extend our model to the collective
motion of large numbers of electrons. Making a few simple and
easily justified approximations, we arrive at Ohm’s Law with an
understanding of how it is rooted in simple physical processes. My
goal is to help students see physics as a coherent whole, rather
than a collection of arbitrary formulae to be memorized and
manipulated.
I try to carry this approach on through the major sequence, with
the level of complexity increasing in the higher-level classes. In
Physics 122, I assign several problems that require students to
make explicit approximations in order to describe realistic
situations. For example, they calculate the difference in time
between a clock at the equator and a clock at the North Pole, due
to the rotation of the Earth; the change is small enough that
students must make an approximation in order to solve it with a
normal calculator. I have also started using Mathematica to
explore problems that can only be solved with a computer, such as
finding the allowed energy states of a finite square well
potential. For this activity, students need to determine the
boundary conditions that allow the computer to solve the
Schrödinger equation for this system, and also develop a
procedure for determining which solutions are physically valid
wavefunctions. Successfully finding the allowed energy states
requires understanding not just the equations involved, but also
the procedure for finding solutions and the physical meaning of
the wavefunction.
For my module of our advanced laboratory class (Physics 300),
taught to junior and senior physics majors, I do not provide
detailed step-by-step instructions for the experiment. Instead, I
ask students to develop their own experimental procedure by
reading journal articles, as they would if they were working
scientists. Replicating and extending the work of others is a
critical part of the practice of science, and this lab lets them
start learning that skill.
All of these tasks are intended to give students a better
understanding of what it means to think like a physicist. Not only
is this good training for students in the major, it also helps
students outside the major see physics as an active and vital
discipline, and not merely a set of mathematical formulae and dry
facts. The best indication of success I have seen was a comment
from a student in Physics 120 in Winter 2005, who wrote, “I wish
I had taken physics earlier than this year so I could have taken
more.”
Undergraduate Research
For students who do plan to major in physics, there is no
more important part of learning to think like a physicist than
participation in research. Learning to do research is an essential
part of the training of a physics major, and one of the chief
advantages a small college like Union offers is the chance for
students to work closely with faculty on research projects. My
experience working on research projects while at Williams was one
of the most important factors that convinced me to pursue a career
in physics, and served as excellent preparation for graduate
school.
I view student involvement in research as not only an important
part of the research program, but an absolutely essential part of
our teaching mission. For this reason, I have supervised fifteen
different student research projects in my lab at Union, including
five senior theses (with two more students doing theses this
year), and seven summer research projects. Three students have
worked with me in two different summers. I have co-authored one
publication with a student, Colin F., and two students
have presented their results at national meetings: Colin F.
at the National Conference on Undergraduate Research in 2003, and
Mike M. at the Division of Atomic, Molecular, and
Optical Physics meeting of the American Physical Society in 2006.
Students have been involved in every phase of the construction of
my laboratory. The lasers I use were designed and built by Pat
S. and Eric G.. Ryan M. designed and
built a tapered electromagnet and assembled the main vacuum system
as part of his thesis research. Mike M. has assembled and
tested an entirely new system to develop a new type of atom source
for future experiments and will continue that work for his thesis.
These students benefit from their research experience not only by
learning specific lab skills, but also by learning the process of
doing physics. They learn how to design an experiment, how to
build apparatus (my student projects almost always involve some
work in the machine shop), and how to collect and analyze data.
They also learn to be more independent, as working on a research
problem is different than anything they experience elsewhere in
the curriculum. To paraphrase a colleague at Williams, the hardest
thing for new research students to learn is that research is not a
three-hour lab. Even in our advanced laboratory course, students
know that the experiment they are doing will work, if they
just follow the established procedure. With real research
problems, experiments are much more open-ended, and there is no
guarantee that any given experiment will ever work. This
requires a much more flexible and independent approach than a
laboratory class, teaching research students not just how to
follow a set procedure, but how to modify the procedure in order
to reach a desired goal, and even when to abandon the procedure
entirely in favor of a different method.
These are skills that are absolutely critical not only for careers
in physics, but for almost any career imaginable. Some of my
students have gone on to graduate school in physics or
engineering. Others have gone on to professional school in another
field, or directly into a career in industry. Whatever their
chosen career, I am confident that they are all well served by
their research experience. In the end, some of the most important
teaching I do takes place not in the classroom, but in my research
lab.