Does more experience make
you a better teacher?
I
really have very mixed feelings about getting more teaching experience. I mean, yes, it would be nice to feel more
comfortable – to have more of a background to know when to worry and when to
just relax. And yes, to a certain
extent teaching is a skill, a craft, and like any skill you improve with
practice. But when I look over the
teachers that I had at Eastern and CU, there was certainly not any one-to-one
correlation between more experience and better teaching. Often the best teachers I had were not the
most experienced ones. My best teachers
injected a real energy, enthusiasm, a passion for the subject. I think that experience can make you a
competent teacher, but not a great one.
Experience can teach you about organization, structure, common
difficulties with the material, et cetera.
If
teaching is a craft, a skill, then there is no progress in teaching from
generation to generation, and I believe in progress. I believe that any teacher today should be better than any
teacher from fifty years ago, because I believe that we can treat teaching as a
science, where innovation and experimentation can allow us to develop new
techniques that make us all better teachers.
Experience can only refine the practice of existing teaching
methodologies – it can never find new techniques that advance the state of
teaching as a whole.
With
my teaching I want to accomplish a whole lot more than directly educating the
students I will see over the course of my career. I want to use them as a testing ground for new teaching methods –
methods of lecture, the structure of homework, uses of technology, other uses
of class time – methods that I can evaluate, and if successful methods that can
be adopted by others and advance the state of math/physics teaching as a whole.
If
anything I'm actually a little bit afraid of becoming experienced. To be innovative you have to see things with
fresh eyes, seeing new possibilities, new perspectives, new ways of doing things
in the classroom that no one has ever done before. As I become more experienced, I'm afraid that I will become more
complacent, less able to see new things, and more traditional in my teaching. That's not useful if my goal is to
revolutionize the teaching of math and physics in this country.
Can there really be
progress in teaching?
Teaching
can be treated as a science, because we can formulate it into a quantitatively
measurable system: Given the finite
time and energy that teacher has to devote to a class, how do they allocate
that time and energy in order to maximize the amount of student learning that
occurs? Student learning is a
measurable quantity – we do it all the time with assignments and exams. By testing different teaching methods we can
objectively demonstrate which are better.
For
instance, until the 19th century, college instruction was usually done with the
instructor standing at a podium and reading their notes to the class. At this point the chalkboard was introduced
as a new technology. It was quickly
discovered that if the professor wrote on the board during the lecture then
students learned the material better – they both saw and heard the material, so
it was more memorable. This also
afforded teachers the ability to work examples of mathematics problems for the
students visually – which was discovered to be better than merely describing
how the problems could be done in words.
This made any teacher of the blackboard-using generation superior to the
pre-blackboard generation: No matter
how experienced the two teachers were, using a blackboard increases the total
learning that takes place in the classroom in measurable ways that can be
measured with exams. Thus real progress
did take place.
Can learning be objectively
measured?
Some
college educators might argue it's really not fair to evaluate teaching methods
by measuring student learning, because the most important part of learning is
immeasurable. It's unquantifiable,
ineffable. There's no way you can put a
number on a student's comprehension of Newton's laws – not a fair or meaningful
number anyway.
I
think this is tremendously hypocritical for an educator to say this. A large part of our job is to quantify
student learning. I often grade fifty
papers a day, and I give each a numerical score, which I used to quantify how
well the student has comprehended the material. We give them assignments, papers, quizzes, exams, and finally at
the end of it all we give them a total grade, with which we attempt to put a
number on how well they have mastered the totality of the course. Either this whole operation is a sham, or
learning is quantifiable. It is
inconsistent for us to spend hours every day quantifying student learning, but
then when we are asked to take our students work together to quantify our
teaching, to cry foul! Of course it
would be nice if we could say that success in the classroom, the teaching
process, is completely unquantifiable -- because then that saves us from the
difficulty of trying to improve some objective standard, but as one who assigns
grades to students this is the epitome of academic hypocrisy.
Grades
and tests are imperfect measurements of student learning to be sure. There are a great many factors which
contribute to how well a given student does on a given test (how well they are
feeling that day, whether they happened to glance over a particular topic just
before the exam) in addition to their real understanding, but that doesn't mean
we throw them out. There is no quantity
in the universe that we can measure perfectly, with no noise, no sources of
error. You just make repeated
measurements -- lots of homeworks, lots of quizzes, a wide variety of questions
on the test -- the more data you have, the more likely that these will together
tell you something useful about the student's understanding. And then to evaluate your own teaching, you
average together all the students in the class. Proper use of statistics can allow us to overcome the problems of
imperfect testing.
But aren’t the most
important aspects of learning unquantifiable?
Any type of learning on which you grade your students, is the result of a type of teaching that you can quantitatively evaluate. If you assign grades to your students, then you can use those same methods to evaluate yourself. You can't quantitatively evaluate every aspect of your teaching, any more than you can quantitatively evaluate every aspect of your students' learning. But every bit of their learning that you can objectively measure corresponds to your teaching, which you can measure in an identical way.
Not
everything good that is accomplished in the classroom is quantifiable. There are aspects of learning and personal
growth that really are impossible to measure by some objective standard. For these aspects of learning, I agree that
teaching will forever be folklore, a craft, an art. There will be no progress, no innovation. Perhaps one person believes that moral character
is what makes someone a great teacher in these respects. Another person might believe that it is
experience, another enthusiasm, another youth and a fresh perspective. For those unquantifiable aspects to
learning, there will never be any way to arbitrate between these perspectives,
no way to evaluate what really makes the best teacher. In the words of Karl Popper, these ideas are
`unfalsifiable.' I find this
depressing.
However! There are aspects to learning which really
are quantifiable. For these there can
be real progress. We can objectively
test different teaching methods and really advance, really find better ways of
doing things in the classroom. That's
tremendously exciting! That's why I
know that I can be a better teacher than Isaac Newton, Michael Faraday, or
Richard Feynman -- all great glorious titans of my field. But I can be a better teacher in the
objective ways because the psychology of learning has advanced since their day.
But in order to do this, we
have to choose to treat teaching as a science.
We have to hold our own teaching up to objective standards, and have the
courage to evaluate ourselves against the cold light of the numbers. It is a frightening prospect, but through
this door we can find real progress. We
can have students leave our classes knowing more philosophy or more physics
than their peers did a generation ago.
I believe that people learn when they are active, when they are involved,
explaining, solving, talking, trying, working, and struggling. People learn when they are figuring things
out for themselves, rather than expecting others to teach them. As a teacher, I promote active learning in
and out of the classroom, and I present my students with open-ended problem
solving challenges. As a student of
teaching, I work to learn the best new ideas and methods that other teachers
are using, and I approach teaching as a field of serious scientific research,
where education experiments can point the way to new methods and techniques.
So how do you get students to be active? How do you gently demand that they take
responsibility for their own learning?
I have taught six college courses now, in both astronomy and physics at
the University of Colorado at Boulder and Front Range Community College, and
here are some specific things I like to do:
I love open-ended assignments,
because they encourage creativity and challenge students to think
analytically. One assignment that I
have designed begins by having each student write a two page letter to NASA
proposing a new space probe to be sent somewhere in our solar system. Next, everyone receives copies of the
proposals from five of their peers.
They must rank the proposals 1-5 and write a one page paper justifying
their rankings. Finally, during class
the students form committees of five, all having read the same papers. Together, they must discuss the proposals
and come to a consensus about the final committee rankings. Not only does this
take them through an important part of the modern scientific process, it forces
them to think critically, to discuss, to argue, to question, and to persuade
their peers.
I have had a lot of fun designing new assignments and
projects for my classes, but even better,
I’ve learned to be a “good thief.”
I have used the web, journals, and the old fashioned grapevine to find
out what new teaching techniques are out there, such as this one from Paul
Francis at Australian National University:
First, I pose a mystery to the class (for example, a blackbody spectrum
with emission and absorption lines).
Then each group of 3 or 4 students receives a briefing sheet, making
them an expert on some topic, giving them one piece to the puzzle (e.g. atomic
energy levels or photon theory). To
solve the mystery, each group must verbally trade knowledge with the other
groups one by one, and the first group to figure out the entire puzzle wins a
prize. This activity motivates students with their own competitive spirit to
turn just another lecture into a high stakes race.
I believe that to become better educators, we should
treat teaching as a field of scientific research, and perform classroom
experiments to study the effectiveness of different teaching practices. I conducted my first serious education
experiment last summer, while teaching introductory astronomy at the University
of Colorado. I incorporated small group
activities into every class, but I wondered whether the composition of these
learning groups was important: Is it
better to group students of approximately equal ability, so that they will go
at the same pace, and all equally contribute?
Or should the groups be mixed, so that the stronger students can help
the others? I designed a pre-test to
assess the strength of the students coming into the class and used it to assign
my students to either homogeneous or heterogeneous learning groups. The students spent about 30 minutes of each
class doing assignments in these groups throughout the course. On the last day of class I gave the same
test again, and was able to compare 51 pre/post scores. The mean improvement in test scores, as a
percentage of the possible gain, (post-pre) / (100-pre), was 56.7% for the
homogenous groups, and 57.1% for the heterogeneous groups: No significant difference at all! The next time I teach this class, I will
simply group the students arbitrarily.
In the future I would like to study issues such as the effectiveness of
small frequent homework assignments versus more challenging infrequent ones,
and compare different ways of balancing class time between lecture, discussion,
and in class assignments.
I have not yet had the opportunity to teach upper
division classes. However for the past
three years I have worked with upper division students, acting as “coach” for
the University of Colorado’s teams in the Mathematical Contest in
Modeling. In this competition,
undergraduate students work in teams of three, at colleges and universities all
over the world, spending a weekend in February using mathematical modeling to
solve a real world problem, then writing a paper describing their results. To prepare our students, I organized weekly
meetings, where we would discuss strategies, problem solving techniques, useful
references, important mathematical ideas, and brainstorm on problems from previous
years. I would like to teach upper
division classes in a similar style, designing each class around a series of
real-world, open ended problems. The
students will write up their work on these projects in a mathematical
narrative, a paper which uses calculations and data to persuasively make an
argument. Good upper division classes
must demand higher level thinking skills, by asking students to apply the
methods we teach in novel situations, and to evaluate the strengths and
weaknesses of work done by others. The
lectures, in such a class, are thus motivated by the problems, becoming a way
of giving the students the tools they need.
In summary, our students learn when they are actively figuring things out, trying to teach themselves, not passively drifting through a lecture, expecting to be taught. I design my classes not around what I will do, but what the students will do, to let them take command of their own learning, and to teach physics and mathematics as a way of thinking, a way of learning about the world around us.