TITLE: If You Can't Teach It, You May Not Understand It. Or Else...
AUTHOR: Eugene Wallingford
DATE: June 09, 2016 4:05 PM
an interesting article
about words and concepts, Elisa Gabbert repeats a familiar
sentiment about teaching:
... the physicist Richard Feynman reportedly said, after
being asked to prepare a freshman lecture on why spin-1/2
particles obey Fermi-Dirac statistics, "I couldn't reduce
it to the freshman level. That means we really don't
When I read this, my inner
thought, "With the data at hand, you really can't draw that
conclusion. All you can say with absolute certainty is that
you don't understand it."
Actually, I empathize deeply Feynman's sentiment, which has been
attributed to many famous people and stated in one form or other
by many people who have tried to teach a challenging topic to
others. Most teachers have had the experience of trying to
explain an idea they think they know cold, only to find
themselves stumbling over concepts or relationships that seem so
obvious in their expert mind. I experience this feeling almost
every semester. When I was a young teacher, such experiences
disconcerted me. I soon learned that they were opportunities
to understand the world better.
But I think that, at a logical level, people sometimes draw an
invalid conclusion from statements of the sort Feynman
reportedly made. It's certainly true that if we don't really
understand a complex subject, then we probably won't be able to
reduce it to a level appropriate for first-year students. But
even if you do understand it really well, you still
may have difficulty explaining it to beginners.
Teaching involves two parties: the teacher and the learner.
Effective teaching requires being able to communicate new ideas
in a way that connect with what the learner knows and can do.
To be effective teachers, we need two kinds of knowledge:
This latter understanding comes at two levels. First, we might
know a specific individual well and be able to connect to his or
her own personal experiences and knowledge. Second, we might
understand a group, such as freshman CS students, based on some
common background and maturity level.
Teaching individuals one-on-one can be most effective, but it
takes a lot of time and doesn't scale well. As a result, we
often find ourselves teaching a group of people all at once or
writing for a mass audience. Teaching a class means being able
to communicate new ideas to a group of students in a way that
prepares most or all of them to learn on their own after they
leave the classroom and begin to do their individual work.
Most people who try to teach find out that this is a lot harder
than it looks. Over time, we begin to learn what a generic
freshman CS student knows and is like. We build up a cache of
stories for reaching them in different ways. We encounter
pedagogical patterns of effective learning and learn ways to
implement them in our teaching. We also begin to learn
techniques for working with students individually so that, in
our office after class, we can drop down from generic teaching
to more intimate, one-on-one instruction.
If you want to find out simultaneously how well your students
are understanding what you are teaching and how well you
understand what you are teaching, let them ask questions. I am
often amazed at the questions students ask, and equally amazed
at how hard they can be to answer well. On truly glorious days,
I surprise myself (and them!) with an answer or story or
example that meets their needs perfectly.
However well I understand a topic, it always takes me time to
figure out how to communicate effectively with a new audience.
Once I understood that this was natural, it allowed me to take
some of the pressure to be perfect off myself and get down to
the business of learning how to teach and, often, learning
computer science at a deeper level.
So, if we can't reduce some topic to the freshman level, it may
well mean that we don't really understand it. But it may also
mean that you don't yet understand your audience well enough.
Figuring out which is true in a given case is yet another
challenge that every teacher faces.
- an understanding of the content to be communicated
- an understanding of how to reach our intended audience