TITLE: If You Can't Teach It, You May Not Understand It. Or Else... AUTHOR: Eugene Wallingford DATE: June 09, 2016 4:05 PM DESC: ----- BODY: In 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 understand it."
When I read this, my inner Sheldon Cooper 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. -----